Answer:
The dimensions are 25 * 50 feet.
Step-by-step explanation:
The 3 sides of the pen will measure (2x + y) feet where x is the width and y is the length.
2x + y = 100
y = 100 - 2x
The area A = xy = x(100 - 2x) ft^2.
Finding the maximum area.
A = x(100 - 2x)
A = 100x - 2x^2 Finding the derivative:
A' = 100 - 4x
For maximum value of A this equals zero:
100 - 4x = 0
4x = 100
x = 25 ft, so this is the width.
The length is 100 - 2(25) = 50 ft.
Answer:
48 flowers
Step-by-step explanation:
Since, the ratio of tulips to daisies are the same.
Hence, if we have x number of daisies, then the number of tulips will also be x.
Therefore, with number of tulips being 21 and equal ratio of daisies will also mean that Anna has 21 daisies .
The total number of flowers will be :
Number of tulips + Number of daisies
21 + 21 = 42 flowers
The average rate of change from x = -1 to x = 2 is 2
<u>Solution:</u>
Given function is:
f(x) = 2x - 1
We have to find the average rate of change from x = -1 to x = 2
<em><u>The average rate of change is given as:</u></em>
<em><u>The average rate of change from x = -1 to x = 2 is given by formula:</u></em>
<em><u>Find f(2) and f( - 1)</u></em>
<em><u>Substitute x = 2 in given function</u></em>
f(2) = 2(2) - 1 = 4 - 1 = 3
<em><u>Substitute x = -1 in given function</u></em>
f( - 1) = 2(-1) - 1 = -2 - 1 = -3
<em><u>Substitute the values in above formula,</u></em>
Thus average rate of change from x = -1 to x = 2 is 2
Answer:
C. Q=−31, P = -2
Step-by-step explanation:
2x+Q = Px−31
A. Q = −2 and P=2
2x+Q=Px−31
2x - 2 =2x - 31
0x = -29
0 ≠ -29 : NO SOLUTION
B.Q=31 and P=2
2x+Q=Px−31
2x + 31 = 2x - 31
0x = -62
0 ≠ -62 : NO SOLUTION
C. Q=−31, P = -2
2x+Q=Px−31
2x - 31 = -2x - 31
4x = 0
x = 0 : ONE SOLUTION
D. Q=-31 and P=2
2x+Q=Px−31
2x - 31 = 2x - 31
0x = 0
0 = 0: Infinitely many solutions
Answer:
C. Q=−31, P = -2
This is a right triangle
so
Cos x = 109 / 134 then x = cos⁻¹ (109/134) = 35.567°
sin y = 109 / 134 then y = sin⁻¹ (109/134) = 54.433°
and
the third side = √(134² - 109²) = 77.94
