Calculate had a net income of 5 million dollars in 2010, while a small competing company, Computate, had a
net income of 2 millions dollars. The management of Calculate develops a business plan for future growth
that projects an increase in net income of 0.5 million per year, while the management of Computate
develops a plan aimed at increasing its net income kshy15% each year.
a. Create standard mathematical model (table, graph, or equations) for the projected net income for the
next 10 years for both companies. Make sure that each model is accurate and labeled properly so that it
represents the situation
b. If both companies were able to meet their net income growth goals, which company would you choose
to invest in? Why?
c. When, if ever, would your projections suggest that the two companies have the same net income? How
did you find this? Will they ever have the same net income again?

Let's write this question as a systems of equations to solve.

x-y=7 (the difference)

x+y=23 (the sum)

Through the process of elimination we get

2x=30

x=15.

With that value of x, we can plug it back into any of the previous equations to get the value of y.

(15)-y=7 (Solve for y)

y=8.

The two numbers are 15 and 8.

Answer:

pfft no lol

Step-by-step explanation:

yeah no

have a good day!  :)

plz give me brainliest

Answer:

yes

Step-by-step explanation:

i think,because it goes past the center it all

Answer:

210%

Step-by-step explanation:

dat was too easy

Answer:

210% or 21% or 2.10%

its all about what 2.10 is out of (example:   /1=210%  /10= 21%  /100=2.1%

edit: if your wondering what the "/" means it means " out of"                (example: 1 out of 100 is 1%)

Answer:

30

Step-by-step explanation:

Perimeter of rectangle = 5y - 1 + 4y + 2 + 5y - 1 + 4y + 2

                                      = 18y + 2

18y + 2 = 128

18y = 128 - 2

     = 126

y = 126 ÷ 18

y = 7

Length of AD = 4y + 2

                      = 4(7) + 2

                      = 28 + 2

                      = 30

$8.75 because 26.25 divided by 3 equals $8.75.

hope this helps

Answer:

See below for Part A.

Part B)

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

Step-by-step explanation:

Part A)

The parabola given by the equation:

[tex]y^2=4ax[/tex]

From 0 to h is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

[tex]y=f(x)=\sqrt{4ax}[/tex]

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]

Where r(x) is the distance between f and the axis of revolution.

From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:

[tex]r(x)=y(x)=\sqrt{4ax}[/tex]

Now, we will need to find f’(x). We know that:

[tex]f(x)=\sqrt{4ax}[/tex]

Then by the chain rule, f’(x) is:

[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]

For our limits of integration, we are going from 0 to h.

Hence, our integral becomes:

[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]

Combine roots;

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]

Integrate. We can consider using u-substitution. We will let:

[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]

We also need to change our limits of integration. So:

[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]

Hence, our new integral is:

[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]

Simplify and integrate:

[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

FTC:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]

Simplify each term. For the first term, we have:

[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]

We can factor out the 4a:

[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

For the second term, we have:

[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =(2a)^3[/tex]

Hence:

[tex]\displaystyle =8a^3[/tex]

Thus, our equation becomes:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]

We can factor out an 8a^(3/2). Hence:

[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Hence, we have verified the surface area generated by the function.

Part B)

We have:

[tex]y^2=36x[/tex]

We can rewrite this as:

[tex]y^2=4(9)x[/tex]

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

We can write:

[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]

Solve for h. Simplify:

[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]

Divide both sides by 8π:

[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]

Isolate term:

[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]

Raise both sides to 2/3:

[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]

Hence, the value of h is:

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

You seem to have left out that 0 ≤ x ≤ h.

From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is

[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]

We have

y(x) = 2√(ax)   →   y'(x) = 2 • a/(2√(ax)) = √(a/x)

so the integral is

[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]

[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]

[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]

[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]

Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :

[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]

[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]

[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]

[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]

[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]

Answer:

Each dose should be of 5.05 milligrams.

Step-by-step explanation:

To solve the present problem, it is necessary to first establish the equivalence between pounds and kilograms. Thus, 1 pound is equal to 0.453 kilograms. Therefore, the dog weighs about 30.35 kilograms (67 x 0.453), with which, since 3 milligrams must be applied for each kilogram of the animal's weight, 10.1 milligrams of Benadryl (30.35 / 3) should be applied.

Now, since Benadryl is applied in two doses, each of these doses should be 5.05 milligrams (10.1 / 2).

