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2 years ago

11

(Q9) Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using

limits. y=0.8^x

1 answer:

Artemon [7]2 years ago

6 0

Answer:

C

Step-by-step explanation:

A function in the form $y=a*b^x$ is an exponential function. If

a > 0, and b > 1 -- this is exponential growth function
a > 0, and 0 < b < 1 -- this is exponential decay function

The given function can be written as $y=1*0.8^x$ , so a > 0 and 0 < b < 1, hence this is exponential decay function.

For end behavior, we take limits from -∞ and from ∞. If we do that we can see that C is the correct answer. Also, looking at the graph explains it. Attached is the graph.

<em>From the graph, as we move towards negative infinity, the graph goes towards positive infinity and as we move towards positive infinity, the graph goes towards 0.</em>

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Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl

Wittaler [7]

Answer:

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

Step-by-step explanation:

The equation of a circle of radius $5$ centered at $(0,0)$ is:

$x^{2} + y^{2} = 5^{2}$ .

$x^{2} + y^{2} = 25$ .

Differentiate implicitly with respect to $x$ to find the slope of tangents to this circle.

$\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]$

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0$ .

Apply the power rule and the chain rule. Treat $y$ as a function of $x$ , $f(x)$ .

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0$ .

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0$ .

That is:

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0$ .

Solve this equation for $\displaystyle \frac{dy}{dx}$ :

$\displaystyle \frac{dy}{dx} = -\frac{x}{y}$ .

The slope of the tangent to this circle at point $(3, 4)$ will thus equal

$\displaystyle \frac{dy}{dx} = -\frac{3}{4}$ .

Apply the slope-point of a line in a cartesian plane:

$y - y_0 = m(x - x_0)$ , where

$m$ is the gradient of this line, and
$(x_0, y_0)$ are the coordinates of a point on that line.

For the tangent line in this question:

$\displaystyle m = -\frac{3}{4}$ ,
$(x_0, y_0) = (3, 4)$ .

The equation of this tangent line will thus be:

$\displaystyle y - 4 = -\frac{3}{4} (x - 3)$ .

That simplifies to

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

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3 years ago

Zalia meets her friend at the science museum to see a special exhibition. The admission to the museum is $12.50 plus tax. Zalia

diamong [38]

I did the math on calculator and got A.

Hope I could help (:

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2 years ago

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Let 0 be an acute angle of a right triangle. Evaluate the other five trigonometric functions of 0.

Paraphin [41]

Answer:

sin θ = (√119)/12

tan θ = (√119)/5

csc θ = 12/(√119)

cot θ = 5/(√119)

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2 years ago

What is the area of the kite?

Kazeer [188]

Multiply 4.93m by 8.5m to get 41.905m to the second power.

You do this because there are 2 identical triangles on the top. And if you put those two triangles together, you get a rectangle. The length of the rectangle is 8.5m while the width would be 4.93. Multiplying the length and width gives you the area.

Then multiply 10.2m by 8.5m to get 86.7m to the second power.

You do this because there are 2 identical triangles on the bottom. And if you put those two triangles together, you get another rectangle. The length of the rectangle is 8.5m while the width would be 10.2m. Multiplying those together gives you the area.

You then add the two areas, 41.905m to the second power and 86.7m to the second power, to get the area of the entire figure.

After adding, you get 128.605 m to the second power. That's the answer

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2 years ago

Ratio of x and 2 is not greater than 14

allochka39001 [22]

The ratio of x and 2=x:2
not greater than is <

So I'd say the answer would be x:2<14

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2 years ago