Posted in Mathematics

The second pattern is in prime numbers. Each number is a prime number in a successive order.
2,3,5,7,11,13, [17,19,23,29,31], 37, 41, etc..


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Posted in Mathematics

I NEED HELP FAST!!!!!Monique is factoring the expression 4x+16xy Her work is shown below. Factors of 4x: 1, 2, 4, x Factors of 16xy: 1, 2, 4, 8, 16, x, y GCF: 4x Factored expression: 4x(0+4y) Which best describes the accuracy of Monique’s solution? A. Monique’s solution is accurate. B. Monique made an error when listing the factors, which affected the GCF and the factored expression. C. Monique made an error when determining the GCF from her list of factors. D. Monique made an error when writing the factored expression.

Answer with explanation:

Monique is factoring the expression 4x+16xy Her work is shown below.  

Factors of 4 x→: 1, 2, 4, x

Factors of 16 x y:→ 1, 2, 4, 8, 16, x, y

G CF: 4 x

Factored expression: 4 x(0+4 y)→Incorrect

→4 x +16 x y= 4* x + 4 *4* x* y

  = 4* x* (1+4 y)

while writing the factored expression, we have to break the terms into smaller  terms that is into monomials and  then we should take out the common factor between the two terms.

Option D:  Monique made an error when writing the factored expression.

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Posted in Mathematics

If f(x) = 9x + 1, find f–1 (f (3))

Answer:

The value of f^{-1}(f(3))is 3.

Step-by-step explanation:

Here, the given function is,

f(x)=9x+1-----(1)

For finding f^{-1}(f(3)) we have to find out the inverse of f(x),

The steps are as follows,

Step 1 : Replace f(x) by y,

y=9x+1

Step 2 : Switch x and y,

x=9y+1

Step 3 : Isolate y in the left side,

-9y=1-x

implies y = frac{x-1}{9}

Step 4 : replace y by f^{-1}(x),

f^{-1}(x)=frac{x-1}{9}------(2)

Now,

f^{-1}(f(3))=f^{-1}(9times 3+1)   ( From equation (1) )

=f^{-1}(28)

=frac{28-1}{9}     ( From equation (2) )

=frac{27}{9}

=3

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Posted in Mathematics

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = -7. y=x^2, x=y^2.

Attached is a diagram setting up the problem.
Because the axis of rotation is horizontal and we are using shell method, the radius will be in the y-direction and integration will need to be in terms of “y”.

The general formula for shell method is:
2 pi  intlimits^a_b {r(y) h(y)} , dy

r(y) is the radius as shown in diagram and is equal to the distance from y=-7 to upper curve x=y^2. This is distance from y=-7 to x-axis plus y-value along curve.
—> r(y) = y+7

h(y) is height of shell represented as x-distance between the 2 curves.
y =x^2 –> x = sqrt(y),   x = y^2
—-> h(y) = sqrt(y) – y^2

The limits are determined by y-values of intersection of 2 curves.
y^2 = sqrt(y) —> y^3 -y = 0   —–> y = 0,1

Now we can write the integral:
V = 2 pi  intlimits^1_0 {(y+7)(sqrt{y} -y^2)} , dy
V =2 pi  intlimits^1_0{(-y^3-7y^2+y^{3/2}+7y^{1/2})} , dy
V = 2 pi  |^1_0 (-frac{1}{4}y^4 -frac{7}{3}y^3 +frac{2}{5}y^{5/2}+frac{14}{3}y^{3/2})
V = 2pi frac{149}{60} = frac{149}{30} pi

Posted in Mathematics

The first five terms of an arithmetic sequence are shown below: 20, 17, 14, 11, 8, . . . Let n represent the term number and f(n) the term in the sequence.

Answer:

It’s f(n)=-3n+23 and the points on the graph are..:.(given for problem)

X:1,2,3,4,5

Y:20,17,14,11,8

answer for plots on the graph:

X:1,2,3,4,5

Y:10,17,14,11,8

you need to just plot the given numbers onto the graph.

I hope this helped!

Step-by-step explanation:

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