An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 feet from each corner and turning up the edges. If the box is to hold 864 cubic feet, what should be the dimensions of the sheet metal?

Answers

Answer 1

Answer:

Answer:

24 feet

Step-by-step explanation:

We are given that an open box is to be constructed from a square piece of sheet metal by removing a square side 6 feet from each corner and turning up the edges.

We have to find the dimensions of the sheet metal

Let x feet be the side of square metal sheet

Length of box=x-12 feet (because 6 feet removed from each corner)

Width of box=x-12 feet

Height of box=6 feet

Volume of box=864 cubic feet

We know that volume of cuboid= $l* b* h$

Box is in cuboid shaped

Therefore, volume of box= $6(x-12)(x-12)$

$6(x^2-24x+144)=864$

$x^2-24x+144=(864)/(6)$

$x^2-24x+144=144$

$x^2-24x+144-144=0$

$x(x-24)=0$

Then , $x=0 , x-24=0$

$x=24$

x=0 is not possible because side of square metal sheet can not be zero

Therefore, x=24

All sides of square metal sheet are equal.

Hence, side of square metal sheet =24 feet

Answer 2

Answer:

Final answer:

The original sheet of metal from which an open box holding 864 cubic feet is constructed by removing 6-foot squares from each corner and folding up the edges should be a square with a side length of 26 feet.

Explanation:

To answer your question about the open box constructed from a square piece of sheet metal, let's assume the original side length of the sheet metal is x feet. When squares of length 6 feet are removed from each corner and the edges are turned up, we're left with a box with length and width of (x - 2*6) feet and height of 6 feet.

Given that the volume of the box is 864 cubic feet, we set up this equation to find x:

(x - 12 feet)(x - 12 feet)*6 feet = 864 cubic feet.

Solving this equation gives us a value for x, which is the side length of the original square piece of sheet metal. Doing the math, we find x = 26 feet. So, the dimensions of the original sheet metal are 26 feet by 26 feet.

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Multiply your answer should be a monomial in standard form (-4x^2)(7x^3)

Answers

answer: -28x^5

exlaningtion:I used my brain dhdhdishdhdhdhdhdh

Two joggers, one averaging 7 mph and one averaging 5 mph, start from a designated initial point. The slower jogger arrives at the end of the run 45 minutes after the other jogger. Find fhe distance of the run.

Answers

22.5 miles long

basically all you have to do is count out the factors until you reach two number of 45 apart

  DIFFERENCE
7MPH 5MPH BETWEEN THEM

7 5 2
14 10 4
21 15   6
28 20 8
35 25 10
42 30 12
49 35 14
56 40 16
63 45 18
70 50   20
77 55   22
84 60   24
91 65 26
98    70 28
105    75 30
112    80 32
119 85 34
126 90 36
133 95 38
140    100 40
147 105 42
154 110 44
161 115 46

considering the differences are even it means it has to fall in the middle. if you count from the top it is 22.5 numbers down giving you the number of miles.
I'm sure there is an easier way but this is how i would solve it. :)

Final answer:

The distance of the run is 13.125 miles. The total time for the slower jogger was found to be 2.625 hours. Thus, both joggers ran the same distance, but at different speeds resulting in different finish times.

Explanation:

The problem deals with the concept of relative speed in mathematics. To find the distance of the run, we first need to figure out the time it took for each jogger to finish the run. We know that the slower jogger finished 45 minutes after the faster one. Since the speed equivalence is expressed in miles per hour (mph), let's convert 45 minutes into hours by dividing 45 by 60, giving us 0.75 hours.

Given that the slower jogger runs at 5 mph, and they took 0.75 hours longer than the faster one, we know they ran for a certain time 't', so we can represent this as t = total time of slower jogger's run.

The faster jogger ran at 7 mph. Since the jogger was 0.75 hours ahead of the slower one, the time would be represented by t - 0.75 hours = total time of faster jogger's run. The distance travelled by each jogger is 'speed x time'.

Following this, we equal these distances because it's the same course: 5t = 7(t - 0.75).

Solving this equation gives us t = 2.625 hours (total time for slower jogger). To find the run's distance, we can now substitute total time into either jogger's speed x time calculation. We'll use the slower jogger here: Distance = 5t = 5*2.625 = 13.125 miles.

