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Kazeer [188]
3 years ago
8

An artist cuts 4 squares with side length x ft from the corners of a 12 ft-by-18 ft rectangular piece of sheet metal. She bends

up the sides and
welds the comers to form a rectangular garden fountain that is x ft high. Write and simplify a function for the volume of the fountain in terms
of x.
V(x) =
x+
x+

Mathematics
1 answer:
Kruka [31]3 years ago
8 0

Answer:

V=4x^3-60x^2+216x

Step-by-step explanation:

<u>Volume And Function s</u>

Geometry can usually be joined with algebra to express volumes as a function of some variable. The volume of a parallelepiped of dimensions a,b,c is

V=abc

Our problem consists in computing the volume of a box made with some sheet of metal 12 ft by 18 ft. The four corners are cut by a square distance x as shown in the image below .

If the four corners are to be lifted and a box formed, the base of the box will have dimensions (12-2x)(18-2x) and the height will be x. The volume of the box is

V=x(12-2x)(18-2x)

Operating and simplifying

V=4x^3-60x^2+216x

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Help me please! (Look at image.)
Svetradugi [14.3K]
4^2 = 16
so x must be greater than 16
answer
E. 17
F. 19
8 0
2 years ago
The diameter of Circle \(Q\) terminates on the circumference of the circle at \((3,0)\) and \((-4,0)\). Write the equation of th
Dahasolnce [82]

The equation of the given circle in the standard form is given as <u>(x + 0.5)² + y² = 3.5²</u>.

In the question, we are given that the diameter of Circle \(Q\) terminates on the circumference of the circle at \((3,0)\) and \((-4,0)\).

We are asked to write the equation of the circle in standard form.

The equation of the circle in standard form is given as (x - h)² + (y - k)² = r, where (h, k) is the center of the circle, and r is the radius of the circle.

The center of the circle can be found using the midpoint formula, as the center is the midpoint of the diameter.

Thus, the center is at ( (3 + (-4))/2, (0 + 0)/2 ) = ( -1/2, 0 ).

The length of the diameter can be calculated using the distance formula.

Thus, the length of the diameter of the circle is √((-4 - 3)² + (0 - 0)²) = √((-7)²) = √49 = 7.

The radius is half the length of the diameter.

Thus, the radius, r = 7/2.

Now, we have the center (h, k) = (-1/2, 0), and the radius, r = 7/2.

Thus, the equation of the circle in the standard form, (x - h)² + (y - k)² = r can be shown as:

(x - (-1/2))² + (y - 0)² = (7/2)²,

or, (x + 0.5)² + y² = 3.5².

Thus, the equation of the given circle in the standard form is given as <u>(x + 0.5)² + y² = 3.5²</u>.

Learn more about the equation of the circle at

brainly.com/question/1559324

#SPJ4

8 0
1 year ago
HELP PLELASE I DONT UNDERSTAND
jeyben [28]

Answer:

The scale factor is 1/4

Step-by-step explanation:

18/72 = 10/40 = 11/44

simplify all of those and you get 1/4.

5 0
3 years ago
A new savings account is opened with $800 and gains 4.5% annual interest continuously. How much is in the account after 3 years
alexira [117]
A=800×e^(0.045×3)
A=915.63
7 0
3 years ago
Read 2 more answers
Question 6 of 10
jeka57 [31]

Answer:

  A)  6

Step-by-step explanation:

The ratio is found by dividing a sequence value by the one before. It is "common" if it is the same for any pair of sequence values.

  r = y2/y1 = 36/6 = 6

The common ratio is 6.

3 0
2 years ago
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