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2 years ago

Find, in terms of π, the surface area of a sphere generated by rotating a semicircle of radius 6 inches about its diameter.

Mathematics

1 answer:

Minchanka [31]2 years ago

6 0

Answer:

$144\pi in^2$

Step-by-step explanation:

Given

Shape: Circe

Radius = 6 inches

Required

What is the surface area of a sphere when the circle

When a circle is rotated about its diameter, the resulting sphere maintains the same radius and diameter as the circle, before rotation;

This implies that

Radius [of sphere] = 6 inches

$Surfare\ Area = 4\pi r^2$

Substitute 6 for r

$Surfare\ Area = 4\pi* 6^2$

$Surfare\ Area = 4\pi* 6 * 6$

$Surfare\ Area = 4\pi*36$

$Surfare\ Area = 144\pi$

Hence, the surface area of the resulting sphere is 144 pi inches square

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A line segment of length k is divided into 3 equal parts what is the distance between midpoints of the first and third segments

anastassius [24]

Line segment of length k is divided into 3 equal parts.

so first segment is 0-k/3 and third segment is 2/3k-k

so mid-pt of 1st = k/6 and 3rd = 5/6k

so the distance in between = 5/6k-k/6 = 4/6k = 2/3k

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2 years ago

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2 years ago

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Y=-2(x+5)^2-30 In standard form

Trava [24]

Answer:

y = -2 ( (x^2) + (2*x*5) + (5^2)) - 30

y = -2 ( x^2 + 10x + 25) - 30

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y = -2x^2 - 20x - 50 - 30

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3 0

3 years ago

Select all instances in which the variable described is binomial.

tino4ka555 [31]

Answer: a. , c. , d., e.

Step-by-step explanation:

A variable that counts how many times a certain event occurs in a particular number of trials is known as binomial random variable.

For each trial, there exist only two outcomes .

The probability of for each event is the same on each trial.

a. Event has two outcomes with same probability as 0.50, therefore the random variable represents the total number of flips required to get tails is a binomial random variable.

b. Total guidelines are 5.

Here total outcomes are not 2 , it does not meet with the conditions of binomial.

c. The random variable represents the total number of children from this pair of parents with blue eyes has two outcomes (where has or not.)

also, the probability of having blue eyes is same in each trial, so it represents binomial random variable.

d. The random variable represents the total number out of 567 customers with a checking account has two outcomes (checking or savings).

So, it represents binomial random variable.

e. The random variable represents the total number of ace cards observed has two outcomes ( ace or not ace).

So it represents the binomial random variable.

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2 years ago

The sum of two numbers is 36. Twice the first number minus the second is 6. Find the numbers.

kkurt [141]

Hey there!!

Let's take the two numbers as 'x' and 'y'

The sum of these two numbers is 36.

... x + y = 36

Twice the first number minus the second is 6.

... 2x - y = 6

Now, we have two equations.

_______________________________________________________

... x + y = 36

... 2x - y = 6

Now, let's add both the equations.

... 3x = 42

Divide each side by 3.

... x = 42 / 3

... x = 14

Hence, the first number is'14'.

We know the sum of both the numbers is 36.

... x + y = 36

... 14 + y = 36

Subtract 14 on both sides.

... y = 36-14

... y = 22

Hence, the second number is 22.

The numbers are 14 and 22.

Hope my answer helps!!

3 0

2 years ago