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1 year ago

Find the average rate of change of the function defined by the following table. x y -2 -5 2 35 6 75 10 115

Mathematics

1 answer:

Pani-rosa [81]1 year ago

6 0

By definition we have that the average rate of change of the function is:

$AVR = \frac{f(x2) - f(x1)}{x2 - x1}$

Evaluating the function for the complete interval we have that the AVR is given by:

$AVR = \frac{115 - (-5)}{10 - (-2)}$

Rewriting we have:

$AVR = \frac{115+5}{10+2}$

Simplifying the expression we have:

$AVR = \frac{120}{12}$

$AVR = 10$

Answer:

the average rate of change of the function defined by the table is:

$AVR = 10$

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Use polar coordinates to find the volume of the given solid. bounded by the paraboloid z = 9 + 2x2 + 2y2 and the plane z = 15 in

mina [271]

Answer:

Z = 8 + 2x2 + 2y2

Convert to polar coordinates

Z = 8 + 2r2

Now theta will go from 0 to pi/2 because it's in the first quadrant.

R will go from 0 to the radius of the circle formed at the intersection of the plane and the paraboloid.

14 = 8 + 2r2

r = sqrt(3)

So r goes from 0 to sqrt(3).

You integrate 14-z where 0<r<sqrt(3) and 0<theta<pi/2.

It is 14-z and not z because just z would give the volume under the paraboloid.

Step-by-step explanation: please go answer my recent question

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1 year ago

Which of the following shows the extraneous solution to the logarithmic equation? log Subscript 4 Baseline (x) + log Subscript 4

vekshin1

Given:

The given equation is $\log _{4}(x)+\log _{4}(x-3)=\log _{4}(-7 x+21)$

We need to determine the extraneous solution of the equation.

Solving the equation:

To determine the extraneous solution, we shall first solve the given equation.

Applying the log rule $\log _{c}(a)+\log _{c}(b)=\log _{c}(a b)$ , we get;

$\log _{4}(x(x-3))=\log _{4}(-7 x+21)$

Again applying the log rule, if $\log _{b}(f(x))=\log _{b}(g(x))$ then $f(x)=g(x)$

Thus, we have;

$x(x-3)=-7 x+21$

Simplifying the equation, we get;

$x^2-3x=-7 x+21$

$x^2+4x=21$

$x^2+4x-21=0$

Factoring the equation, we get;

$(x-3)(x+7)=0$

Thus, the solutions are $x=3, x=-7$

Extraneous solutions:

The extraneous solutions are the solutions that does not work in the original equation.

Now, to determine the extraneous solution, let us substitute x = 3 and x = -7 in the original equation.

Thus, we get;

$\log _{4}(3)+\log _{4}(3-3)=\log _{4}(-7 \cdot 3+21)$

$\log _{4}(3)+\log _{4}(0)=\log _{4}(0)$

Since, we know that $\log _{a}(0)$ is undefined.

Thus, we get;

Undefined = Undefined

This is false.

Thus, the solution x = 3 does not work in the original equation.

Hence, x = 3 is an extraneous solution.

Similarly, substituting x = -7, in the original equation. Thus, we get;

$\log _{4}(-7)+\log _{4}(-7-3)=\log _{4}(-7(-7)+21)$

$\log _{4}(-7)+\log _{4}(-10)=\log _{4}(49+21)$

$\log _{4}(-7)+\log _{4}(-10)=\log _{4}(70)$

Simplifying, we get;

Undefined = $\log _{4}(70)$

Undefined = 3.06

This is false.

Thus, the solution x = -7 does not work in the original solution.

Hence, x = -7 is an extraneous solution.

Therefore, the extraneous solutions are x = 3 and x = -7

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1 year ago

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Natali [406]

Answer:

f(x) = $3^{x}$ + 10

Step-by-step explanation:

Year one would be 10 + 3

Year two would be (3*3)+10

year three would be (3*3*3)+10

Which easily simplifies into $3^{x}$ + 10.

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2 years ago

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Sunny_sXe [5.5K]

Answer:

3.876943x10^9

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Step-by-step explanation:

3,876,943,000

Put the decimal at the end

3,876,943,000.

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3.876943000

We moved it 9 places, so that is the exponent

We moved it to the left, so the exponent is positive

The three zeros at the end can be dropped because they are the last numbers to the right of the decimal

3.876943x10^9

0.0007317

Move it so only 1 number is before the decimal

00007.317

We moved it 4 places, so that is the exponent

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7.317x10^-4

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A right rectangular prism and an oblique triangular prism are both 12 centimeters tall and have the same volume. What statement

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This is the concept of volumes of solid figures, given that the height of the right rectangular prism and the oblique triangular prism are 12 cm and both prisms have the same volume, we can conclude that:
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2 years ago

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