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
Distribute -10
-10n - 50 = 40
Add 50 to both sides
-50 + 50 would cancel
- 50 + 40 = -10
Divide by -10
-10/-10 = 1
N=1
Answer:
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of triangle plus the area of semicircle
so
we have
Find the height of the right triangle applying the Pythagorean Theorem
The radius of the semicircle is half the height of triangle
substitute in the formula
To find a volume of a cylinder we use the following formula:
Plug in the values:
Take the square:
Multiply the numbers:
Answer:
B
Step-by-step explanation:
-5[ (x³+1)(x+4) ] = -5[ x³*(x+4) + 1*(x+4) ]
= -5 [ x³*x + x³*4 + 1*x + 1*4 ]
= -5 [ x⁴ + 4x³ + x + 4]
= -5*x⁴ + (-5)*4x³ + (-5)*x + (-5) * 4
= -5x⁴ - 20x³ - 5x - 20
