A triangular frame is being built as the support for a ramp. The longest part of the
frame will sit on the ground. The second longest side is 2'3" and forms an 18°
angle with ground. The smallest side is 10" long. Determine the angle the
smallest side will make with the ground.
Answers
The smallest side of the triangle makes an angle of approximately 20.6 degrees with the ground.
To determine the angle the smallest side will make with the ground, we can use the law of sines. The law of sines states that for any triangle ABC:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.
Let's label the sides of our triangle as follows:
The longest side (sitting on the ground) is side c
The second longest side is side b
The smallest side is side a
We know that side b is 2'3" long, which is equivalent to 27 inches. We also know that side a is 10 inches long. We can use the law of sines to solve for the angle opposite side a:
sin(A) = (a/c) * sin(C)
We can solve for sin(C) by using the fact that the sum of the angles in any triangle is 180 degrees:
C = 180 - A - B
We know that angle B is 18 degrees, so we can substitute that into our equation for C:
C = 180 - A - 18
C = 162 - A
Substituting this expression for C into our equation for sin(A), we get:
sin(A) = (a/c) * sin(162 - A)
We know that c is the longest side of the triangle and therefore opposite the largest angle. Since we are interested in the angle opposite side a, we can assume that angle A is the smallest angle in the triangle. We can use this assumption to simplify our equation for sin(A):
sin(A) = (a/c) * sin(162)
Plugging in the values for a, c, and sin(162), we get:
sin(A) = (10/27) * 0.951
sin(A) = 0.352
Taking the inverse sine of both sides, we get:
A = sin^-1(0.352)
A ≈ 20.6 degrees
Therefore, the smallest side of the triangle makes an angle of approximately 20.6 degrees with the ground.
To learn more about smallest visit:
https://brainly.com/question/14677993
#SPJ11
Related Questions
estimate the error that is made by approximating the sum of the given series by the series the fitst 5 terms 1/k^3
Answers
The error involved in approximating the sum of the given series by the sum of the first five terms of the series is `R5 = 1/6³ + 1/7³ + ...`.
To estimate the error that is made by approximating the sum of the given series by the series the first 5 terms 1/k³, we can use the remainder term of a convergent series.
The given series is ∑ 1/k³ from k = 1 to infinity.We have to find the error involved in approximating the sum of the given series by the sum of the first five terms of the series.
That is, we need to find the difference between the actual sum of the series and the sum of the first five terms of the series.
The sum of the series is given by: `S = 1/1³ + 1/2³ + 1/3³ + 1/4³ + ... + 1/n³ + ...` We can use the remainder term of the series to find the error in approximation.
The remainder term `Rn` is given by: `Rn = Sn - S` where `Sn` is the sum of the first `n` terms of the series. Thus, we have to find the remainder term for `n = 5`.
The remainder term `Rn` is given by: `Rn = S - Sn = 1/6³ + 1/7³ + ...` Since the given series is convergent, the remainder term `Rn` tends to zero as `n` tends to infinity.
So, if we take the sum of the first five terms of the series, the error involved in approximation is given by the remainder term `R5`.
The error involved in this approximation is very small and can be neglected.
To learn more about : terms
https://brainly.com/question/30643700
#SPJ8
What is the y-intercept of the quadratic function f(x) = (x-8)(x+3)
Answers
Answer:
-24
Step-by-step explanation:
To find the y intercept, plug x in as 0.
Answer:
-24
Step-by-step explanation:
Y intercept is where graph cuts the y axis and it satisfies x=0
So put x=0 in your equation
F(0)= -8 x 3
F(0)= -24
Therefore y-intercept= -24
According to the graph, what is the value of the constant in the equation
below?
A. 60
B. 30
C. 15
D. 72
Answers
\( \sf \dag \: \red{Answer :-}\)
Let us consider point A,
We are given that,
\( \sf : \implies \: height = \frac{constant}{width} \: \: \: \: \: \: \\ \therefore \sf constant = height \: \times width\)
Now, we can simply put the given values at Point A,
\( \sf \: constant = 30 \times 2 = 60\)
To verify, let's move on to next point, i.e. point B,
\( \sf \: costant = 10 \times 6 = 60\)
Hence, verified, the constant is \( \sf \red{60}\).
Hope it helps you :)
there are 3 plots in Kevin's garden. Last year Kevin planted 10 lilies in one plot. This year, there are 30 lilies on each plot. How many total lilies are on Kevin's land now?
Answers
Answer:He used 6 plots of land.
explanation:
total no. of plots =10 (land was divided in 10 equal parts)
used plots = 3/5 of 10 =3/5*10 =6
Step-by-step explanation:
neil uses 41-cent stamps and 8-cent stamps to mail a gift card to a friend. if the postage is $1.95, how many of each stamp did neil use?
