Ask question

Ask question

All categories

3 years ago

13

the radius of the Outer Circle is 2x cm and the radius of the inside circle is 6 cm the area of the Shaded region is 288 Pi cent

imeters squared. What is the value of x

1 answer:

Alexeev081 [22]3 years ago

5 0

For this case we have that by definition, the area of a circle is given by:

$A = \pi * r ^ 2$

Where:

r: It is the radius of the circle.

So, we have that the area of the shaded region is given by:

$\pi * (2x) ^ 2- \pi * 6 ^ 2 = 288 \pi\\4x ^ 2-36 = 288\\4x ^ 2 = 288 + 36\\4x ^ 2 = 324$

We divide between 4 on both sides of the equation:

$x ^ 2 = 81$

We apply root to both sides:

$x = \pm \sqrt {81}$

We choose the positive value of the root:

$x = \sqrt {81}\\x = 9$

Finally, the value of "x" is 9

Answer:

$x = 9$

You might be interested in

A term for a geometric figure that is enclosed by a circle.

Verizon [17]

A geometric figure enclosed by a circle is called an inscribed figure.

6 0

3 years ago

Read 2 more answers

The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

5 0

2 years ago

A red marble is selected at random from a bag containing 2 blues and 9 red marbles and is not replaced.the probability that a se

meriva

Answer:

So the probability of drawing a second red marble is 8 out 10 or 0.8.

Step-by-step explanation:

It seems to me that if one red marble is already gone, there are 8 red marbles left out of a total of 10 marbles.

So the probability of drawing a second red marble is 8 out 10 or 0.8.

3 0

2 years ago

Read 2 more answers

Which graph represents the inverse sine function?

hichkok12 [17]

Answer: A.
The inverse sine function is written as sin−1(x) or arcsin(x). Inverse functions swap x- and y-values, so the range of inverse sine is − π/2 to π/2 and the domain is −1 to 1. When evaluating problems, use identities or start from the inside function.
(REFER TO CHART BELOW)

6 0

2 years ago

What is the slope of this line

Rashid [163]

Answer:

Slope = 2/3

Step-by-step explanation:

Slope = Change over y (rise) over change over x (run)

Pick two dot points on the line

Count how many units over they are until you get to the next dot, then count how many units up until you reach the next dot

Remember: Y runs vertically, X runs horizontally

Put the unit number that ran vertically on the top, then put the unit number that runs horizontally on the bottom

If needed simplify

The slope is 2/3

5 0

3 years ago