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Juliette [100K]
3 years ago
5

How does the volume of an oblique cone change if the height is reduced to 2/3 of its original size and the radius is doubled

Mathematics
1 answer:
spayn [35]3 years ago
3 0

The volume of oblique cone =\frac{1}{3} \pi r^{2} h

Now radius is doubled is now it is 2r

And height is reduced to 2/3 of its original size that is 2/3 h

So plugging the values we get volume

New Volume = \frac{1}{3} \pi (2r)^2 (\frac{2}{3} h)

= \frac{1}{3} \pi 4r^2 (\frac{2}{3} h) = \frac{8}{6} \pi r^{2} h =\frac{8}{2} (\frac{1}{3} \pi r^{2} h )=4*(\frac{1}{3} \pi r^{2} h )

It means the volume becomes 4 times

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Find angle D if angle B = 50
Mariana [72]
<h3>Answer:  80 degrees</h3>

============================================================

Explanation:

I'm assuming that segments AD and CD are tangents to the circle.

We'll need to add a point E at the center of the circle. Inscribed angle ABC subtends the minor arc AC, and this minor arc has the central angle AEC.

By the inscribed angle theorem, inscribed angle ABC = 50 doubles to 2*50 = 100 which is the measure of arc AC and also central angle AEC.

----------------------------

Focus on quadrilateral DAEC. In other words, ignore point B and any segments connected to this point.

Since AD and CD are tangents, this makes the radii EA and EC to be perpendicular to the tangent segments. So angles A and C are 90 degrees each for quadrilateral DAEC.

We just found angle AEC = 100 at the conclusion of the last section. So this is angle E of quadrilateral DAEC.

---------------------------

Here's what we have so far for quadrilateral DAEC

  • angle A = 90
  • angle E = 100
  • angle C = 90
  • angle D = unknown

Now we'll use the idea that all four angles of any quadrilateral always add to 360 degrees

A+E+C+D = 360

90+100+90+D = 360

D+280 = 360

D = 360-280

D = 80

Or a shortcut you can take is to realize that angles E and D are supplementary

E+D = 180

100+D = 180

D = 180-100

D = 80

This only works if AD and CD are tangents.

Side note: you can use the hypotenuse leg (HL) theorem to prove that triangle EAD is congruent to triangle ECD; consequently it means that AD = CD.

5 0
3 years ago
Given: 3x+7+2(4x+1) = 3(x-1) -4 prove: x=-2
denis23 [38]

Answer:

x = -2, proven below.

Step-by-step explanation:

3x + 7 + 2(4x+1) = 3(x-1) - 4

3x + 7 + 8x + 2 = 3x - 3 - 4

9 + 11x = 3x - 7

16 + 11x = 3x

16 = - 8x

-2 = x

7 0
3 years ago
Last month Jim drove his car 2,718.3 miles. That brought the car’s total mileage to 87,416. What was the car’s mileage before la
stich3 [128]

To solve this problem you must apply the proccedure shown below:

1. You have that Jim drove the car 2,718.3 miles for a total mileage of 87,416.

2. Then, to calculate the mileage before last month, you only need to substract the total mileage given in the exercise above and the mileage drove last month, as following:

87,416miles-2,718.3miles=84,697.7miles

Therefore, the answer is: 84,697.7 miles.

3 0
3 years ago
"What is the difference between a ratio and its related rate and unit rate?"
Vinil7 [7]

Answer:

Step-by-step explanation:

The ratio is the relationship of two numbers. ... A rate is a little bit different than the ratio, it is a special ratio. It is a comparison of measurements that have different units, like cents and grams. A unit rate is a rate with a denominator of 1.

7 0
2 years ago
What is the value of x in the equation 8x+16
nevsk [136]

Answer:2

Step-by-step explanation:

4 0
3 years ago
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