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Diano4ka-milaya [45]
3 years ago
12

savannah bought two 24 packs of tim bits. she is hanging out with 4 friends. what is the greatest number of timbits each of them

can get, if shared evenly. is the quotient rational or irrational? explain how you know..
Mathematics
1 answer:
lilavasa [31]3 years ago
5 0
6.It is a rational quotient. You know because 24 tim bits divided by four friends equals six.
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I'm have some issues with the problem shown in the screenshot and would love some help.
KiRa [710]

The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

  • Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.

  • Maximum volume of the box is approximately 1048.6 in.³

<h3>How can the dimensions and volume of the box be calculated?</h3>

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let <em>x </em>represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, <em>V</em>, of the box is therefore;

V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x

By differentiation, at the extreme locations, we have;

\frac{d V }{dx}  =  \frac{d( 4 \cdot \:  {x}^{3}  - 106 \cdot \:  {x}^{2}  + 630\cdot \:  {x} )  }{dx} = 0

Which gives;

\frac{d V }{dx}  =12\cdot \:  {x}^{2}  -  212\cdot \:  {x} + 630 = 0

6•x² - 106•x + 315 = 0

x  =  \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6}

Therefore;

x ≈ 4.55, or x ≈ -5.55

When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

  • Width ≈ 18 - 2×4.55 in. = 8.89 in.

  • Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.

  • Height = x ≈ 4.55 in.

  • The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³

Learn more about differentiation and integration here:

brainly.com/question/13058734

#SPJ1

7 0
1 year ago
The ratio of foreign students to American students at a college is 2 to 35. How many foreign students attend this college if the
oee [108]
You have to divide 1575 by 35 which equals 45 and then multiply that by 2 which equals 90. There are 90 foreign students
3 0
3 years ago
Read 2 more answers
A customer in a store had two 50% off coupons. She tried to buy a purse with them, gave them to the cashier
antoniya [11.8K]

Answer:

Well, I think that the 50% coupons would give you only 50% off of your entire purchace. Not 100% off.

Step-by-step explanation:

8 0
2 years ago
Ms.Lopez has created a floor plan of a dollhouse. The area of the entire dollhouse is 576 square inches
harina [27]

Answer:

(a)Area of the bedroom=96 square inches

(b)Area of the living room =144 square inches

(c)Area of the dollhouse that is not of the bedroom or living room =336 square inches.

Step-by-step explanation:

The area of the bedroom is 1/6 the area of the entire dollhouse

The area of the living room is 3/2 times the area of the bedroom.

The area of the entire dollhouse is 576 square inches

Let the area of bedroom=b

Let the area of living room=l

(a) The area of the bedroom is 1/6 the area of the entire dollhouse

b=\frac{1}{6}X576=96 square inches

(b)The area, in square inches, of the living room

The area of the living room is 3/2 times the area of the bedroom

l= \frac{3}{2}X96=144 square inches

(c)The total area of the house =576 square inches

Area of the bedroom=96 square inches

Area of the living room =144 square inches

Area of the dollhouse that is not of the bedroom or living room

=576-(96+144)=576-240=336 square inches.

The area of the living room is 3/2 times the area of the bedroom

This is gotten by subtracting the area of the bedroom and living room from the total area of the house.

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3 years ago
What is 8 gallons in pints
nikitadnepr [17]

Answer:

64 pints is 8 gallons

Step-by-step explanation:

7 0
3 years ago
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