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4 years ago

What is the equation of a circle whose center is at the origin and whose radius is 9?

Mathematics

2 answers:

Rashid [163]4 years ago

3 0

A=πr2=π·92≈254.469. I think this is what your looking for

erma4kov [3.2K]4 years ago

3 0

√x²+y²=9 or (x²+y²) = 9² Man that was hard to type

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The dimensions of a rectangle are such that its length is 3 in. more than its width. If the length were doubled and if the width

Kay [80]

Answer:

The length of the rectangle is 11 inch and its width is 8 inch.

Step-by-step explanation:

Given:

Rectangle $(R_1)$ and rectangle $(R_2)$ .

Let the width of the rectangle be 'x' inch.

Its length = '(x+3)' inch

Area of the rectangle = $(A_1)$

⇒ $A_1$ = $(x)(x+3)$

Now for rectangle $(R_2)$ its width is decreased by 1 inch and length is doubled,the area $(A_2)$ will increased by 66 sq-inch.

So,

$A_2=A_1+66$

According to the question.

⇒ Area of rectangle $(R_2)$ with width '(x-1)' and length '2(x+3)'='(2x+6)' .

⇒ $A_2=(x-1)(2x+6)$

Plugging the values of $A_2$ in terms of $A_1$ .

⇒ $A_1+66= (x-1)(2x+6)$

Plugging $A_1$ = $(x)(x+3)$ into the equation.

⇒ $(x)(x+3)+66=(x-1)(2x+6)$

⇒ $x^2+3x+66=2x^2+6x-2x-6$

⇒ $x^2-2x^2+3x-6x+2x+6+66=0$

⇒ $-x^2-x+72=0$

Now using quadratic formula we can find the value of 'x'.

Quadratic formula, (x)= $\frac{\pm b+\sqrt{b^2-4ac} }{2a}$

x= -9 and x= 8

Discarding the negative value.

Our width = 'x' = 8 inches.

So the length of the rectangle = 11 inches and width of the rectangle = 8 inches.

7 0

3 years ago

Solve. 3 x+2y−z=8 2x+2z=−4 x+3y=4 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. ( , , )

marshall27 [118]

Answer:

x = 1 , y = 1 , z = -3

Step-by-step explanation:

Solve the following system:

{3 x + 2 y - z = 8

2 x + 2 z = -4

x + 3 y = 4

Hint: | Choose an equation and a variable to solve for.

In the third equation, look to solve for x:

{3 x + 2 y - z = 8

2 x + 2 z = -4

x + 3 y = 4

Hint: | Solve for x.

Subtract 3 y from both sides:

{3 x + 2 y - z = 8

2 x + 2 z = -4

x = 4 - 3 y

Hint: | Perform a substitution.

Substitute x = 4 - 3 y into the first and second equations:

{3 (4 - 3 y) + 2 y - z = 8

2 (4 - 3 y) + 2 z = -4

x = 4 - 3 y

Hint: | Expand the left hand side of the equation 3 (4 - 3 y) + 2 y - z = 8.

3 (4 - 3 y) + 2 y - z = (12 - 9 y) + 2 y - z = 12 - 7 y - z:

{12 - 7 y - z = 8

2 (4 - 3 y) + 2 z = -4

x = 4 - 3 y

Hint: | Expand the left hand side of the equation 2 (4 - 3 y) + 2 z = -4.

2 (4 - 3 y) + 2 z = (8 - 6 y) + 2 z = 8 - 6 y + 2 z:

{12 - 7 y - z = 8

8 - 6 y + 2 z = -4

x = 4 - 3 y

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for y:

{12 - 7 y - z = 8

8 - 6 y + 2 z = -4

x = 4 - 3 y

Hint: | Isolate terms with y to the left hand side.

Subtract 12 - z from both sides:

{-7 y = z - 4

8 - 6 y + 2 z = -4

x = 4 - 3 y

Hint: | Solve for y.

Divide both sides by -7:

{y = 4/7 - z/7

8 - 6 y + 2 z = -4

x = 4 - 3 y

Hint: | Perform a substitution.

Substitute y = 4/7 - z/7 into the second equation:

{y = 4/7 - z/7

8 - 6 (4/7 - z/7) + 2 z = -4

x = 4 - 3 y

Hint: | Expand the left hand side of the equation 8 - 6 (4/7 - z/7) + 2 z = -4.

8 - 6 (4/7 - z/7) + 2 z = 2 z + ((6 z)/7 - 24/7) + 8 = (20 z)/7 + 32/7:

{y = 4/7 - z/7

(20 z)/7 + 32/7 = -4

x = 4 - 3 y

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for z:

{y = 4/7 - z/7

(20 z)/7 + 32/7 = -4

x = 4 - 3 y

Hint: | Isolate terms with z to the left hand side.

Subtract 32/7 from both sides:

{y = 4/7 - z/7

(20 z)/7 = -60/7

x = 4 - 3 y

Hint: | Solve for z.

Multiply both sides by 7/20:

{y = 4/7 - z/7

z = -3

x = 4 - 3 y

Hint: | Perform a back substitution.

Substitute z = -3 into the first equation:

{y = 1

z = -3

x = 4 - 3 y

Hint: | Perform a back substitution.

Substitute y = 1 into the third equation:

{y = 1

z = -3

x = 1

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = 1 , y = 1 , z = -3

3 0

3 years ago

the diameter of a cone-shaped container is 4 inches, and its height is 6 inches .How much grater is the volume of a cylinder-sha

sveticcg [70]

The radius r used in below equations would equal 2in because it is half the given diameter of 4in.
The volume of the cone would be
$V = \frac{1}{3} \pi r^2h \\ \\ V = \frac{1}{3} \pi (2in)^2(6in) = 8 \pi\ in^3$

The volume of a cylinder with the same dimensions would be
$V = \pi r^2h \\ 
V = \pi (2in)^2(6in) = 24 \pi in^3$

The cylinder is 24 - 8 = 16 cubic inches greater.

3 0

3 years ago

The weight of 10 identical samples of a substance is 0.01 pounds what is the weight of 100 samples

valentina_108 [34]

Hola!!

If 10 = 0.01
then you could divide 100 by 10 which is 10
So then you multiply 0.01 by 10 which is 0.1

So the answer is 0.1

Get another answer to be sure. c:

5 0

3 years ago

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What is the answer to 8+4x+3(6x)+2

Tatiana [17]

The answer to the question is 10+22x

6 0

3 years ago

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