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3 years ago

Identify the y intercept and asymtote for the exponential function f(x)=3^x+2

1 answer:

5 0

Y-intercept occurs at x = 0.
y = 1 + 2 = 3

$f(x) = 3^{x} + 2$
$\text{Asymptote: } \lim_{x \to \infty} 3^{x} + 2$
$= 2$

Thus, there is a horizontal asymptote at x = 2.

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It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours. How long doe

lina2011 [118]

Answer:

Time taken by the un powered raft to cover this distance is T = 192.12 hr

Step-by-step explanation:

Let speed of boat = u $\frac{km}{hr}$

Speed of current = v $\frac{km}{hr}$

Let distance between A & B = 100 km

Time taken in downstream = 32 hours

$32 = \frac{100}{u +v}$

$u + v = \frac{100}{32}$

u + v = 3.125 ------ (1)

Time taken in upstream = 48 hours

$48 = \frac{100}{u -v}$

$u -v = \frac{100}{48}$

u - v = 2.084 ------- (2)

By solving equation (1) & (2)

u = 2.6045 $\frac{km}{hr}$

v = 0.5205 $\frac{km}{hr}$

Now the time taken by the un powered raft to cover this distance

$T = \frac{100}{v}$

Because un powered raft travel with the speed of the current.

$T = \frac{100}{0.5205}$

T = 192.12 hr

Therefore the time taken by the un powered raft to cover this distance is

T = 192.12 hr

3 0

4 years ago

Read 2 more answers

Use the Product Property for Exponents to explain why x · x = x2.

Lubov Fominskaja [6]

Whenever there is no exponent on a variable,

you can give it an exponent of 1.

So we can rewrite the x's in this problem as x¹.

When we multiply two terms together

with like bases, we add their exponents.

So now just add their exponents to get x².

3 0

3 years ago

What is the answer to the question. Solve for x

slega [8]

Answer:

Answer:

$x=\frac{75}2$

Step-by-step explanation:

Give letters, as in the attached image.

The triangles ABE and CDE are similars (AAA). In particular $AE:CE=BE:DE \rightarrow 46:30=(x+20):x \rightarrow 46x=30(x+20) \rightarrow 23x=15x+300 \rightarrow 8x=300\rightarrow x=\frac{75}2$

5 0

2 years ago

4. Find the standard from of the equation of a hyperbola whose foci are (-1,2), (5,2) and its vertices are end points of the dia

Ad libitum [116K]

The standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

<h3>How to find the standard equation of a hyperbola</h3>

In this problem we must determine the equation of the hyperbola in its standard form from the coordinates of the foci and a general equation of a circle. Based on the location of the foci, we see that the axis of symmetry of the hyperbola is parallel to the x-axis. Besides, the center of the hyperbola is the midpoint of the line segment with the foci as endpoints:

(h, k) = 0.5 · (- 1, 2) + 0.5 · (5, 2)

(h, k) = (2, 2)

To determine whether it is possible that the vertices are endpoints of the diameter of the circle, we proceed to modify the general equation of the circle into its standard form.

If the vertices of the hyperbola are endpoints of the diameter of the circle, then the center of the circle must be the midpoint of the line segment. By algebra we find that:

x² + y² - 4 · x - 4 · y + 4= 0

(x² - 4 · x + 4) + (y² - 4 · y + 4) = 4

(x - 2)² + (y - 2)² = 2²

The center of the circle is the midpoint of the line segment. Now we proceed to determine the vertices of the hyperbola:

V₁(x, y) = (0, 2), V₂(x, y) = (4, 2)

And the distance from the center to any of the vertices is 2 (semi-major distance, a) and the semi-minor distance is:

b = √(c² - a²)

b = √(3² - 2²)

b = √5

Therefore, the standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

To learn more on hyperbolae: brainly.com/question/27799190

#SPJ1

5 0

2 years ago

How many lines of symmetry, if any, exist for trapezoid ABCD?

galben [10]

I think the answer is 1 but I can’t see the picture

8 0

4 years ago

Read 2 more answers