Standard form for circle with radius r and center (h,k) is
(x-h)^2+(y-k)^2=r^2
r=36
center at -2,-7
(x-(-2))^2+(y-(-7))^2=36^2
(x+2)^2+(y+7)^2=1296
firts option
Answer: Senior: $8, Child: 14
Step-by-step explanation:
3s + c = 38
3s + 2c = 52
c = 14
3s + 14 = 38
3s = 24
s = 8
7. x=3 is the midpoint between the roots. The other root is x = 2*3 -(-5) = 11.
8a) f(x) = (x +3)^2 -49. The vertex is (-3, -49). The roots are -10, 4.
8b) y = (x+4)^2 -1. The vertex is (-4, -1). The roots are -5, -3.
8c) f(x) = 2(x +3)^2 -34. The vertex is (-3, -34). The roots are -3±√17.
Answer:
_____________________
a(6,-7) m(7,-5) letb(p,q)
Now,
Let a(6,-7) be x1 ,y1
Let b(p,q) be x2,y2
x,y = (7,-5)
Using Mid point Formula,
x = x1+x2 y= y1+y2
_____ , _____
2 2
7 = 6+p -5 = -7+q
___ , ____
2 2
or, 7×2=6+p , -5×2= -7+q
or, 14=6+p , -10= -7+q
or, p=14-6 , q= -7+10
p=8 , q= 3
Step-by-step explanation:
So , The coordinate of B(8,3)
Thank you
Let P be Brandon's starting point and Q be the point directly across the river from P.
<span>Now let R be the point where Brandon swims to on the opposite shore, and let </span>
<span>QR = x. Then he will swim a distance of sqrt(50^2 + x^2) meters and then run </span>
<span>a distance of (300 - x) meters. Since time = distance/speed, the time of travel T is </span>
<span>T = (1/2)*sqrt(2500 + x^2) + (1/6)*(300 - x). Now differentiate with respect to x: </span>
<span>dT/dx = (1/4)*(2500 + x^2)^(-1/2) *(2x) - (1/6). Now to find the critical points set </span>
<span>dT/dx = 0, which will be the case when </span>
<span>(x/2) / sqrt(2500 + x^2) = 1/6 ----> </span>
<span>3x = sqrt(2500 + x^2) ----> </span>
<span>9x^2 = 2500 + x^2 ----> 8x^2 = 2500 ---> x^2 = 625/2 ---> x = (25/2)*sqrt(2) m, </span>
<span>which is about 17.7 m downstream from Q. </span>
<span>Now d/dx(dT/dx) = 1250/(2500 + x^2) > 0 for x = 17.7, so by the second derivative </span>
<span>test the time of travel, T, is minimized at x = (25/2)*sqrt(2) m. So to find the </span>
<span>minimum travel time just plug this value of x into to equation for T: </span>
<span>T(x) = (1/2)*sqrt(2500 + x^2) + (1/6)*(300 - x) ----> </span>
<span>T((25/2)*sqrt(2)) = (1/2)*(sqrt(2500 + (625/2)) + (1/6)*(300 - (25/2)*sqrt(2)) = 73.57 s.</span><span>
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</span><span>mind blown</span>
