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Vesnalui [34]
3 years ago
5

A sphere with a diameter of 30 inches is placed in a cube. The sphere touches the lateral faces

Mathematics
1 answer:
Nina [5.8K]3 years ago
5 0

Answer:

a) 30 inches × 30 inches × 30 inches

b) 27,000 inches³

c) 14,130 inches³

d) 12,870 inches³

Step-by-step explanation:

Edge of the cube = diameter = 30 inches

Volume of cube = s³

30³ = 27000 inches³

Radius = 30/2 = 15

Volume of sphere:

(4/3) × 3.15 × 15³

14130 inches³

Difference:

27000 - 14130

12870 inches³

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6x^2+x-12 in factored form
pychu [463]
6x²+x-12

the first thing we need to do is find 2 numbers that add up to equal the middle term (1) but multiply together to get a product of -72 (-12*6)

two numbers that would fit this is 9 and -8
so now we placed 9x and -8x in place of the middle term

6x²+9x-8x-12

now we look for whats common between the first two numbers and divide them out

6x²+9x = 3x(2x+3)

now we do the same with the last two numbers

-8x-12 = -4(2x+3)

notice how the numbers in brackets are the same (2x+3)
we will keep (2x+3) and then combine the numbers on the outside

once we do that you should get an answer of 

(3x-4)(2x+3)

hope this helped!


5 0
3 years ago
Ava and Sara both started getting an allowance 12 weeks ago, and they haven't spent a cent! They get $1 for each year of their a
4vir4ik [10]

Answer:

Ava is 10 years old

Step-by-step explanation:

Sara is 8

Sara=$8 per week for 12 weeks

$8×12 weeks=$96

Ava has $24 more than Sara

x*12=96$+$24

12x=120

x=120/12

x=10

Ava's age is 10

6 0
3 years ago
The price of an Item has been reduced by 80%. The original price was $65. What is the price of the item now?​
PIT_PIT [208]

Answer:

$13

Step-by-step explanation:

multiply 65 by 80 then divide by 100, you get 52, so subtract 65 from 52 you get 13

5 0
3 years ago
In the graph of an inequality, the region to the right of a dashed vertical line
lara31 [8.8K]

Answer:

x is greater than -4

Step-by-step explanation:

8 0
3 years ago
Start with the basic function f(x)=2x. If you have an initial value of 1, then you end up with the following iterations. f(1)=2*
denpristay [2]
<span>f(x)=2x

f(1)=2*1=2

f^2(1)=2*2*1=4

f^3(1) =2*2*2*1=8

1. If you continue this pattern, what do you expect would happen to the numbers as the number of iterations grows?

I expect the numbers continue growing multiplying each time by 2.

Check your result by conducting at least 10 iterations.

f^4(1) = f^3(1) * f(1) = 8*2 = 16

f^(5)(1) = f^4(1) * f(1) = 16 * 2 = 32

f^6 (1) = f^5 (1) * f(1) = 32 * 2 = 64

f^7 (1) = f^6 (1) * f(1) = 64 * 2 = 128

f^8 (1) = f^7 (1) * f(1) = 128 * 2 = 256

f^9 (1) = f^8 (1) * f(1) = 256 * 2 = 512

f^10 (1) = f^9 (1) * f(1) = 512 * 2 = 1024

2. Repeat the process with an initial value of −1. What happens as the number of iterations grows?

f(-1) = 2(-1) = - 2

f^2 (-1) = f(-1) * f(-1) = - 2 * - 2 = 4

f^3 (-1) = f^2 (-1) * f(-1) = 4 * (-2) = - 8

f^4 (-1) = f^3 (-1) * f(-1) = - 8 * (-2) = 16

f^5 (-1) = f^4 (-1) * f(-1) = 16 * (-2) = - 32

As you see the magnitude of the number increases, being multiplied by 2 each time, and the sign is aleternated, negative positive negative positive ...
</span>
4 0
3 years ago
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