You are standing 40 meters from the base of the Empire state building. You estimate that the angle of elevation to the top of the 86th floor is 82 degrees. If the total height of the building is another 123 meters above the 86th floor what was the appropriate height of the building? Draw a picture and show work.
Answers
The total height of the building will be calculated as
\(H=y+123m\)Step 1: Calculate y using the trigonometric ratio tan
\(\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \text{where,} \\ \theta=82^0 \\ \text{opposite}=DB=y \\ \text{adjacent}=AB=40m \end{gathered}\)By substituting the values, we will have
\(\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 82^0=\frac{y}{40m} \\ \text{cross multiply, we will have} \\ y=40\times\tan 82^0 \\ y=284.6m \\ y\approx285m \end{gathered}\)Therfore,
The height of the building will be
\(\begin{gathered} H=y+123m \\ H=285m+123m \\ H=408m \end{gathered}\)Hence,
The Approximate height of the building = 408m
Related Questions
The speed limit is 35 mph
Which equation represents the statement?
\(a. \: s < 35\)
\(b. \: s \leqslant 35\)
\(c. \: s > 35\)
\(d. \: s \geqslant 35\)
Answers
Answer:
\( b.~~s \le 35 \)
Step-by-step explanation:
The speed limit is the maximum allowed speed. If the speed limit is 35 mph, you can drive at 35 mph or less than 35 mph. You need to show a speed that is less than or equal to 35 mph.
Answer:
\( s \le 35 \)
Find the next two positive and two negative angles that are coterminal with the given quadrantal angle.
Answers
Answer:
(1). 450 degree and 90 degree.
(2). - 270 degree and - 990 degree.
Step-by-step explanation:
So, we are given the the following data or parameters in this question or problem; A = -630 degree, and we are to look for the next two positive and two negative angles that are coterminal with the given quadrantal angle.
For the positive(+ve) angles we have that;
- 630 degree + 1080 degree = 450 degree; and - 630 degree + 720 degree= 90 degree.
For the negative(-ve) angles we have that;
- 630 degree + 360 degree= - 270 degree and - 630 degree - 360 degree = - 990 degree.
Lawrence purchased a used pickup truck for $16,550 by paying cash. If he had financed the truck with an installment plan, he would have had to pay a $3,000 down paymentand 48 monthly installments of $390. How much did he save by paying cash?$4,850$6,790$7.240$5,170None of these choices are correct.
Answers
Lawrence purchased a used pickup truck for $16,550 by paying cash. If he had financed the truck with an installment plan, he would have had to pay a $3,000 down payment
and 48 monthly installments of $390. How much did he save by paying cash?
$4,850
$6,790
$7.240
$5,170
None of these choices are correct.
we have that
3,000+48(390)=$21,720 ----> If he had financed the truck with an installment plan
Find out the difference
21,720-16,550=$5,170
therefore
answer is $5,170Someone please answer this!!!
Answers
Answer:
1. 2 eggs 2. 53 mph 3. $8 per hour 4. 1 \(\frac{3}{4}\) gal per hour
Step-by-step explanation:
1. There are 4 eggs used in 2 batches. For one batch, you divide 4 eggs by 2 batches to get 2 eggs for each batch.
2. There are 265 miles in total, so to get the average speed each hour, you divide the total by 5 hours to get 53 miles per hour.
3. In 7 hours, he got $56. Divide 56 by 7 to get the pay each hour, which would be $8 per hour.
4. In a half hour, the swimming pool has leaked a certain amount of water. Double that to get how many gallons per hour. \(\frac{7}{8} * 2= 1 \frac{3}{4}\) gallons per hour.
please answer i am stuck
Answers
(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).
In 2011 the assets are about $669.6 billion
(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).
In 2016 the assets are about $931.5 billion.
(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).
In 2019 the assets are about $1135.4 billion.
How to estimate the cost of the assets in 2011?Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:
\(A(x)=324e^{0.066x}\)
where:
A(x) is in billions of dollars.x = 7 corresponds to the year 2007.For the year 2011, the cost (in billions of dollars) is given by;
x = (2011 - 2007) + 7
x = 4 + 7
x = 11 years.
