Sam is 27 years old. His age is 6 years greater than 3 times Brandon's age. Which method

A box without a top is to be made from a rectangular piece of cardboard, with dimensions 9 in. by 10 in., by cutting out square

mariarad [96]

Answer:

The optimal volume is 63.1142 in3, with a cut of 1.5767 inches

Step-by-step explanation:

If we make a cut of x inches to create the box, the dimensions of the box will be:

Length = 10 - 2x

Width = 9 - 2x

Height = x

So the volume of the box would be:

Volume = (10 - 2x) * (9 - 2x) * x

Volume = 4x3 - 38x2 + 90x

To find the maximum volume, we need to take the derivative of the volume and find the values of x where it is equal to zero:

dV/dx = 12x2 - 76x + 90 = 0

6x2 - 38x + 45 = 0

Using Bhaskara's formula, we have:

Delta = 38^2 - 4*6*45 = 364

sqrt(Delta) = 19.08

x1 = (38 + 19.08) / 12 = 4.7567

x2 = (38 - 19.08) / 12 = 1.5767

Testing these values in the volume equation, we have:

Volume1 = 4*(4.7567)^3 - 38*(4.7567)^2 + 90*(4.7567) = -1.1883

(Negative value for the volume is not valid)

Volume1 = 4*(1.5767)^3 - 38*(1.5767)^2 + 90*(1.5767) = 63.1142

So the optimal volume is 63.1142 in3, with a cut of 1.5767 inches

7 0

3 years ago

What is(14x2-27x+9)/(7x-3)?

Ann [662]

Answer:

(-7x - 3) • (2x + 3)

Step-by-step explanation:

7 0

3 years ago

A small plane travel at a rate of 125 kilometers per hour. find the distance traveled in 3 hours

sveta [45]

The answer is 375 kilometers in 3 hours

7 0

3 years ago

Marlin bought 4 ham sandwiches and 2 bags of chips for $22.50 . If the chips cost $0.75 per bag how much did each sandwich cost

Masteriza [31]

first work out the value of 2 bags of chips which is: 0.75 + 0.75 = 1.50p

take that away from the total: 22.50-1.50=21 pounds

since what is left (21) is how much 4 ham sandwiches cost we can just divide 21 by 4 which is 5.25

so each sandwich costs 5.25 pounds

3 0

3 years ago

Read 2 more answers

The graph represents the normal distribution of recorded weights, in pounds, of cats at a veterinary clinic.

marshall27 [118]

Please consider the graph.

We have been given that graph represents the normal distribution of recorded weights, in pounds, of cats at a veterinary clinic. We are asked to choose the weights, which are within 2 standard deviations of the mean.

We can see from our graph that mean of the weights is 9.5 and standard deviation in 0.5.

The data point that would be below two standard deviation is: $9.5-2\times 0.5$ that is $9.5-1=8.5$ .

The data point that would be above two standard deviation is: $9.5+2\times 0.5$ that is $9.5+1=10.5$ .

Now we need to check the data points that lie within 8.5 and 10.5.

Upon looking at our given choices, we can see that 8.9, 9.5 and 10.4 pounds lie within 2 standard deviation of the mean.

Therefore, 8.9 lbs, 9.5 lbs and 10.4 lbs are correct choices.

8 0

3 years ago

Read 2 more answers