All categories

3 years ago

Troy cycled 57 miles in 3 hours. if he cycled at a constant rate, what was his rate in mph?

Mathematics

2 answers:

Digiron [165]3 years ago

8 0

57 miles / 3 hours = 19 mph

Nimfa-mama [501]3 years ago

7 0

Divide 57 by 3 to get 19mph

You might be interested in

Find the values of m and b that make the following function differentiable. the piecewise function f of x equals x cubed when x

aalyn [17]

$f(x)=\begin{cases}x^3&\text{for }x\le1\\mx+b&\text{for }x>1\end{cases}$

$f$ must be continuous in order to be differentiable, so we need to have

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$

By its definition, $f(1)=1^3=1$ , and

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}x^3=1$

$\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}(mx+b)=m+b$

so that $\boxed{m+b=1}$ .

We want the derivative to exist at $x=1$ , which requires that we pick an appropriate value for $f'(1)$ so that $f'(x)$ is also continuous. At the moment, we know

$f'(x)=\begin{cases}3x^2&\text{for }x1\end{cases}{/tex]so we need to pick [tex]f'(1)$ such that

$\displaystyle\lim_{x\to1^-}f'(x)=\lim_{x\to1^+}f'(x)$

We have

$\displaystyle\lim_{x\to1^-}f'(x)=\lim_{x\to1}3x^2=3$

$\displaystyle\lim_{x\to1^+}f'(x)=\lim_{x\to1}m=m$

so that $\boxed{m=3}$ (which means we need to pick $f'(1)=3$ ) and so $m+b=1\implies\boxed{b=-2}$

5 0

3 years ago

Eugene has five payments left to make on his computer. If each payment is $157.90, how much does he still owe?

puteri [66]

$157.90 x 5 = $789.50

He still owes $789.50

3 0

2 years ago

A game is played by rolling a fair six-sided die once. If the

Art [367]

The value of the game will be $ 0.08. Then the correct option is B.

<h3>What is probability?</h3>

Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.

A game is played by rolling a fair six-sided die once.

If the die lands on a 1 the player win $8 otherwise the player loses $1.50.

Then the value of the game will be

The probability of success will be

p = 1/6

The probability of failure will be

p = 5/6

Then the value of the game will be

Value of game = 8p - 1.5q

Value of game = 8 x 1/6 - 1.5 x 5/6

Value of game = 1.3333 - 1.25

Value of game = 0.08333