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MAXImum [283]
3 years ago
13

What is the volume of the largest box that can be made from a square piece of cardboard with side lengths of 24 inches by cuttin

g equal squares from each corner and turning up the sides?
Mathematics
2 answers:
Kitty [74]3 years ago
5 0

Answer:

1024 in³

Step-by-step explanation:

Volume = (24 - 2x)(24 - 2x)(x)

= 576x - 96x² + 4x³

dV/dx = 576 - 192x + 12x² = 0

x² - 16x + 48 = 0

x² - 12x - 4x + 48 = 0

x(x - 12) - 4(x - 12) = 0

(x - 12)(x - 4) = 0

x = 4, x = 12

x can not be 12,

Because 24 - 2(12) = 0

So x = 4

Volume = (24 - 8)(24 - 8)(4)

= 1024

SVEN [57.7K]3 years ago
3 0

You need to subtract the two cutouts on each side, so the side of the box would be 24- 2x. X would then become the height of the box once folded.

The volume is found by multiplying the 4 dimensions:

The volume becomes x(24-2x)^2

Now take the derivative of the formula to solve for x

Dv/dx= (24-2x)^2 + x^2(24-2x)*-2

= 24-2x(24-2x-4x)=0

X =12 or 4

24-2x = 24-2(4) = 24-8=16

Volume = 16 x 16 x 4 = 1024 cubic inches.

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Find the area of the figure. round your answer to the nearest hundredth
liraira [26]

Answer: 84.14

Step-by-step explanation:

Area of the rectangle is L*W=B*H

14*5=70

To find the area of the half circle we must use the formula pi r^2/2

r=radius

and the radius is 6 because we add 4 and 4 and need to get to 14

because the line below it is 14 and it is a rectangle so the lengths are the same.

Diameter=6

So radius =3

pi (3)^2/2=

9/2 pi + 70=

84.14

6 0
3 years ago
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Savatey [412]
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8 0
2 years ago
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What is the diameter of the cirlce if the radius is 7
Liono4ka [1.6K]

Answer:

14

Step-by-step explanation:

The diameter of a circle is twice its radius

d=2r

Substitute 7 in for r

d=2*7

d=14

So, the diameter is 14

Hope this helps! :)

7 0
3 years ago
Read 2 more answers
PLEASE ANSWER i WILL PUT MOST BRAINLIEST!
galina1969 [7]

Answer:

The correct option is;

c. Because the p-value of 0.1609 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.

Step-by-step explanation:

Here we have the values

μ = 275 mL

275.4

276.8

273.9

275

275.8

275.9

276.1

Sum = 1928.9

Mean (Average), = 275.5571429

Standard deviation, s = 0.921696159

We put the null hypothesis as H₀: μ₁ = μ₂

Therefore, the alternative becomes Hₐ: μ₁ ≠ μ₂

The t-test formula is as follows;

t=\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}

Plugging in the values, we have,

Test statistic = 1.599292

t_{\alpha /2} at 7 - 1 degrees of freedom and α = 0.05 = ±2.446912

Our p-value from the the test statistic = 0.1608723≈ 0.1609

Therefore since the p-value = 0.1609 > α = 0.05, we fail to reject our null hypothesis, hence the evidence suggests that the mean does not differ from 275 mL.

4 0
3 years ago
Choose the best description for the real number 35
Natalija [7]

Answer:

A) Irrational, because it is not a terminating or repeating decimal.

Step-by-step explanation:

Every time a square root results in a decimal, it will always never end, and never repeat. The square root of 35 qualifies for both of these qualities, therefore, making the answer (A). Hope this helps!

5 0
3 years ago
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