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Naily [24]
3 years ago
11

Ben jogged 4 and 1/2 miles in 1 and 1/4 hours at a constant rate. How far did Ben jog in one hour? *

Mathematics
1 answer:
Mrac [35]3 years ago
7 0

let's firstly convert the mixed fractions to improper fractions and then proceed.

\stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}}~\hfill \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill

\begin{array}{ccll} miles&hours\\ \cline{1-2} \frac{9}{2}&\frac{5}{4}\\[1em] x&1 \end{array}\implies \cfrac{~~ \frac{9}{2}~~}{x}=\cfrac{~~ \frac{5}{4}~~}{1}\implies \cfrac{~~ \frac{9}{2}~~}{\frac{x}{1}}=\cfrac{5}{4}\implies \cfrac{9}{2}\cdot \cfrac{1}{x}=\cfrac{5}{4} \\\\\\ \cfrac{9}{2x}=\cfrac{5}{4}\implies 36=10x\implies \cfrac{36}{10}=x\implies \cfrac{18}{5}=x\implies 3\frac{3}{5}=x

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Let the length of the radius = r feet.

Diameter = 2r = 2 x 6.8 = 13.6 feet

Circumference = 2\pir = 2 x 3.14 x 6.8 = 42.704 feet = approx. 42.7 feet

6 0
3 years ago
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The quadratic function modeling the height of a ball over time is symmetric about the line , where t is time in seconds. Which s
Rashid [163]

Answer:

A. The height of the ball is the same after 1 second and 3 seconds.

Step-by-step explanation:

The quadratic equation function modeling is used to analyze the relationship between variables in the equation. If the ball is at height and t is time then the ball is on symmetric line which will move for initial 1 second then stabilizes at 3 seconds.

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3 years ago
1. Jeremy has $12000 cash to invest in the bank compounded at 4% interest annually.
gavmur [86]

Answer:

A(x) = 12000(1.04)^x

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

A(t) = P(1 + \frac{r}{n})^{nt}

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

$12000 cash

This means that P = 12000

Compounded at 4% interest annually.

This means that r = 0.04, n = 1

What equation will calculate the value in x years?

A(t) = P(1 + \frac{r}{n})^{nt}

A(x) = P(1 + \frac{r}{n})^{nx}

A(x) = 12000(1 + 0.04)^x

A(x) = 12000(1.04)^x

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Answer:

To satisfy the hypotheses of the Mean Value Theorem a function must be continuous in the closed interval and differentiable in the open interval.

Step-by-step explanation:

As f(x)=2x3−3x+1 is a polynomial, it is continuous and has continuous derivatives of all orders for all real x, so it certainly satisfies the hypotheses of the theorem.

To find the value of c, calculate the derivative of f(x) and state the equality of the Mean Value Theorem:

dfdx=4x−3

f(b)−f(a)b−a=f'(c)

f(x)x=0=1

f(x)x=2=3

Hence:

3−12=4c−3

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