geometry...?

Question

1.If the point (-3, 7) is dilated with a scale factor of ____, and the center of the dilation is at the origin, then the image of that point is (-12.75, 29.75).

2.To the nearest unit, the approximate distance between the points (-2, 3, -5) and (2, -7, 4) is how many units?

3. The diameter of the base of a right cone is 8 cm. If the total surface area of the cone is 164 radius cm2, how many centimeters must the slant height be?

4.Which is the equation of a 20 cm diameter circle with its center at (3,-6)?
A.(x-3)^2+(y+6)^2=100
B.(x-3)^2+(y+6)^2=400
C.(x+3)^2+(y-6)^2=400
D.(x+3)^2+(y-6)^2=100

5.What is the volume of a sphere that has a 12 m diameter?

A.
509 m3

B.
904 m3

C.
4070 m3

D.
7230 m3

when answering please make sure you are positive of your answer please and thankyou to all who answer!

Answer 1

1. To dilate, you multiply the original point (-3, 7) by some factor to get (-12.75, 29.75).

-3d = -12.75
d = 4.25

7d = 29.75
d = 4.25

(those d's should be equal... I just did both to double check.)

So, the scale factor is 4.25 or 17/4.
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2)
(-2, 3, -5) and (2, -7, 4)

Use the distance formula:
d = sqrt [(x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2]
d = sqrt [(-2 - 2)^2 + (3 - -7)^2 + (-5 - 4)^2]
d = sqrt [(-4)^2 + (10)^2 + (-9)^2]
d = sqrt [16 + 100 + 81]
d = sqrt [197] = 14.03566 = 14 units
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3) if d = 8, then r = 4

SA = (pi)(r)(slant height) + (pi)(r^2)
164 = (pi)(4)(slant height) + (pi)(4^2)
164 = (pi)(4)(slant height) + 16(pi)
164 - 16(pi) = pi(4)(slant height)
(164 - 16pi) / 4pi = slant height
9.05 = slant height
==========================
4)
Center of a circle (h, k) is
(x - h)^2 + (y - k)^2 = r^2

So the answer is B.
==============================
5) if d = 12, r = 6
Volume = (4/3)(pi)(r^3)
= (4/3)(pi)(6^3)
= (4/3)(pi)(216)
= 904.7786

Answer 2

1. To dilate from the origin means that you would multiply the coordinates of the points by some constant. Divide the coordinates of the second by the first and you'll get 4.25 both times. This means that the scale factor is 4.25.

2. The distance between two points in 3-space is SQRT((change in x's)^2 + (change in y's)^2 + (change in z's)^2)

Using (-2, 3, -5) and (2, -7, 4) SQRT((4)^2 + (-10)^2 + (9)^2)
= SQRT (16 + 100 + 81) = SQRT (197)

which is approx. 14.036

3. The total surface area of a cone is pi(r)(L) + pi(r^2) where L is the slant-height. If the diameter is 8 cm then the radius is 4 cm.

(I am assuming radius was a typo.. and that you mean't pi)

164 pi = pi(4)(L) + pi(4^2)
164 = 4L + 16
148 = 4L
37 = L

The slant height is 37 cm.

4. If the diameter is 20 cm, then the radius is 10.

(x - h)^2 + (y - k)^2 = r^2 is the equation of a circle centered at (h, k) with a radius of r,

so answer A.(x - 3)^2 + (y + 6)^2 = 100 is correct.

5. Volume of a sphere is (4/3)pi(r^3). If the diameter is 12 m, then the radius is 6 m.

V = (4/3)pi(6)^3 = 288pi m^3 which is closest to answer B.

Answer 3

I start the first one.
1.If the point (-3, 7) is dilated with a scale factor of _4.25___, and the center of the dilation is at the origin, then the image of that point is (-12.75, 29.75).

Answer 4

incredibly, the only concern that i will discover in basic with sacred geometry and alchemy is they the two handle styles of spirituality. Sacred geometry bargains with using geometric types and shapes interior the layout and shape of church homes, temples, mosques or everywhere of non secular accumulating. those particular shapes mean particular issues, reckoning on the religion or perception device. for occasion, the pentagram in Christianity refers back to the 5 senses. In Catholicism, it may each now and then communicate with the devil, or the Evil One. Alchemy bargains with the technique of turning metals into gold, utilising chemical components and technological understanding. besides the fact that, Alchemy is likewise a perception in looking the appropriate awareness by way of chemistry. subsequently, alchemy is a spirituality all its very own. All in all, the only concern that i will make sure in basic between the two is they the two handle a type, or types, of spirituality.

Answer 5

1. 4.25
2. 14
good luck with the rest