Help with inverse variation?

A truck is being filled with cube-shaped packages that have side lengths of 1/4 foot. The part of the truck that is being filled

n200080 [17]

Answer:

24000 pieces.

Step-by-step explanation:

Given:

Side lengths of cube = $\frac{1}{4} \ foot$

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

$Volume\ of\ cube =a^{3}$

$=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot$

Length = 8 foot, Breadth = $6\frac{1}{4} =\frac{25}{4} \ foot$ , Height = $7\frac{1}{2} =\frac{15}{2} \ foot$

$Volume\ of\ rectangular\ prism =length\times breadth\times height$

$=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot$

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = $\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube$

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.

7 0

2 years ago

4x + 3y = 6 3x + 5y = -1 Solve the simultaneous equations. y= z=

Kisachek [45]

Answer:

x=3, y= -2

Step-by-step explanation:

Multiplying :

(4x+3y =6)*-3

(3x+5y =-1)*4

-12x -9y= -18

12x+20y= -4

Add the equations

20y-9y = -4-18

11y = -22

y= -22/11 = -2

3x +5* -2= -1

3x -10 = -1

3x = 10-1

x= 9/3 =3

4 0

2 years ago

Which relation is a function?

Ksivusya [100]

B. To see if it’s a function, it has to pass the vertical line test. That means draw a vertical line (going up and down) through any point on the graph and it can only go through one point. If it goes through more than 1, it’s not a function. Like in graph A, if you draw a vertical line at x=-2, it will go through two points, same at x=2. For graph b, no matter where you move a vertical line, it only passes through one point at a time, so it passes the vertical line test.

8 0

1 year ago

If the value of x=4, y=3 and z= -2 find the value of 2x+3z

Oksana_A [137]

Answer:

Step-by-step explanation:

To find value:

2x + 3z

Given values:

x = 4, y = 3 and z = -2

Solution:

2x + 3z

(Putting the values of x = 4 and z = -2)

= 2(4) + 3(-2)

= 8 - 6

= 2 (Ans)

8 0

2 years ago

Read 2 more answers

Pleaseee Help me 20 pts

Simora [160]

Answer:

Tax is C 4.12

Tip is E 15.00

total =94.10

Step-by-step explanation:

Tax = bill * tax rate

= 74.98 * 5.5%

= 74.98 * .055

= 4.1239

To the nearest cent = 4.12

Tip = bill * tip rate

= 74.98 * 20%

= 74.98 *.2

= 14.996

To the nearest cent = 15.00

The total bill is

Final = bill + tax+ tip

= 74.98 + 4.12+15

= 94.10

7 0

2 years ago