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3 years ago

Solve this equation and explain the steps 9-2x= 7x

Mathematics

1 answer:

Hunter-Best [27]3 years ago

3 0

Answer:

x = 1

Step-by-step explanation:

Step 1: Write equation

9 - 2x = 7x

Step 2: Solve for x

Add 2x on both sides: 9 = 9x

Divide both sides by 9: x = 1

Step 3: Check

Plug in x to verify it's a solution.

9 - 2(1) = 7(1)

9 - 2 = 7

7 = 7

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alisha [4.7K]

Answer:

If it's not too late by now, the answer is 19.9 $mm^{2}$

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3 years ago

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

What's ur guys' mbti im tired

Vinvika [58]

Answer:

i ndo0nt nwjrefilaqwebriuhgyowafh vnh3e4iyufrawgevtc87ayimcawhuebovaetyert

Step-by-step explanation:

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3 years ago

If the given values in a right triangle are cos A =

Vlad1618 [11]

See the picture attached to better understand the problem

we know that
in the right triangle ABC
cos A=AC/AB
cos A=1/3
so
1/3=AC/AB----->AB=3*AC-----> square----> AB²=9*AC²----> equation 1

applying the Pythagoras Theorem
BC²+AC²=AB²-----> 2²+AC²=AB²---> 4+AC²=AB²----> equation 2

substitute equation 1 in equation 2
4+AC²=9*AC²----> 8*AC²=4----> AC²=1/2----> AC=√2/2
so
AB²=9*AC²----> AB²=9*(√2/2)²----> AB=(3√2)/2

the answer is
the hypotenuse is (3√2)/2

5 0

4 years ago

The radius of a circle is 4.6 millimeters. Find the diameter.

kramer

Hi :)

Radius is half the diameter

4.6 mm (2) = 9.2 mm

The diameter of the circle is 9.2 mm.

4 0

3 years ago