Mathematics, 11.09.2019 06:20 weeblordd

** a rock is thrown upward from the top of
a 25 foot tower with an initial upward
velocity of 100ft/sec. the height of a rock
above the ground as a function of time can
be modeled by the equation: h(t) =
- 16t? + 100t + 25. how long does it take
for the rock to fall back to the ground?

Answers: 3

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Answers

Answer from: espinosajoselyn

The rocket will take 6.49 seconds to fall back to the ground

Step-by-step explanation:

* Lets explain how to solve the problem

- A rock is thrown upward from the top of a 25 foot tower with an initial

upward velocity of 100 ft/sec

- That means at t = 0 the height of the rock is 25 feet above the ground

- A function of time can be modeled by the equation:

h(t) = - 16t² + 100t + 25, where h is the height of the rocket from the

ground at time t

∵ h(t) = -16t² + 100t + 25

- The height of the rocket is 25 feet above the ground when it

is thrown up

∴ h(t) = 25 at t = 0 ⇒ initial position of the rocket

- The height of the rocket when hits the ground is zero

∴ h(t) = 0 when the rocket hits the ground ⇒ final position of it

- We need to find the time that the rocket takes to fall back to

the ground

∵ h(t) = 0

∵ h(t) = -16t² + 100t + 25

∴ -16t² + 100t + 25 = 0

- Lets solve it to find the value of t

∵ -16t² + 100t + 25 = 0

- Multiply both sides by -1 to make the coefficient of t² positive

∴ 16t² - 100t - 25 = 0

- Use your calculator to find the values of t

∴ t = 6.49 sec and t = -0.24 sec

∵ We will reject the value of t = -0.24, because time can not be

negative value

∴ The rocket will take 6.49 seconds to fall back to the ground

Answer from: Quest

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

$\tan\left(x\right)=\frac{\left[altitude\right]}{\left[base\right]}=\frac{p}{r}$

$\tan\left(x\right)=\frac{p}{r}$

$\frac{p}{r}=tan(x)$

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

Answer from: Quest

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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** a rock is thrown upward from the top of
a 25 foot tower with an initial upward
veloci...

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