Answer:
I think the answer of this question is,
Step-by-step explanation:
The 20th term may be 1048576
Answer:
The volume of the solid is 
Step-by-step explanation:
In this case, the washer method seems to be easier and thus, it is the one I will use.
Since the rotation is around the y-axis we need to change de dependency of our variables to have 
. Thus, our functions with 
as independent variable are:
For the washer method, we need to find the area function, which is given by:
![A=\pi\cdot [(\rm{outer\ radius)^2 -(\rm{inner\ radius)^2 ]](https://tex.z-dn.net/?f=A%3D%5Cpi%5Ccdot%20%5B%28%5Crm%7Bouter%5C%20radius%29%5E2%20-%28%5Crm%7Binner%5C%20radius%29%5E2%20%5D)
By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function 
and the inner one by 
. Thus, the area function is:
![A(y)=\pi\cdot [(\sqrt{y} )^2-(y^2)^2]\\A(y)=\pi\cdot (y-y^4)](https://tex.z-dn.net/?f=A%28y%29%3D%5Cpi%5Ccdot%20%5B%28%5Csqrt%7By%7D%20%29%5E2-%28y%5E2%29%5E2%5D%5C%5CA%28y%29%3D%5Cpi%5Ccdot%20%28y-y%5E4%29)
Now we just need to integrate. The integration limits are easy to find by just solving the equation 
, which has two solutions 
and 
. These are then, our integration limits.
500 liters is the answer..............
Answer:
-3
1 + 4 sqrt( 241 )
1 - 4 sqrt( 241 )
Step-by-step explanation:
We need minus lambda on the entries down the diagonal. I'm going to use m instead of the letter for lambda.
[-43-m 0 80]
[40 -3-m 80]
[24 0 45-m]
Now let's find the determinant
(-43-m)[(-3-m)(45-m)-0(80)]
-0[40(45-m)-80(24)]
+80[40(0)-(-3-m)(24)]
Let's simplify:
(-43-m)[(-3-m)(45-m)]
-0
+80[-(-3-m)(24)]
Continuing:
(-43-m)[(-3-m)(45-m)]
+80[-(-3-m)(24)]
I'm going to factor (-3-m) from both terms:
(-3-m)[(-43-m)(45-m)-80(24)]
Multiply the pair of binomials in the brackets and the other pair of numbers;
(-3-m)[-1935-2m+m^2-1920]
Simplify and reorder expression in brackets:
(-3-m)[m^2-2m-3855]
Set equal to 0 to find the eigenvalues
-3-m=0 gives us m=-3 as one eigenvalue
The other is a quadratic and looks scary because of the big numbers.
I guess I will use quadratic formula and a calculator.
(2 +/- sqrt( (-2)^2 - 4(1)(-3855) )/(2×1)
(2 +/- sqrt( 15424 )/(2)
(2 +/- sqrt( 64 )sqrt( 241 )/(2)
(2 +/- 8 sqrt( 241 )/(2)
1 +/- 4 sqrt( 241 )
Answer:
Step-by-step explanation:
Multiplicative reciprocal of x is 1/x
Eg: Multiplicative reciprocal of 4 is 1/4
Multiplicative reciprocal of 1/8 = 8/1 = 8
Multiplicative reciprocal of 89 is 1/89
When we multiply a number and its Multiplicative reciprocal , the result will be 1
4*1/4 = 1
