1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kruka [31]
3 years ago
12

A water sprinkler sends water out in a circular pattern. How large is the watered area if the radius of the watering pattern is

19 ​ft?
Mathematics
1 answer:
leva [86]3 years ago
7 0

A water sprinkler sends water out in a circular pattern. Determine how large an area is watered. The radius of watering is 19 feet. Use 3.14 for radius

 

area=l*b =3.14*19


You might be interested in
The diameter of a circle is 12 inches. What is the circle's circumference?<br> Use 3.14 for .
frozen [14]
The formula to find circumference is 2(3.14)r
For this problem, first you take half of the diameter to get radius. Then, putting this into the formula, you get 2(3.14)(6) = 37.699
5 0
3 years ago
Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of
kifflom [539]

Looks like we have

\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k

which has divergence

\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2

By the divergence theorem, the integral of \vec F across S is equal to the integral of \nabla\cdot\vec F over R, where R is the region enclosed by S. Of course, S is not a closed surface, but we can make it so by closing off the hemisphere S by attaching it to the disk x^2+y^2\le1 (call it D) so that R has boundary S\cup D.

Then by the divergence theorem,

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV

Compute the integral in spherical coordinates, setting

\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi

so that the integral is

\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5

The integral of \vec F across S\cup D is equal to the integral of \vec F across S plus the integral across D (without outward orientation, so that

\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S

Parameterize D by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath

with 0\le u\le1 and 0\le v\le2\pi. Take the normal vector to D to be

\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=-u\,\vec k

Then we have

\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4

Finally,

\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}

6 0
4 years ago
To decrease an amount by 8 percent, what single multiplier would you use?
Alchen [17]
That's far more problems than I usually accept in a single question, but since you're new and obviously a beginner, I'll try to help. 

<span>To Increase an amount by 7% what single multiplier would you use </span>
<span>We want 7% more than 100% of the amount, so the multiplier is </span>
<span>(100% + 7%) = 107% = 1.07 </span>
<span>[Remember that "percent" means "per hundred," so we divide a percentage by 100 to get the numerical equivalent.] </span>

<span>To Decrease an amount by 7% what single multiplier would you use </span>
<span>We want 7% less than 100% this time, so the multiplier is </span>
<span>(100% - 7%) = 93% = 0.93 </span>

<span>5 ÷ 0.1 </span>
<span>= 50 </span>

<span>(To One Decimal Place) (0.3 x 2.8)Squared </span>
<span>[Notation: around here we usually write "squared" as ^2, where the ^ is an exponentiation sign.] </span>
<span>(0.3 x 2.8)^2 = 0.84^2 = 0.7056 </span>
<span>which is 0.7 when rounded to one decimal place. </span>

<span>6.38 + 4.52 ÷ 4.71 +9.53 </span>
<span>= 6.38 + (4.52 ÷ 4.71) + 9.53 [assuming operations in the usual order] </span>
<span>= about 6.38 + 0.96 + 9.53 </span>
<span>= 16.87 </span>

<span>Expand and Simplify </span>
<span>(x + 2)(x + 3) </span>
<span>= x^2 + 2x + 3x + 6 </span>
<span>= x^2 + 5x + 6 </span>

<span>Expand and Simplify </span>
<span>(x + 2)(x - 3) </span>
<span>= x^2 + 2x - 3x - 6 </span>
<span>= x^2 - x - 6 </span>

<span>x + 1 < 5 </span>
<span>x < 4 [subtracting 1 from both sides] </span>

<span>Make n the subject of the formula.... M=3n </span>
<span>3n = M </span>
<span>n = M/3</span>
5 0
3 years ago
if a 14 foot tree casts a 8 foot long shadow. how tall is a tree that casts a 4 foot long shadow?
kvasek [131]

7-foot

EXPLANAT

Given:

14 foot tree

8foot shadow

4foot shadow

Let h be the height of a tee that casts a 4 foot long shadow.

Using proportion;

14 foot = 8 ft shadow

h = 4 ft shadow

Cross - multiply

8h = 56

Divide both-side by 8

h = 7 foot.

Hence, the tree is 7-foot.

4 0
1 year ago
A group of biologists found a total of 15 loggerhead turtle nests along a beach during a certain season. This was 20% of the tot
Andre45 [30]
20% also equals 1/5, right?

So in order to find the total number of turtle nests, just find 5/5, or multiply 15 by 5.

15 x 5 = 75

There were 75 total nests
6 0
4 years ago
Other questions:
  • Please help ASAP!!!!!!!!!
    14·1 answer
  • What are the slope and y-intercept of the linear function graphed to the left? slope: –2; y-intercept: 2 slope: ; y-intercept: 1
    7·3 answers
  • Kenya has 2 hours to make a 104 mile road trip. What rate must she average to make the trip in 2 hours?
    13·1 answer
  • Which number line plots the integers –12, -3, and 7?<br> 12, 3, -7
    14·2 answers
  • 12,925 rounded to the nearest ten thousand
    10·2 answers
  • Question
    14·1 answer
  • 3. The point D(3, -2) is
    14·1 answer
  • The second floor of a house consists of a master bedroom, kid's bedroom, and bathroom.
    10·1 answer
  • 1. X2+7X-8<br><br><br> I need help ASAP right answers only
    11·2 answers
  • Convert 19/9 to decimal. Round your answer to the nearest thousandths.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!