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
Answer:
Step-by-step explanation:
Answer: No
Step-by-step explanation:
According to triangle inequality theorem which state that: the sum of any 2 sides of a triangle must be greater than the measure of the third side.
Now let's test the given parameters if they obey this theorem
4 inches, 5 inches and 1 inch
4 + 5 = 9
9 > 1 correct
5 + 1 = 6
6 > 4 correct
4 + 1 = 5
5 not > 5 wrong
Therefore he won't be able to create the triangular component with these toothpicks without modifying any of the lengths
Answer:
4608 cubes
Step-by-step explanation:
It is very important to note that:
1 cube in a Rectangular Prism has a side length of 1/4
The volume of 1 cube = (side length)³
= (1/4)³ cubic units
We are told in the above question that:
A rectangular prism has a volume of 72 cubic units.
The number of unit cubes that will fill the rectangular prism exactly is calculated as:
72 cubic units ÷ (1/4)³ cubic units
= 72 cubic units ÷ (1/64) cubic units
= (72 × 64 ) cubes
= 4608 cubes
Therefore, the number of unit cubes that will fill the rectangular prism exactly is 4608 cubes
