3
Select the correct answer.
The angle of depression between the top of a 100-foot cliff and a ship approaching the shore is 37°.
cliff top
37°
100
feet
37°
ship
d
What is the approximate distance, d, between the bottom of the cliff and the ship?
ÐÐ
166. 2 feet
OB. 60. 2 feet
ÐС.
75. 4 feet
OD.
132. 7 feet
Reset
Next
Answers
The correct answer is (D) 132.7 feet.
From the given information, we can draw a diagram as follows:
A
/|
/ |
/ | 37°
/ |
/ |
/ |
/ |
/_ _ _ _|
d B
Where A represents the top of the cliff, B represents the ship and d represents the distance between the ship and the bottom of the cliff.
Since we know that the angle of depression is 37 degrees, then the angle CAB is also 37 degrees. We also know that AB is 100 feet, which is the height of the cliff. We want to find the distance d between the bottom of the cliff and the ship.
We can use the tangent function to find d:
tan(37°) = AB/BD
tan(37°) = 100/d
d = 100/tan(37°)
Using a calculator, we can find that:
d ≈ 132.7 feet
Therefore, the correct answer is (D) 132.7 feet.
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Related Questions
For the polynomial function find the following: (i) Degree of the polynomial; (ii) All intercepts; (iii) The intercept.
y = x^2 + 169
Degree of a Polynomial:
When our polynomial is written in expanded form, we can determine its degree by stating the highest exponent on our variable. If our polynomial is factored, the degree is instead equal to the sum of the number of factors, though if any factor is taken to an exponent, we count that factor as many times as indicated by the value of the exponent.
Answers
(i) The highest exponent on the variable x is 2. Therefore, the degree of the polynomial is 2. (ii) There are no x-intercepts for this polynomial. (iii) Since there are no x-intercepts, there is no intercept to be determined for this polynomial.
For the polynomial function \(y = x^2 + 169\):
(i) Degree of the polynomial:
The highest exponent on the variable x is 2. Therefore, the degree of the polynomial is 2.
(ii) All intercepts:
To find the intercepts, we set y = 0 and solve for x.
When y = 0:
\(x^2 + 169 = 0\)
This equation has no real solutions because the term x^2 is always non-negative, and adding 169 to it will result in a positive value. Therefore, there are no x-intercepts for this polynomial.
(iii) The intercept:
Since there are no x-intercepts, there is no intercept to be determined for this polynomial.
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Assume that 40% of students at SCC receive A or B’s, 35% receive C’s, and 25% receive
D or F’s. A survey of 300 r/s UC Davis students indicates that 100 of them received A or
B’s, 130 received C’s, and 70 received D or F’s. Do these results provide strong evidence
that the overall percentages of the 3 grade categories at UC Davis are not all the same as
the ones at SCC? Perform a hypothesis test and use a p-value to draw and explain your
conclusion
Answers
We have sufficient evidence to conclude that the over all percentages of 3 categories are not same.
What is meant by percentage?The percentage refers to a specific percentage out of a hundred. It is a fraction with the denominator 100, and the sign for it is 1%.
The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian phrase per cento, which means "for a hundred," gradually shrank to become the symbol for "percent," which is now used globally. It finally vanished totally. The word "per" was frequently shortened to "p." The contemporary "%" symbol was created by condensing the "cento" to two circles divided by a horizontal line.
Category Observed(\(O_{i}\)) Expected(\(E_{i}\)) (\(O_{i}\)-\(E_{i}\))²/\(E_{i}\)
A or B 100 120 3.333
C 130 105 5.9524
D or F 70 75 0.056
Total 300 300 9.3417
H₀:over percentages are same at UC Davis and at SSC
H₁:They are not same
Test statistic
X²=∑ (\(O_{i}\)-\(E_{i}\))²/\(E_{i}\)
=9.3417
P-value=P(X²(n-1)>9.3417)
=0.0094
Here we can see that the P-value is very low(<0.05 and <0.01)
So, we reject the null hypothesis H₀.
Therefore, we have sufficient evidence to conclude that the over all percentages of 3 categories are not same.
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a sample of 1500 computer chips revealed that 69% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that 72% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.05 level to dispute the company's claim? state the null and alternative hypotheses for the above scenario.
Answers
At a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.
What is the null hypothesis in statistics?
