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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 tur

den301095 [7]

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= $l\times b\times h$

Box is in cuboid shaped

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

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

$x^2-24x+144=\frac{864}{6}$

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

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

$x(x-24)=0$

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

4 0

4 years ago

If a ball is thrown upward at 29.4 meters per second from the top of a building that is 80 meters high, the height of the ball c

RoseWind [281]

Answer:

Step-by-step explanation:

29.4 per sec > Building 80m

Height = S = 4.9t^2 + 29.4t + 80

Solve for t:

t = 1.24 (approximately)

If t needed coordinates / solve using the quadratic formula:

t = (1.24 , -7.24)

<h3>The ball's maximum height is 124.1 meters.</h3>

7 0

3 years ago

The cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use over 900 min. For amonth

Helen [10]

Answer:

1022 minutes

Step-by-step explanation:

Let x be the number of minutes the executive used the phone

There is a base charge of $35 and only minutes greater than 900 min are charged at the rate of $0.40 per minute

So total bill A = 35 + 0.4(x-900)

We know the bill was $83.80

So we can rewrite the equation as

35 + 0.4(x-900) = 83.30

and solve for x

To make it easier for computational purposes

1) Multiply both sides by 10

$35\cdot \:10+0.4\left(x-900\right)\cdot \:10=83.8\cdot \:10$

2) Perform individual multiplication

$350+4\left(x-900\right)=838$

3) Subtract 350 from both sides

$350+4\left(x-900\right)-350=838-350$

4) Simplify

$4\left(x-900\right)=488$

5) Divide both sides by 4

$\frac{4\left(x-900\right)}{4}=\frac{488}{4}$

6) Simplify

$x-900=122$

7) Add 900 to both sides to isolate x

$x-900+900=122+900$

8) Simplify to obtain x

$x=1022$

Answer: The executive used the phone for 1022 minutes that month

6 0

2 years ago

The sample space for flipping a coin three times is given. Let H represent Heads and T represent Tails

Phantasy [73]

Here's the answer:
A. There are 3 favorable outcome for 2 heads, 1 tail (3/8 or 0.375 probability)B. There is 1 favorable outcome for 3 heads (1/8 or 0.125 probability)C. There are 3 favorable outcome for 2 tails, 1 head (3/8 or 0.375 probability)D. There is 1 favorable outcome for 3 tails (1/8 or 0.125 probability)E. Sum of probabilities = A+B+C+D
Sum of probabilities = 0.375 + 0.125 + 0.375 + 0.125Sum of probabilities = 1

A and C are the same, they both have 3/8 probability. As well as B and D, both have 1/8 probability.

6 0

3 years ago

Four girls helped Mr.Day plant garden for their help hr gave the girls $24 to share equally later Mrs day gave each girl $2 for

katrin [286]

Answer:$8

Step-by-step explanation: there is 4 girls and $24 they split it equally so you would do 24/4 and that gives you 6. Then it says Mrs. Day gave each girl $2 so then you add 6+2 and then you get 8.

3 0

3 years ago

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