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shtirl [24]
3 years ago
5

An open box is made from a square piece of cardboard 30 inches on a side by cutting identical squares and turning up the sides.

A) express the volume of the box as V, as a function of the length of the side of the square cut from each corner, x. B) Find and interpert V(3), V(4), V(5),V(6),V(7). What is happening to the volume of the box as th elength of the side of the square cut from each corner increases? C) Find the domain of V
Mathematics
1 answer:
pychu [463]3 years ago
3 0

Step-by-step explanation:

A)

The length of the box is 30 − 2x inches.

The width of the box is 30 − 2x inches.

The height of the box is x inches.

So the volume is:

V = x (30 − 2x)²

B)

V(3) = 3 (30 − 6)² = 1728

V(4) = 4 (30 − 8)² = 1936

V(5) = 5 (30 − 10)² = 2000

V(6) = 6 (30 − 12)² = 1944

V(7) = 7 (30 − 14)² = 1792

As x increases, the volume of the box increases to a maximum and then decreases.

C)

The ends of the domain occur when V = 0.

0 = x (30 − 2x)²

x = 0 or 15

So the domain is (0, 15).

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shutvik [7]

Answer:

No.

If y is greater than 3, it is not a solution to the system of inequalities. (7,5) has a y value of 5, therefore it is is not a solution.

8 0
3 years ago
In a game of poker a hand of five cards is dealt to each player from a deck of 52 cards. find the probablility of a hand contain
aalyn [17]

Answer:

0.00597

Step-by-step explanation:

Given,

Total number of cards = 52,

In which flush cards = 20,

Also, the number of spade flush cards = 5,

Since,

\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}

Thus, the probability of a hand containing a spade flush, if each player has 5 cards

=\frac{\text{Ways of selecting a spade flush card}}{\text{Total ways of selecting five cards}}

=\frac{^{20}C_5}{^{52}C_5}

=\frac{\frac{20!}{5!15!}}{\frac{52!}{5!47!}}

=\frac{15504}{2598960}

= 0.00597  

7 0
3 years ago
Mario invests £2000 for 3 years at 5% per annum compound interest. Calculate the value of the investment at the end of 3 years.
Delicious77 [7]

Answer:

$2315.25

Step-by-step explanation:

Given data

Principal=  £2000

Time= 3 years

Rate= 5%

The compound interest expression is

A= P(1+r)^t

substitute

A= 2000(1+0.05)^3

A= 2000(1.05)^3

A= 2000*1.157625

A= 2315.25

Hence the Amount is $2315.25

7 0
3 years ago
-8-3x=-8(1-7x) how many solutions will mark barilest
Lina20 [59]

Answer:

x=0

Step-by-step explanation:

-8-3x=-8(1-7x)

add 8 to both sides =( -3x=56x)

subtract 56x from both sides (-59x=0)

divide both sides by -59 = (x=0)

5 0
3 years ago
PLEASE HELP ME BRAINLIEST TO RIGHT ANSWER
N76 [4]

Can you put it in any form instead of a point so I can correctly plot it in

3 0
3 years ago
Read 2 more answers
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