we have the inequality
step 1
Find out the first solution (positive case)
The first solution is all real numbers less than or equal to 1.20
Interval (-infinite,1.20]
step 2
Find out the second solution (negative case)
Multiply by -1 both sides
The second solution is all real numbers greater than or equal to -2.8
the interval [-2.8, infinite)
step 3
Find out the solution to the given inequality
The solution is
[-2.8, infinite) ∩ (-infinite,1.20]=[-2.8,1.20]
the solution is the interval [-2.8,1.20]
see the attached figure to better understand the problem
Answer:
(a) 120 square units (underestimate)
(b) 248 square units
Step-by-step explanation:
<u>(a) left sum</u>
See the attachment for a diagram of the areas being summed (in orange). This is the sum of the first 4 table values for f(x), each multiplied by 2 (the width of the rectangle). Quite clearly, the curve is above the rectangle for the entire interval, so the rectangle area underestimates the area under the curve.
left sum = 2(1 + 5 + 17 + 37) = 2(60) = 120 . . . . square units
<u>(b) right sum</u>
The right sum is the sum of the last 4 table values for f(x), each multiplied by 2 (the width of the rectangle). This sum is ...
right sum = 2(5 +17 + 37 +65) = 2(124) = 248 . . . . square units
You need to divide the total amount by $75, to see how many DVD players she could buy with the $568.
568÷75= 7 remaining 43
This means that Julia can buy 7 DVD players, and will have $43 extra dollars left over.