Next, we would substitute 11 for x in the exponential function:
\(A(11)=324e^{0.066 \times 11}\)
A(11) = $669.6 billions.
Part b.
For the year 2016, the cost (in billions of dollars) is given by;
x = (2016 - 2007) + 7
x = 9 + 7
x = 16 years.
Next, we would substitute 16 for x in the exponential function:
\(A(16)=324e^{0.066 \times 16}\)
A(16) = $931.5 billions.
Part c.
For the year 2019, the cost (in billions of dollars) is given by;
x = (2019 - 2007) + 7
x = 12 + 7
x = 19 years.
Next, we would substitute 19 for x in the exponential function:
\(A(19)=324e^{0.066 \times 19}\)
A(19) = $1135.4 billions.
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A computer training institute has 625 students that are paying a course fee of $400. Their research shows that for every $20 reduction in the fee, they will attract another 50 students. Which equation could be used to represent this situation, where x is the course fee and R(x) is the total revenue?
R(x) = −2.5x2 + 1625x
R(x) = −3x2 + 1650x
R(x) = 3x2 − 1650x
R(x) = 2.5x2 − 1625x
Answers
The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²
What is an Equations?Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
N(x) = 625 + 2.5x
The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:
R(x) = (625 + 2.5x)(400 - x)
Simplifying the expression, we get:
R(x) = 250000 + 375x - 2.5x²
Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:
R(x) = 250000 + 375x - 2.5x²
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An open box is to be made from a 5 ft by 9 ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have.
Answers
Answer: 21 ft³
Step-by-step explanation:
Let x represent the height of the box.
Then the 5 ft width of cardboard is (5 - 2x) when creating the box
and the 9 ft length of cardboard is (9 - 2x) when creating the box.
Volume = length x width x height
= (9 - 2x)(5 - 2x)(x)
= 45x - 28x² + 4x³
Using Calculus to solve for x, set the derivative equal to zero and use the quadratic formula to solve for x:
V' = 45 - 56x + 12x²
0 = 12x² - 56x + 45
x = 3.6, x = 1.0
Use those values to find the width, length, and volume:
height(x) × width (5 - 2x) × length (9 - 2x) = Volume
3.63 × -2.26*
1 × 3 × 7 = 21
*width cannot be negative so the height cannot be 3.63
Please please help me with this i have 40 missing assignments, if you help YOUR AMAZING
Answers
The volume of the prisms are:
1. 432 yd³
2. 36in³
3. 252 m³
4. 240 ft³
5. 576 mm³
6. 144 cm³
7. 343 m³
8. 120 yd³
9. 150 in³
How to determine the volumeThe formula for calculating the volume of a rectangular prism is expressed as;
V = lwh
such that;
l is the lengthw is the widthh is the heightNow, substitute the value for each of the prisms, we have;
1. Volume = 6 × 6 ×12
Multiply
Volume = 432 yd³
2. Volume = 2 ×9 × 2
Multiply
Volume = 36in³
3. Volume = 9 × 4 × 7
Multiply
Volume = 252 m³
4. Volume = 10 × 8 × 3
Multiply
Volume = 240 ft³
5. Volume = 4 × 12 × 12
Multiply the values
Volume = 576 mm³
6. Volume = 6 × 8 × 3
Volume = 144 cm³
7. Volume = 7 × 7 ×7
Volume = 343 m³
8. Volume = 8 × 3 × 5
Volume = 120 yd³
9. Volume = 5 × 6 × 5
Volume = 150 in³
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Martinez' General Store is having a 45% off sale on men's clothing. John paid $70.95 for a jacket that was on sale. What was the original price of the jacket?
Answers
Answer:
$129
Step-by-step explanation:
We can use this equation:
x - 0.45x = 70.95
0.55x = 70.95
x = $129
A taxi charges a flat rate of $3.50 plus an additional $0.75 per mile. If Nataly has $8, what is the furthest she can travel?
