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Pani-rosa [81]
3 years ago
12

4. What is the volume of the cylinder? Express answer in terms of a (hold and

Mathematics
1 answer:
Vladimir [108]3 years ago
4 0

Given:

Base area = 4π mm²

Height = 10 mm

To find:

The volume of the cylinder.

Solution:

Base of the cylinder is circle.

Area of the base = πr²

πr² = 4π

Volume of the cylinder = πr²h

Substitute 4π in place of πr².

                                      = 4π × 10

                                      = 40π mm³

The volume of the cylinder is 40π mm³.

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f(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, [infinity]) and g(x) = 2x^2
iren2701 [21]

Answer with Step-by-step explanation:

We are given that function f(x) which is quadratic function.

x -intercept of function f(x) at (-1,0) and (-3,0)

x-Intercept of f means zeroes of f

x=-1 and x=-3

Range of f =[-4,\infty)

g(x)=2x^2+8x+6=2(x^2+4x+3)

g(x)=0

2(x^2+4x+3)=0

x^2+4x+3=0

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x(x+3)+1(x+3)=0

(x+1)(x+3)=0

x+1=0\implies x=-1

x+3=0\implies x=-3

Therefore, x-intercept of g(x) at (-1,0) and (-3,0).

Substitute x=-2

g(-2)=2(-2)^2+8(-2)+6=8-16+6=-2

g(x)=2(x^2+4x)+6

g(x)=2(x^2+2\times x\times 2+4-4)+6=2(x^2+2\times x\times 2+4)-8+6

g(x)=2(x+2)^2-2

By comparing with the equation of parabola

y=a(x-h)^2+k

Where vertex=(h,k)

We get vertex of g(x)=(-2,-2)

Range of g(x)=[-2,\infty)

Zeroes of f and g are same .

But range of f and g are different.

Range of f contains -3 and -4 but range of g does not contain -3 and -4.

f and g are both quadratic functions.

3 0
3 years ago
The product of (3 − 4i) and____is 25.
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9a+16a=75\\\\25a=75\qquad\text{divide both sides by 25}\\\\\boxed{a=3}\qquad\text{put the value of a to}\ b=\dfrac{4}{3}a:\\\\b=\dfrac{4}{3}(3)\\\\\boxed{b=4}\\\\Answer:\ \boxed{(3-4i)\underline{(3+4i)}=25}

6 0
3 years ago
15 points! Please answer rigghtt
Scorpion4ik [409]

Answer:

20 hours

Step-by-step explanation:

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170 divided by 8.50 is 20.

The answer is 20.

If this helped please consider marking it brainliest :3

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