MATHEMATICS HIGH SCHOOL

Suppose the surface area of a sphere is 324π square units. What is the volume, in cubic units, of this sphereA) 9π
B) 81π
C) 324π
D) 972π

Answers

Answer 1

Answer:

Answer:

Option D is correct

$972 \pi$ is the volume, in cubic units, of this sphere

Step-by-step explanation:

Surface area of sphere(S) and volume of sphere (V) is given by:

$S = 4 \pi r^2$

$V = (4)/(3) \pi r^3$ .....[1]

As per the statement:

Suppose the surface area of a sphere is 324π square units

⇒S = 324π square units

then;

$324 \pi = 4 \pi r^2$

Divide both side by $4 \pi$ we have;

$81 = r^2$

$r^2= 81$

⇒ $r = √(81) = 9$ units

We have to find the volume, in cubic units, of this sphere.

Substitute the given value in [1] we have;

$V = (4)/(3) \pi \cdot 9^3 = (4)/(3) \pi \cdot 729$

Simplify:

$V = 4 \cdot \pi \cdot 243 = 972 \pi$ cubic units

Therefore, $972 \pi$ is the volume, in cubic units, of this sphere

Answer 2

Answer: D would be the answer

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Multiplying a number by which of the following would result in a smallest number? 10^-1 10^0 10^1 10^2

Answers

Answer:

To obtained the smallest number multiply the number with $(10)^(-1)$ .

Step-by-step explanation:

Given : $(10)^(-1),\ (10)^0,\ (10)^1,\ (10)^2$

We have to find when we multiply any number with the given number which number will give the smallest value.

Consider the given numbers,

$(10)^(-1),\ (10)^0,\ (10)^1,\ (10)^2$

We find the values of each number one by one,

1) consider $(10)^(-1)$ , using property of exponents $a^(-m)=(1)/(a^m)$ , we have

$(10)^(-1)=(1)/(10)=0.1$

2) $(10)^0$ we know any thing to power 0 is always 1.

$(10)^0=1$

3) $(10)^1$ is same as itself that is 10.

4) $(10)^2$ is $(10)* 10=100$

Thus, To obtained the smallest number multiply the number with $(10)^(-1)$ .

10^-1 would be the smallest answer...

10^-1= .1
10^0= 1
10^1= 10
10^2= 100

If the common difference in an arithmetic sequence is 4, and the 20th term is 36, what is the first term?

Answers

The sum of an arithmetic sequence can be found using the formula S = n/2(a + l) where S equals sum, n equals # terms, a equals the first term and l equals last term we know enough of these to find the missing pieces S = -15n = 20a = 4 -15 = 20/2 (4 + l) now we only have one unknown -15 = 10 (4 + l)-15 = 40 + 10l-55 = 10l l = -5.5 so the last term is -5.5 now we can use anothe formula to find the common difference l = a + (n-1) d so the last term equals the first term (a) plus # terms -1 times (d) the common difference -5.5 = 4 + (20-1) d -9.5 = 19 d d = -.5 so your common difference is -.5

What value is 4 to the second power

Answers

Answer:

Step-by-step explanation:

4² = 4 × 4 = 16

Answer:

4^2= 4*4 = 16 is the answer

20% of 160. Please help ? How to find the percent of it

Answers

20% of 160

Solve

20/100 = .20
.20*160 = 32

Answer: 32

so it wold be 20 over 100 and x over 160 so you wold cross multiply then divide

x 20
-- --
160 100 cross mulltiply

3200/100= 32 32=answer

Suppose contact lenses cost $300 for a year’s supply or $30 for a month’s supply. Which is less expensive to order per year, paying for 12 months at one time or paying for 1 month at a time?(1 point) month(s) at a time

Answers

Answer: Buying them for the year- 300 dollars

Step-by-step explanation:

30 x 12 is equal to 360 dollars, which is more expensive than 300 dollars.

Is (2,4) a solution of the equation y=x-2

Answers

4 = 2 - 2
4 = 0
Is it a solution for y = x - 2?
No.

Final answer:

To determine if a point is a solution to an equation, substitute the values of the coordinates into the equation. The point (2,4) was found to not be a solution to the equation y=x-2.

Explanation:

To test if the point (2,4) is a solution to the equation y=x-2, we replace the 'x' with '2' and 'y' with '4' in the equation.

So if y is indeed equal to x - 2, then, replacing x and y should leave you with a true statement. That will be 4 = 2 - 2. But this results in, 4 = 0 which is not true.

So, (2,4) is not a solution to the equation y=x-2.