32 is 4 more than twice a<br> number. What is the number?

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: A linear model with ordered pairs at 0, 60 and 2, 75 and 4, 75 and 6, 40 and 8, 20 and 10, 0 and 12, 0 and 14, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet. Part A: During what interval(s) of the domain is the water balloon's height increasing? (2 points) Part B: During what interval(s) of the domain is the water balloon's height staying the same? (2 points) Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points) Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds.

Answer:

Part A:

Between 0 and 2 seconds, the height of the balloon increases from 60 feet to 75 feet at a rate of 7.5 ft/s

Part B:

Between 2 and 4 seconds, the height stays constant at 75 feet.

Part C:

Between 4 and 6 seconds, the height of the balloon decreases from 75 feet to 40 feet at a rate of -17.5 ft/s

Between 6 and 8 seconds, the height of the balloon decreases from 40 feet to 20 feet at a rate of -10 ft/s

Between 8 and 10 seconds, the height of the balloon decreases from 20 feet to 0 feet at a rate of -10 ft/s

Hence it fastest decreasing rate is -17.5 ft/s which is between 4 to 6 seconds.

Part D:

From 10 seconds, the balloon is at the ground (0 feet), it continues to remain at 0 feet even at 16 seconds.

3 0

3 years ago

A telephone pole has a wire to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor po

Bumek [7]

Answer:

The height of the pole is 105ft,

Step-by-step explanation:

Let us call $h$ the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is $h - 49$ .

The wire length $d$ is 14 ft longer than height $h$ , hence

$d= h+14$ .

Thus we get a right triangle with hypotenuse $d= y+14$ , perpendicular $h$ , and base $h-49$ ; therefore, the Pythagorean theorem gives

$(h-49)^2+h^2 = (h+14)^2$

which upon expanding we get:

$h^2-98h+2401 = h^2+28h+196$

further simplification gives

$h^2-126h+2205=0$ ,

which is a quadratic equation with solutions

$h =21ft\\h = 105ft.$

Since the first solution $h =21ft$ will give the triangle base length of $21ft-49ft = -28ft$ which is negative; therefore, we disregard it and pick the solution $h = 105ft$ .

Hence, the height of the pole is 105ft.

3 0

2 years ago

Type the correct answer in the box. Round your answer to two decimal places.

Vlad [161]

Find the square root of 13, which is 3.6

5 0

3 years ago

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32 is 4 more than twice a number. What is the number?