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PolarNik [594]
3 years ago
12

Plz help...do both plz

Mathematics
1 answer:
Gemiola [76]3 years ago
3 0
The answer for number 4 is 13 and number 6 is 121 and the last problem for number 7 is 112
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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
tekilochka [14]

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

4 0
3 years ago
What is the surface area of a cube with a side of length 14 meters?
prisoha [69]
SA = 6a^2

Where 'a' is the side length.

Plug in what we know:

SA = 6(14)^2

Simplify the exponent:

SA = 6(196)

Multiply:

SA = 1176
3 0
3 years ago
Solve the system of equations.<br><br><br> y+4z=0<br> 4x+y-2z=2<br> -3x-3z=-9
antoniya [11.8K]

Step-by-step explanation:

y+4z=0

4x+y-2z=2

-3x-3z=-9

3 0
1 year ago
Read 2 more answers
Help me with this quick!
lara [203]

6g+10≤35

Hope that helps!!! :D

3 0
2 years ago
Write a thesis statement for your argument aginst online learning
Marina86 [1]

Answer:

Online Learning is bad because it can cause social Isolation, it requires strong self-motivation and time management skills , Lack of communication skill development in online students and cheating prevention during online assessments is very complicated.

Step-by-step explanation:

3 0
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