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alekssr [168]
2 years ago
7

A) BCD is a straight line.

Mathematics
1 answer:
otez555 [7]2 years ago
3 0

Answer:

x = 46°

Step-by-step explanation:

Since Δ ABC is equilateral then interior angles = 60°

Since CE = DE then Δ CDE is isosceles and the base angles are congruent, so

∠ ECD = \frac{180-32}{2} = \frac{148}{2} = 74°

BCD is a straight line, then the 3 angles on it sum to 180°, that is

60° + 74° + x = 180°

134° + x = 180° ( subtract 134° from both sides )

x = 46°

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Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP​
-Dominant- [34]

Option A: The height of the cylinder is equal to the diameter of the sphere.

Option C: The radius of the sphere is half the height of the cylinder.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Solution:

The sphere is inside the cylinder.

Let r be the radius of the sphere.

Option A: The height of the cylinder is equal to the diameter of the sphere.

The sphere is fully occupied the cylinder.

If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.

Option B: The height of the cylinder is two times the diameter of the sphere.

That is h = 2d. From the above option, we know that h = d.

So, it is not true.

Option C: The radius of the sphere is half the height of the cylinder.

we know that diameter = 2 × radius (d = 2r)

From option A, we have h = d.

Substitute d = 2r, we get

⇒ h = 2r

Divide by 2 on both sides, we get

$\Rightarrow \frac{h}{2}=r

Therefore, it is true.

Option D: The diameter of the sphere is equal to the radius of the cylinder.

It is not true, because diameters of both cylinder and sphere are equal.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Radius of cylinder and sphere = r

Height of cylinder h = 2r (by option C)

Volume of cylinder = Volume of sphere

  $\Rightarrow \pi r^2 h = \frac{4}{3} \pi r^3 (formula)

$\Rightarrow \pi r^2 (2r) = \frac{2\times2}{3} \pi r^3

$\Rightarrow 2 \pi r^3= \frac{2}{3} \times 2\pi r^3

Hence it is true.

Option A, option C and option E are true.

6 0
3 years ago
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What’s the probability?
son4ous [18]

Answer:

\frac{1}{8}

Step-by-step explanation:

The probability for a flip on either side of the coin is always 50% or \frac{1}{2}

So to get the probability for the three flips just do:

(\frac{1}{2}) ^{3}  or \frac{1}{2} × \frac{1}{2} × \frac{1}{2}

Either way you solve it the answer is \frac{1}{8}

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2 years ago
I need help please...
nekit [7.7K]

Answer: What is the question?

Step-by-step explanation:

3 0
3 years ago
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What is the answer to -3(9-x)+6x
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Answer: 9−27

Step-by-step explanation:

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3 years ago
Simple math help?<br> Solve for x<br> √x+12 = √x+2
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This is an impossible equation. If sqrt(x) = sqrt(x), and sqrt(x) + 2 = sqrt(x) + 12, then that would mean that 2=12, which is incorrect.
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2 years ago
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