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A box has 6 beads of the same size, but all are different colors. Tania draws a bead randomly from the box, notes its color, and then puts the bead back in the box. She repeats this 3 times. What is the probability that Tania would pick a yellow bead on the first draw, then a blue bead, and finally a yellow bead again?1/216

1/36

1/6

1/2

Answers

The probability that Tania would pick a yellow bead on the first draw, then a blue bead, and finally a yellow bead again is 1/216.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm{Probability=(Desired\ Outcomes)/(Total\ Number\ of\ outcomes\ possible)$

As it is given that the box has 6 beads of the same size, but all are different colours. therefore, the probability of any bead being selected is 1/6.

Now, we know that when Tania picks a bead she puts it back in the box, therefore, the sample size of the box will be the same and also the probability of each bead will be the same as well.

Further, the probability that Tania would pick a yellow bead on the first draw, then a blue bead, and finally a yellow bead again can be written as,

$\rm Probability = (1)/(6) * (1)/(6) * (1)/(6) = (1)/(216)$

Hence, the probability that Tania would pick a yellow bead on the first draw, then a blue bead, and finally a yellow bead again is 1/216.

Learn more about Probability:

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Each specific bead color has (each time) a probability $\frac{1}6$ of being drawn.

Hence the final probability is $\frac{1}6\cdot\frac{1}6\cdot\frac{1}6=\boxed{(1)/(216)}$

What is the equation of a line passing through the point (a, b) and having a slope of b?

Answers

From the slope form of a line;
$(y-b)/(x-a) =b$
y-b=bx-ab
y=bx-ab+b
y=bx-b(a-1)

Answer:

The equation is y-a= b(x-b)

Step-by-step explanation:

I use bold for the slope so you can differentiate the slope term b from the y coordinate value b.

The equation of a line passing through a specific point and having a specific slope can be obtained using the point slope form of a line :

y-y1=m(x-x1) where m is the slope and (x1,y1) is your specific point.

So replacing your values, the point (x1,y1) =(a,b) and m=b, in this equation we havE:

y-a= b(x-b)

That can be expressed in point slope form and explicit for as.

y = b(x-b) + a = bx -bb +a =

y= bx + (a -bb)

Convert 372 in Quinary number

Answers

Answer:

372₁₀ = 2442₅

Step-by-step explanation:

372 : 5 = 74 r 2

74 : 5 = 14 r 4

14 : 5 = 2 r 4

2 : 5 = 0 r 2 ↑

write down the remainders in the reverse order

372₁₀ = 2442₅

Write the standard form of the equation of the hyperbola 4x2 − 9y2 − 16x − 36y − 56 = 0.

Answers

The standard form of the equation of the hyperbola:

$((x - 2)^2)/(5) - ((y + 2)^2)/(20/9) = 1$

How did we get the values?

To write the standardform of the equation of a hyperbola, you need to rearrange the given equation into the following form:

$((x-h)^2)/(a^2) - ((y-k)^2)/(b^2) = 1$

Where (h, k) is the center of the hyperbola, and "a" and "b" are positive constants related to the shape and size of the hyperbola.

Start by completing the square for both the x and y terms:

1. Group the x terms and y terms separately:

4x² - 16x - 9y2 - 36y - 56 = 0

2. Complete the square for the x terms by adding and subtracting the appropriate constant inside the first bracket:

4(x² - 4x + 4) - 9y² - 36y - 56 = 0

3. Complete the square for the y terms by adding and subtracting the appropriate constant inside the second bracket:

4(x² - 4x + 4) - 9(y² + 4y + 4) - 56 + 36 = 0

4. Now, rewrite the equation and simplify:

4(x² - 4x + 4) - 9(y² + 4y + 4) - 20 = 0

5. Factor the squares:

4(x - 2)² - 9(y + 2)² - 20 = 0

6. Divide both sides by the constants to isolate the equation:

$((x - 2)^2)/(5) - ((y + 2)^2)/(20/9) = 1$

Now, you have the standard form of the equation of the hyperbola:

$((x - 2)^2)/(5) - ((y + 2)^2)/(20/9) = 1$

The center of the hyperbola is at (h, k) = (2, -2), "a" is the square root of 5, and "b" is the square root of 20/9.

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Answer:

(x-2)^2/3^2 - (y+2)^2/2^2 =1

Step-by-step explanation:

Plato

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An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 feet from each corner and turning up the edges. If the box is to hold 864 cubic​ feet, what should be the dimensions of the sheet​ metal?

Answers

Final answer:

Explanation:

Learn more about Open Box Construction here:

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Final answer:

Explanation:

Learn more about Relative Speed here:

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What is Probability?

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How did we get the values?

An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 feet from each corner and turning up the edges. If the box is to hold 864 cubic feet, what should be the dimensions of the sheet metal?