Answers
If Neil uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend , then the number of 41 cent stamp used is 3 and number of 6 cent stamps used is 12 .
Let number of 41 cents stamps used be = x ;
and let number of 6 cents stamps used be = y ;
converting amount 41-cents in dollars is = $0.41 ;
and converting amount 6-cents in dollars is = $0.06 ;
the amount for which Neil used 41-cent stamps , 6-cent stamps is = $1.95 ;
this situation in equation form is written as ⇒ 0.41x + 0.06y = 1.95
Multiplying on both sides by 100 , we get
⇒ 41x + 6y = 195 ;
⇒ y = (195 - 41x)/6 ;
We will test this equations for values of x and y , the number of stamps must be whole numbers .
If x = 1 , then value of y is = 25.66
If x = 2 , then value of y is = 18.833
If x = 3 , then value of y is = 12
If x = 4 , then value of y is = 5.166 .
the only value of x and y which shows a whole number as an output is : If x = 3 , then y = 12 .
Therefore , Neil used "3" 41-cents stamps and "12" 6-cent stamps .
Learn more about Equations here
https://brainly.com/question/14532602
#SPJ4
At the Planetarium, tickets cost $9 for adults and $7 for kids under 12. What would be the total cost for 2 adult tickets and 16 kids tickets? What would be the total cost for aa adult tickets and kk kids tickets?
Answers
$9 adults
$7 kids
9×2=18 ($) parents/adults
16×7=112 ($) kids
I don't understand the last question
Answer:
126 sir :3
Step-by-step explanation:
point) Suppose f' (x) is a differentiable increasing function for all x. In each of the following pairs, which number is the larger? For each, enter A or B_ 1. Comparing A. f'(7) and B. f'(8) is larger 2. Comparing A f "(7) and B. 0 : is larger 3. Comparing A_ f(7 + Ax) and B. f(7) +f'(7)Ax is larger For each, make sure that you can explain why:
Answers
B. f'(8) is larger.Since f'(x) is an increasing function, it means that its slope is increasing as x increases.
Therefore, since we are comparing the slope at x = 7 and x = 8, we can conclude that the slope at x = 8 (B) is larger than the slope at x = 7 (A). This is because as x increases from 7 to 8, the slope of f'(x) is increasing.
A. f "(7) is larger.Since f'(x) is an increasing function, it means that its slope is always positive.
Therefore, its second derivative f "(x) represents the rate of change of the slope of f'(x). If f "(7) is positive, it means that the slope of f'(x) is increasing, which implies that the function is becoming steeper.
On the other hand, if f "(7) is zero, it means that the slope of f'(x) is not changing, which implies that the function is not becoming steeper. Hence, A is larger.
A. f(7 + Ax) is larger.
Using the first-order Taylor approximation, we have:
f(7 + Ax) ≈ f(7) + f'(7)Ax + O(Ax)^2
where O(Ax)^2 represents the higher-order terms that are negligible as Ax approaches zero. Therefore, if we neglect the higher-order terms, we can say that:
f(7 + Ax) ≈ f(7) + f'(7)Ax
Now, since f'(x) is an increasing function, it means that its slope is positive for all x. Therefore, when Ax is positive (i.e., when we move to the right from x = 7), f(7 + Ax) will be larger than f(7) + f'(7)Ax.
This is because f(7 + Ax) represents the actual function value at 7 + Ax, while f(7) + f'(7)Ax represents the linear approximation of the function at 7 + Ax. Hence, A is larger.
For more questions like Function click the link below:
https://brainly.com/question/21145944
#SPJ11
solve the square: x^2-4x+8=0
Answers
Answer:
(x-2)^2+4.
Hope this helps!
24x27= Will give brainless
Answers
Answer:
648
Step-by-step explanation:
here u go
Answer:
648
Step-by-step explanation:
24 x 27 = 648
hey need help fast!!!
Answers
Answer:
MN║OP
Step-by-step explanation:
From the picture attached,
MP and OP are the two lines and OT is a transversal intersecting these lines at R and S.
Angles on the same side of transversal OT measure the same as 45°
By the converse of corresponding angles theorem,
"If the corresponding angles formed by the transversal with the lines, are equal in measure, then the lines are parallel."
Therefore, MN║OP is the answer.
Andre went online and visited websites for two banks to check their interest rates on savings accounts. For a $750 deposit, he can either earn 4.5% for 3 years at Bank A or 5%for 2 years at Bank B. How much would Andre earn from Bank B?
