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3 years ago

The graph below shows the water level of a tank that is emptying over time.

Mathematics

1 answer:

Allisa [31]3 years ago

3 0

From inspecting the graph, you can identify the y-intercept and the slope of the line shown.

The y-intercept is 200 gallons.
The slope is

75-200
m = ------------- = -12.5 gallons/minute
10 - 0

Thus, y = 200 gallons - [12.5 gallons/minute ]t

To answer the 2nd question, let t = 12 minutes and calculate y(12).

To determine how long it wld take to empty the tank, set the above formula equal to zero and solve the resulting equation for t.

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A baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the vol

k0ka [10]

The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

Given the following data:

Volume of box = 224 cubic inches.

Translating the word problem into an algebraic expression;

$W = 3 + L$ ......equation 1

$H = 4 + L$ ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

$Volume = length * width * height$ .....equation 3.

Substituting the values into equation, we have;

$224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}$

Rearranging the polynomial, we have;

$L^{3} + 7L^{2} + 12L - 224 = 0$

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

$(x - 3) = 0\\x = 3$

$P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9) + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0$

We would try with 4;

$P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16) + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224 - 224 = 0$

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

Find more information on polynomial here: brainly.com/question/10689855

3 0

3 years ago

How to integrate sqrt(1+x^3)?

Karolina [17]

First integrate the entire thing by letting multiplying by 1/2 the entire expression raised to exponent 1/2 - 1. That is,
0.5(1 + x³)^-0.5
Then, multiplying this by the derivative of those inside the parentheses. The final answer would be,
(0.5)((1 + x³)^-0.5)(3x²)

8 0

3 years ago

Simplify each expression 2x+5y+7x=

dimaraw [331]

You add 2x and 7x to get 9x
so the answer is 9x+5y

6 0

3 years ago

The value -2 is a lower bound for the zeros of the function shown below.

Tju [1.3M]

Answer:

False

Step-by-step explanation:

f(x) = 4x³ - 12x² - x + 15

Set output to 0.

Factor the function.

0 = (x + 1)(2x - 3)(2x - 5)

Set factors equal to 0.

x + 1 = 0

x = -1

2x - 3 = 0

2x = 3

x = 3/2

2x - 5 = 0

2x = 5

x = 5/2

-2 is not a lower bound for the zeros of the function.

7 0

3 years ago

Glven: F(x) = 2x - 1; G(X) = 3x + 2; H(x) = x2 Find F/G/H(2) 121 27 71

Sergio039 [100]

Answer:

3/32

Step-by-step explanation:

One approach to doing this probelm is to evaluate all three functions F, G and H at x = 2:

F(2) = 2(2) - 1 = 3

G(2) = 3(2) + 2 = 8

H(2) = (2)^2 = 4

3/8

Then (F/G)(2) = (3/8), and (F/G/H) = -------- = 3/32

8 0

3 years ago