Answer:
Step-by-step explanation:
We want to calculate the right-endpoint approximation (the right Riemann sum) for the function:
On the interval [-1, 1] using five equal rectangles.
Find the width of each rectangle:
List the <em>x-</em>coordinates starting with -1 and ending with 1 with increments of 2/5:
-1, -3/5, -1/5, 1/5, 3/5, 1.
Since we are find the right-hand approximation, we use the five coordinates on the right.
Evaluate the function for each value. This is shown in the table below.
Each area of each rectangle is its area (the <em>y-</em>value) times its width, which is a constant 2/5. Hence, the approximation for the area under the curve of the function <em>f(x)</em> over the interval [-1, 1] using five equal rectangles is:
Step-by-step explanation:
Perimeter of a rectangle = 2(L+W)
L is the length of the rectangle:
W is the width of the rectangle.
Given
Perimeter = 214feet
If the length is 41 ft longer than the width, then L = 41+W
Substitute L = 41+W into the formula:
P = 2(L+W)
214 = 2(41+W+W)
214 = 2(41+2W)
214 = 82+4W
4W = 214-82
4W = 132
W = 132/4
W = 33 feet
Since L = 41+W
L = 41+33
L = 74 feet
Hence the dimension of the field is 74ft by 33ft
<em>The width of the playing field is 33feet</em>
small frames ($8): s
large frames ($15): L
Cost: 8s + 15L = 239 ⇒ 1(8s + 15L = 239) ⇒ 8s + 15L = 239
Quantity: s + L = 22 ⇒ -8( s + L = 22) ⇒ <u> -8s -8 L = -176 </u>
7L = 63
L = 9
Quantity: s + L = 22 ⇒ s + (9) = 22 ⇒ s = 13
Answer: 13 small frames, 9 Large frames
3+(-5)x=19
Subtract 3 from both sides of the equation.
-5x= 16
Divide by -5 on both sides
X= -3.2
