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Answer:
Question 1)
Cristina is traveling 11 miles per hour and Kori is traveling 20 miles per hour.
Question 2)
Four hours.
Question 3)
Paige spent two hours biking and six hours walking.
Step-by-step explanation:
Question 1)
Let Cristina's speed be <em>x</em>.
Kori travels 9 miles per hour faster than Cristina. So, Kori's speed is (<em>x</em> + 9).
After six hours, Cristina would have traveled 6<em>x</em> miles and Kori would have traveled 6(<em>x</em> + 9) miles.
Since Kori traveled in the opposite direction, we can place a negative to represent this. So, after six hours, Kori is -6(<em>x</em> + 9) miles away from the restaurant while Cristina is 6<em>x</em> miles away from the restaurant.
Since the distance between them is 186 miles, the difference of the two expressions is 186. Hence:
Distribute:
Distribute:
Simplify:
Hence:
Cristina's speed is 11 miles per hour. Thus, Kori's speed is 20 miles per hour.
Question 2)
Let <em>h</em> represent the amount of time that has passed in hours.
Carrie left the restaurant traveling 12 miles per hour.
Four hours later, Leah left traveling in the same direction at 24 miles per hour.
After four hours, Carrie would have traveled 12(4) = 48 miles.
Carrie would still be traveling at 12 miles per hour. So, her distance from the restaurant is given by:
Since Leah just left and is traveling at a rate of 24 miles per hour, her distance from the restaurant is given by:
Leah will catch up when the two expressions are equivalent. Hence:
Solve for <em>h: </em>
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Leah will catch up with Carrie in four hours.
Question 3)
Let <em>x</em> represent the amount of hours spent biking and <em>y</em> represent the amount of hours spent walking.
The total trip to the mall took eight hours. Hence:
The mall is a total of 46 miles away. Since Paige bikes at a rate of 8 miles per hour and walks at a rate of five miles per hour:
Solve the system. We can use elimination. Multiply the first equation by -5:
We can add this to the second equation:
Hence:
Using the first equation again:
So, Paige spent two hours biking and six hours walking.
Answer:
Step-by-step explanation:
The similar triangles are drawn in the figure attached.
As shown in the figure, the smaller triangle ΔABC, and the larger triangle ΔA'B'C' share the same slope; therefore, the slope of the hypotenuse is the length of the triangle ΔA'B'C' divided by its base:
Therefore, the equation of the hypotenuse is
Where the function f is discontinuous and continuous is mathematically given as
- f(x) is not continuous at x = 0.
- f(x) is left continuous at x = 1
- f(x) is right continuous for all x =5
Generally, the equation for is mathematically given as
Since x+1, 1/x, and (x-5), the function does not "break" since these three terms are continuous. at
- x = 1
- x = 5.
According to the dictionary definition of continuity, the function f(x) is continuous at x = a if:
lim (x->a-) f(x) = lim (x->a+) f(x) = f(a).
for x = 0
lim (x->0-) f(x)
= lim (x->0-) (x+1),
since f(x) = x+1 for
f(x<=1) = 1 + 0
f(x<=1)= 1
lim (x->0+) f(x)= lim (x-->0+) ( √(x-5) ), since f(x)
lim (x->0+) f(x)= √(x-5 for x>=5
lim (x->0+) f(x)= 5
In conclusion,
- f(x) is not continuous at x = 0.
- f(x) is left continuous at x = 1
- f(x) is right continuous for all x =5
Read more about discontinuous
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Complete Question
Find the numbers at which f is discontinuous. Then determine whether f is continuous from the right, from the left, or neither at each point of discontinuity.
f(x)={ x+1 if x< 1
1/x if 1<x<5
√(x-5) if x> 5