Answer:

Step-by-step explanation:
given,
y=5√sinx
Volume of the solid by revolving

a and b are the limits of the integrals
now,



![V =25\pi [-cos x]_{\pi/4}^{\pi/2}](https://tex.z-dn.net/?f=V%20%3D25%5Cpi%20%5B-cos%20x%5D_%7B%5Cpi%2F4%7D%5E%7B%5Cpi%2F2%7D)
![V =25\pi [-cos (\pi/2)+cos(\pi/4)]](https://tex.z-dn.net/?f=V%20%3D25%5Cpi%20%5B-cos%20%28%5Cpi%2F2%29%2Bcos%28%5Cpi%2F4%29%5D)
![V =25\pi [0+\dfrac{1}{\sqrt{2}}]](https://tex.z-dn.net/?f=V%20%3D25%5Cpi%20%5B0%2B%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5D)

volume of the solid generated is equal to 
Answer:
p ∈ IR - {6}
Step-by-step explanation:
The set of all linear combination of two vectors ''u'' and ''v'' that belong to R2
is all R2 ⇔
And also u and v must be linearly independent.
In order to achieve the final condition, we can make a matrix that belongs to
using the vectors ''u'' and ''v'' to form its columns, and next calculate the determinant. Finally, we will need that this determinant must be different to zero.
Let's make the matrix :
![A=\left[\begin{array}{cc}3&1&p&2\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%261%26p%262%5Cend%7Barray%7D%5Cright%5D)
We used the first vector ''u'' as the first column of the matrix A
We used the second vector ''v'' as the second column of the matrix A
The determinant of the matrix ''A'' is

We need this determinant to be different to zero


The only restriction in order to the set of all linear combination of ''u'' and ''v'' to be R2 is that 
We can write : p ∈ IR - {6}
Notice that is
⇒


If we write
, the vectors ''u'' and ''v'' wouldn't be linearly independent and therefore the set of all linear combination of ''u'' and ''b'' wouldn't be R2.
Answer:
a⁴b⁴ - c⁴
Step-by-step explanation:
The difference of squares formula states that (a - b)(a + b) = a² - b². In this case, a = a²b² and b = c² so a² - b² = (a²b²)² - (c²)² = a⁴b⁴ - c⁴.
This chart represents a proportional relationship. The rate of change will be 4.
<h3>What is the constant of proportionality?</h3>
Firstly, there is a proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called the constant of proportionality.
Given;
x y
1 4
2 8
3 12
4 16
Here, x = ky
put the first value
k = 1/4
This chart represents a proportional relationship.
So the rate of change will be

Learn more about proportional ;
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Its the third option y-9=-1/4(x+2) because the equation for point slope form is y-y1= m(x-x1) so because there is a negative 2 it is a positive 2. Remember a negative minus a negative is a positive. Hope this helped :)!