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kap26 [50]
2 years ago
11

A rocket was launched into the air from a podium 6 feet off the ground. The rocket path is represented by the equation h(t)=-16t

^2+120t+6, where h(t) represents the height, in feet, and t is the time, in seconds. Find the average rate of change from the initial launch to the maximum height.
Mathematics
1 answer:
Arte-miy333 [17]2 years ago
6 0

Answer:

60

Step-by-step explanation:

The given function is:

h(t)=-16t^2+120t+6

The average rate of change of h(t) from t=a to t=b is given by:

\frac{h(b)-h(a)}{b-a}

We can rewrite this function as: h(t)=-16(t-3.75)^2+231

The maximum height of the rocket is 231 and it occurs at t=3.75

\implies h(3.75)=231

The initial launch occurs at: t=0

and h(0)=-16(0)^2+120(0)+6=6

The average rate of change from the initial launch to the maximum height is

\frac{h(3.75)-h(0)}{3.75-0}=\frac{231-6}{3.75-0} =60

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saveliy_v [14]

We have been given an equation ae^{ct}=d. We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

\frac{ae^{ct}}{a}=\frac{d}{a}

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Now we will take natural log on both sides.

\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})

Using natural log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})

We know that \text{ln}(e)=1, so we will get:

ct\cdot 1=\text{ln}(\frac{d}{a})

ct=\text{ln}(\frac{d}{a})

Now we will divide both sides by c as:

\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}

t=\frac{\text{ln}(\frac{d}{a})}{c}

Therefore, our solution would be t=\frac{\text{ln}(\frac{d}{a})}{c}.

5 0
2 years ago
Which point shows the location of 5 – 2i on the complex plane below? On a coordinate plane, points A, B, C, and D are shown. Poi
Romashka-Z-Leto [24]

Answer:

The Point C shows the location of 5-2i in the complex plane: 5 points to the right of the origin and 2 points down from the origin.

Step-by-step explanation:

We have the complex number 5-2i and we have to show the location of the point that represents that number in the complex plane

In the complex plane the real numbers are located in the horizontal axis, increasing to the right. The positives real numbers are at the right of the origin and the negatives to the left.

The complex numbers are located in the vertical axis, with the positives over the origin and the negatives below the origin.

This complex number 5-2i is the sum of a real part (5) and a imaginary part (-2i), so the point will be 5 units rigth on the horizontal axis (for the real part) and 2 units down in the vertical axis (for the imaginary part).

8 0
2 years ago
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Matt Adams is the best player in his college baseball team. In his last few games, Matt has hit 70%, 77% 81% and 88% of balls th
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79 is the answer ........
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2 years ago
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Noah is writing an exam for his 8th grade students. The exam is worth 100 points and Noah wants 35 questions on the exam. He pla
MaRussiya [10]

Answer: the system of equations are

x + y = 35

3x + 2y = 100

Step-by-step explanation:

Let x= the number of short answer questions.

Let y= the number of multiple choice questions.

Noah wants 35 questions on the exam. This means that

x + y = 35

He plans to mix short answer questions, worth 3 points, with multiple choice questions worth 2 points. This means that x short answer questions will give 3x points and y multiple choice questions will give 2y points

Since the exam is worth 100 points, then,

3x + 2y = 100 - - - - - - - -1

Substituting x = 35 - y into equation 1, it becomes

3(35 - y) + 2y = 100

105 - 3y + 2y = 100

y = 105 - 100 = 5

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3 0
2 years ago
While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 40 degrees. After w
NARA [144]
Draw a diagram to illustrate the problem as shown in the figure below.

Let h = the height of the hill.
At position A, the angle of elevation is 40°, and the horizontal distance to the foot of the hill is x.
By definition,
tan(40°) = h/x
h = x tan40 = 0.8391x             (1)

At position B, Joe is (x - 450) ft from the foot of the hill. His angle of elevation is 40 + 18 = 58°.
By definition,
tan(58°) = h/(x - 450)
h = (x - 450) tan(58°) = 1.6003(x-450)
h = 1.6003x - 720.135          (2)

Equate (1) and (2).
1.6003x - 720.135 = 0.8391x
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x = 946.0523

From (1), obtain
h = 0.8391*946.0523 = 793.8 ft

Answer:  The height of the hill is approximately 794 ft (nearest integer)

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