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Liono4ka [1.6K]

3 years ago

10

Sherman has 1 cat and 4 dogs. He wants to buy a toy for each of his pets. Sherman has $16 to spend on pet toys. How much can he

spend on each pet? Enter the answer as a fraction in simplest form and then as an amount in dollars and cents.

1 answer:

algol133 years ago

5 0

Answer:

He can spend 16/5 on each pet.

amount=3 dollar and 2 cents

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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

A mural is painted on the walls of a local business. It measures 7.5 ft long and 3.5 ft wide. The owner would like

Afina-wow [57]

Answer:

24 sections

Step-by-step explanation:

8 + 8 = 16

4+ 4 = 8

16 + 8 = 24

5 0

2 years ago

If a student has an average exam score between 70 and 79, he will earn a grade of C in his algebra course. Suppose he has three

goldenfox [79]

Answer:

(64,86.5)

Step-by-step explanation:

find the case where he gets 70 and the case where he gets 79

if his average is 70:

(75+62+85+2x)/5=70

(222+2x)/5=70

222+2x=350

2x=128

x=64

if his average is 79:

(75+62+85+2x)/5=79

(222+2x)/5=79

222+2x=395

222+2x=395

2x=173

x=86.5

7 0

3 years ago

What is “One third of the opposite of a number is less than 12?”

nirvana33 [79]

Answer:

$\frac{1}{3}(-x)$ <12

4 0

3 years ago

1) There are 43 girls and 25 boys in the Valley View Middle School chorus. What is the ratio of girls to boys? 43 to 25, or 43:2

Arturiano [62]

Answer:

Oh gosh. Im not positive but I think it would be 43:25. Please dont get mad at me if its wrong!

Step-by-step explanation:

I am so sorry if its wrong but im not very sure :-(

6 0

2 years ago