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Feliz [49]
3 years ago
15

How to find the volume of a quarter-sphere?

Mathematics
1 answer:
Ganezh [65]3 years ago
7 0

As the word suggests, a quarter-sphere is a quarter of a sphere, and thus the volume of a quarter-sphere is a quarter of the volume of the sphere.

The volume of a sphere is computed as

\dfrac{4}{3} \pi r^3

So, the volume of a quarter-sphere is

\dfrac{1}{4}\cdot \dfrac{4}{3} \pi r^3 = \dfrac{1}{3} \pi r^3

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karie builds a skate ramp with 2 metres of wood. she wants the vertical height of the ramp to be 1 metre. what does the angle el
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Answer:

  30°

Step-by-step explanation:

The relationship between triangle sides and angles can be remembered using the mnemonic SOH CAH TOA. Here, we're interested in the relationship involving the hypotenuse and the side opposite the angle:

  Sin = Opposite/Hypotenuse

For a ramp 1 m high and 2 m long, we have ...

  sin(x) = (1 m)/(2 m) = 1/2

  x = arcsin(1/2) = 30°

The elevation angle of the ramp needs to be 30°.

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3 years ago
Write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros
Kitty [74]

The factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)

<h3>How to determine the factored form?</h3>

The given parameters are:

  • Leading coefficient, a = 1
  • Zeros = -3, -3, 4, and 2.

Rewrite the zeros as:

x = -3, x = -3, x = 4 and x = 2

Set the zeros to 0

x + 3 = 0, x + 3 = 0, x - 4 = 0 and x - 2 = 0

Multiply the zeros

(x + 3) * (x + 3) * (x - 4) *(x - 2) = 0

Express as a function

y(x) = a(x + 3) * (x + 3) * (x - 4) *(x - 2)

Substitute 1 for a

y(x) = (x + 3)²(x - 4)(x - 2)

Hence, the factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)

Read more about polynomials at:

brainly.com/question/4142886

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In a recent poll, 700 people were surveyed. 77% of them said they opposed the current war. How many people stated they were in o
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Step-by-step explanation:


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Since ABCD is a parallelogram, the two pairs of _________ sides (AB¯ and CD¯, as well as AD¯ and BC¯) are congruent. Then, since
Marysya12 [62]

Answer:

1. Opposite

2. angle-side-angle criterion

Step-by-step explanation:

Since ABCD is a parallelogram, the two pairs of <u>(opposite)</u> sides (AB¯ and CD¯, as well as AD¯ and BC¯) are congruent. Then, since ∠9 and ∠11 are vertical angles, it can be concluded that ∠9≅∠11. Since ABCD is a parallelogram, AB¯∥CD¯. Since ∠2 and ∠5 are alternate interior angles along these parallel lines, the Alternate Interior Angles Theorem allows that ∠2≅∠5. Since two angles of △AEB are congruent to two angles of △CED, the Third Angles Theorem supports that ∠8≅∠3. Therefore, using the <u>(angle-side-angle criterion)</u>, it can be stated that △AEB≅△CED. Then, applying the definition of congruent triangles, it can be stated that AE¯≅CE¯, which makes E the midpoint of AC¯. Use a similar argument to prove that △AED≅△CEB; then it can be concluded that E is also the midpoint of BD¯. Since the midpoint of both line segments is the same point, the segments bisect each other by definition. Match each number (1 and 2) with the word or phrase that correctly fills in the corresponding blank in the proof.

A parallelogram posses the following features:

   1. The opposite sides are parallel.

   2. The opposite sides are congruent.

   3. It has supplementary consecutive angles.

   4. The diagonals bisect each other.

7 0
3 years ago
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