MATHEMATICS HIGH SCHOOL

"A solid machine part is to be manufactured as shown in the figure. The part is made by cutting a small cone off the top of a larger cone. The small cone has a base radius of 3 inches and a height of 5 inches. The larger cone has a base radius of 5 inches and had a height of 12 inches prior to being cut. What is the volume of the resulting part illustrated in the figure?"-------------------------
I keep doing the math for it and get 359 cubed inches (rounded to the closest whole number) when including the pi, and 114pi cubed inches when I exclude it. The answer choices are 60pi cubed inches, 65pi cubed inches, 85pi cubed inches, and 90*pi cubed inches. Can someone go through the math of this?

Answers

Answer 1

Answer:

Large cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 9^2 x 15

= 1272.3 cubic inches

Smaller cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 3^2 x 5

= 47.1 cubic inches

1272.3 - 47.1 = 1225.2 cubic inches

1272/3.14 ≈ 390

The answer is 390 × pi.

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What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?–10
–5
–3
–1

Answers

If you would like to solve the inequation 2 * (3x - 1) >= 4x - 6, you can do this using the following steps:

2 * (3x - 1) >= 4x - 6
2 * 3x - 2 * 1 >= 4x - 6
6x - 2 >= 4x - 6
2x >= - 6 + 2
2x >= - 4
x >= - 2

The correct result would be x >= - 2, so - 1.

The value of x in the solution is -1. Option D

How to determine the value of x

2(3x – 1) ≥ 4x – 6

From the given equation, make 'x' the subject by expanding the brackets

6x - 2 ≥ 4x - 6

Collect like terms

6x -4x ≥ -6 + 2

2x ≥ -4

x ≥ -4/ 2

x ≥ -2

If x ≥ -2, then x = -1

Therefore, the value of x in the solution is -1.Option D

Learn more about inequalities here:

brainly.com/question/25275758

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Find the range of the following piecewise function.[0,11)
(-4,6]
(0,11]
[-4,6)

Answers

Given:

The piecewise function is

$f(x)=\begin{cases}x+4 & \text{ if } -4\leq x<3 \n 2x-1 & \text{ if } 3\leq x<6 \end{cases}$

To find:

The range of given piecewise function.

Solution:

Range is the set of output values.

Both functions $f(x)=x+4$ and $f(x)=2x-1$ as linear functions.

Starting value of $f(x)=x+4$ is at x=-4 and end value is at x=3.

Starting value: $f(-4)=-4+4=0$

End value: $f(3)=3+4=7$

Starting value of $f(x)=2x-1$ is at x=3 and end value is at x=6.

Starting value: $f(3)=2(3)-1=5$

End value: $f(6)=2(6)-1=11$

Least range value is 0 at x=-4 and 0 is included in the range because -4 is included in the domain.

Largest range value is 11 at x=6 and 11 is not included in the range because 6 is not included in the domain.

So, the range of the given piecewise function is [0,11).

Therefore, the correct option is A.

How many unit tiles need to be added to the expressionx2 + 4x + 3 in order to form a perfect square trinomial

Answers

In the question "How many unit tiles need to be added to the expression x2 + 4x + 3 in order to form a perfect square trinomial" the correct answer is 1 unit tile. Because, to make the expression x^2 + 4x + 3 a perfecr square trinomial we have x^2 + 4x + 3 + 1 = x^2 + 4x + 4 = (x + 2)^2

Answer:

A) 1

Step-by-step explanation:

If: 2=6, 3=12, 4=20, 5=30, 6=42, 9=??

Answers

2*3=6, 3*4=12, 4*5=20, 5*6=30, 6*7=42, 7*8=56, 8*9=72, 9*10=90. 90 is your final answer

your answer would be 9=72 they are just multiplying the first number by 3 then 4 then 5 and so on and so on

The sum of two number is 17. their driffrence is 27.write a system of equations that describe this situation. solve to find the two numbers

Answers

A) x + y = 17
B) x - y = 27
Adding both equations:2x = 44
x = 22
y = -5

You have a coupon good for $5 off the price, p, of any large pizza. You also get a 15% discount on any pizza if you show your student ID. How much more would you pay for a large pizza if the cashier applies the coupon first, rather than the 15% discount first? Please show steps to this composite function.

Answers

If the coupon is applied first.
Amount paid = $0.85(p - 5)

If the discount is applied first.
Amount paid = $0.85p - 5

Amount paid more if the coupon is applied first is 0.85(p - 5) - (0.85p - 5) = 0.85p - 4.25 - 0.85p + 5 = 0.75

Therefore, you will pay $0.75 more if the coupon is applied first rather than the 15% discount first.

Answer:

3; all real numbers except x=2

0.75

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