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vladimir2022 [97]
2 years ago
7

James ran 4 laps and walked 2 laps When running his average speed was 2.5 minutes per lap When walking his average speed was 4.9

minutes per lap How long did it take James to complete 6 laps? 7.4 minutes 9.9 minutes 14.8 minutes Or 19.8 minutes
Mathematics
1 answer:
lutik1710 [3]2 years ago
5 0

Answer:

19.8 minutes

Step-by-step explanation:

Total time the 4 laps was completed = 4 x 2.5 = 10 minutes

Total time the 2 laps was completed = 2 x 4.9 = 9.8 minutes

total time = 10 minutes + 9.8 minutes = 19.8 minutes

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Answer:

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Step-by-step explanation:

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Answer:

log(11 {x}^{2} )

Step-by-step explanation:

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Alexeev081 [22]

Answer:

  • x-intercept:  (-0.1, 0)
  • Horizontal Asymptote: y = -3
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(First answer option)

Step-by-step explanation:

<u>General form of an exponential function</u>

y=ab^x+c

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Given <u>exponential function</u>:

y=4(10)^x-3

<h3><u>x-intercept</u></h3>

The x-intercept is the point at which the curve crosses the x-axis, so when y = 0.  To find the x-intercept, substitute y = 0 into the given equation and solve for x:

\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}

Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.

<h3><u>Asymptote</u></h3>

An <u>asymptote</u> is a line that the curve gets infinitely close to, but never touches.

The <u>parent function</u> of an <u>exponential function</u> is:

f(x)=b^x

As<em> </em>x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.

Therefore, there is a horizontal asymptote at y = 0.

This means that a function in the form  f(x) = ab^x+c always has a horizontal asymptote at y = c.  

Therefore, the horizontal asymptote of the given function is y = -3.

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A graph representing exponential growth will have a curve that shows an <u>increase</u> in y as x increases.

A graph representing exponential decay will have a curve that shows a <u>decrease</u> in y as x increases.

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The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.

Learn more about exponential functions here:

brainly.com/question/27466089

brainly.com/question/27955470

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