Write the equation of a vertical line that goes through (2,-1)

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much

Y_Kistochka [10]

Answer:

x = ∛ 2*V/5

y = ∛ 2*V/5

h = V/ ∛ 4*V²/25

Step-by-step explanation:

Dimensions of the aquarium base is x*y

We call c₁ cost per unit area of the sides, then cost per unit area of slate is equal 5c₁.

let call h the height of the aquarium then volume of the aquarium is:

V = x*y*h where h = V / x*y

As the base is a rectangular one there are 2 sides x*h . and 2 sides y*h

According to this:

Ct (cost of aquarium ) = cost of the base + cost of the sides

cₐ ( cost of the base) = 5*c₁*x*y

c₆ (cost of the sides ) = c₁*2*x*h + c₁*2*y*h

C(t) = 5*c₁*x*y +2* c₁*x* V/x*y + 2* c₁*y* V/x*y or

C(t) = 5*c₁*x*y + 2*c₁*V/y *2*c₁* V/x

Taking partial derivatives en x and y we have:

C´(x) = 5*c₁*y - 2*c₁*V/x²

C´(y) = 5*c₁*x - 2*c₁*V/y²

C´(x) = C´(y) ⇒ 5*c₁*y - 2*c₁*V/x² = 5*c₁*x - 2*c₁*V/y²

or 5*y - 2*V/x² = 5*x - 2*V/y²

(5*y*x² - 2*V)/x² = ( 5*y²x - 2*V) /y²

(5*y*x² - 2*V)*y² = ( 5*y²x - 2*V)*x²

5*y³*x² - 2*V*y² = 5*y²x³ - 2*V*x²

5*y³*x² - 5*y²x³ = 2*V * ( y² - x²)

by symmetry x = y

Then using x = y and plugging that value on the derivatives

C´(x) = 5*c₁*y - 2*c₁*V/x²

C´(x) = 5*c₁*x - 2*c₁*V/x²

C´(x) = 0 ⇒ 5*c₁*x - 2*c₁*V/x² = 0

5*x - 2*V/x² = 0 ⇒ 5*x³ - 2*V = 0 ⇒ 5*x³ = 2*V ⇒ x³ = 2*V/5

x = ∛ 2*V/5 and y = ∛ 2*V/5 and h = V/ x*y h = V/ ∛ 4*V²/25

7 0

3 years ago

There are 650 sixth graders in the school and 338 of them are girls. What percent of the 6th grade students are girls?

Evgesh-ka [11]

Answer:

52% are girls

Step-by-step explanation:

We know that there are 650 sixth-graders and 338 of them are girls, we are then asked to find the percentage of how many are girls.

We have the fraction 338 over 650 but need to reduce it.

To solve this, we need to find the GCF of 650 and 338, which is 26, so divide both the numerator and denominator by 26.

$\frac{338/26}{650/26}$

$\frac{13}{25}$

Now divide the 13 and 25 :

13 / 25 = 0.52

0.52 * 100 = 52%

Therefore, 52% of the sixth-graders in the school are girls

4 0

2 years ago

Read 2 more answers

WILL GIVE BRAINLIEST!!! The two larger segments below are perpendicular. Find the area of the shaded region to the nearest integ

snow_lady [41]

Answer:

I wont be able to help much and get you till all the way to the end but here is what i know:

Step-by-step explanation:

The radius of the smaller circle is 6, and the longer segment adds up to 12 since 6 + 6 = 12. the area of the whole bigger circle would be 452.389, by using the formula of the area of a circle "πr²". This is what i can tell and the only part I'm confused in how to find the area of JUST the shaded part. I hope this helped a bit!

5 0

2 years ago

1. y = log x

Nuetrik [128]

Answer:

Domain {x : x > 1}

Range {y : y ∈ R}

Vertical asymptote x = 0

x-intercept (1, 0)

End behavior consistent

Graph attached down

Step-by-step explanation:

Let us study the equation:

∵ y = log(x)

→ It is a logarithmic function, so no negative values for x

∴ Its domain is {x : x > 1}

∴ Its range is {y : y ∈ R}, where R is the set of the real numbers

→ An asymptote is a line that a curve approaches, but never touches

∵ x can not be zero

∴ It has a vertical asymptote whose equation is x = 0

→ x-intercept means values of x at y = 0, y-intercept means

values of y at x = 0

∵ x can not be zero

∴ There is no y-intercept

∵ y can be zero

∴ The x-intercept is (1, 0)

→ The end behavior of the parent function is consistent.

As x approaches infinity, the y-values slowly get larger,

approaching infinity

∵ y = log(x) is a parent function

∴ The end behavior is consistent

→ The graph is attached down

6 0

3 years ago

The equation Y=KX show you would make $41.09 for recycling 7 pounds of cans. How much would you make if you recycled 4 pounds

Reika [66]

41.09 divide by 7 = 5.87

5.87*4 = 23.48

6 0

3 years ago