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svetoff [14.1K]
2 years ago
10

Daryl measures the angle of elevation to be 62 degrees. Frances measures the angle of elevation to be 54 degrees. if the two ent

husiasts are 28m apart, how far off the ground is the helicopter.

Mathematics
1 answer:
Leya [2.2K]2 years ago
5 0

Answer:

<em>The helicopter is 27.38 m far off the ground</em>

Step-by-step explanation:

The drawing shown in the image below has all the measures and variables needed to solve the problem.

We need to find R, the height of the helicopter. We'll use the law of sines to find the length of side a.

\displaystyle \frac{28}{\sin X}=\frac{a}{\sin 54^\circ}

The angle X is the measure needed to complete 180°:

X = 180° - 54° - 62° = 64°

Solving for a:

\displaystyle a=\frac{28}{\sin 64^\circ}\cdot \sin 54^\circ

Calculating:

a = 31.11 m

Now using the sine ratio in the right triangle to the left side:

\displaystyle \sin 62^\circ=\frac{R}{a}

Solving for R:

R=a\sin 62^\circ

R=31.11*0.88

R = 27.38 m

The helicopter is 27.38 m far off the ground

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Do u have a problem that went with this?

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You have a total of ​$1760 to invest. Account A pays 7​% annual interest and account B pays 4​% annual interest. How much should
posledela

Answer:

You should invest $820 in account A and $940 in account B

Step-by-step explanation:

* Lets use the system of linear equations to solve the problem

- Simple Interest Equation I = Prt , Where:

# P = Invested Amount

# I = Interest Amount

# r = Rate of Interest per year in decimal; r = R/100

# t = Time Period involved in months or years

* Lets solve the problem

- The total money invested is $1760

- Account A pays 7​% annual interest

- Account B pays 4​% annual interest

- Let A represent the amount of money invested in the account A

- Let B represent the amount of money invested in the account B

- You would like to earn $ 95 at the end of one year

∴ The interest from both accounts at the end of one year is $95

- Lets write the equations

# Account A :

∵ Account A has $A invested

∴ P = $A

∵ Account A pays 7​% annual interest

∴ r = 7/100 = 0.07

∵ t = 1 year

∵ I = Prt

∴ I = A(0.07)(1) = 0.07A

# Account B :

∵ Account B has $B invested

∴ P = $B

∵ Account A pays 4​% annual interest

∴ r = 4/100 = 0.04

∵ t = 1 year

∵ I = Prt

∴ I = B(0.04)(1) = 0.04B

- The total amount of interest from both accounts at the end of one

  year is $95

∴ I from A + I from B = 95

∴ 0.07A + 0.04B = 95 ⇒ multiply both sides by 100

∴ 7A + 4B = 9500 ⇒ (1)

- The total money to invest in both accounts is $1760

∵ Account A has $A invested

∵ Account B has $B invested

∴ A + B = 1760 ⇒ (2)

* Lets solve the system of equations to find the amount of money

  invested in each account

- Multiply equation (2) by -4 to eliminate B

∵ A + B = 1760 ⇒ × -4

∴ -4A - 4B = -7040 ⇒ (3)

- Add equation (1) and (3)

∵ 7A + 4B = 9500 ⇒ (1)

∵ -4A - 4B = -7040 ⇒ (3)

∴ 7A - 4A = 9500 - 7040

∴ 3A = 2460 ⇒ divide both side by 3

∴ A = 820

- Substitute the value of A in equation (1) or (2)

∵ A + B = 1760 ⇒ (2)

∴ 820 + B = 1760 ⇒ subtract 820 from both sides

∴ B = 940

- From all above

* You should invest $820 in account A and $940 in account B

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3 years ago
What 23.427 rounded to the nearst whole number
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23, you have to round down. If it was 23.527 it would be 24.
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Talja [164]

Answer:

13 and 27

Step-by-step explanation:

y= x+14

x+y=40

x+ x+14=40

2x+14=40

40-14=26

so, 2x=26

26/2

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so, x=13 and

and y equal 40-13

y=27

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2 years ago
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The first one is 4, and the second one is 3.7
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