Answer: The larger integer is 42 and the smaller integer is 14
Step-by-step explanation:
14 x 2 + 14 = 42
42 + 14 = 56
Answer:
45 minutes
Step-by-step explanation:
At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...
t = d/s
t = (7.5 mi)/(10 mi/h) = 0.75 h
to catch Peter.
Mitchell will catch Peter in 45 minutes.
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<em>Alternate Solution</em>
Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:
3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter
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You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.
<span>Simplifying
15 + 5x = 0
Solving
15 + 5x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-15' to each side of the equation.
15 + -15 + 5x = 0 + -15
Combine like terms: 15 + -15 = 0
0 + 5x = 0 + -15
5x = 0 + -15
Combine like terms: 0 + -15 = -15
5x = -15
Divide each side by '5'.
x = -3
Simplifying
x = -3</span>
Answer:
a=1.29 approx
Step-by-step explanation:
To check for continuity at the edges of each piece, you need to consider the limit as
approaches the edges. For example,

has two pieces,
and
, both of which are continuous by themselves on the provided intervals. In order for
to be continuous everywhere, we need to have

By definition of
, we have
, and the limits are


The limits match, so
is continuous.
For the others: Each of the individual pieces of
are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.