The null hypothesis in inferential statistics states that two possibilities are the same. The null hypothesis states that the observed difference is solely due to chance. The likelihood that the null hypothesis is true can be calculated using statistical tests.
Sample size, n =1500
The sample proportion of the chips that do not fail in the first 1000 hrs of their use, \(\hat{p} = 0.69\)
Null Hypothesis, H0: p=0.72
Alternate Hypothesis, \(Ha: p \neq 0.72\)
Test statistic,
\(z= \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} - \frac{0.69-0.72}{\sqrt{\frac{0.72(1-0.72)}{1500}}} = -2.5877\)
Critical Value,
\(Z_{0.05/2} =\)±1.96
Now, since the absolute value of the test statistic i.e, 2.5877 is greater than the absolute value of the critical value i.e, .1.96, thus we will reject the null hypothesis.
Thus at a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.
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What is the arithmetic mean of the following numbers?
1,2, 10, 6, 4,4,6,3,1,4
Answers
Answer:
The quadratic mean (rms) of a set of numbers is the square root of the sum of the squares of the numbers divided by the number of terms.
⎷
(
1
)
2
+
(
2
)
2
+
(
10
)
2
+
(
6
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2
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Step-by-step explanation:
One to any power is one.
√
1
+
(
2
)
2
+
(
10
)
2
+
(
6
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2
+
(
4
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2
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(
4
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2
+
(
6
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2
+
(
3
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2
+
(
1
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2
+
(
4
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2
10
Raise
2
to the power of
2
.
√
1
+
4
+
(
10
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2
+
(
6
)
2
+
(
4
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2
+
(
4
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2
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(
6
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2
+
(
3
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2
+
(
1
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2
+
(
4
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2
10
Raise
10
to the power of
2
.
√
1
+
4
+
100
+
(
6
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2
+
(
4
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2
+
(
4
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2
+
(
6
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2
+
(
3
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2
+
(
1
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2
+
(
4
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2
10
Raise
6
to the power of
2
.
√
1
+
4
+
100
+
36
+
(
4
)
2
+
(
4
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2
+
(
6
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2
+
(
3
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2
+
(
1
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2
+
(
4
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2
10
Raise
4
to the power of
2
.
√
1
+
4
+
100
+
36
+
16
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
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2
+
(
4
)
2
10
Raise
4
to the power of
2
.
√
1
+
4
+
100
+
36
+
16
+
16
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise
6
to the power of
2
.
√
1
+
4
+
100
+
36
+
16
+
16
+
36
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise
3
to the power of
2
.
√
1
+
4
+
100
+
36
+
16
+
16
+
36
+
9
+
(
1
)
2
+
(
4
)
2
10
One to any power is one.
√
1
+
4
+
100
+
36
+
16
+
16
+
36
+
9
+
1
+
(
4
)
2
10
Raise
4
to the power of
2
.
√
1
+
4
+
100
+
36
+
16
+
16
+
36
+
9
+
1
+
16
10
Add
1
and
4
.
√
5
+
100
+
36
+
16
+
16
+
36
+
9
+
1
+
16
10
Add
5
and
100
.
√
105
+
36
+
16
+
16
+
36
+
9
+
1
+
16
10
Add
105
and
36
.
√
141
+
16
+
16
+
36
+
9
+
1
+
16
10
Add
141
and
16
.
√
157
+
16
+
36
+
9
+
1
+
16
10
Add
157
and
16
.
√
173
+
36
+
9
+
1
+
16
10
Add
173
and
36
.
√
209
+
9
+
1
+
16
10
Add
209
and
9
.
√
218
+
1
+
16
10
Add
218
and
1
.
√
219
+
16
10
Add
219
and
16
.
√
235
10
Cancel the common factor of
235
and
10
.
Tap for fewer steps...
Factor
5
out of
235
.
√
5
(
47
)
10
Cancel the common factors.
Tap for fewer steps...
Factor
5
out of
10
.
√
5
⋅
47
5
⋅
2
Cancel the common factor.
√
5
⋅
47
5
⋅
2
Rewrite the expression.
√
47
2
Rewrite
√
47
2
as
√
47
√
2
.
√
47
√
2
Multiply
√
47
√
2
by
√
2
√
2
.
√
47
√
2
⋅
√
2
√
2
Combine and simplify the denominator.
