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evablogger [386]
3 years ago
13

I bought 16 cupcakes and then last week i bought 9 keep the pattern going

Mathematics
1 answer:
lana [24]3 years ago
4 0

Answer:

25

Step-by-step explanation:

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Read 2 more answers
Find the point P on the line yequals=33x that is closest to the point (60 comma 0 )(60,0). What is the least distance between P
scoray [572]

Answer:

18\sqrt{10}$ units

Step-by-step explanation:

We are given the equation of the line y=3x and a point, say Q(60,0) outside of that line.

We want to find the point on the line y=3x which is closest to Q.

Let P(x,y) be the desired point. Since it is on the line y=3x, it must satisfy the line.

If x=a, y=3a, so the point P has the coordinates (a,3a).

Distance between point Q and P

=\sqrt{(60-a)^2+(0-3a)^2}\\D =\sqrt{10a^2-120a+3600}

To minimize D, we find its derivative

\dfrac{dD}{da}=\dfrac{10a-60}{\sqrt{10a^2-120a+3600} }\\$Setting \dfrac{dD}{da}=0\\10a-60=0\\10a=60\\a=6

Therefore, the y-coordinate for P is 3*6=18.

The point P=(6,18).

Next, we calculate the distance between P(6,18) and (60,0).

D =\sqrt{10(6)^2-120(6)+3600}\\=\sqrt{3240}\\=18\sqrt{10}$ units

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4 years ago
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