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3 years ago

5) Tim loves reading fiction, and he can read 100 pages in 2 hours. How many pages he can read in 48 minutes?

Mathematics

2 answers:

Aleonysh [2.5K]3 years ago

6 0

Answer:

40 pages

Step-by-step explanation:

Lets change hours to minutes

1 hours = 60 minutes

2 hours = 120 minutes

We will use ratios to solve

100 pages x pages

------------------- = --------------

120 minutes 48 minutes

Using cross products

100 * 48 = 120 * x

Divide each side by 120

100 *48/120 = 120x/120

40 =x

Tim can read 40 pages

IrinaVladis [17]3 years ago

5 0

Answer:

$40\ pages$

Step-by-step explanation:

Remember that

1 hour=60 minutes

2 hours=120 minutes

Using proportion

$\frac{100}{120}\frac{pages}{minutes}=\frac{x}{48}\frac{pages}{minutes}\\ \\x=100*48/120\\ \\x=40\ pages$

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3 years ago

Given f(x) =

sergejj [24]

Answer:

Step-by-step explanation:

We are given the function:

$\displaystyle f(x) = \left\{ \begin{array}{ll} 2\cos(\pi x) \text{ for } x \leq -1 \\ \\ \displaystyle \frac{2}{\cos(\pi x)}\text{ for } x > -1 \end{array} \right.$

And we want to find:

$\displaystyle \lim_{x\to -1}f(x)$

So, we need to determine whether or not the limit exists. In other words, we will find the two one-sided limits.

Left-Hand Limit:

$\displaystyle \lim_{x\to-1^-}f(x)$

Since we are approaching from the left, we will use the first equation:

$\displaystyle =\lim_{x\to -1^-}2\cos(\pi x)$

By direct substitution:

$=2\cos(\pi (-1))=2\cos(-\pi)=2(-1)=-2$

Right-Hand Limit:

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

Since we are approaching from the right, we will use the second equation:

$=\displaystyle \lim_{x\to -1^+}\frac{2}{\cos(\pi x)}$

Direct substitution:

$\displaystyle =\frac{2}{\cos(\pi (-1))}=\frac{2}{\cos(-\pi)}=\frac{2}{(-1)}=-2$

So, we can see that:

$\displaystyle \displaystyle \lim_{x\to-1^-}f(x)=\displaystyle \lim_{x\to -1^+}f(x) =-2$

Since both the left- and right-hand limits exist and equal the same thing, we can conclude that:

$\displaystyle \lim_{x \to -1}f(x)=-2$

Our answer is A.

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