Tap for fewer steps...
Multiply
√
47
√
2
and
√
2
√
2
.
√
47
√
2
√
2
√
2
Raise
√
2
to the power of
1
.
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47
√
2
√
2
1
√
2
Raise
√
2
to the power of
1
.
√
47
√
2
√
2
1
√
2
1
Use the power rule
a
m
a
n
=
a
m
+
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to combine exponents.
√
47
√
2
√
2
1
+
1
Add
1
and
1
.
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47
√
2
√
2
2
Rewrite
√
2
2
as
2
.
Tap for fewer steps...
Use
n
√
a
x
=
a
x
n
to rewrite
√
2
as
2
1
2
.
√
47
√
2
(
2
1
2
)
2
Apply the power rule and multiply exponents,
(
a
m
)
n
=
a
m
n
.
√
47
√
2
2
1
2
⋅
2
Combine
1
2
and
2
.
√
47
√
2
2
2
2
Cancel the common factor of
2
.
Tap for more steps...
√
47
√
2
2
1
Evaluate the exponent.
√
47
√
2
2
Simplify the numerator.
Tap for fewer steps...
Combine using the product rule for radicals.
√
47
⋅
2
2
Multiply
47
by
2
.
√
94
2
The result can be shown in multiple forms.
Exact Form:
√
94
2
Decimal Form:
4.84767985
…
A restaurant offers the following menu items.how many different meals are possible if each meal includes one main course, one side dish and drink
Answers
18 different meals are possible if each includes one main course, one side dish and drink.
How do we solve for the combination of meals?From the provided menu, there are:
3 choices for the main course (Grilled Chicken, Turkey Sandwich, Pasta Salad). 2 choices for the side dish (Salad, Applesauce). 3 choices for the drink (Milk, Juice, Water)
The total numbr of possible meals combination is therefore
3 (main courses) ×2 (side dishes) × 3 (drinks) = 18 different meals.
Here is a list of all the possible meals:
A list of the meal will be
Grill chicken, salad, milk
Grill chicken, salad, juice
Grill chicken, salad, water
Grill chicken, applesauce, milk
Grill chicken, applesauce, juice
Grill chicken, applesauce, water
Turkey sandwich, salad, milk
Turkey sandwich, salad, juice
Turkey sandwich, salad, water
Turkey sandwich, applesauce, milk
Turkey sandwich, applesauce, juice
Turkey sandwich, applesauce, water
Pasta salad, salad, milk
Pasta salad, salad, juice
Pasta salad, salad, water
Pasta salad, applesauce, milk
Pasta salad, applesauce, juice
Pasta salad, applesauce, water
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please help me answer this question asap
Answers
Answer:
It's quite easy
Step-by-step explanation:
people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23
Therefore there are 23 people less than 30 years old.
pls mark me as brainliest pls.
a microorganism measures 5 μm in length. its length in mm would be?
Answers
The length of the microorganism in millimeters is 0.005 mm.
The theory behind converting length units from one unit to another is based on the conversion factor principle. In the International System of Units (SI), the conversion factor between two units of length can be obtained by comparing the number of meters represented by each unit. For example, 1 millimeter is equal to 0.001 meters, and 1 micrometer is equal to 0.000001 meters.
To convert from one unit of length to another, we multiply the length by the appropriate conversion factor. In this case, to convert from micrometers to millimeters, we multiply the length in micrometers by 0.001 to obtain the length in millimeters.
To convert the length of the microorganism from micrometers (μm) to millimeters (mm), we divide by 1000.
5 μm / 1000 = 0.005 mm
Therefore, the length of the microorganism in millimeters is 0.005 mm.
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how many solutions does this system for equations have ? PLZ HELP ASAP !
Answers
Answer:
Infinitely many solutions
Multiply.