Answer:

2, 4, and 6 (b, d, f)

Step-by-step explanation:

dont  really know how to explain

Answer:

149

Step-by-step explanation:

149 and the angle beside b are supplementary (Let's call it A)

180-149=A=31

180-31=149

149=B

Answer:

x = 26

Step-by-step explanation:

m<B = m<E = (x + 17)°

180 - (25 + 112) = (x + 17) (sum of ∆)

180 - 137 = x + 17

43 = x + 17

Subtract both sides by 17

43 - 17 = x

x = 26

Answer:

yes 40

Step-by-step explanation:

she got it correct

Answer:

11 sqrt(2)

Step-by-step explanation:

We know that in a 45 45 90 triangle, the lengths of the sides are x, x ,x sqrt(2)

the length of x is 11

so the lengths of the sides are 11, 11, 11 sqrt(2)

The hypotenuse is 11 sqrt(2)

Answer:

She uses 162 millitiers if Solution B.

Step-by-step explanation:

180 - 10% = 162

Solution A = 18 milliliters

Soultion B = 162 millitiers

Answer:

A, 2 5/8 cups

Step-by-step explanation:

Since six dozen brownies is three times as much as two dozen, we can multiply 7/8 cups by 3. 3 x 7/8 = 21/8 If we simplify this fraction, it is 2 5/8. Therefore the answer is A, 2 5/8 cups.

Answer:

The price would be $51.75.

Step-by-step explanation:

Since Joe is marking up by 15%, the price will increase for the pair of shoes.  Multiply 45 by 1.15 since you are increasing the price by 15% to get your final answer which is $51.75.

Answer:

[tex]y = 320x +2080[/tex]

Step-by-step explanation:

Given

Population in 1995 = 2400

Population in 2000 = 4000

Required

Determine the linear equation

Let the years be represented with x.

In 1995, x = 1 i.e. the first year

In 2000, x = 6

Let y represents the population

When x = 1; y = 2400

When x = 6; y = 4000

First, we calculate the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{4000 - 2400}{6 - 1}[/tex]

[tex]m = \frac{1600}{5}[/tex]

[tex]m = 320[/tex]

Next, we calculate the line equation as follows:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex]y - 2400 = 320(x - 1)[/tex]

[tex]y - 2400 = 320x - 320[/tex]

[tex]y = 320x - 320 + 2400[/tex]

[tex]y = 320x +2080[/tex]

Answer:

about 7.0710678cm

Step-by-step explanation:

it's a square so the sides are equal.

the diagonal is 100cm

This makes a right triangle with two sides

since the sides are equal, they both are equal to the square root of 50, which is half of 100

the square root of 50 is about 7.0710678cm

Answer:

y=8

Step-by-step explanation:

because 3×8 is 24

and 8 would be the missing number

Answer:

Fraction form: it snowed 2 1/10 inches in total, decimal form: in other words it snowed 2.1 inches.

Step-by-step explanation:

Answer:

30.5 + 1.5s

Step-by-step explanation:

Answer:

sure easy man the carrot is blue and green and orange there naswer soled

Answer:

C.  G' (4,-7), R' (2,-3), T'(6,-4)

Step-by-step explanation:

Get a piece of paper and draw 2 intersecting lines, like how a graph looks like. Then get another paper that's transparent enough, and place a dot roughly where R would be. Rotate it 270* clockwise (3 times around 90 degrees), and R would be in the bottom right area. That means the figure would be around that area and you can base the coordinates from that.

Answer:

[tex]\boxed{0}[/tex]

Step-by-step explanation:

x² = (Q - A)(Q - B)(Q - C) ... (Q - Z)

x² =  (Q - A)(Q - B)(Q - C) ... (Q - P)(Q - Q)(Q - R) ... (Q - Z)

x² = (Q - A)(Q - B)(Q - C) ... (Q - P)(0)(Q - R) ... (Q - Z)

x² = 0

x = 0

Answer:

t8y8 uv7g7 ug8 ugy ug h 7 v jvu utyc7 . hit u ut taj h

Step-by-step explanation:

fucjvjvi j jvu jvivu igigi ivigi iigihi ivigi igih

Answer:

f(3)=g(3)

Step-by-step explanation:

the only one i see is that

f(3)=g(3)

because the two functions intersect there

that means the two values are the same

Answer:

What dose this mean

Step-by-step explanation:

Thx for the free points

Answer:

3

Step-by-step explanation:

i think 5-2

Answer:

Step-by-step explanation:

E

Answer:

$120

Step-by-step explanation:

Answer:

The mixed number 1 1/6 converted into an improper fraction is 7/6.

Step-by-step explanation:

The improper fraction representation after converting of 1 1/6 is 7/6 where numerator is 7 and denominator is 6

To convert a mixed number to an improper fraction, we follow these steps:

Multiply the whole number by the denominator of the fraction.

In this case,  multiply 1 (the whole number) by 6 (the denominator), which gives  6.

Add the numerator to the result obtained in step 1.

The numerator in this case is 1. Adding 1 to 6 gives 7.

Place the result from step 2 as the numerator of the fraction, and keep the denominator the same.

The denominator remains 6.

Therefore, the improper fraction representation of 1 1/6 is 7/6.

Learn more about converting  fractions here:

https://brainly.com/question/15743041

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