Help ASAP
Answers
Answer:75.00
Step-by-step explanation:750 x 5% x 2 = 75
Determine the value of x.
Question 1 options:
A)
8
B)
4
C)
4
D)
Answers
\(\huge{\underline{\underline{\boxed{\sf{\purple{Answer:-}}}}}}\)
option c is correct\(\huge{\underline{\underline{\boxed{\sf{\purple{Explanation:-}}}}}}\)
\(\large\huge\green{\sf{Given:-}}\)
in a right triangle:-hypotenuse= 8 unitbase= x\(\large\huge\green{\sf{ToFind:-}}\)
base= x=??\(\large\huge\green{\sf{FormulaRequired:-}}\)
\( sec Q= \frac{hypotense}{base} \)value of sec 30°= 2/√3\(\large\huge\green{\sf{Solution:-}}\)
\( \red {\mathbb{ \underline { \tt By \: Using \: Trigonometric\: Formula:-}}}\)
\( sec Q= \frac{hypotense}{base} \)value of sec 30°= 2/√3➡2/√3= 8/x
➡x= 8√3/2
➡x= 4√3
➡Hence, required answer is 4√3
Krutika and Natasha win some money and share it in the ratio 4:3. Krutika gets £7 more than Natasha. How much did they get altogether?
Answers
Answer:
49
Step-by-step explanation:
The computation of the total amount is shown below:
Let us assume the natasha be 4x
And, the krutika be 3x
Now as per the situation
4x = 3x + £7
x = £7
For natasha = 4(7) = 28
For krutika = 3(7) = 21
So, the total amount is
= 28 + 21
= 49
Dana has 8 baseball cards, 10 football cards, 4 hockey cards, and 14 basketball cards. All the cards are the same size and shape. Dana will select one card at random.
What is the probability that the care selected will be a hockey card?
A. 1/9
B. 1/8
C. 1/4
D. 1/3
Answers
Answer:1/8
Step-by-step explanation:
well the total amount you have of cards is 36 so you will have 4/36 now you just need to reduce and you will get 1/8
$(x^2-4x+2)^{x^2-5x+2} = 1.$
;PPP
Answers
It shows how you kind of get the answer and kind of explains it.
find the value of the potential at 16.0 cmcm from the center of the sphere.
Answers
The value of the potential at 16.0 cm from the center of the sphere is 1.581 × 10⁸ volts
To find the value of the potential at 16.0 cm from the center of the sphere, let's apply the equation of electric potential for a solid sphere:V = k Q / R where k is the Coulomb constant, Q is the charge of the sphere, and R is the radius of the sphere.
We know that the sphere is electrically charged, so the equation will be:
V = k Q / R
We are given that the radius of the sphere is R = 15.0 cm.
We need to find the value of Q, the charge of the sphere.
To find the value of Q, let's apply the equation for the electric field due to a charged sphere:
r < R: E = k Q r / R³r > R: E = k Q / r²
In this case, we need to find the value of the potential at 16.0 cm from the center of the sphere, which means that r > R (since R = 15.0 cm).So, we can use the second equation:
V = k Q / rwhere r = 16.0 cm.
We need to express k in terms of Coulombs law: k = 1 / 4πε₀ where ε₀ is the electric constant.
ε₀ = 8.85 × 10⁻¹² F/m²k = 1 / 4πε₀ = 9 × 10⁹ N m² / C²
Now we can substitute the known values into the equation:
V = k Q / rV = (9 × 10⁹ N m² / C²) Q / (16 × 10⁻² m)
V = 5.625 × 10⁷ Q (in volts)
We still need to find the value of Q.
For that, we can apply the equation for electric field:r < R: E = k Q r / R³r > R: E = k Q / r²
Since we know that the electric field at r = R is σ / ε₀, where σ is the surface charge density, we can use this information to find Q.r = R:
E = σ / ε₀σ = Q / (4πR²)
E = k Q / R³σ / ε₀
= k Q / R²Q
= σ R⁴ / ε₀
Now we can substitute the known values into the equation:
Q = σ R⁴ / ε₀
Q = (1.5 × 10⁻⁸ C/m²) (0.15 m)⁴ / (8.85 × 10⁻¹² F/m²)
Q = 2.804 C
Finally, we can substitute the value of Q into the equation for V:
V = 5.625 × 10⁷ (2.804)V
= 1.581 × 10⁸ volts
Therefore, the value of the potential at 16.0 cm from the center of the sphere is 1.581 × 10⁸ volts.