2x^4 (3x³ − x² + 4x)
Answers
Answer: A
Step-by-step explanation:
When multiplying: Numbers multiply with numbers and for the x's, add the exponents
If there is no exponent, you can assume an imaginary 1 is the exponent
2x⁴ (3x³ − x² + 4x)
= 6x⁷ -2x⁶ + 8x⁵
Answer:
A. \(6x^{7} - 2x^{6} + 8x^{5}\)
Step-by-StepLabel the parts of the expression:
Outside the parentheses = \(2x^{4}\)
Inside parentheses = \(3x^{3} -x^{2} + 4x\)
You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses
\(2x^{4}\) × \(3x^{3}\)
\(2x^{4}\) × \(-x^{2}\)
\(2x^{4}\) × \(4x\)
First, multiply the whole numbers of each value before the variables
2 x 3 = 6
2 x -1 = -2
2 x 4 = 8
Now you have:
6\(x^{4}x^{3}\)
-2\(x^{4}x^{2}\)
8\(x^{4} x\)
When you multiply exponents together, you multiply the bases as normal and add the exponents together
\(6x^{4+3}\) = \(6x^{7}\)
\(-2x^{4+2}\) = \(-2x^{6}\)
\(8x^{4+1}\) = \(8x^{5}\)
Put the numbers given above into an expression:
\(6x^{7} -2x^{6} +8x^{5}\)
Key Wordsdistribution
variable
like exponents
You spin a spinner and flip a coin. Find the probability of the events.
15. Spinning a 4 and flipping heads
16. Spinning an even number and flipping tails
17. Spinning a multiple of 3 and flipping heads
18. Spinning white and not flipping heads
Answers
WILL MARK BRAINLIEST!!!
1. Describe three different ways to solve a quadratic equation. Describe the strengths and limitations of each method, and explain how you would decide which one to use to solve a particular problem.
2. Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
Divide all terms in the equation by a.
Subtract the constant (the term without an x) from both sides.
Add a constant (in terms of a and b) that will complete the square.
Take the square root of both sides of the equation.
Solve for x.
3. Write a linear equation that intersects y = x2 at two points. Then write a second linear equation that intersects y = x2 at just one point, and a third linear equation that does not intersect y = x2. Explain how you found the linear equations.
Thank You!!
Answers
The ways that can be used to solve a quadratic equation include:
Factorization
Using the quadratic formula.
Completing the squares.
What is a quadratic equation?It should be noted that a quadratic equation simply means an algebraic equation of the second degree in x.
Here, the factorization, using the quadratic formula, and completing the squares method can be used.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer: 2.5, 5.3
Step-by-step explanation:
\(-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3\)
(8x3 - 30x + 21) / (4x -6)
Answers
Answer:
\( \frac{ {8x}^{3} - 30x + 21 }{2(2x - 3)} \)
Step-by-step explanation:
1) Factor out the common terms 2.
\( \frac{8x^{3} - 30x + 21}{2(2x - 3)} \)
Therefor, the answer is 8x³ - 30x + 21 / 2 ( 2x - 3 ).
Answer:
8x3 - 30x + 21
————————
2 • (2x - 3)
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): "x3" was replaced by "x^3".
8x3 - 30x + 21
Simplify —————————
4x - 6
Pull out like factors :
4x - 6 = 2 • (2x - 3)
Find roots (zeroes) of : F(x) = 8x3 - 30x + 21
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 8 and the Trailing Constant is 21.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4 ,8
of the Trailing Constant : 1 ,3 ,7 ,21
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 43.00
-1 2 -0.50 35.00
-1 4 -0.25 28.38
-1 8 -0.12 24.73
-3 1 -3.00 -105.00
Note - For tidiness, printing of 27 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Polynomial Long Division
Dividing : 8x3 - 30x + 21
("Dividend")
By : 2x - 3 ("Divisor")
dividend 8x3 - 30x + 21
- divisor * 4x2 8x3 - 12x2
remainder 12x2 - 30x + 21
- divisor * 6x1 12x2 - 18x
remainder - 12x + 21
- divisor * -6x0 - 12x + 18
remainder 3
Quotient : 4x2 + 6x - 6
Remainder : 3
Answer: 8x3 - 30x + 21
————————
2 • (2x - 3)
Three less than the product of 2 and a number is equal to 5
Answers
Answer:
3<2*x=5
Step-by-step explanation:
Hope this helped, Have a Wonderful Day/Night!!
( btw the astric means multiplication )
The unknown number will be equal to 4.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that three is less than the product of 2 and a number is equal to 5. The unknown number will be calculated as:-
2x - 3 = 5
2x = 5 + 3
2x = 8
x = 8 / 2 = 4
Therefore, the unknown number will be equal to 4.
