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1 year ago

Write the prime factorization of 27. Use exponents when appropriate and order the factors from least to greatest

Mathematics

1 answer:

MakcuM [25]1 year ago

7 0

Answer:

27 = 3³

Step-by-step explanation:

The prime factorization of 27 is ...

27 = 3×3×3 = 3³

The exponent of 3 signifies the factor is repeated 3 times.

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Write the equation of a circle centered at the

Fudgin [204]

Answer:

$(x+4)^2+(y+6)^2=100$

Step-by-step explanation:

Given a circle centred at the point P(-4,-6) and passing through the point

R(2,2).

To find its equation, we follow these steps.

Step 1: Determine its radius, r using the distance formula

For point P(-4,-6) and R(2,2)

$\text{Distance Formula=}\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\text{Radius=}\sqrt{(2-(-4))^2+(2-(-6))^2} \\=\sqrt{(2+4))^2+(2+6)^2}\\=\sqrt{6^2+8^2}\\=\sqrt{100}\\Radius=10$

Step 2: Determine the equation

The general form of the equation of a circle passing through point (h,k) with a radius of r is given as: $(x-h)^2+(y-k)^2=r^2$

Centre,(h,k)=P(-4,-6)

r=10

Therefore, the equation of the circle is:

$(x-(-4))^2+(y-(-6))^2=10^2\\\\(x+4)^2+(y+6)^2=100$

3 0

2 years ago

A fence must be built to enclose a rectangular area of 20,000 ft^2. Fencing material costs $4 per foot for the two sides facing

Marysya12 [62]

The cost of the least expensive fence is $3200

Step-by-step explanation:

The given is:

A fence must be built to enclose a rectangular area of 20,000 ft²
Fencing material costs $4 per foot for the two sides facing north and south and $8 per foot for the other two sides

We need to find the cost of the least expensive fence

Assume that the length of each side opposite to North or South is x feet and the length of each other sides is y feet

∵ The length of the rectangle = x feet

∵ The width of the rectangle = y feet

∵ The rectangular area is 20,000 ft²

- Area of a rectangle = length × width

∴ x × y = 20,000

- Divide both sides by x to find y in terms of x

∴ $y=\frac{20,000}{x}$

The fence's length is equal to the perimeter of the rectangular area

∵ Perimeter of the rectangle = 2 length + 2 width

∴ Perimeter of the rectangle = 2x + 2y

∵ Fencing material costs $4 per foot for the two sides facing

North and South

∴ x costs $4 per foot

∵ The cost of the other two sides is $8 per foot

∴ y costs $8 per feet

The cost of the fence is the sum of the products of 4 , 2x and 8 , 2y

∵ The cost of the fence (C) = 4(2x) + 8(2y)

∴ C = 8x + 16y

- Substitute y by its value above

∴ $C=8x+16(\frac{20,000}{x})$

∴ $C=8x+\frac{320,000}{x}$

To find the least expensive differentiate C with respect to x and equate the answer by 0 to find the value of x

∵ $\frac{320,000}{x}$ can be written as $320,000x^{-1}$

∴ $C=8x+320,000x^{-1}$

∵ $\frac{dC}{dx}=8(1)x^{1-1}+320,000(-1)x^{-1-1}$

∴ $\frac{dC}{dx}=8-320,000x^{-2}$

- Equate $\frac{dC}{dx}$ by zero

∴ $8-320,000x^{-2}=0$

∵ $-320,000x^{-2}=-\frac{320,000}{x^{2}}$

∴ $8-\frac{320,000}{x^{2}}=0$

- Subtract 8 from both sides

∴ $-\frac{320,000}{x^{2}}=-8$

- Multiply both sides by x²

∴ - 320,000 = - 8x²

- Divide both sides by -8

∴ 40,000 = x²

- Take √ for both sides

∴ 200 = x

Substitute x in the equation of C to find the least cost of fence

∵ $C=8(200)+\frac{320,000}{(200)}$

∴ C = 1600 + 1600

∴ C = 3200

The cost of the least expensive fence is $3200

Learn more:

You can learn more about the differentiation in brainly.com/question/4279146

#LearnwithBrainly

5 0

2 years ago

This table shows the population of caribou in an area over a period of years . a. What is the growth factor? b. Write an equatio

elena55 [62]

Answer:

I Think its B

Step-by-step explanation:

Edge 2021

3 0

3 years ago

PLEASE ANSWER FAST!! FIRST CORRECT ANSWER MARKED BRAINLIST. I NEED TO PASS THIS CLASS

soldier1979 [14.2K]

Answer:

6900%

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

What is the power of x? <br> A) 2 <br> B) 3 <br> C) 6 <br> D) 7

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

They are basically wanting the value of x.

These are 2 secant lines drawn. Secant Line is a line that intersects the circle at 2 points.

To solve this, we have to use secant-secant theorem.

Secant-Secant Power Theorem tells us that if 2 secant lines are drawn from external point (here, E) to a circle, then, product of measure of one secant's external part and total secant is equal to other secants external part and whole secant.

In algebra, that is:

$(x+1)(x+1+11)=(x+4)(x+4+1)$

Let's multiply and find the value of x:

$(x+1)(x+1+11)=(x+4)(x+4+1)\\(x+1)(x+12)=(x+4)(x+5)\\x^2 + 13x + 12=x^2+9x+20\\13x+12=9x+20\\13x - 9x = 20 - 12\\4x = 8\\x = 2$

Hence, the correct answer choice is A

8 0

3 years ago