Know more about the Coulomb constant
https://brainly.com/question/506926
#SPJ11
Shane plans on finding a summer job so he can earn enough money to buy a new laptop that costs $595. He has already saved $150. If Shane
finds a summer job that pays him $7.50 an hour after taxes are withheld, what is the minimum number of hours he will have to work in order to
purchase the laptop?
80
79
60
59
Answers
Answer:
59
Step-by-step explanation: x=number of hours
150+7.50x=595
7.50x=595-150
7.50x/7.50=445/7.50
x=59
Plz Help (ASAP) Thanks
Answers
Answer:
x^4 - 3x^2 + x^2 - 4
Step-by-step explanation:
hope it helps
Let V and W be vector spaces, and let T:V→→W be a linear transformation. Given a subspace U of V, let T(U) denote the set of all images of the form T(x), where x is in U. Show that T(U) is a subspace of W.To show that T(U) is a subspace of W, first show that the zero vector of W is in T(U). Choose the correct answer below.A. Since V is a subspace of U, the zero vector of U, 0, is in V. Since T is linear, T(0)=Ow, where 0w is the zero vector of W. So Oy is in T(U ). B. Since U is a subspace of W, the zero vector of W, Ow, is at U. Since T is linear, T(0) = 0, where 0, is the zero vector of V. So Ow is at T( U).C. Since V is a subspace of U, the zero vector of V, Oy, is in U. Since T is linear, T(0)=0w, where 0w is the zero vector of W. So 0 is in T(U ).D. Since U is a subspace of V, the zero vector of V, 0y, is at U. Since T is linear, T(0)=0, where 0 is the zero vector of W. So 0w is at T(U ).
Answers
T(U) is a subspace of W Since V is a subspace of U, the zero vector of V, 0, is in U. As T is linear, \(T(0) = 0_w\) , where \(0_w\) is the zero vector of W. Therefore, \(0_{w}\) is in T(U).
It can be proved Since U is a subspace of V, the zero vector of V, 0y, is in U. Since T is linear, \(T(0_{y}) = 0_{w}\) , where \(0_{w}\) is the zero vector of W. So\(0_{w}\) is in T(U).
To show that T(U) is a subspace of W, we also need to show that T(U) is closed under vector addition and scalar multiplication. Let u1, u2 be vectors in U, and let c be a scalar. Then we have: \(T(u1 + u2) = T(u1) + T(u2)\) (since T is linear)
\(T(cu1) = cT(u1)\) (since T is linear)
Since U is a subspace of V, we have \(u1 + u2\) and \(cu1\) are also in U. Therefore, \(T(u1 + u2)\) and \(T(cu1)\) are both in T(U), which shows that T(U) is closed under vector addition and scalar multiplication.
Thus, T(U) is a subspace of W.
To practice more about the vector spaces:
https://brainly.com/question/13045843
#SPJ11
Which expression should you simplify to find the 90% confidence interval,
given a sample of 65 people with a sample proportion of 0.42?
O A. 0.42
1.645-0.42
165
OB. 0.42 65
0.42(1–0.42
1.645
O c. 0.42 +1.645.
0.42(1-0.42)
65
O D. 0.42 +1.645.
V0.42(1–0.42)
65
Answers
Answer:
i think is would be D
hope that helps if not i can change it
Step-by-step explanation:
Allen has been asked to replicate a scientific diagram in his notebook. The teacher has told him that variations in lengths of up to 2 centimeters are acceptable. If a test tube is 7 centimeters long in the original diagram, write an equation to help Allen find the maximum and minimum acceptable lengths of the test tube in his diagram. (Let x represent the length of the test tube in the new diagram.)
Answers
Answer:
7 ± 2 = x
Step-by-step explanation:
± means plus or minus
A ladder is leaning against a tall wall with the foot of the ladder placed at 7 feet from the base of the wall and the angle of elevation is 73' 30' 40"
Answers
Complete question is;
A 21 ft ladder is leaning against a tall wall with the foot of the ladder placed at 7 feet from the base of the wall and the angle of elevation is?
Answer:
θ = 70.5°
Step-by-step explanation:
The angle of elevation simply means the angle that the ladder makes with the ground. Let's call this angle θ.
I've attached a diagram showing the triangle made by this ladder and the wall.
From the attached diagram, we can see the triangle formed by the ladder and the wall.
We can find the angle of elevation θ from trigonometric ratios.
Thus;
7/21 = cos θ
cos θ = 0.3333
θ = cos^(-1) 0.3333
θ = 70.5°
Harlon recorded this set of data, which contains an outlier.
163, 97, 184, 199, 169, 175
What is the range of this set of data?
12
97
102
172
Answers
Answer:
Answer C: 102
Step-by-step explanation:
The correct answer for the question is 102. I did the quiz and got it right.
