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3 years ago

A room has an area of 216 square feet. One dimension is 6 feet more than the other. Find the length of the longer side.

2 answers:

3 0

The dimensions would be x and x+6. The area is 216.

x(x+6) = 216
x^2 + 6x - 216 = 0
(x-12)(x+18) = 0

x = 12---Yes---
x = -18---No, sides cannot be negative---

If one side is 12, the other side is 18. To check:

12 * 18 = 216
216 = 216

Correct

kicyunya [14]3 years ago

3 0

He correct cause I just did it. ;)

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suppose the mean height for men is 70 inches with a standard deviation of 2 inches. What percentage of men are less than 74 inch

Ratling [72]

Answer:

97.7 %

Step-by-step explanation:

TWO standard deviations above the mean

z - score = 2 corresponds to .9772 97.7 %

3 0

2 years ago

A small rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 righ

jonny [76]

Let $\vec r(t),\vec v(t),\vec a(t)$ denote the rocket's position, velocity, and acceleration vectors at time $t$ .

We're given its initial position

$\vec r(0)=\langle0,0,10\rangle\,\mathrm m$

and velocity

$\vec v(0)=\langle250,450,500\rangle\dfrac{\rm m}{\rm s}$

Immediately after launch, the rocket is subject to gravity, so its acceleration is

$\vec a(t)=\langle0,2.5,-g\rangle\dfrac{\rm m}{\mathrm s^2}$

where $g=9.8\frac{\rm m}{\mathrm s^2}$ .

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

$\vec v(t)=\left(\vec v(0)+\displaystyle\int_0^t\vec a(u)\,\mathrm du\right)\dfrac{\rm m}{\rm s}$

$\vec v(t)=\left(\langle250,450,500\rangle+\langle0,2.5u,-gu\rangle\bigg|_0^t\right)\dfrac{\rm m}{\rm s}$

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

$\boxed{\vec v(t)=\langle250,450+2.5t,500-gt\rangle\dfrac{\rm m}{\rm s}}$

and

$\vec r(t)=\left(\vec r(0)+\displaystyle\int_0^t\vec v(u)\,\mathrm du\right)\,\rm m$

$\vec r(t)=\left(\langle0,0,10\rangle+\left\langle250u,450u+1.25u^2,500u-\dfrac g2u^2\right\rangle\bigg|_0^t\right)\,\rm m$

$\boxed{\vec r(t)=\left\langle250t,450t+1.25t^2,10+500t-\dfrac g2t^2\right\rangle\,\rm m}$

b. The rocket stays in the air for as long as it takes until $z=0$ , where $z$ is the $z$ -component of the position vector.

$10+500t-\dfrac g2t^2=0\implies t\approx102\,\rm s$

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

$\boxed{\|\vec r(102\,\mathrm s)\|\approx64,233\,\rm m}$

c. The rocket reaches its maximum height when its vertical velocity (the $z$ -component) is 0, at which point we have

$-\left(500\dfrac{\rm m}{\rm s}\right)^2=-2g(z_{\rm max}-10\,\mathrm m)$

$\implies\boxed{z_{\rm max}=125,010\,\rm m}$

7 0

3 years ago

100% of will give me 93

Art [367]

Answer:

Hi Wdym m=by 100% of will give me 93

Step-by-step explanation:

5 0

2 years ago

Tricia spends $4.89 on 3 snack packs.

lesantik [10]

Answer:

$1.63

Step-by-step explanation:

Divide 4.89 by 3

Answer: $1.63

Simple

Hope it helps ♥️♥️

5 0

3 years ago

11. Shrimp are often found in tropical climates and can be raised on farms or caught in the wild.

seropon [69]

Answer:

3/83

Step-by-step explanation:

Probability: the ways to get the desired result / all of the possible results.

To solve, plug in the values they give.

There are 6 packages of wild-caught shrimp from Honduras. (The desired result)

Now, to find all of the possible results, add the total number of packages together.

27 + 40 + 52 + 13 + 6 + 28 = 166

6/166 = 3/83

Thus, the answer is a 3/83 chance of getting a package of wild-caught shrimp came from Honduras.

7 0

2 years ago