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3 years ago

Solve the equation of e^x-2=(1/e^6)^x+3.

Mathematics

1 answer:

Aliun [14]3 years ago

5 0

Answer:

x = -16/7

Step-by-step explanation:

The equation as written reduces to finding the solution to a 7th-degree polynomial. The one real solution, found using a graphing calculator, is ...

x ≈ 1.60945071137

_____

Since this is beyond the scope of most algebra courses, we suspect you want the solution to ...

e^(x-2) = (1/e^6)^(x+3)

x -2 = -6(x +3) . . . . . . . . take the natural log of both sides

x -2 = -6x -18 . . . . . . . . . eliminate parentheses

7x -2 = -18 . . . . . . . . . . . add 6x

7x = -16 . . . . . . . . . . . . . add 2

x = -16/7

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Suppose y varies inversely with x, and y = -1 when x = 6. What inverse variation equation relates x and y?

snow_tiger [21]

Answer:

$\displaystyle \text{d. }y=\frac{-6}{x}$

Step-by-step explanation:

If two values $x$ and $y$ are inversely proportional, their product is always some maintained constant (the product of $x$ and $y$ is always maintained). This way, if one goes up, the other must go down by the same extent. By definition, this represents an inversely proportional relationship.

Therefore, we can simply find this constant by multiplying the given values of $x$ and $y$ :

$xy=k,\\6\cdot (-1)=-6$

The constant $-6$ must be maintained as the product of $x$ and $y$ for all values of $x$ and $y$ for them to be inversely proportional. Thus, we have the equation:

$xy=-6$

Divide both sides by $x$ to isolate $y$ :

$\boxed{y=\frac{-6}{x}}$

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chubhunter [2.5K]

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Step-by-step explanation:

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2 years ago

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I need help ASAP PLEASE!!!

Nat2105 [25]

I’m just guessing but since 13/4=3.25 that means that the triangle dialated by 3.25 so you multiply 8 by 3.25 and X might be 26

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3 years ago

A line with a slope of 2 passes through the points (0,4) and (-6,v). What is the value of v?

krok68 [10]

To solve this problem, we should create an equation using the given information. To do this, we should calculate the slope between the two points as if they were regular points, giving us:

change in y/change in x = (v-4)/(-6-0) = (v-4)/(-6)

Since we know that the slope is 2, we can set our calculated value for the slope of the line for the equation (v-4)/(-6) equal to 2, as shown below:

(v-4)/(-6) = 2

To solve this equation, we should multiply both sides of the equation by -6 to get rid of the denominator on the left side of the equation.

v-4 = -12

Next, we should add 4 to both sides of the equation to get the variable v alone on the left side of the equation, as shown below:

v = -8

Therefore, v =-8 is your answer.

Hope this helps!

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