Answers
8.00 - 3.50 = 4.50
4.50 / .75 = 6
Nataly can travel 6 miles
choose the inequality that represents the following graph
Answers
Answer:
A
Step-by-step explanation:
if the hole is not shaded that means it can not equal 5 and due to the fact that the line stops at 5 means it's less than 5 so the answer is A
StartFraction 32 Over 8 EndFraction = StartFraction 28 Over x EndFraction
a.
x = 4
c.
x = 8
b.
x = 28
d.
x = 7
Answers
Answer:
d. x = 7
Step-by-step explanation:
\(\frac{32}{8} = \frac{28}{x}\)
Cross multiply, the denominator "8" is multiplied by numerator "28", while the numerator "32" is multiplied by denominator "x":
8 * 28 = 224
32 * x = 32x
\(32x = 224\)
Divide both sides by 32:
\(\frac{32}{32} = \frac{224}{32}\)
[x = 7]
Which inequality represents the situation described below?
The distance, d, is less than 200 miles.
A. d ≥ 200
B. d > 200
C. d ≤ 200
D. d < 200
Answers
Hello!
The distance, d, is less than 200 miles.
B. d > 200
I don’t know how to do this
Answers
Answer:
A
Step-by-step explanation:
Pick ONE of the two problems below to solve. The longest side of a trapezoid is 7 cm longer than the shortest side. The remaining two sides are both three times as long as the shortest side. If the perimeter of the trapezoid is 32 cm, write and solve an equation to find the lengths of all four sides of the trapezoid. Let s represent the length of the shortest side
Answers
Answer:
Let s be the length of the shortest side, then the length of the longest side is s+7cm, and the lengths of the remaining sides are both equal to 3s.
Now, recall that the perimeter of a trapezoid is the sum of the lengths of its sides, therefore we can set the following equation:
\(s+7cm+s+3s+3s=32cm\text{.}\)Adding like terms in the above equation we get:
\(8s+7cm=32cm\text{.}\)Subtracting 7cm from the above equation we get:
\(\begin{gathered} 8s+7cm-7cm=32cm-7cm, \\ 8s=25cm. \end{gathered}\)Dividing the above equation by 8 we get:
\(\begin{gathered} \frac{8s}{8}=\frac{25cm}{8}, \\ s=3.125cm\text{.} \end{gathered}\)Therefore the length of the shortest side is 3.125cm.
The length of the longest side is
\(3.125\operatorname{cm}+7\operatorname{cm}=10.125\operatorname{cm}\text{.}\)The lengths of the remaining two sides are:
\(3\times3.125\operatorname{cm}=9.375\operatorname{cm}\text{.}\)
Which of the following values are in the range of the function graphed below?Check all that apply.10+-10. 1002O A. -1OB. 2O C. 1O D. -6E. -2
Answers
The answer is (5, - 4) (Option D)
We are required to solve the system of equations:
\(\begin{gathered} 4x+y=16\text{ (Equation 1)} \\ 2x+3y=-2\text{ (Equation 2)} \end{gathered}\)In order to solve the equations, we need to make sure that one of the terms in both equations is the same.
In (Equation 1), there is a 4x term. In (Equation 2), there is a 2x term.
We can make 2x in (Equation 2), the same as 4x in (Equation 1), by multiplying the whole of (Equation 2) by 2
Let us perform this multiplication below:
\(\begin{gathered} 4x+y=16\text{ (Equation 1)} \\ 2x+3y=-2\text{ (Equation 2)} \\ \text{ Multiply (Equation) 2 by 2} \\ 2\times(2x+3y)=-2\times2 \\ 4x+6y=-4\text{ (Equation 3)} \\ \\ \text{Now we have two equations with 4x as a common term. They are:} \\ \\ 4x+y=16\text{ (Equation 1)} \\ 4x+6y=-4\text{ (Equation 3)} \end{gathered}\)Now that we have a similar term in both (Equation 1) and (Equation 2), we can subtract both equations to eliminate that term and then find the value of y.
