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3 years ago

10

Suppose there is a 1.6°F drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on

the ground is 64.5°F, what will be the temperature when the plane reaches an altitude of 9,000 ft?

1 answer:

Vesnalui [34]3 years ago

7 0

Answer:

50.1 deg F

Step-by-step explanation:

1.6deg F for every 1,000ft. You need to get to 9,000ft. 1.6degx9=14.4

64.5deg-14.4deg=50.1degF

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A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

so

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

so

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0

3 years ago

Please answer this quick

Darya [45]

$(3x + 20degrees ) = 180degrees$

180 degress because a stranight angle equals that

3 0

3 years ago

What is .74 repeating as a fraction?

Sedaia [141]

The answer to your question is 74/99:D

8 0

3 years ago

Using 50 observations, the following regression output is obtained from estimating y = β0 + β1x + β2d1 + β3d2 + ε. Coefficients

pickupchik [31]

Answer:

The answer is "789.03 and 806.16".

Step-by-step explanation:

$y\^ \ \ = -0.45 + 3.78(x) -11.88(d_1) + 5.25(d_2)$

For point a:

Calculating the value for $y\^ \ \ x = 212,\ \ d_1 = 1, and \ \ d_2 = 0$

$y\^ = -0.45 + 3.78(212) -11.88(1) + 5.25(0)$

$= -0.45 + 801.36 -11.88 + 0\\\\= 789.03$

For point b:

Calculating the value of $y\^ \ \ for \ \ x = 212, \ \ d_1 = 0, and \ \ d_2 = 1$

$y\^ = -0.45 + 3.78(212) -11.88(0) + 5.25(1)$

$= -0.45 + 801.36 -0 + 5.25\\\\= 806.16$

3 0

3 years ago

If you can answer this u are the best

spayn [35]

Answer:

47

Step-by-step explanation:

if there are 100 total and 45 are girls, then there are 55 boys enrolled. since 8 are absent- 55-8=47

5 0

3 years ago