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Travka [436]
3 years ago
11

Use the table below of the function f(x) = x4 − 2x3 to answer this question:

Mathematics
2 answers:
DiKsa [7]3 years ago
8 0

<u>ANSWER</u>

The average rate of change from x=-1 to x=2  is -1

<u>EXPLANATION</u>

The average rate of change from x=-1 to x=2

=\frac{f(2)-f(-1)}{2-(-1)}


From the table,

f(2)=0 and f(-1)=3.


So we substitute in to the above expression for average rate of change.



Average\:Rate\:of\:Change=\frac{0-3}{2+1}


=\frac{-3}{3}


=\-1


The correct answer is B



denpristay [2]3 years ago
6 0
-1 hope this helpz man
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Hello i need some help please!​
Oksi-84 [34.3K]

Answer:

2x + 8

Step-by-step explanation:

8 more means too add and twice means multiplication so therefore it would be 2x plus 8 as the answer hope this helps.

3 0
3 years ago
Read 2 more answers
Determine the radius of a cone that has a volume of 230 ft' and a height of 15 ft.
VLD [36.1K]

Answer:

the formula for finding cone volume is V=πr²× 1/3

Step-by-step explanation:

230=3.14×x²×1/3

we have to solve for X that is our radius

14.8

3 0
3 years ago
1. A tank is 3/5 full of water. After 330 litres of water is drawn out, it becomes 2/7 full. Find the capacity of the tank in li
Andreas93 [3]

Answer:

1050

Step-by-step explanation:

Let x = full capacity

\frac{3}{5} x=\frac{2}{7} x+330

Move the variable to the left side by subtracting both sides by \frac{2}{7} x

\frac{3}{5} x-\frac{2}{7}x=\frac{2}{7} x+330 -\frac{2}{7}x

\frac{3}{5} x-\frac{2}{7} x=330

Combine the like terms (don't forget about common denominator)

\frac{21}{35} x-\frac{10}{35} x=330

\frac{11}{35} x=330

Multiply both sides by \frac{35}{11} to isolate the x

(\frac{35}{11})\frac{11}{35} x=330(\frac{35}{11})

x = 1050

5 0
3 years ago
Calculate the total area of the shaded region.
LUCKY_DIMON [66]

so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

\stackrel{f(x)}{2x^3-x^2-5x}~~ = ~~\stackrel{g(x)}{-x^2+3x}\implies 2x^3-5x=3x\implies 2x^3-8x=0 \\\\\\ 2x(x^2-4)=0\implies x^2=4\implies x=\pm\sqrt{4}\implies x= \begin{cases} 0\\ \pm 2 \end{cases}

so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.

\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill

\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}

7 0
2 years ago
Given that y varies directly as x and y = 18 when x = 6
sergey [27]

Answer:   y = 15,    x = 10

<u>Step-by-step explanation:</u>

NOTE: "varies directly" is of the form    \dfrac{y}{x}=k  where k is the constant of proportionality.

First, input the given x and y-values to find k

\dfrac{y}{x}=k\qquad \qquad \text{Given: y=18, x=6}\\\\\dfrac{18}{6}=k\\\\\boxed{3=k}

Next, input the given value and k = 3 to solve for the missing variable.

x = 5\\\\\dfrac{y}{5}=3\\\\\large\boxed{y = 15}\\\\\\y=30\\\\\dfrac{30}{x}=3\\\\\dfrac{30}{3}=x\\\\\large\boxed{10 = x}

4 0
4 years ago
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