MATHEMATICS COLLEGE

What is the answer to a10/a3 ?

Answers

Answer 1

Answer:

Answer:

a^7

Step-by-step explanation:

$(a^(10))/(a^3)\n\n\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=x^(a-b)\n(a^(10))/(a^3)=a^(10-3)\n\n=a^7$

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Which is better 32 miles or 12.7 kilometers and why

Answers

Answer:

32 miles

Step-by-step explanation:

32 miles is equal to 51.499008 Kilometers

12.7 kilometers is equal to 7.891414 miles

Translate the following into algebraic expressions: The first class has a kids in it, the second has b kids in it, and the third class has c kids in it. The kids from all three classes are divided equally between two buses. How many kids are in each bus?

Answers

Answer:

(a + b + c)/2

Step-by-step explanation:

Number of kids in first class: a

Number of kids in second class: b

Number of kids in third class: c

The total number of kids in all classes is: a + b + c

The total number of kids is divided equally between 2 buses:

(a + b + c)/2

Answer:

(a + b + c)/2

Step-by-step explanation:

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A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.Suppose the paper is 7"-wide by 9"-long.
a. Estimate the maximum volume for this box?
b. What cutout length produces the maximum volume?

Answers

To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.

The solution is:

a) V (max) = 36.6 in³

b) x = 1.3 in

The volume of a cube is:

V(c) = w×L×h ( in³)

In this case, cutting the length "x" from each side, means:

wide of the box ( w - 2×x ) equal to ( 7 - 2×x )

Length of the box ( L - 2×x ) equal to ( 9 - 2×x )

The height is x

Then the volume of the box, as a function of x is:

V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x

V(x) = ( 63 - 14×x - 18×x + 4×x²)×x

V(x) = 4×x³ - 32×x² + 63×x

Tacking derivatives, on both sides of the equation

V´(x) = 12×x² - 64 ×x + 63

If V´(x) = 0 then 12×x² - 64 ×x + 63 = 0

This expression is a second-degree equation, solving for x

x₁,₂ = [ 64 ± √ (64)² - 4×12*63

x₁ = ( 64 + 32.74 )/ 24

x₁ = 4.03 this value will bring us an unfeasible solution, since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)

x₂ = ( 64 - 32.74)/24

x₂ = 1.30 in

The maximum volume of the box is:

V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3

V(max) = 4.4 × 6.4 × 1.3

V(max) = 36.60 in³

To chek for maximum value of V when x = 1.3

we find the second derivative of V V´´, and substitute the value of x = 1.3, if the relation is smaller than 0, we have a maximum value of V

V´´(x) = 24×x - 64 for x = 1.3

V´´(x) = 24× 1.3 - 64 ⇒ V´´(x) < 0

Then the value x = 1.3 will bring maximum value for V

Related Link: brainly.com/question/13581879

Final answer:

The maximum volume of the box that can be formed is approximately 17.1875 cubic inches. The cutout length that would result in this maximum volume is approximately 1.25 inches.

Explanation:

To solve this problem, we will use optimization in calculus. Let's denote the length of the square cutout as 'x'. When you cut out an x by x square from each corner and fold up the sides, the box will have dimensions:

Length: 9 inches (the original length) - 2x (the removed parts)
Width: 7 inches (the original width) - 2x
Height: x inches (the height is the cutout's length)

So the volume V of the box can be given by the equation: V = x(9-2x)(7-2x). We want to maximize this volume.

To find the maximum, differentiate V with respect to x, equate to zero and solve for x. V' = (9-2x)(7-2x) + x(-2)(7-2x) + x(9-2x)(-2) = 0. We obtain x=1.25 inches, but we need to verify whether this value gives us a maximum. Second differentiation, V'' = -12 is less than zero for these dimensions so the V is maximum.

a. So, when we solve, the maximum volume will be approximately 17.1875 cubic inches.

b. The cutout length that would produce the maximum volume is therefore about 1.25 inches.

Learn more about Optimization here:

brainly.com/question/37742146

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40hrs $11.00/hr15%
8%
7%
What were each tax totals. What is the gross pay. What is the net pay. Show your work

Answers

Answer:

$440
$66, $35.20, $30.80
$308

Step-by-step explanation:

Gross pay means the amount of money you get without any tax reductions.

40 * 11 = $440

Find the value of all the taxes.

440 * 0.15 = $66

440 * 0.08 = $35.20

440 * 0.07 = $30.80

Net pay means the amount of money you get with tax reductions.

440 - 66 - 35.20 - 30.80 = $308

Best of Luck!

If three out of every fourteen trick-or-treaters that came to your house last Halloween were dressed as pirates, what proportion of trick-or-treaters were not dressed as pirates?

Answers

Answer:

Explanation:

Given that three out of every fourteen trick-or-treaters were dressed as pirates

The proportion of the tick-or-treaters that were not dressed as pirates is the subtraction of the proportion of the people d

Dressed as pirates = 3/14

Not dressed as pirates = 14/14 - 3/14

= 11/14

The distance a vehicle travels can be found by using the formula d = rt, where d is the total distance traveled, r is the rate of speed, and t is the amount of time spent traveling. Grace drives her truck a distance of 80 miles at a steady speed of 50 miles per hour. To the nearest hour, how many hours does she spend driving?