SOLUTION: 1. An ice-cream manufacturer has decided on a new logo for her company.
It consists of a triangle and 2 circles representing a wafer cone and two balls of ice cream.
Placed o
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Question 388498: 1. An ice-cream manufacturer has decided on a new logo for her company.
It consists of a triangle and 2 circles representing a wafer cone and two balls of ice cream.
Placed on a set of rectangulat axes the logo is modelled .
The triangle has coordinates P(-3,-6), Q(-4,6) and R(2,8).
A is the midpoint of QR
1(a). Find the equation of PA.
1(b). When PA is extended it intersects with the larger circle at B and C. If the larger circle has its equation x²+y²-10x-20y+105=0, find the coordinates of C.
1(c). Given that C is the centre of the smaller circle and that its radius is exactly half of the larger circle, find the equation of the smaller circle.
2. A curve has its equations y=x³-kx²-16x+32
2(a). If the curve crosses the x-axis at A(2,0), find k.
2(b). The point B(p,35) also lies on this curve, find the value of p.
2(c). Calculate the size of the angle between the line AB and the x-axis in the positive direction. Give the answer to the nearest degree.
3. Express 3cos(x°)+5sin(x°) in the form kcos(x°-a°), where k>0 and 0≤a≤360
Can you provide full working with the solutions please.
Many Thanks,
Andrew Rankin.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You have something written wrong. If A is the midpoint of QR, then the coordinates of A have to be (-1,7). But the extended line through P(-3,-6) and A(-1,7) does NOT intersect the circle:
.
On the other hand, it DOES intersect the circle
.
(just barely) Is that what you really meant? By the way, you are only allowed one question per post. Repost the other question separately from the correction to this question.
John
My calculator said it, I believe it, that settles it
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