Ask question

Ask question

All categories

3 years ago

12

Two runners in a marathon determine that the angles of elevation of a news helicopter covering the race are 38 degrees and 45 de

grees. If the helicopter is 1700 feet above the finish line, how far apart are the runners? (Round your answer to the nearest foot) *

1 answer:

rjkz [21]3 years ago

6 0

Answer:

476 feet

Step-by-step explanation:

The given problem when graphically depicted forms a right triangle which has been attached below.

We want to determine the distance between Runner A and Runner B in the diagram.

Using Trigonometric Ratios

In Right Triangle AHC

$\tan 38^\circ =\dfrac{1700}{AC} \\$Cross multiply$\\AC *\tan 38^\circ =1700\\AC =\dfrac{1700}{\tan 38^\circ}\\\\=2175.9$ feet$

In Right Triangle BHC

$\tan 45^\circ =\dfrac{1700}{BC} \\$Cross multiply$\\BC *\tan 45^\circ =1700\\BC =\dfrac{1700}{\tan 45^\circ}\\\\=1700$ feet$

The distance between the two runners,

AB=AC-BC

=2175.9-1700

=475.9

=476 feet ( to the nearest foot)

You might be interested in

Evaluate the expression (-1/2)^3

Vinil7 [7]

-1/8 is the anwser. Hope this helps!

6 0

3 years ago

Read 2 more answers

Simplify 3x⁵y³ ÷2y² step by step

seropon [69]

Answer:

3/2 x^5 y

Step-by-step explanation:

3x^5y^3

----------------

2y^2

Simplify the y terms

y^3 / y^2 = y^(3-2) = y

3/2 x^5 y

8 0

3 years ago

Read 2 more answers

HELP HELP WILL MARK RIGHT AND FIRST ANWSSER BRANLIEST

Liono4ka [1.6K]

It should be option A! I hope this helps you!

5 0

3 years ago

Water is pumped into a tank at a rate of r (t)=30(1−e− 0.16t) gallons per minute, where t is the number of minutes since the pum

Vlad1618 [11]

Answer:

The total volume of the water in the tank after 20 minutes = 1220 gallons

Step-by-step explanation:

Rate of water pumped into the tank r (t) = 30 (1 - $e^{-0.16 t}$ )

Initial volume of water in the tank = 800 gallons

The water in the tank after 20 minutes = Initial volume of water in the tank + Volume of water being pumped in the tank

$V_{total} = V_{i} + V_{pump}$

$V_{pump}$ = $\int\limits^a_b {r(t)} \, dt$

Where a = 0 , b = 20

Put the value of r (t) in above equation we get

$V_{pump}$ = $\int\limits^a_b {30 (1 - e^{-0.16t} )} \, dt$

$V_{pump}$ = $30 [ t + \frac{e^{-0.16t} }{0.16} ]$

$V_{pump}$ = $30[ (20- 0) + \frac{1}{0.16}(e^{-0.16 (20)}- e^{0} )$

$V_{pump}$ = 420 gallon

Now, total volume in the tank

$V_{total} = V_{i} + V_{pump}$

$V_{total} = 800 + 420$

$V_{total} = 1220 \ gallon$

Therefore the total volume of the water in the tank after 20 minutes = 1220 gallons

3 0

4 years ago

Nicolas has $6,500 to deposit into an account which earns 3.25% interest compounded annually. How interest will he have earned a

agasfer [191]

We have been given that Nicolas has $6,500 to deposit into an account which earns 3.25% interest compounded annually. We are asked to find amount of interest earned at the end on 8 years.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nt}$ , where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

$3.25\%=\frac{3.25}{100}=0.0325$

$A=6500(1+\frac{0.0325}{1})^{1\cdot 8}$

$A=6500(1+0.0325)^{8}$

$A=6500(1.0325)^{8}$

$A=6500(1.2915775352963673)$

$A=8395.253979$

Now we will subtract principal amount from final amount to find amount of interest as:

$\text{interest}=8395.253979-6500$

$\text{interest}=1895.253979\approx 1895.25$

Therefore, Nicolas would have earned $1895.25 in interest at the end of 8 years.

7 0

3 years ago