A boat traveled 27 miles in 2 hours. at this rate, how many miles will the boat travel in 1 2 hour

Can you please help me with this question.

blondinia [14]

Answer:

Step-by-step explanation:

this my answer is perfect yap

4 0

3 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

How to find the circumference of a cirlcle

Otrada [13]

$\sf{Circumference = 2\times\pi\times~r}$

Where r is the radius of the circle.

7 0

3 years ago

kimmy earns a $200 commission on all sales plus a base salary of $30,000 her total income last year was $80,000. I need an equat

brilliants [131]

I think the answer is:
30,000+200s = 80,000
where s represents the sales

6 0

3 years ago

Hey can anyone pls answer these math problems!!

Zepler [3.9K]

Answer:

1={5 and 3} 2={0} 3={0.209 and 4.791} 4={-3 and 4} 5={1 and 9} 6={-4.303 and -0.697}

Step-by-step explanation:

Your probably confused on what a, b, and c means.

The problems are written like this.

$ax^2+bx+c=0$

That formula finds the zeros.

For example 1:

$x^2-8x+15=0\\ax^2-bx-c\\a=1\\b=-8\\c=15$

Then use the formula

$x=\frac{-b+-\sqrt{b^2-4ac} }{2a} \\\\x=\frac{-(-8)+-\sqrt{-8^2-4(1)(15)} }{2} \\x=\frac{8+-\sqrt{64-60} }{2} \\\\x=\frac{8+-2}{2}\\$

If plus then 5, if minus then 3

CHECK:

$x^2-8x+15=0\\5^2-8(5)+15=0\\25-40+15=0\\0=0\\3^2-8(3)+15=0\\9-24+15=0\\0=0$

Hope this helps you understand how to do this by yourself. Now to do the rest ;-;

5 0

2 years ago