This is done below:
\(\begin{gathered} 4x+y=16 \\ -(4x+6y)=-(-4)_{} \\ \\ 4x+y=16 \\ -4x-6y=4 \\ \\ 4x-4x+y-6y=16+4 \\ -5y=20\text{ (Divide both sides by -5)} \\ \\ \therefore y=-\frac{20}{5}=-4 \end{gathered}\)Now that we have the value of y, we can substitute this value into Equation 1 to get the value of x
This is done below:
\(\begin{gathered} \text{Equation 1:} \\ 4x+y=16 \\ \text{but y = -4} \\ \\ 4x+\text{ -4= 16} \\ 4x-4=16 \\ \\ \text{add 4 to both sides} \\ \\ 4x-4+4=16+4_{} \\ 4x=20\text{ (Divide both sides by 4)} \\ \\ x=\frac{20}{4}=5 \end{gathered}\)Therefore, the solution to the system of equations is:
x = 5, y = -4
Thus the final answer is (5, - 4) (Option D)
Find domain Range Y-intercept X- intercept Vertical asymptote Horizontal asymptote Pic attached below note write domain and range in interval notation
Find domain
Range
Y-intercept
X intercept
Vertical asymptote
Horizontal asymptote
Pic attached below
Answers
The key features of this rational function include the following:
Domain: (-∞, -1) ∪ (-1, ∞)
Range: (-∞, -2) ∪ (-2, ∞)
Y-intercept: 1.
X-intercept: 1/2.
Vertical asymptote: x = -1.
Horizontal asymptote: y = -2.
What is an asymptote?In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).
In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.
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HELP!!!!!! WHAT DID I do wrong????
Answers
Answer:
Y = 1/4x + 0 or Y = 1/4x
Step-by-step explanation:
Teacher circles the 4 because the point was (1,4)
Slope is rise over run
You risen 1 unit on the y-axis, then you went over 4 units on the axis, making the slope 1/4x
PLEASE CLICK ON THIS IMAGE I NEED HELP
Answers
Answer:
The answer is C. the number of cups sold
Step-by-step explanation:
Answer:
The number of cups sold is the answer
Step-by-step explanation:
Y = The total earnings
0.5 = The price per cup
x= The amount of cups being sold
Help please f/18 = -6
Answers
Answer:
f=-108
Step-by-step explanation:
f/18=-6
f= -6 x 18
f= -108
Answer:
f=-108
Step-by-step explanation:
Since F divided by 18 is -6, just multiply -6 and 18 to get the answer
Which number has a 4 with a value ten times less than the 4 in the number 123,469?
Answers
The number that has a 4 in the hundred places.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
A 4 with a value ten times less than the 4 in the number 123,469.
First, the value of the 4 in the number 123,469 can be found by separating each digit as:
123,469 = 100,000 + 20,000 + 3,000 + 400 + 60 + 9
Then the value of the 4 is 400.
Now we want a number that has a 4 with a value then times less than 400. Then we have
400/10 = 40
Then we want a number that has a 4 in the hundred places.
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What is the solution to the system of equations graphed below?
o
A. (1,1)
B. (0, -4)
C. (2.5)
D. (-5.-3)
Answers
Answer: b
Step-by-step explanation:
Find the domain and solve.
(d) log₄²(1+x²)=0.25
Answers
The domain and the solution of the equation log₄²(1+x²)=0.25 are x = ±1
How to determine the domain and the solution?From the question, we have the following parameters that can be used in our computation:
log₄²(1+x²)=0.25
In this case, the domain of the expression and the solution are the same
So, we start by taking the square root of both sides
log₄(1+x²) = 0.5
Next, we apply the change of base law of logarithm
So, we have
1 + x² = 4⁰°⁵
Evaluate the exponent
1 + x² = 2
Evaluate the like terms
x² = 1
Take the square root of both sides
x = ±1
Hence, the domain and the solution are x = ±1
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You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second,
determine how long it will take for the object to hit the ground below. NEAREST TENTH
Answers
You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second, 64.23 feet/second long it will take for the object to hit the ground below. This can be solved using the concept of law of conservation of energy.
What is law of conservation of energy?Three fundamental quantities all maintain their original values. Energy, momentum, and angular momentum are these. Energy is a conserved quantity, which could surprise you if you've read instances in previous pages, such the kinetic energy of charging elephants. The first law of thermodynamics, generally known as the law of conservation of energy, stipulates that the energy of a closed system must remain constant and cannot rise or fall on its own without external intervention.
