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Alexeev081 [22]
3 years ago
11

The altitude of a plane is 1200 meters. From a point on the ground, the angle of elevation of an airplane is 25º. What is the di

stance from point P to the airplane, to the nearest tenth of a meter? Explain your answer.
Mathematics
1 answer:
gtnhenbr [62]3 years ago
8 0

Answer:

2839.4 meters

Step-by-step explanation:

Given that:

Altitude = 1200 m

Using trigonometry :

The distance from point P to the airplane :

Using trigonometric relation :

Sin θ = opposite / hypotenus

Sin θ = altitude / x

Sin θ = 1200 m / x

Sin 25 = 1200 / x

0.4226182 = 1200 / x

x = 1200 / 0.4226182

x = 2839.4423

Distance from P to airplane = 2839.4 meters

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The regression equation is \^y = 1.56\^x + 1.29, and it will take 31 weeks to have $50.00

<u>(a) The linear regression equation</u>

To do this, we make use of a graphing calculator;

From the graphing calculator, we have the following calculation summary:

  • The sum of X = 45
  • The sum of Y = 83
  • Mean X = 4.5
  • Mean Y = 8.3
  • Sum of squares (SSX) = 82.5
  • Sum of products (SP) = 128.5

The regression equation is then represented as:

\^y = b\^x + a

Where:

b = \frac{SP}{SSX} and a = M_Y - bM_X

So, we have:

b = \frac{128.5}{82.5}

b = 1.55758

Approximate

b = 1.56

a= 8.3 - (1.56 \times 4.5)

a= 1.29091

Approximate

a= 1.29

This means that, the regression equation is \^y = 1.56\^x + 1.29

<u>(b) Predict the time to have $50.00</u>

This means that:

\^y = 50

So, we have:

50 = 1.56\^x + 1.29

Subtract 1.29 from both sides

48.71 = 1.56\^x

Divide both sides by 1.56

31.22 = \^x

Rewrite as:

\^x = 31.22

Approximate

\^x = 31

Hence, it will take 31 weeks to have $50.00

Read more about linear regression models at:

brainly.com/question/14585820

8 0
2 years ago
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Hope this helps!
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The world population in 2000 was approximately 6.08 billion. The annual rate of increase
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