![\frac{3}{5} p](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7D%20p)
- 4 = 25
First, simplify
![\frac{3}{5} p](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7D%20p)
to
![\frac{3p}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3p%7D%7B5%7D%20)
/ Your problem should look like:
![\frac{3p}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3p%7D%7B5%7D%20)
- 4 = 25
Second, multiply both sides by 5. / Your problem should look like: 3p - 20 = 125
Third, add 20 to both sides. / Your problem should look like: 3p = 125 + 20
Fourth, simplify 125 + 20 to get 145. / Your problem should look like: 3p = 145
Fifth, divide both sides by 3. / Your problem should look like: p =
![\frac{145}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B145%7D%7B3%7D%20)
Answer as fraction: p =
Answer as decimal: 48.3333
your answer is part A ....
Answer:
-0.2,-2.2,-0.2, 0.8, 1.8
Step-by-step explanation:
Given :Five people were asked approximately how many hours of TV they watched per week.
Their responses were as follows. 6 4 6 7 8
To Find : Find the deviations from the mean for these five data values
Solution :
Mean = ![\frac{\text{Sum of all observations}}{\text{Total no. of observations}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BSum%20of%20all%20observations%7D%7D%7B%5Ctext%7BTotal%20no.%20of%20observations%7D%7D)
Mean = ![\frac{6+4+6+7+8}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B6%2B4%2B6%2B7%2B8%7D%7B5%7D)
Mean = ![6.2](https://tex.z-dn.net/?f=6.2)
The deviations from the mean for these five data values: 6-6.2,4-6.2,6-6.2,7-6.2,8-6.2=-0.2,-2.2,-0.2, 0.8, 1.8
Hence the deviations from the mean for these five data values is -0.2,-2.2,-0.2, 0.8, 1.8
Answer:
Step-by-step explanation:
The question asks you to graph the inequality
<em>The steps of drawing the inequality are the same steps of drawing the equation except the area of the solution</em>
→ The solution of the equation is just all the points lie on the line
→ The solution of the inequality is one of these cases:
- All the points on the line and on the area down the line if the inequality y ≤ ......
- All the points on the line and on the area over the line if the inequality y ≥ .......
- All the points on the area down the line if the inequality y < ......
- All the points on the area over the line if the inequality y > .......
∵ The inequality is 4x - 3y ≤ 6
∴ The equation of the line is 4x - 3y = 6
Your drawing is right, BUT you must shade the area over the line because the solution of the inequality is all the points on the line and over the line
The coefficient of y is -3 which means we will divide the sides of the inequality by a negative number, so sign the inequality must e reversed
I attached the figure of the inequality to show you the explanation above.
The red shaded is the area of the solution of the inequality.
1. Observe that
![\nabla \dfrac{x^2y^2w^2}2 = \langle xy^2w^2, x^2yw^2, x^2y^2w\rangle](https://tex.z-dn.net/?f=%5Cnabla%20%5Cdfrac%7Bx%5E2y%5E2w%5E2%7D2%20%3D%20%5Clangle%20xy%5E2w%5E2%2C%20x%5E2yw%5E2%2C%20x%5E2y%5E2w%5Crangle)
is a gradient field, so the gradient theorem holds and the integral in question is indeed path-independent. Its value is
![\dfrac{x^2y^2w^2}2\bigg|_{x=1,y=3,w=2}^{x=2,y=4,w=1} = 32 - 18 = \boxed{14}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2y%5E2w%5E2%7D2%5Cbigg%7C_%7Bx%3D1%2Cy%3D3%2Cw%3D2%7D%5E%7Bx%3D2%2Cy%3D4%2Cw%3D1%7D%20%3D%2032%20-%2018%20%3D%20%5Cboxed%7B14%7D)
2.
is an exact differential if we can find a scalar function
such that
![\dfrac{\partial f}{\partial x} = 3x^2 (x^2+y^2) = 3x^4 + 3x^2y^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%20%3D%203x%5E2%20%28x%5E2%2By%5E2%29%20%3D%203x%5E4%20%2B%203x%5E2y%5E2)
![\dfrac{\partial f}{\partial y} = 2y(x^3+y) = 2x^3y + 2y^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%20%3D%202y%28x%5E3%2By%29%20%3D%202x%5E3y%20%2B%202y%5E2)
Integrating both sides of the first equation with respect to
yields
![f(x,y) = \dfrac35 x^5 + x^3 y^2 + g(y)](https://tex.z-dn.net/?f=f%28x%2Cy%29%20%3D%20%5Cdfrac35%20x%5E5%20%2B%20x%5E3%20y%5E2%20%2B%20g%28y%29)
Differentiating with respect to
gives
![\dfrac{\partial f}{\partial y} = 2x^3y + \dfrac{dg}{dy} = 2x^3y + 2y^2 \\\\ \implies \dfrac{dg}{dy} = 2y^2 \implies g(y) = \dfrac23y^3 + C](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%20%3D%202x%5E3y%20%2B%20%5Cdfrac%7Bdg%7D%7Bdy%7D%20%3D%202x%5E3y%20%2B%202y%5E2%20%5C%5C%5C%5C%20%5Cimplies%20%5Cdfrac%7Bdg%7D%7Bdy%7D%20%3D%202y%5E2%20%5Cimplies%20g%28y%29%20%3D%20%5Cdfrac23y%5E3%20%2B%20C)
and we ultimately find
![f(x,y) = \boxed{z = \dfrac35 x^5 + x^3y^2 + \dfrac23 y^3 + C}](https://tex.z-dn.net/?f=f%28x%2Cy%29%20%3D%20%5Cboxed%7Bz%20%3D%20%5Cdfrac35%20x%5E5%20%2B%20x%5E3y%5E2%20%2B%20%5Cdfrac23%20y%5E3%20%2B%20C%7D)
(We can also use the same method here to determine the scalar function in part (1).)
Then the integral is path-independent, and its value is
![f(2,1) - f(1,2) = \dfrac{418}{15} - \dfrac{149}{15} = \boxed{\dfrac{269}{15}}](https://tex.z-dn.net/?f=f%282%2C1%29%20-%20f%281%2C2%29%20%3D%20%5Cdfrac%7B418%7D%7B15%7D%20-%20%5Cdfrac%7B149%7D%7B15%7D%20%3D%20%5Cboxed%7B%5Cdfrac%7B269%7D%7B15%7D%7D)