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2 years ago

Suppose you drop a tennis ball from a height of 15 feet.

Mathematics

1 answer:

kiruha [24]2 years ago

4 0

9.2 feet

Hope this helps.

Brainliest plz

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What is the value of b in the equation b+8=13?

DanielleElmas [232]

Answer:

Step-by-step explanation:

b = 13 - 8 = 5

6 0

2 years ago

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PLEASE HELP!!!!<br> Which of these pair of functions are inverse functions?

Mamont248 [21]

Answer:

Option B and C are correct.

Step-by-step explanation:

Inverse function: If both the domain and the range are R for a function f(x), and if f(x) has an inverse g(x) then:

$f(g(x)) = g(f(x)) = x$ for every x∈R.

Let $f(x) = \frac{1}{2}(\ln(\frac{x}{2}) -1)$ and $g(x) = 2e^{2x+1}$

Use logarithmic rules:

$ln e^a = a$

$e^{lnx} = x$

$\ln a^b = b\ln a$

then, by definition;

$f(g(x)) = f(2e^{2x+1}) =\frac{1}{2}(\ln(\frac{2e^{2x+1}}{2})-1)$ = $\frac{1}{2}(\ln(e^{2x+1}}){-1) = \frac{1}{2} (2x+1-1) =\frac{1}{2}(2x) = x$

$g(f(x)) = g(\frac{1}{2}(\ln(\frac{x}{2}) -1)) = 2e^{2({\frac{1}{2}(\ln(\frac{x}{2}) -1})+1$ $2e^{(\ln(\frac{x}{2}) -1+1}=2e^{\ln(\frac{x}{2})} =2\cdot \frac{x}{2} = x$

Similarly;

for $f(x) = \frac{4 \ln(x^2)}{e^2}$ and $g(x) = e^{\frac{e^2 \cdot x}{8} }$

then, by definition;

$f(g(x)) = f(e^{\frac{e^2 \cdot x}{8}}) =\frac{4 \ln {(\frac{e^2 \cdot x}{8})^2}}{e^2}$ = $\frac{8 \ln {(\frac{e^2 \cdot x}{8})}}{e^2} =\frac{8\frac{e^2\cdot x}{8} }{e^2}=\frac{8e^2 \cdot x}{8e^2}=x$

Similarly,

g(f(x)) = x

Therefore, the only option B and C are correct. As the pairs of functions are inverse function.

3 0

3 years ago

The graph of g(x) is the graph of f(x)=5x+15 compressed horizontally by a factor of 1/5 .

Vlad [161]

Consider the value of f at x=2.

f(2)=5*2+15=10+15=25. Thus, we have the point (2, 25) in the graph of f.

The graph of g is the graph of f compressed horizontally by a factor of 1/5.

So at 2, the y-coordinate is 25(1/5=5). That is, we have the point (2, 5).

All pairs (x, y) in f can be described by (x, 5x+15), thus, all pairs (x, y) in g can be described by (x, (5x+15)/5), that is (x, x+3). Thus, the rule for g is :

g(x)=x+3.

Answer: <span>A) g(x)=x+3</span>

7 0

3 years ago

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Baily is training to run a marathon. The number of minutes it takes to run the marathon after t weeks of training is M= 300(0.95

Whitepunk [10]

Answer:

300=initial time and 0.05 is the amount of time shaved off of the initial time to run the marathon

Step-by-step explanation:

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3 years ago

Which of the following correctly completes the square for: x^2+2x=48

Ket [755]