The complete question is given below:-
Three less than the product of 2 and a number is equal to 5. Calculate the unknown number.
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A football team carried out a report to see the impact of stretching on preventing injury. Of the 32 footballers in the squad 25 stretch regularly. Of those who stretch, 3 got injured last year. There was a total of 8 injured players last year. The results can be presented in a frequency tree. What fraction of players are not stretching regularly?
Answers
Answer:
1/16
Step-by-step explanation:
Total = 32 footballers
25 stretch regularly.
3 injure last year
now, 22 stretch regularly.
out of 32, 8 are injured. Therefore, 32-8=24 should stretch regularly but only
22 stretch regularly. Therefore, 24-22 =2 are not stretching regularly.
fraction of players are not stretching regularly = 2/32 =1/16
A pair of Jordans sold at retail for $180 and now sell for $330 after market. A. Is this a percent INCREASE or DECREASE, what is the PERCENT change?
Answers
Answer:
This is a percent INCREASE
The percent change is 83.33%
Step-by-step explanation:
Let us solve the question
∵ A pair of Jordans sold at retail for $180
∴ The initial price = 180
∵ Now it sells for $330 aftermarket
∴ The new price = 330
→ That means the new price is greater than the initial price
∵ The new price is greater than the initial price
∴ This is a percent INCREASE
∵ The percent of change = (amount of increase ÷ initial amount) × 100%
∵ The amount of increase = new price - initial price
∴ The amount of increase = 330 - 180 = 150
→ Substitute it in the rule of percent of increase above
∵ The percent change = \(\frac{150}{180}\) × 100%
∴ The percent change = \(\frac{5}{6}\) × 100%
∴ The percent change = 83.33%
Sam is on a game show with a score of -250. If he scores 450 points what is his new score?
Answers
Answer:
200 points
Step-by-step explanation:
1. Since 450 is a positive value, we have to add 450 to -250 to get the new total.
2. (Solving)
\(-250 + 450\) \(-250 + 450 = 450 - 250\) \(450 - 250\) \(200\)Therefore, Sam's new score is 200 points.
Mary and Bill both are saving money. Mary already has $30 and is able to save $5.50 every week. Bill already has $45 and is able to save $4.25 every week. When will Mary and Bill have the same amount of money?
Answers
Answer: 12 weeks
Step-by-step explanation:
Let the week that both of them will have thesame amount of money be represented by x.
Since Mary already has $30 and is able to save $5.50 every week, this will be denoted as: 30 + 5.50x
Since Bill already has $45 and is able to save $4.25 every week, this will be debited by 45 + 4.25x. Then we'll equate both equations and this will be:
30 + 5.50x = 45 + 4.25x
5.50x - 4.25x = 45 - 30
1.25x = 15
x = 15/1.25
x = 12
They'll have thesame amount of money in 12 weeks.
What's the circumference of a
circle with a diameter of 31 inches?
Use 3.14 for pi.
Answers
Answer:
circumference = 97.34
Step-by-step explanation:
circumference = diameter x Pi
31 x 3.14 = 97.34 inches
The circumference of the circle with a diameter of 31 inches is approximately 97.34 inches.
The circumference of a circle can be calculated using the formula C = πd, where C represents the circumference and d represents the diameter of the circle.
Given that the diameter of the circle is 31 inches, we can substitute this value into the formula:
C = 3.14 * 31
C ≈ 97.34 inches
Therefore, the circumference of the circle with a diameter of 31 inches is approximately 97.34 inches.
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4. The ratio of students who made
the honor roll to the total number
of students is 1:50. If there are
500 students in total, how many
made the honor roll?
Answers
Answer: 10 made the honor roll
Step-by-step explanation:
Michael and Christopher ran a total of 8.4 miles. Christopher ran 4.1 miles and Michael ran m miles. How many miles did Michael run?
Answers
Answer:
michael ran 4.3 miles
Step-by-step explanation:
8.4-4.1=4.3
Answer:
he ran 4.3 miles i think but i am not sure
8.4-4.1=4.3
PLEASE HELP! I NEED ALL OF THEM ANSWERED! FIRST GETS BRAINLIEST!
Answers
The angle measures for this problem are given as follows:
A = 63º.B = 138º.C = 117º.D = 114º.Then the four letter code is given as follows:
FBCA.