Hope this helps you!
~Me ^^
time-use data show that married american women have cut their housework time roughly in half over the last half-century, while men have:
Answers
Over the last half-century, time-use data has shown that married American women have significantly reduced their housework time, cutting it roughly in half.
This change can be attributed to various factors such as advancements in home appliances, shifting gender roles, and increased participation of women in the workforce. On the other hand, men have gradually increased their contributions to housework during this period.
This shift in housework responsibilities can be attributed to societal changes that promote a more equitable distribution of domestic tasks between partners. As gender norms have evolved, men are increasingly taking on roles that were once predominantly associated with women, leading to a more balanced approach to housework within households. Additionally, the rise in dual-income families has necessitated a more equal division of domestic responsibilities.
In summary, over the past 50 years, married American women have seen a considerable decrease in housework time, while men have increased their contributions. This change reflects evolving gender roles and societal expectations, promoting a more equal division of labor within households.
Learn more about predominantly here:
https://brainly.com/question/521450
#SPJ11
Solve the system by substitution.
y = x
y = 23 - 8
Answers
Answer:
x=15, y=15
Step-by-step explanation:
y=23-8
y=x, thus x=23-8 and y and x are the same thing (given from the first equation)
23-8=15
So, y and x are both 15
X=Y so they are the same thing
Y=23-8
23-8=15
in 2010, haiti was hit by a devastating earthquake, which registered at 7.0
Answers
Answer:Richter scale measures intensity of earthquake as power of 10. The intensity of the Chilean earthquake( year 1960) was approx 316.23 times greater than the earthquake in Haiti (year 2010)How to measure the greatness of earthquakes from Richter scale's intensities?Suppose that the first measured earthquake was of intensity (on Richter scale)Suppose the second measured earthquake was of intensity(on Richter scale).It is a fact that each unit of the the Richter scale measurement increases as the power of 10.So if b = a + 1, then the second earthquake was 10 times greater than the first earthquake.If we have b = a + x, then we have:Second earthquake was times greater than the first earthquake.As it was given that the earthquake in Haiti was of 7.0 intensity on Richter scale, and that the Chilean earthquake was about 9.5 intensity on Richter scaleThe difference is 9.5 - 7 = 2.5
Step-by-step explanation:
The table below shows an inequality and a number by which to multiply both sides. Inequality Multiply each side by Negative 2 less-than 3 Negative 5 What is the resulting true inequality? Negative 10 less-than negative 15 Negative 10 greater-than negative 15 10 less-than negative 15 10 greater-than negative 15
Answers
Answer:
(D) 10>-15
Step-by-step explanation:
Answer:
Answer is D 10 > -15
Step-by-step explanation:
the interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model. t or f
Answers
True. the interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.
what is slope in statistics?The slope and intercept of a line reveal the steepness of the line and the location in which it intersects an axis. The slope and intercept of the logistic relationship of the two variables can be utilized to get the average change rate. The ratio of a change in the variable y to the rise in the x component is known as the the line's slope.
Briefing:Y = a + bX, where X seems to be the mediating variable and Y is the response variable, is the equation of a linear regression line. A is the intersection (the result of y for x = 0), and b is the line's slope.
To learn more about slope visit:
https://brainly.com/question/29690915
#SPJ4
you are ordering shirts for a club at your school. the function f(x)=8x+12 represents the cost of ordered x shirts how much would it cost to buy 32 shirts
Answers
The cost of ordering shirts for a club is 268 units.
Define Function.
A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.
This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).
The statement that f is a function from X to Y using the function notation f: X→Y
The function that represents the cost of the shirts(x) is f(x) = 8x+12
Now, for x = 32
f(x) = 8x+12
f(32) = 8(32) + 12
= 256 +12
f(32) = 268 units
.
To know more about Function visit:
brainly.com/question/12431044
#SPJ1
The table and graph show the height (y), in feet, of water in a cattle tank at the end of each day (x) after it is filled.
Which of the following statements is not a valid conclusion from this information?
Answers
The invalid conclusion from the given information is -
It does not represent a exponential relationship.The initial amount of water in the cattle tank is not zero.What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a table and graph show the height (y), in feet, of water in a cattle tank at the end of each day (x) after it is filled.
The invalid conclusion from the given information is -
It does not represent a exponential relationship.The initial amount of water in the cattle tank is not zero.Therefore, the invalid conclusion from the given information is -
It does not represent a exponential relationship.The initial amount of water in the cattle tank is not zero.To solve more questions on algebraic expressions, visit the link below-
brainly.com/question/1041084
#SPJ1