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Kobotan [32]
2 years ago
10

How tall is a building that casts a 71​-ft shadow when the angle of elevation of the sun is 29 degrees​?

Mathematics
1 answer:
TiliK225 [7]2 years ago
4 0
We can use trigonometry to solve the problem. First draw a picture of the situation to understand what is going on (See the attached photo).

Next, we can use the tangent  function to solve for the height of the building:

tan(29^{\circ})= \frac{h}{71}

Next, rearrange the problem to solve for h:

h = 71tan(29^{\circ})

h = 39.356 ft

You might be interested in
What is the domain of the function y= square root x - 5 - 1
IrinaK [193]

Answer:

x\geq 5

Step-by-step explanation:

The function that we have to study in this problem is

y=\sqrt{x-5}-1

The domain of a function is defined as the set of all the possible values of x that the function can take.

For a square-root function, there are some limitations to the possible value of the argument in the root.

In particular, the argument of a square root must be equal or greater than zero, because the square root of a negative number is not defined.

Therefore, in this case, we have to set the following condition for the domain:

x-5\geq 0

And by solving, we get

x\geq 5

which means that the domain of this function is all real numbers equal or greater than 5.

5 0
3 years ago
Andrew has a four-year college loan for $20,000. The lender charges a simple interest rate of 5 percent. How much interest will
Olegator [25]

Given that loan amount P=20000

Interest rate r=5% = 0.05

Time of loan t=4 years

Now to find the interest amount we just plug those values into formula

simple interest = P × r × t

simple interest = 20000* 0.05* 4

simple interest = 1000 * 4

simple interest = 4000

Hence final answer is choice b. $4000.

7 0
3 years ago
Read 2 more answers
107 = 7 - 2(7b - 1) what does b equal?
topjm [15]

107 = 7 -2 (7b - 1)

First, distribute -2 to all terms within the parenthesis

-2(7b - 1) = -14b + 2

107 = 7 -14b + 2

Combine like terms

107 = -14b (+7 + 2)

107 = -14b + 9

Isolate the b. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

Subtract 9 from both sides

107 (-9) = -14b + 9 (-9)

107 - 9 = -14b

98 = -14b

Isolate the b. Divide -14 from both sides

(98)/-14 = (-14b)/-14

98/-14 = b

b = −7

-7 is your answer

hope this helps

5 0
3 years ago
What is the average speed for the interval t=1 hour to t=3 hours
inysia [295]

Answer:

7.5 miles per hour

Step-by-step explanation:

Average speed over the interval [1, 3] = (distance at 3 hrs -distance at 1 hr)/(3 hrs - 1 hr)

From the graph:

Distance at 3 hrs = 30 => (3, 30)

Distance at 1 hr = 15 => (1, 15)

Average speed = (30 - 15)/(3 - 1)

Average speed = 15/2

= 7.5

Therefore, average speed = 7.5 miles per hour

5 0
2 years ago
Please help with algebra problem
kumpel [21]
Number of weekend minutes used: x
Number of weekday minutes used: y

This month Nick was billed for 643 minutes:
(1) x+y=643

The charge for these minutes was $35.44
Telephone company charges $0.04 per minute for weekend calls (x)
and $0.08 per minute for calls made on weekdays (y)
(2) 0.04x+0.08y=35.44

We have a system of 2 equations and 2 unkowns:
(1) x+y=643
(2) 0.04x+0.08y=35.44

Using the method of substitution
Isolating x from the first equation:
(1) x+y-y=643-y
(3) x=643-y

Replacing x by 643-y in the second equation
(2) 0.04x+0.08y=35.44
0.04(643-y)+0.08y=35.44
25.72-0.04y+0.08y=35.44
0.04y+25.72=35.44

Solving for y:
0.04y+25.72-25.72=35.44-25.72
0.04y=9.72

Dividing both sides of the equation by 0.04:
0.04y/0.04=9.72/0.04
y=243

Replacing y by 243 in the equation (3)
(3) x=643-y
x=643-243
x=400

Answers:
The number of weekends minutes used was 400
The number of weekdays minutes used was 243
6 0
3 years ago
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