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kodGreya [7K]
3 years ago
6

What is the volume of a cone with a radius of 4 centimeters and a height of 5 centimeters?

Mathematics
1 answer:
vovangra [49]3 years ago
8 0

Answer:

83.79 cm²

Step-by-step explanation:

(please refer to attached)

recall that the volume of a cone is given by

V = (1/3) π r² h

where

r = radius = given as 4 cm

h = height = given as 5 cm

assume π = 3.142

substituting the values into the formula:

V = (1/3) π r² h

V = (1/3) (3.14) (4)² (5)

V = 83.79 cm²

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Please show the steps​
notka56 [123]

Answer:

  x = -3, 0, or 7

Step-by-step explanation:

After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.

__

<h3>Step 1</h3>

Write the equation in standard form.

  4x³ -16x² -84x = 0

<h3>Step 2</h3>

Factor out the common factor from all terms.

  = 4x(x² -4x -21) = 0

<h3>Step 3</h3>

Compare to the factored form of a quadratic:

  (x +a)(x +b) = x² +(a+b)x +ab

This tells you the constants 'a' and 'b' in the factors can be found by considering ...

  (a+b) = -4 . . . . the coefficient of the x term of the quadratic

  ab = -21 . . . . . the constant term of the quadratic

It is often helpful to list factor pairs of the constant:

  -21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum

The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...

  a = -7, b = 3

<h3>Step 4</h3>

Put it all together.

  4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation

<h3>Step 5</h3>

Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:

  4x = 0   ⇒   x = 0

  x -7 = 0   ⇒   x = 7

  x +3 = 0   ⇒   x = -3

Solutions to the equation are x ∈ {-3, 0, 7}.

_____

<em>Additional comment</em>

What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.

A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.

3 0
2 years ago
Pls help me!! this is for a study guide :)
inn [45]

Answer:

x° = 149°

Step-by-step explanation:

According to the <u>Triangle Sum Theorem</u>, the sum of the measures of the angles in every triangle is 180°. Since we are given two angles with measures of m < 86° and m < 63°, then the third angle must be:

m < 86° + m < 63° + m < (angle 3) = 180°

149° + m < ? = 180°

Subtract 149° from both sides to solve for m < (angle 3)

149° - 149° + m < (angle 3)   = 180° - 149°

m < ?   = 31°

Therefore, the measure of the third angle is 31°.

To find x°, we can reference the <u>Triangle Exterior Angle Postulate</u>, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

In other words, the measure of x° = m < 86° + m < 63°

x° = 149°

By the way, m< (angle 3) and x° are also supplementary angles whose sum equal 180°:

x° + m < (angle 3) = 180°

149° +  31° = 180°

6 0
2 years ago
A beach volleyball court is 9 meters wide and 18 meters long. The rope used
HACTEHA [7]

Answer:

14.22

Step-by-step explanation: 1.58x9 meters=14.22 meters

7 0
2 years ago
Read 2 more answers
QUICK QUESTION! PLEASE ANSWER FAST!
mr_godi [17]
A^2 + B^2 = C^2
7^2 + B^2 = 25^2
49 + B^2 = 625
-49 -49
B^2 = 576
Square root both sides
B = 24
4 0
3 years ago
Read 2 more answers
Please help. I have no idea how to do this. Find the measure of
vagabundo [1.1K]

m∠A = 40

Step-by-step explanation:

Given AB =AC and  m∠B = 70

Since AB =AC , Triangle ABC is an isosceles Triangle and the corresponding angles B and C are equal.

So m∠B = m∠C = 70

The sum of the 3 Angles of a triangle is 180°.

=> m∠A  + m∠B + m∠C = 180

=> 140 + m∠C = 180

=> m∠C = 40

Hence the answer is  m∠C = 40

6 0
3 years ago
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