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3 years ago

If f(x)=3x^2+1 and g(x)=1-x, what is the value of (f-g)(2)?

Mathematics

2 answers:

Sav [38]3 years ago

6 0

Answer:

$(f-g)(2)=28$

Step-by-step explanation:

Given:

$f(x)=3x^2+1$

$g(x)= 1-x$

To find the equivalent expression of $(f-g)(2)$ .

$(f-g)(2) = f(2) - g(2)$

Find g(x)

$g(x)=1-x$

Sub x for 2

$g(2)=1-2$

$g(2)=-1$

Find f(x)

$f(x)=3x^2+1$

Sub x for 2

$f(2)=3(2)^2+1$

$f(2)=12+1$

$f(2)=13$

Solve for the giving value

$(f-g)(2)$

$(13- (-1)) (2)$

$14(2)$

stepladder [879]3 years ago

3 0

The answer should be 14.

You just have to substitute x with the given number and finish the equation.

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A soup can in the shape of a right circular cylinder is to be made from two materials. The material for the side of the can cost

Advocard [28]

Answer:

Radius = 1.12 inches and Height = 4.06 inches

Step-by-step explanation:

A soup can is in the shape of a right circular cylinder.

Let the radius of the can is 'r' and height of the can is 'h'.

It has been given that the can is made up of two materials.

Material used for side of the can costs $0.015 and material used for the lids costs $0.027.

Surface area of the can is represented by

S = 2πr² + 2πrh ( surface area of the lids + surface are of the curved surface)

Now the function that represents the cost to construct the can will be

C = 2πr²(0.027) + 2πrh(0.015)

C = 0.054πr² + 0.03πrh ---------(1)

Volume of the can = Volume of a cylinder = πr²h

16 = πr²h

$h=\frac{16}{\pi r^{2}}$ -------(2)

Now we place the value of h in the equation (1) from equation (2)

$C=0.054\pi r^{2}+0.03\pi r(\frac{16}{\pi r^{2}})$

$C=0.054\pi r^{2}+0.03(\frac{16}{r})$

$C=0.054\pi r^{2}+(\frac{0.48}{r})$

Now we will take the derivative of the cost C with respect to r to get the value of r to get the value to construct the can.

$C'=0.108\pi r-(\frac{0.48}{r^{2} })$

Now for C' = 0

$0.108\pi r-(\frac{0.48}{r^{2} })=0$

$0.108\pi r=(\frac{0.48}{r^{2} })$

$r^{3}=\frac{0.48}{0.108\pi }$

r³ = 1.415

r = 1.12 inch

and h = $\frac{16}{\pi (1.12)^{2}}$

h = 4.06 inches

Let's check the whether the cost is minimum or maximum.

We take the second derivative of the function.

$C"=0.108+\frac{0.48}{r^{3}}$ which is positive which represents that for r = 1.12 inch cost to construct the can will be minimum.

Therefore, to minimize the cost of the can dimensions of the can should be

Radius = 1.12 inches and Height = 4.06 inches

5 0

3 years ago

Identify the variable(s), set up your equation(s), and solve. Richard has an elder sister who is twice his age and a younger sis

alexdok [17]

Answer:

7 years

Step-by-step explanation:

Given that:

Let Richard's age = x

Elder sister's age = 2x

Youngwr sister's age = x - 2

Product of sisters ages = 70

2x * (x - 2) = 70

2x² - 4x = 70

2x² - 4x - 70 = 0

x² - 2x - 35 = 0

x² - 7x + 5x - 35 = 0

x(x - 7) +5(x - 7) = 0

(x - 7) or (x + 5) = 0

x = 7 or x = - 5

X can't be negative

Hence, x = 7

Richard is 7 years

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2 years ago

What are the solutions of the system y=x^2+3x-4 y=2x+2

ra1l [238]

Hope this would help you

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3 years ago

I need help with this math question :(

Ray Of Light [21]

Answer:

k = 5,

y = 5x

Step-by-step explanation:

If y is proportional to x,

y ∝ x

Then the equation will be

y = kx

Her k = proportionality constant.

Now we choose a point from the given table.

Let the point is (2, 10).

By putting the values of x and y in the equation,

10 = 2×k

k = $\frac{10}{2}$

k = 5

This will be true for any point we choose from the table.

And the equation will be y = 5x

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Evgesh-ka [11]

The answer is 3.3 hope this helps you .Skateboards

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