The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant. the volume of a rectangular prism is 672 cubic centimeters. the figure has a length of 8 centimeters and a width of 14 centimeters. a second prism has a length of 12 centimeters and a width of 8 centimeters. what is the volume of the second prism?
576 cubic centimeters
768 cubic centimeters
784 cubic centimeters
1,344 cubic centimeters

The volume of the second rectangular  prism is  576 cm³ .

Step-by-step explanation:

As given

The volume of a rectangular prism varies jointly with the length and width when the height remains constant.

Let us assume that the length is denoted by L .

Let us assume that the Breadth is denoted by B.

Thus

V = L × B ×  H

where H is the constant of variation

The volume of a rectangular prism is 672 cubic centimeters and has a length of 8 centimeters and a width of 14 centimeters.

Volume (V) = 672 cm

Length (L) = 8 cm

Width (B) = 14 cm

Put all the values in the above

672 = 8 × 14 ×  H

672 = 112H

H = 6

As given

A second prism has a length of 12 centimeters and a width of 8 centimeters.

Length = 12 cm

Width =  8 cm

Height = 6cm

Put all the values in V = L × B ×  H .

V = 12 × 8  ×  6

V = 576 cm³

Therefore the volume of the second rectangular  prism is  576 cm³ .

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

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