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3 years ago

Find the inverse of f(x)=e^2x-1

1 answer:

3 0

$f(x)=e^{2x-1}\\\\y=e^{2x-1}\\\\\text{replace x with y and y with x}\\\\x=e^{2y-1}\\\\\text{solve for y}\\\\e^{2y-1}=x\ \ \ \ |\ln\\\\\ln e^{2y-1}=\ln x\\\\2y-1=\ln x\ \ \ |+1\\\\2y=\ln x+1\ \ \ |:2\\\\y=\dfrac{\ln x+1}{2}\\\\Answer:\ \boxed{f^{-1}(x)=\dfrac{\ln x+1}{2},\ x > 0}$

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You previously found the mean of this data set. Use that in answering the question. 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25,

kicyunya [14]

Answer:

Sum of squares of differences = 11239.74

Step-by-step explanation:

We are given the following data set:

63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79

We have to calculate the sum of square of the data set.

Formula:

$\text{Sum of square of differences} = \sum (x_i -\bar{x})^2$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{962}{15} = 64.13$

Sum of squares of differences =

1.284444444 + 618.3511113 + 776.5511113 + 78.61777778 + 221.0177779 + 61.88444445 + 908.0177776 + 791.4844443 + 892.017778 + 1860.484444 + 1531.417778 + 833.2844446 + 1775.217777 + 669.0844446 + 221.0177779

= 11239.74

3 0

3 years ago

6 mi Find the volume for the shape above. Use 3.14 for pi. Round to the nearest whole number.

vodka [1.7K]

Answer:

Step-by-step explanation: does anyone know? I really need this

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3 years ago

Find the vertex of the graph of f(x) = x2 + 4x - 5.

Fofino [41]

You can solve this in two ways.

1. Graphical. Plot the graph for x between -5 and 1 (see attachement).
The vertex of the graph is the peak of the curve, which has the coordinates x=-2, y=-9.

2. Analytical. Calculate the derivative of the function f(x)
$\frac{df}{dx}=2x+4$
Solve the equation:
$2x+4=0$
will give the solution x=-2.
Replace x=-2 in the f(x) function and you'll get the value of y:
$(-2)^2+4 \cdot (-2)-5=4-8-5=-9$

You get the same answer: x=-2, y=-9

So the answer is
<span>B. (-2, -9)</span>

7 0

4 years ago

What is (2x^2+6x-3) added to (2x^3-3x+2)?

Bas_tet [7]

2x² + 6x - 3 + 2x³ - 3x + 2

Combine like terms

2x³ + 2x² + 6x - 3x - 3 + 2

Final answer:
2x³ + 2x² + 3x - 1

8 0

3 years ago

Read 2 more answers

What is the answer of X2/3??

Yuri [45]

1/3x^2

hope this helps

7 0

4 years ago