a woodworker builds a picture frame that is 2 feet by 3 feet. find the perimeter of the frame in feet.

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

Please answer correctly !!!!!!!!!!! Will mark 50 points brainliest !!!!!!

Ket [755]

Answer:

In your console (ctrl + shift + j), the letter a would appear. Beneath that, the letter c would appear.

Step-by-step explanation:

This is because the val2 is not less than or equal to 3. The second condition that's inside the first condition is true but since the first condition is false, the second condition would not run.

3 0

2 years ago

Solve For 1/4 + 1/2 + x = - 3/4

ivann1987 [24]

Answer:

x= negitive 6/8

Step-by-step explanation:

Ok think about it 1/4 plus 1/2 is 3/4

so how do i go to negitives?

you double the amount of it and then minus it

because 3/4- 3/4 would be zero

so you have to double it to get that answer

have a wonderful day filled with only joy!

5 0

3 years ago

How much of a radioactive kind of thorium will be left after 14,680 years if you start with

babymother [125]

Answer:

8978 grams

Step-by-step explanation:

The equation to find the half-life is:

$N(t)= N_{0}e^{-kt}$

N(t) = amount after the time <em>t</em>

$N_{0}$ = initial amount of substance

t = time

It is known that after a half-life there will be twice less of a substance than what it intially was. So, we can get a simplified equation that looks like this, in terms of half-lives.

$N(t)= N_{0}e^{-\frac{ln(\frac{1}{2}) }{t_{h} } t}$ or more simply $N(t)= N_{0}(\frac{1}{2})^{\frac{1}{t_{h} } }$