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Andre45 [30]
3 years ago
11

Which logarithmic equation is equivalent to the exponential equation below e^2x=7

Mathematics
1 answer:
Zarrin [17]3 years ago
4 0
\bf log_{{  a}}{{  b}}=y \iff {{  a}}^y={{  b}}\qquad\qquad 
%  exponential notation 2nd form
{{  a}}^y={{  b}}\iff log_{{  a}}{{  b}}=y \\\\
-----------------------------\\\\
e^{2x}=7\iff log_e(7)=2x\iff ln(7)=2x
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What is the vertex of g(x) = –3x2 + 18x + 2?
blsea [12.9K]

Answer:

(3,29)

Step-by-step explanation:

There is a formula that can be used to find the x-value of the vertex of the parabola. This formula is x=\frac{-b}{2a}

We have the function g(x)=-3x^2+18x+2

From this function, we can find that

a=-3\\b=18\\c=2

We can plug in our know values into the formula to get

x=\frac{-18}{2(-3)\\} \\x=\frac{-18}{-6} \\\\x=3

Then we can plug in our x-value to find the y-value of the vertex

g(3)=-3(3)^2+18(3)+2\\\\g(3)=-3(9)+54+2\\\\g(3)=-27+54+2\\\\g(3)=29

This means that the vertex would be (3,29)

6 0
3 years ago
Which multiplication equation can be used to solve 1/6 ÷ 5? ​
Anna [14]

Answer:

1/6 x 1/5 = multiplication equation

8 0
2 years ago
The inner orbit is designated by the number __________.
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The inner orbit is designated by the number 1
7 0
3 years ago
Can you show me the answer?​
MatroZZZ [7]

Answer:

I can't even see the picture. I'm sorry.

Step-by-step explanation:

7 0
3 years ago
If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in
Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume (V), in cubic centimeters, and surface area (A_{s}), in square centimeters, of the box with a square base are described below:

A_{s} = l^{2}+h\cdot l (1)

V = l^{2}\cdot h (2)

Where:

l - Side length of the base, in centimeters.

h - Height of the box, in centimeters.

By (2), we clear h within the formula:

h = \frac{V}{l^{2}}

And we apply in (1) and simplify the resulting expression:

A_{s} = l^{2}+ \frac{V}{l}

A_{s}\cdot l = l^{3}+V

V = A_{s}\cdot l -l^{3} (3)

Then, we find the first and second derivatives of this expression:

V' = A_{s}-3\cdot l^{2} (4)

V'' = -6\cdot l (5)

If V' = 0 and A_{s} = 30000\,cm^{2}, then we find the critical value of the side length of the base is:

30000-3\cdot l^{2} = 0

3\cdot l^{2} = 30000

l = 100\,cm

Then, we evaluate this result in the expression of the second derivative:

V'' = -600

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

V = 30000\cdot l - l^{3}

V = 2000000\,cm^{3}

The largest possible volume of the box is 2000000 cubic meters.

4 0
2 years ago
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