How to obtain the angle measures?For angle A, first we have that (2x + 35)º and (8x - 40)º are vertical angles, hence the value of x is obtained as follows:
8x - 49 = 2x + 35
6x = 84
x = 84/6.
x = 14
This means that the measure of angle A is obtained as follows:
m<A = 2(14) + 35 = 28 + 35 = 63º.
For angle B, the two angles are supplementary, hence the value of x is given as follows:
10x - 18 + 15x + 48 = 180
25x = 150
x = 150/25
x = 6.
Then the measure of angle B is given as follows:
m < B = 15x + 48 = 15(6) + 48 = 138º.
For angle C, the alternate interior angles are congruent, hence the value of x is obtained as follows:
7x + 5 = 12x - 75
5x = 80
x = 16.
Then the measure of angle C is obtained as follows:
m<C = 7x + 5 = 7(16) + 5 = 117º.
For item 4, the angles form a linear pair, meaning that they are supplementary and the value of x is obtained as follows:
27x - 21 + 10x + 16 = 180
37x = 185
x = 185/37
x = 5.
Then angle D is calculated as follows:
m < D = 27x - 21 = 27(5) - 21 = 114º.
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find the exact length of the curve.x = 1/3 √y (y - 3), 16 ≤ y ≤ 25
Answers
The length of the curve x = 1/3 √y (y − 3) is 64/3.
What is arc length?The distance between two point along a segment of a curve is known as the arc length.
The equation of the curve is given by:
x = 1/3 √y (y − 3), 16 ≤ y ≤ 25
Length of the curve y = f(x) between point x =a to x = b is given by:
\(\int\limits^b_a {\sqrt{1+[f'(x)]^2} } \, dx\)
√1 + [f′(x)]2 dx.
x = 1/3 √y (y − 3)
x = 1/3 * \(y^\frac{3}{2}\) - \(y^\frac{1}{2}\)
Let's find the first derivative of x.
dx/dy = 1/3. 3/2. \(y^\frac{1}{2}\)- 1/2 . \(y^\frac{1}{2}\)
dx/ dy = 1/2 ( \(y^\frac{1}{2}\) - \(y^\frac{-1}{2}\))
(dx/dy)^2= 1/4 ( \(y^\frac{1}{2}\) - \(y^\frac{-1}{2}\))^2
= 1/4(y + \(y^-^1\)-2)
1 + {f′(x)}2 = 1 + 1/4(y +\(y^-^1\)-2)
= 1/4 y + 1/4\(y^-^1\)+ 1/2
1 + {f′(x)}2= 1/4 (y + \(y^-^1\) + 2)
√[1 + {f′(x)}2] = 1/2 ( \(y^\frac{1}{2}\) + \(y^\frac{-1}{2}\))
Length of curve is given by:
25
∫ \(\frac{\sqrt{y} }{2} +\frac{1}{2\sqrt{y} }\) dy
16
= \(\left \{ {{y=25} \atop {x=16}} \right.\) [\(y^\frac{3}{2}\)/3 + √y]
= [(25)3/2 /3 + √25] - [(16)3/2 /3 + √16]
= [125/3 + 5] - [64/3 + 4]
= 140/3 - 76/3
= (140 - 76)/3
= 64/3
So the length of the curve is 64/3
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if 26 children were to be born in a hospital on a given day, how many combinations of 6 boys and 20 girls would exist? 230,230 4 x 10^26 500,000 15 Z
Answers
The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.
]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.
In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.
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You have $1000 to invest in an account and need to have $2000 in one year. What interest rate would you need to have in order to have this if the amount is compounded weekly? Round your answer to the nearest percent.
Answers
Answer:
\(\large \boxed{\sf \ \ 70\% \ \ }\)
Step-by-step explanation:
Hello,
We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :
\(1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})\)
For the second week
\(1000\cdot (1+\dfrac{r}{5200})^2\)
After 52 weeks
\(1000\cdot (1+\dfrac{r}{5200})^{52}\)
and we want to be equal to 2000 so we need to solve:
\(1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...\)
Rounded to the nearest percent, the solution is 70%.
If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
4%
Step-by-step explanation:
is 103 perfect square? show your work
Answers
Answer:
yes
Step-by-step explanation:
Could not simplify further
Answer:
No, it's not a perfect square.