Given that,
Height of the cliff, h= 55 Foot
Initial speed of the projectile, u = 85 m/s
Let, the projectile hit the ground with velocity "v"
Applying the law of conservation of energy,
mgh + 1/2 mu² = 1/2 mv²
or, m (gh + 1/2 u²) = 1/2 mv²
or, (gh + 1/2 u²) = 1/2 v²
or, 10 × 55 + (1/2 × (55)²) = 1/2 v²
or, 550 + 1512.5 = 1/2 v²
or, 2062.5 = 1/2 v²
or, 4125 = v²
or, v = 64.23 feet/second
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The price of an item has been reduced by 2.09 The original price was 99.15 What is the price now?
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The current price of the item is 97.06
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Original price of an item = 99.15
The price has been reduced by 2.09.
The current price.
= 99.15 - 2.09
= 97.06
Thus,
The current price of the item is 97.06
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Need Help You Can Get 35 point!!!
The width of a rectangular field is represented by x meters. The length of the field is 10 more than twice its width . The area of the field is 5500m^2
Part A
Write an equation that can be used to determine the dimensions, in meters, of the field.
Part B
What is the width, in meters, of the field?
The width is ( ) meters.
Answers
Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x
Part B: width is 50 meters.
How to determine the valueThe formula for calculating the area of a rectangle is expressed with the equation;
A = lw
Such that the variables are expressed as;
A is the areal is the lengthw is the widthWe then have that;
l = 2x + 10
Substitute the values
5500 = (2x + 10)(x)
expand the bracket
5500 = 2x² + 10x
2x² + 10x - 5500
x² + 5x - 2750
x² + 55x - 50x - 2750
x(x + 55) - 50(x + 55)
x = 50 meters
Length = 2(50) + 10
Length = 100 + 10 = 110 meters
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If f(x)= 2(3 to the power of x) +1 what is the value of f(2)
Answers
Answer:
19
Step-by-step explanation:
f(x)= 2(3^x) + 1
f(2)= 2(3^2) + 1
= 2(9) + 1
= 18 + 1
= 19
Which of the following is an example of the Distributive Property?
2x - 20y = - 20y - 2x
5x2 * 7x2 - 5 + 2= 12x2 - 3
(7xh)k = 7x(hk)
2z2(2y - 5) = 4z2y - 10z2
Answers
Answer:
2z2(2y - 5) = 4z2y - 10z2
Step-by-step explanation:
I hope this helps
Answer:
\(2z^2(2y - 5) = 4z^2y - 10z^2\)
Step-by-step explanation:
Televisions and monitors come in two common aspect ratios, 4:3 and 16:9 (sometimes
16:10 is also used). A 42 inch TV suggests that the main diagonal of the TV is 42 inches.
Determine the dimensions of the screen of a 42 inch TV with a 4:3 aspect ratio.
Answers
Answer:
The dimension of the TV = 11.2 inches × 8.4 inches
Step-by-step explanation:
Let x be the length of the TV
Let y be the width of the TV
x : y = 4:3
\(\frac{x}{y} = \frac{4}{3} \\cross-multiplying\\3x = 4y \\x = \frac{4}{3} y- - - - - (1)\)
From the figure attached:
using Pythagoras theorem
x² + y² = 42²
where:
\(x = \frac{4}{3} y\\(\frac{4}{3}y)^2 + y^2 = 42^2\\\frac{16}{9}y^2 + y^2 = 1764\\ \frac{16y^2}{9} + \frac{y^2}{1} = 1764\\\frac{16y^2 +9y^2}{9}= 1764\\ cross-multiplying\\16y^2 + 9y^2 = 1764\\25y^2 = 1764\\y^2 = \frac{1764}{24}\\y^2 = 70.56\\y = \sqrt{70.56} \\y = 8.4\ inches\\Finding\ x:\\x = \frac{4}{3} y\\x = \frac{4}{3} \times 8.4\\ x = 1.33 \times 8.4\\x = 11.2\ inches\\\therefore\ the\ dimensions\ are\ 11.2\ inches \times 8.4\ inches\)
A 12 oz box of sugar costs $3.10 and a 36 oz box of sugar costs $7.90. Which box of sugar is the better buy?
Answers
Answer: 36 oz box
Step-by-step explanation:
3.1/12=0.258333
7.9/360.291444
Thus, the 36 oz box is the better buy