sales of frozen pizza for a club fund raiser from 500 one year to 715 the next year what was the percent increase

If c is the curve given by \mathbf{r} \left( t \right = \left( 1 5 \sin t \right \mathbf{i} \left( 1 3 \sin^{2} t \right \mathbf

jonny [76]

With the curve $C$ parameterized by

$C:\mathbf r(t)=\underbrace{15\sin t}_{x(t)}\,\mathbf i+\underbrace{13\sin^2t}_{y(t)}\,\mathbf j+\underbrace{12\sin^3t}_{z(t)}\,\mathbf k$

with $0\le t\le\dfrac\pi2$ , and given the vector field

$\mathbf f(x,y,z)=x\,\mathbf i+y\,\mathbf j+z\,\mathbf k$

the work done by $\mathbf f$ on a particle moving on along $C$ is given by the line integral

$\displaystyle\int_C\mathbf f\cdot\mathrm d\mathbf r=\int\limits_{t=0}^{t=\pi/2}\mathbf f(x(t),y(t),z(t))\cdot\frac{\mathrm d\mathbf r(t)}{\mathrm dt}\,\mathrm dt$

where

$\mathrm d\mathbf r=(15\cos t\,\mathbf i+26\sin t\cos t\,\mathbf j+36\sin^2t\cos t\,\mathbf k)\,\mathrm dt$

The integral is then

$\displaystyle\int_0^{\pi/2}(15\sin t\,\mathbf i+13\sin^2t\,\mathbf j+12\sin^3t\,\mathbf k)\cdot(15\cos t\,\mathbf i+13\sin2t\,\mathbf j+18\sin t\sin2t\,\mathbf k)\,\mathrm dt$
$=\displaystyle\int_0^{\pi/2}(432\sin^5t\cos t+338\sin^3t\cos t+225\sin t\cos t$
$=269$

6 0

3 years ago

How to multiply how far would a car go if it travels at 50 km an hour for 3 hours?

ale4655 [162]

1 hour = 50 km
3 hours = 50 x 3 = 150 km

Answer: The car would go for 150 km in 3 hours.

8 0

3 years ago

If the leg of a triangle is 48 and the hypotenuse is 60 what is the length of the other leg

AURORKA [14]

Answer:

The length of the other would be 36.

Step-by-step explanation:

a² + b² = c²

b² = c² - a²

b² = 60² - 48²

b² = 3600 - 2304

b² = 1296

√b² = √1296

b = 36

4 0

3 years ago

Jensen is building a snow fort. Each block in the fort weighs about 1 kilogram. Jensen hopes to make about 40 blocks for the for

babymother [125]

Answer: 13,333 snowflakes

Step-by-step explanation:

For this exercise let be "x" represents the number of snowflakes that will be in the fort.

According to the information given in the exercise, the weight of one block is 1 kilogram. Knowing that the fort must have 40 blocks, the total weight is:

$total\ weight=(1\ g)(40)\\\\total\ weight=40\ g$