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4 years ago

How would you do this??? PLEASE EXPLAIN!!!

Mathematics

1 answer:

vladimir1956 [14]4 years ago

6 0

The volume is 180.32 because if u multiply those three numbers u get 180.32. Also, what do u mean by SA

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A rock thrown vertically upward from the surface of the moon at a velocity of 36m/sec reaches a height of s = 36t - 0.8 t^2 met

Verdich [7]

Answer:

a. The rock's velocity is $v(t)=36-1.6t \:{(m/s)}$ and the acceleration is $a(t)=-1.6 \:{(m/s^2)}$

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

Velocity is defined as the rate of change of position or the rate of displacement. $v(t)=\frac{ds}{dt}$
Acceleration is defined as the rate of change of velocity. $a(t)=\frac{dv}{dt}$

The rock's velocity is the derivative of the height function $s(t) = 36t - 0.8 t^2$

$v(t)=\frac{d}{dt}(36t - 0.8 t^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(36t\right)-\frac{d}{dt}\left(0.8t^2\right)\\\\v(t)=36-1.6t$

The rock's acceleration is the derivative of the velocity function $v(t)=36-1.6t$

$a(t)=\frac{d}{dt}(36-1.6t)\\\\a(t)=-1.6$

b. The rock will reach its highest point when the velocity becomes zero.

$v(t)=36-1.6t=0\\36\cdot \:10-1.6t\cdot \:10=0\cdot \:10\\360-16t=0\\360-16t-360=0-360\\-16t=-360\\t=\frac{45}{2}=22.5$

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

$s(22.5) = 36(22.5) - 0.8 (22.5)^2\\s(22.5) =405$

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height = $\frac{405}{2} =202.5 \:m$

To find the time it reach half its maximum height, we need to solve

$36t - 0.8 t^2=202.5\\36t\cdot \:10-0.8t^2\cdot \:10=202.5\cdot \:10\\360t-8t^2=2025\\360t-8t^2-2025=2025-2025\\-8t^2+360t-2025=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=-8,\:b=360,\:c=-2025:\\\\t=\frac{-360+\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2-\sqrt{2}\right)}{4}\approx 6.59\\\\t=\frac{-360-\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2+\sqrt{2}\right)}{4}\approx 38.41$

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

$36t - 0.8 t^2=0\\\\\mathrm{Factor\:}36t-0.8t^2\rightarrow -t\left(0.8t-36\right)\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\\\t=0,\:t=45$

The rock is aloft for 45 seconds.

5 0

4 years ago

Please help me asap. No links please <br> 8th Grade

Gennadij [26K]

Answer:

Option P √2.5²-1.2²

Step-by-step explanation:

a = distance between Toby's House and the playground = 1.2 inches

b = distance between the playground and Toby's Friend's House = unknown

c = distance between Toby's House and Toby's Friend's House = 2.5 inches

Use the Pythagorean Theorem to calculate the side length of b:

a²+b²=c²

b²=c²-a²

b=√(c²-a²)

b=√(2.5²-1.2²)

Therefore, option P is correct.

5 0

3 years ago

Read 2 more answers

At a bookstore, 960 books were placed on the discount shelf for 70% off the regular price. If 2/3 of the books sold, how many bo

Brrunno [24]

Answer: a. 320 books

Step-by-step explanation:

Given : The total number of books were placed on the discount shelf for 70% off the regular price = 960

The fraction of books sold = $\dfrac{2}{3}$

Then, the number of books sold = $\dfrac{2}{3}\times960=640$

Now, the number of books remain on the discount shelf = $960-640=320$

Hence, the number of books remain on the discount shelf =320

5 0

4 years ago

Name the algebraic property demonstrated in the example below:<br> 3 • (x • y) = (3 • x) • y

Orlov [11]

Answer:

Associative Property

Step-by-step explanation:

hey! This is an example of the associative property because your are changing where the parentheses are located. Just remember that when using the associative property, you are changing who the values are associating themselves with. PLS MARK BRAINLIEST! Thank you! Hope this helps.

4 0

3 years ago

Carolina is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus $6 for each hour of work. Her t

MrRa [10]

Well first the initial fee would be the x, which is what we have to solve for. Each hour of work is $6, and she does four hours of work. This is equal to $32. The equation would look as follows...

x + 6(4) = 32

Once you have the equation start solving. Use the Pemdas method. First you have to multiply, so now the equation looks as follows...

x + 24 = 32

Now you have to get the x by itself. You do that by subtracting 24 from both sides, because what you do to one side, you do to the other. That will get you to the answer of...

x = 8

In conclusion, Carolina has an initial fee of $8.

Hope this helped.

5 0

3 years ago