Describe the 6 ways to transform a function.

1 answer:

6 0

Translate it up, translate it down, translate it to the right, translate it to the left, stretch it vertically, stretch it horizontally

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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$

8 0

4 years ago

10 points - questions #13-15. W/ work please.

vekshin1

13. To find the angle of WZY you would have to grab the angle of a straight line (180) and subtract it from the already shown angle of 105. 180 - 105 = 75. 75 is the measure of WZY
14. WZ has a measure of 24 since the parallel side is also 24 (not too sure about this one)
15. XYZ Has the same angle as its corresponding angle of 105. The angle is also 105

8 0

3 years ago

Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 16cm and a height of 8cm, at the ra

andriy [413]

Let h=height of water
Let r=radius of water surface
r/h=16/8 =2, so r=2h.
The volume of water is:
v=(1/3)×π×r²×h
=(1/3)×π×(2h)²×h
=4/3πh³
dv/dh=4πh^2
By chain rule:
dv/dt=dv/dh×dh/dt
but
dv/dt=4
thus:
4=(4πh)×dh/dt
dh/dt=4/(4πh²)
when h=6cm we have:
dh/dt=4/(4π6²)
=0.00884 cm³/min

8 0

4 years ago

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What is 5.7909 in scientific notation

umka21 [38]

It's already in scientific notation, but it could be written as 5.7909x10^0

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3 years ago

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Express x^2-6x-4 in the form of (x+m)^2+n.

vova2212 [387]

Answer: