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Mkey [24]
3 years ago
9

candy box is made from a piece of cardboard that measures 45 by 24 inches. Squares of equal size will be cut out of each comer.

The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume? inches should be cut away from each corner to obtain the maximum volume. A square with a side of length (Round to the nearest hundredth as needed.)

Mathematics
1 answer:
den301095 [7]3 years ago
6 0

Answer:

Each square should have 5 inches of side and area = 25 square inches.

Step-by-step explanation:

Candy box is made that measures 45 by 24 inches.

Let the squares of equal size x inches has been cut out of each corner.

The sides will then be folded up to form a rectangular box.

Now we have to find the size of square that should be cut from each corner to obtain maximum volume of the box.

Now the box is with length = (45 - 2x) inches

and width = (24 - 2x) inches

and height = x inches

Volume of the candy box = Length × width × height

V = (45 - 2x)(24 - 2x)(x)

V = x(1080 - 48x -90x + 4x²)

  = x(1080 - 138x + 4x²)

  = 4x³ - 138x² + 1080x

Now we will find the derivative of volume and equate it to zero.

\frac{dV}{dx}=12x^{2}-276x+1080=0

12(x² - 23x + 90) = 0

x² - 23x + 90 = 0

x² - 18x - 5x + 90 = 0

x(x - 18) - 5(x - 18) = 0

(x - 5)(x - 18)=0

x = 5, 18

Now for x = 18 Width of the box will be = (24 - 2×18) = 24 - 36 = -12

Which is not possible.

Therefore, x = 5 will be the possible value.

Therefore, square having area 25 square inches should be cut out from each corner to get the maximum volume of candy box.

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never [62]

Answer:

smallest   angle measure 39 degrees

Step-by-step explanation:

the sum of the three interior angles in a triangle is always 180°

x= smallest

x +x+24 + 2x = 180

4x +24 = 180

4x = 156

x = 39

7 0
3 years ago
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A car drives 16 1/2 miles on a gallon of gas. how many miles can it travel on 9 gallons?
Nana76 [90]

Answer:

148.5 miles

Step-by-step explanation:

its 148.5 miles because you times the 16 1/2 to the 9 and get 148.5 miles

5 0
2 years ago
88 feet/second = 60 miles/hour. How many feet per second is 1 mile? (Hint: divide both side of the equation by the same amount.)
zalisa [80]

Answer:

1 mile/hour is equivalent to 1.47 feet/seconds

Step-by-step explanation:

Given

88 ft/s= 60 miles/hr

Required

Determine the equivalent of 1 mile/hour

88\ ft/s= 60\ miles/hr

Express 60 as 60 * 1

88\ ft/s= 60 * 1\ mile/hr

Divide both sides by 60

\frac{88\ ft/s}{60}= \frac{60 * 1\ mile/hr}{60}

\frac{88\ ft/s}{60}= 1\ mile/hr

Reorder

1\ mile/hr = \frac{88\ ft/s}{60}

Divide 88 by 60

1\ mile/hr = 1.46666666667\ ft/s

Approximate to 3 significant figures

1\ mile/hr = 1.47\ ft/s

Hence;

1 mile/hour is equivalent to 1.47 feet/seconds

8 0
2 years ago
The teacher collected some snowfall data during one of the snow days last year. Estimate the total snowfall throughout the day.
Sedaia [141]

The total snowfall throughout the day is the expected value of the distribution.

The estimated total snowfall during the day is 30 inches

Start by calculating the average rate of snow collected on that day.

Rate = \frac{0 + 1.5 + 2.5 + 2.0 +1.0 +0.5}{6}

This gives

Rate = \frac{7.5}{6}

Divide 7.5 by 6

Rate = 1.25

There are 24 hours in a day.

So, the total snowfall is:

Total  = Rate \times Hours

This gives

Total  = 1.25 \times 24

Multiply

Total  = 30

Hence, the estimated total snowfall during the day is 30 inches

Read more about expected values at:

brainly.com/question/13005177

3 0
2 years ago
The graph below represents the function f.
OLEGan [10]

Answer: А.

The function f intersects the x-axis at two points, and the function g never intersects the x-axis.

Step-by-step explanation:

In the graph we can see f(x), first let's do some analysis of the graph.

First, f(x) is a quadratic equation: f(x) = a*x^2 + b*x + c.

The arms of the graph go up, so the leading coefficient of f(x) is positive.

The vertex of f(x) is near (-0.5, -2)

The roots are at x = -2 and x = 1. (intersects the x-axis at two points)

Now, we know that:

g(x) has a positive leading coefficient, and a vertex at (0, 3)

As the leading coefficient is positive, the arms go up, and the minimum value will be the value at the vertex, so the minimum value of g(x) is 3, when x = 0.

As the minimum value of y is 3, we can see that the graph never goes to the negative y-axis, so it never intersects the x-axis.

so:

f(x) intersects the x-axis at two points

g(x) does not intersect the x-axis.

The correct option is A.

6 0
3 years ago
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