Step-by-step explanation:
First of all a perfact square should never end with 2, 3, 7 or 8, if it does than its not a perfect square.
103 ends with "3", so therefore, it's not a perfect square.
A rectangular prism has a width of 4 cm, a height of 3 cm and a depth of 5 cm. What is the volume of the prism?
Answers
We have that the equation of the volume of a rectangular prism is:
\(V=w\cdot h\cdot d\)in this case, we have the following information:
\(\begin{gathered} w=4\operatorname{cm} \\ h=3\operatorname{cm} \\ d=5\operatorname{cm} \end{gathered}\)then, using the formula we have:
\(\begin{gathered} V=4\cdot3\cdot5=12\cdot5=60 \\ V=60\operatorname{cm}^3 \end{gathered}\)therefore, the volume of the prism is 60 cm^3
Which of the following is the approximate measure of one of the sides of the Pentagon?
Answers
5) The circumcircle is the circle we can draw around the pentagon, where the pentagon is inside the circle.
The diameter of that circumcircle is 483.28 meters.
We have to find the length of one of the sides.
The diameter can be converted to a radius dividing it by 2:
\(r=\frac{D}{2}=\frac{483.28}{2}=241.64\)We will need to also know the measure of the interior angle of the pentagon.
For regular polygons we can calculate it as:
\(\begin{gathered} \alpha=\frac{(n-2)}{n}\cdot180\degree \\ \alpha=\frac{(5-2)}{5}\cdot180\degree \\ \alpha=\frac{3}{5}\cdot180\degree \\ \alpha=108\degree \end{gathered}\)We can then draw a right triangle that will let us calculate the side length (a):
As the radius R bisects the interior angle, we have an angle in the triangle that is half the interior angle: 108/2 = 54°.
Then, we can use trigonometric ratios to find a:
\(\begin{gathered} \cos(54\degree)=\frac{Adjacent}{Hypotenuse}=\frac{a\/2}{R} \\ R\cdot\cos(54\degree)=a\/2 \\ a=2R\cdot\cos(54\degree) \\ a\approx2\cdot241.64\cdot0.5877 \\ a\approx284.06 \end{gathered}\)Answer: 284.06 meters.
In ΔGHI, h = 9. 6 cm, g = 9. 3 cm and ∠G=109°. Find all possible values of ∠H, to the nearest 10th of a degree
Answers
The two possible values for angle H in triangle GHI are approximately 93.1 degrees and 273.1 degrees, rounded to the nearest tenth of a degree
How to find possible angle in GHI triangle?To find the possible values of angle H in triangle GHI, we can use the law of cosines.
Let's label angle H as x. Then, we can use the law of cosines to solve for x:
cos(x) = (9.3² + 9.6² - 2(9.3)(9.6)cos(109))/ (2 * 9.3 * 9.6)
Simplifying this equation, we get:
cos(x) = -0.0588
To solve for x, we can take the inverse cosine of both sides:
x = cos⁻ ¹ (-0.0588)
Using a calculator, we can find that x is approximately 93.1 degrees.
However, there is another possible value for angle H. Since cosine is negative in the second and third quadrants,
We can add 180 degrees to our previous result to find the second possible value for angle H:
x = 93.1 + 180 = 273.1 degrees
So the two possible values for angle H are approximately 93.1 degrees and 273.1 degrees, rounded to the nearest tenth of a degree.
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how to make a square with 50px sides tracy
Answers
To create a square with 50px sides, we need to draw four lines that are each 50px long and perpendicular to one another.
A square is a quadrilateral (a four-sided shape) with four equal sides and four equal angles of 90 degrees each. To create a square with 50px sides, we need to follow a few steps.
Step 1: Draw a line that is 50px long using a ruler or any other measuring tool.
Step 2: At the end of the line, draw a second line that is also 50px long and perpendicular to the first line. This will form the first side of the square.
Step 3: From the end of the second line, draw a third line that is also 50px long and perpendicular to the second line. This will form the second side of the square.
Step 4: Finally, draw a fourth line that is 50px long and perpendicular to the third line, connecting back to the starting point of the first line. This will form the remaining two sides of the square.
By following these steps, you have successfully created a square with 50px sides.
In summary, a square is a four-sided shape with four equal sides and angles of 90 degrees each. The resulting shape will be a square with 50px sides.
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