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a_sh-v [17]
3 years ago
9

What are the domain and range of the exponential function below F(x)=3^x+2

Mathematics
1 answer:
mihalych1998 [28]3 years ago
7 0
3 is the x
2 is the y
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2. Consider the circle x² + y2 = 1, given in figure. Let OP makes an angle 30° with the x axis.
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The equation of the tangent line to the circle passing through the point P is; y = (1/√3)x ± 2/√3

<h3>How to find the equation of the tangent?</h3>

I) We are given the equation of the circle as;

x² + y² = 1

Since angle of inclination is 30°, then slope is;

m = tan 30 = 1/√3

Then equation of the tangent will be;

y = (1/√3)x + c

Put  (√3)x + c into the given circle equation to get;

x² + ((1/√3)x + c)² = 1

x² + ¹/₃x² +  (2/√3)cx + c² = 1

⁴/₃x² +  (2/√3)x + (c² - 1) = 0

Since we need to find value of c for equation to become tangent, then the above quadratic equation must have real and equal roots.

Thus;

((2/√3)c)² - 4(⁴/₃)(c² - 1) = 0

⁴/₃c² - ¹⁶/₃(c² - 1) = 0

⁴/₃c² - ¹⁶/₃c² + ¹⁶/₃ = 0

4c² = ¹⁶/₃

c² = ⁴/₃

c = √⁴/₃

c = ±²/√3

Thus, equation of tangent is;

y = (1/√3)x ± 2/√3

II) Radius from the given equation is 1. Thus, we will use trigonometric ratio to find the x and y intercept;

x-intercept is at y = 0;

0 = (1/√3)x ± 2/√3

-(1/√3)x = ±2/√3

Intercept is positive. Thus;

x = (2/√3)/(1/√3)

x = 1

y - intercept is positive at x = 0;

y = (1/√3)0 ± 2/√3

y = 2/√3

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Calculate the ROI, given the following: Andrew invested $20,000 in mutual funds and received a sum of $35,000 at the end of the
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We are given with an initial deposit of  $20,000 and a future worth of <span>$35,000. In this case, we are asked for the return of income (ROI) of the investment. in this case, we assume the number of years equal to 1. hence, 

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A right rectangular pyramid is sliced vertically (down) by a plane passing
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A right rectangular pyramid when sliced vertically, the  shape of the cross-section is known as Triangle.

<h3>What is A triangle?</h3>

This is known to be a kind of shape that is said to be in  a closed form and it is also known to be a 2-dimensional shape that has 3 sides, 3 angles, and also 3 vertices.

Note that when the when the right rectangular pyramid is sliced vertically (down) by a plane passing through the  of the pyramid, the new shape of the cross-section is a triangle.

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A right rectangular pyramid is sliced vertically (down) by a plane passing through the  of the pyramid. What is the shape of the cross-section?

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