Ask question

Ask question

All categories

3 years ago

7

Jessica is walking home from a friend's house. After two minutes she is 1.8 miles from home. Twelve minutes after leaving, she i

s 1.3 miles from home. What is her rate in miles per hour?

1 answer:

yKpoI14uk [10]3 years ago

4 0

I believe Jessica’s rate in miles per hour is 0.9.

You might be interested in

Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 =

sashaice [31]

Let $R$ be the solid. Then the volume is

$\displaystyle\iiint_R\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$

which follows from the facts that

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta$
(by computing the Jacobian)

and

$z=x^2+y^2=r^2\implies z+z^2=72\implies z=-9\text{ or }z=8$
(we take the positive solution, since it's clear that $R$ lies above the $x$ - $y$ plane)
$r^2+z^2=72\implies z=\pm\sqrt{72-r^2}$
(again, taking the positive root for the same reason)
$z=r^2\implies 8=r^2\implies r=\sqrt8$

$\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}r(\sqrt{72-r^2}-r^2)\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}(r\sqrt{72-r^2}-r^3)\,\mathrm dr$
$=\dfrac{32(27\sqrt2-35)\pi}3$

7 0

3 years ago

Determine the intercepts of the line. − 3 x − 4 = − 5 y − 8 −3x−4=−5y−8

True [87]

Answer:

Step-by-step explanation:

6 0

2 years ago

A firefighter places a 29 feet ladder, so that the base of the ladder is 21 feet from the wall. What is the height at which the

Tju [1.3M]

Pythagorean theorem:
a^2+b^2=c^2 (C^2 always is the hypotenuse)

21^2+b^2=29^2
441+b^2=841
841-441=400
square root of 400 is 20
Your answer is 20

6 0

3 years ago

The area of a circle is 100π cm². What is the circumference, in centimeters? Express your answer in terms of \piπ.

Montano1993 [528]

35.45 cm squared. Hope this helps

3 0

3 years ago

Read 2 more answers

cesar left the college traveling 12 mph. Then, 4 hours later, Gabriel left traveling the same direction at 24 mph. How long will

Sloan [31]

Answer:

Step-by-step explanation:

Given that cesar left the college traveling 12 mph. Then, 4 hours later, Gabriel left traveling the same direction at 24 mph.

Before Gabriel started Cesar would have travelled for 4 hours

So distance travelled by Cesar in 4 hours $=4(12) =48 miles$

Thus Cesar is ahead of Gabriel by 48 miles

Difference of speed $=(24-12) =12 mph$

So to catch Cesar time required = 48/difference in speed

= 4 hours

It will take 4 hours.

8 0

3 years ago