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Oksi-84 [34.3K]
3 years ago
5

Does anyone get this!??

Mathematics
1 answer:
stepladder [879]3 years ago
8 0

Hello from MrBillDoesMath!

Answer:

8

Discussion:

Let the number be "n". Then the question states that

3n - 15 = (n/2) + 5             => multiply both sides by 2

6n - 30 = n + 10                => subtract n from both sides

5n - 30 = 10                      => add 30 to both sides

5n = 30 + 10 = 40            => divide both sides by 5

n = 40/5 = 8

Thank you,

MrB

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Find the point P on the line yequals=66x that is closest to the point (74 comma 0 )(74,0). What is the least distance between P
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Answer:

The point P that is closest to the point (74, 0) is P(7.4, 22.2), and the least distance between P and (74, 0) is 70.2

Step-by-step explanation:

Given

y = 66x

And a point A(74, 0)

We are required to find the point on the line that is closest to A, and then find the distance between these points.

Let the point be P(s, t)

Because it's coordinate satisfies the given equation

y = 3x

Let t = 3s, then we have

p(s, t) = P(s, 3s)

Next, we find the distance between P and A

Let the distance be

D = √[(x1 - y1)² + (x2 - y2)²]

Here x1 = 74, x2 = 0, y1 = s, y2 = 3s.

D = √[(74 - s)² + (0 - 3s)²]

= √(s² - 148s + 5476 + 9s²)

= √(10s² - 148s + 5479)

To maximize the distance, we find the derivative of D with respect to s, and set it to 0.

That is dD/ds = 0

dD/ds =

(20s - 148)/2√(10s² - 148s 5479) = 0

=> 20s - 148 = 0

20s = 148

s = 148/20

s = 7.4

Since t = 3s, we have

t = 22.2

So, the point is P(7.4, 22.2)

Finally, we find the distance D.

D = √[(74 - s)² + (0 - 3s)²]

D = √[(74 - 7.4)² + (0 - 3×7.4)²]

D = √(4435.56 + 492.84)

= √4928.4

D = 70.2

Therefore, the distance is 70.2

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