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Ratling [72]
3 years ago
11

An equilateral triangle of side 14 centimeters is revolved about an altitude to form a cone. What is the number of cubic centime

ters in the volume of the cone?
Mathematics
1 answer:
Naddika [18.5K]3 years ago
4 0

First find the height of the triangle using the Pythagorean theorem:

Height = √(14^2 - 7^2)

Height = √(196 - 49)

Height = √147

Height = 7 √3

Now find the volume of the cone:

Volume = PI x r^2 x H/3

Volume = 3.14 x 7^2 x 7√3/3

Volume = 621.8177 cubic cm's.

Round the answer as needed.

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(x-3) (x-4) polynomial
Debora [2.8K]

Answer:

x^{2} -7x +12

Step-by-step explanation:

Using the Foil method

you multiply x times x and get x^{2}

Then you multiply -4 times X and get -4x

Then you multiply -3 times X and get -3x

then you add -4 and -3 together and get -7x

Lastly you multiply -4 and -3 and get 12

And there you have it

x^{2} -7x +12

8 0
3 years ago
Graph the first six terms of a sequence where a1 = 2 and r = 4.
zavuch27 [327]
We are given with
a1 = 2
r = 4

These are components of a geometric series. The first term is 2 and the common ratio is 4. To get the first six terms, we use the formula:
an = a1 r^(n-1)
a1 = 2 (4)^(1-1) = 2
a2 = 2 (4)^(2-1) = 8
a3 = 2 (4)^(3-1) = 32
a4 = 2 (4)^(4-1) = 128
a5 = 2 (4)^(5-1) = 512
a6 = 2 (4)^(6-1) = 2048
8 0
3 years ago
Read 2 more answers
Solve for x.<br><br><img src="https://tex.z-dn.net/?f=x%20%2B%206%20-%202x%20%3D%20x%20-%2024" id="TexFormula1" title="x + 6 - 2
zhenek [66]

<em>Greetings from Brasil...</em>

First degree equation. The variables are in the 1st member and the numbers in the 2nd member.

X + 6 - 2X = X - 24

X - 2X - X = - 24 - 6

- 2X = - 30

<h2>X = 15</h2>

7 0
3 years ago
Triangle ABC is an isosceles right triangle inscribed in a circle. The center of the circle is point D and the diameter of the c
Paha777 [63]

Answer:

* AD is congruent to DC and BD <em>true</em>

* m∠B = 90° <em>true</em>

<u>* The measure of arc AC is equal to the measure of arc AB </u><u><em>not be true</em></u><em> ( The right answer  )</em>

* The measure of arc AB is equal to measure of arc BC <em>true</em>

Step-by-step explanation:

∵ D is the center of the circle and A , B and C are points on the circle

∴ AD , DB and DC are radii on the circle D

∴ AD ≡ DC ≡ DB

∵ AC passing through point D which is the center of the circle

∴ AC is the diameter of the circle D

∵ ∠B is opposite to the diameter of the circle and vertex B lies on the circle

∵ ∠B is an inscribed angle and  ∠ADC  is a central angle subtended by the same arc AC

∴m∠B = half m∠ADC

∵ m∠ADC = 180°

∴ m∠B = 90°

∵ The measure of arc AC = 180°

∵ ΔABC is isosceles and m∠B = 90°

∴ m∠BAC = m∠BCA = (180° - 90°) ÷ 2 = 45°

∵ ∠ACB is an inscribed angle subtended by arc AB

∴ m∠ACB = half measure of arc AB

∵ The measure of arc AB = 45° × 2 = 90°

∴ The measure of arc AC ≠ the measure of arc AB

∵ Δ ABC is an isosceles triangle and m∠B = 90°

∴ AB = BC

∵ AB subtended by arc AB

∵ BC subtended by arc BC

∴ The length of arc AB = the length of arc BC

∵ If two arcs are equal in length, then they will be equal in measure

∴ The measure of arc AB is equal to the measure of arc BC

3 0
3 years ago
Simplify the expression.
Kitty [74]
5(8x - 10) - 10x + 25(8x - 10) - 10x + 2
= (40x - 50) - 10x + (200x - 250) - 10x + 2
= 40x - 50 - 10x + 200x - 250 - 10x + 2
= (grouping like terms together)
= 40x - 10x + 200x - 10x - 50 - 250 + 2
= 220x - 298
5 0
2 years ago
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