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2 years ago

15

Solve x (give answer as fractions or integers). 2^x =1/2

1 answer:

Rudik [331]2 years ago

7 0

Answer:

x = -1

Step-by-step explanation:

When an exponent is negative, you have to move it to the denominator (or to the numerator if it's already on the denominator). Since the answer is $\frac{1}{2}$ , you know that the 2 has been raised to the power of 1 (any number to the power of 1 is the same number), so you just make it negative. Hope that helps!

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Answer:

x=7

Step-by-step explanation:You can plug in the value for x and solve to see if true.

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3 years ago

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2 years ago

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

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3 years ago

Two sides of a parallelogram are 93 feet and 80 feet. The measure of the angle between these sides is 18°. Find the area of the

azamat

<h3>Answer: 2299 square feet</h3>

Work Shown:

area = a*b*sin(C)

area = 93*80*sin(18)

area = 2299.086438

area = 2299 square feet

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2 years ago

A town has a population of 13,000 and grows at 5% every year. What will be the population after 11 years to the nearest whole nu

timofeeve [1]

Answer:

So all you need to do is find 5% of 13000 which is 650.

Now 650 times 11= 7150

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6 0

3 years ago

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