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jarptica [38.1K]
3 years ago
6

A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut from the four corners and the

flaps are folded upward to form an open box. If the volume of the box is 1536 incubed​, what were the original dimensions of the piece of​ metal?
Mathematics
1 answer:
Misha Larkins [42]3 years ago
7 0

Answer:

Step-by-step explanation:

This is good!  The length of the metal is 20 inches longer than the width.  But we fold up 4-inch flaps on each side, so the height of the box is 4 inches, and the length and width will each decrease by 8 inches (4 inches on each side).  Since the length and width decrease by the same amount, the length will still be 20 inches longer than the width.  So the equations would be:

l = w + 20

vol = l x w x h = 1716 in3

1716 = (w + 20)(w)(4)

1716 = 4w2 + 80w

4w2 + 80w - 1716 = 0

4(w2 + 20w - 429) = 0

4(w + 33)(w - 13) = 0

w + 33 = 0, so w = -33

w - 13 = 0, so w = 13

Since the width can't be negative, the width of the box is 13 and the length is 33 (13 + 20).

But remember, the length and width of the piece of metal are each 8 inches longer than the box, so it was 41 inches by 21 inches.

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  • 5√2
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Step-by-step explanation:

<u>Use the property of 45 degree right triangles</u>

  • c = a√2, where c- hypotenuse, a = legs

<u>Top diagram</u>

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<u>Bottom diagram</u>

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2 years ago
(c) Find a solution of the differential equation that satisfies the initial condition y(1) = 5. (d) Find a solution of the diffe
jonny [76]

Answer:

Step-by-step explanation:

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3 years ago
A large aquarium of water is being filled with a hose. Due to a problem, the sensor does not start working until some time into
stira [4]

Answer: The sensor will read 300 liters after 5 minutes.

The sensor sensor should have read 120 liters at time -7 minutes.


Step-by-step explanation:

Given: The amount of water detected by sensor initially= 225 litres

Since, the hose fills the aquarium at a constant rate of 15 liters per minute.

Let x be the time , and y be reading of sensor then

y=225+15x

Therefore, the sensor reads after 5 minutes (put x=5 in the equation)= 225+5(15)=300\ liters

To find the sensor read at time -7 minutes put x=-7 in the equation, we get

y=225+15(-7)=225-105=120

Hence, the sensor should have read 120 liters at time -7 minutes.

8 0
3 years ago
A measurement of fluoride ion in tooth paste from 5 replicate measurements delivers a mean of 0.14 % and a standard deviation of
Nady [450]

Answer:

The confidence interval at 95 % for which we assume that it contains the true value is (0.0962, 0.1838).

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96*\frac{0.05}{\sqrt{5}} = 0.0438

The lower end of the interval is the mean subtracted by M. So it is 0.14 - 0.0438 = 0.0962

The upper end of the interval is the mean added to M. So it is 0.14 + 0.0438 = 0.1838

The confidence interval at 95 % for which we assume that it contains the true value is (0.0962, 0.1838).

5 0
3 years ago
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Answer:

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