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3 years ago

How does the graph y=3^x compare to the graph y=3^-x

Mathematics

1 answer:

LUCKY_DIMON [66]3 years ago

5 0

Answer:

Y = 3x^x is a graph that has exponential growth while y = 3^-x has exponential decay.

Y = 3x^x (-∞, 0) and (∞, ∞).

Y = 3x^-x (-∞, ∞) and (∞, 0).

Step-by-step explanation:

The infinity symbols were being used to represent the x and y values of each graph. I will call y = 3^x "graph 1" and y = 3^-x "graph 2".

When graph 1 had positive ∞ for its x value, its y value was reaching towards positive ∞. When its x was reaching for negative ∞, its y was going for 0.

For graph 2, however, when its x was reaching for positive ∞, its x was reaching for 0. When its x was reaching for negative ∞, its y was going for positive ∞.

Here's an image of the graphs:

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A ball is thrown downward from a cliff. Its position at time t seconds is given by the formula s(t) = 16t2 + 32t, where s is in

Rom4ik [11]

Answer:

It takes 2.8 seconds for the ball to fall 215 ft.

Step-by-step explanation:

We are given a position function s(t) where s stands for the number of feet the ball has fallen, so we have to replace s with the given value of 215 ft and solve for the time t.

Setting up the equation.

The motion equation is given by

$s(t) =16t^2+32t$

We can replace there s = 215 ft to get

$215=16t^2+32t$

Solving for the time t.

From the previous equation we can move all terms in one side to get

$16t^2+32t-215=0$

At this point we can solve for t using quadratic formula.

$t = \cfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

where a, b and c are the coefficients of the quadratic equation

$at^2+bt+c=0$

So we get

$a=16\\b=32\\c=-215$

Replacing on the quadratic formula we get

$t = \cfrac{-32\pm \sqrt{32^2-4(16)(-215)}}{2(16)}$

Using a calculator we get

$t=-4.8 , t = 2.8$

Physically speaking the only result that makes sense is to move forward in time that give us t = 2.8 seconds.

We can conclude that it takes 2.8 seconds for the ball to fall 215 ft.

3 0

3 years ago

A telephone pole is 24 feet tall. Curtis, who is standing some distance away from the telephone pole measures the angle of eleva

taurus [48]

The distance from the base of the telephone pole to Curtis is about 15 feet.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more number and variables.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let d represent the distance from the base of the telephone pole to Curtis, hence:

tan(51.4) = (24 - 5.2) / d

d = 15 feet

The distance from the base of the telephone pole to Curtis is about 15 feet.

Find out more on equation at: brainly.com/question/2972832

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4 0

2 years ago

Prove divisibility 45^45·15^15 by 75^30

Anuta_ua [19.1K]

Answer:

$3^{75}$

Step-by-step explanation:

We are asked to divide our given fraction: $\frac{45^{45}*15^{15}}{75^{30}}$ .

We will simplify our division problem using rules of exponents.

Using product rule of exponents $(a*b)^n=a^n*b^n$ we can write:

$45^{45}=(3*15)^{45}=3^{45}*15^{45}$

$75^{30}=(5*15)^{30}=5^{30}*15^{30}$

Substituting these values in our division problem we will get,

$\frac{3^{45}*15^{45}*15^{15}}{5^{30}*15^{30}}$

Using power rule of exponents $a^m*a^n=a^{m+n}$ we will get,

$\frac{3^{45}*15^{45+15}}{5^{30}*15^{30}}$

$\frac{3^{45}*15^{60}}{5^{30}*15^{30}}$

Using quotient rule of exponent $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{3^{45}*15^{60-30}}{5^{30}}$

$\frac{3^{45}*15^{30}}{5^{30}}$

Using product rule of exponents $(a*b)^n=a^n*b^n$ we will get,

$\frac{3^{45}*(3*5)^{30}}{5^{30}}$

$\frac{3^{45}*3^{30}*5^{30}}{5^{30}}$

Upon canceling out $5^{30}$ we will get,

$3^{45}*3^{30}$

Using power rule of exponents $a^m*a^n=a^{m+n}$ we will get,

$3^{45+30}$

$3^{75}$

Therefore, our resulting quotient will be $3^{75}$ .

8 0

3 years ago

To convert 132 milligrams to grams, you can set up the proportion x/132 mg = 1,000/ 1 g

marin [14]

Answer:

FALSE

Step-by-step explanation: You can convert 132 milligrams by using the KHDUDCM(King Henry Died Unusually Drinking Chocolate Milk) And you will have to add three zeros to 132. (I might be incorrect)

5 0

2 years ago

Read 2 more answers

Which expression is evaluated to -18-64

gogolik [260]

Answer:

-82

Step-by-step explanation:

-18 - 64

-82

Answer: -82

4 0

3 years ago