Answer:
Option C
Step-by-step explanation:
Standard equation:
r^2 = (x-h)^2 + (y-k)^2
Radius: r
Center: (h,k)
Plug the values in.
r^2 = (x+8)^2 + (y-15)^2
Using distance formula, you conclude that the radius is 17 since the distance from (-8,15) to (0,0) is 17.
r^2 = 289
That means option C is the right answer.
289 = (x+8)^2 + (y-15)^2
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Answer:
The area of this parallelogram is 
Step-by-step explanation:
The formula for working out the area of a parallelogram is : 
To work out the area you would multiply the base of 11 by the height of 4, this gives you 44 meters squared. This is because a identical parallelogram and a rectangle would have the same area.
1) Multiply 11 by 4.
namely, how many times does 1/4 go into 3/8?
![\bf \cfrac{3}{8}\div \cfrac{1}{4}\implies \cfrac{3}{\underset{2}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{1}\implies \cfrac{3}{2}\implies 1\frac{1}{2}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B3%7D%7B8%7D%5Cdiv%20%5Ccfrac%7B1%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B%5Cunderset%7B2%7D%7B~~%5Cbegin%7Bmatrix%7D%208%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7D%5Ccdot%20%5Ccfrac%7B~~%5Cbegin%7Bmatrix%7D%204%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7B1%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B2%7D%5Cimplies%201%5Cfrac%7B1%7D%7B2%7D)
Answer:
x = -6
y = -12
minimum y = -16
Step-by-step explanation:
a
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y = 7x - 4x²
<span>7x - 4x² = 0 </span>
<span>x(7 - 4x) = 0 </span>
<span>x = 0, 7/4 </span>
<span>Find the area of the bounded region... </span>
<span>A = ∫ 7x - 4x² dx |(0 to 7/4) </span>
<span>A = 7/2 x² - 4/3 x³ |(0 to 7/4) </span>
<span>A = 7/2(7/4)² - 4/3(7/4)³ - 0 = 3.573 </span>
<span>Half of this area is 1.786, now set up an integral that is equal to this area but bounded by the parabola and the line going through the origin... </span>
<span>y = mx + c </span>
<span>c = 0 since it goes through the origin </span>
<span>The point where the line intersects the parabola we shall call (a, b) </span>
<span>y = mx ===> b = m(a) </span>
<span>Slope = m = b/a </span>
<span>Now we need to integrate from 0 to a to find the area bounded by the parabola and the line... </span>
<span>1.786 = ∫ 7x - 4x² - (b/a)x dx |(0 to a) </span>
<span>1.786 = (7/2)x² - (4/3)x³ - (b/2a)x² |(0 to a) </span>
<span>1.786 = (7/2)a² - (4/3)a³ - (b/2a)a² - 0 </span>
<span>1.786 = (7/2)a² - (4/3)a³ - b(a/2) </span>
<span>Remember that (a, b) is also a point on the parabola so y = 7x - 4x² ==> b = 7a - 4a² </span>
<span>Substitute... </span>
<span>1.786 = (7/2)a² - (4/3)a³ - (7a - 4a²)(a/2) </span>
<span>1.786 = (7/2)a² - (4/3)a³ - (7/2)a² + 2a³ </span>
<span>(2/3)a³ = 1.786 </span>
<span>a = ∛[(3/2)(1.786)] </span>
<span>a = 1.39 </span>
<span>b = 7(1.39) - 4(1.39)² = 2.00 </span>
<span>Slope = m = b/a = 2.00 / 1.39 = 1.44</span>
