Mathematics, 15.12.2020 09:20 j015

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Answer from: carolyvillanueva

Step-by-step explanation:

We can see that our figure is composed of a cylinder and a cone.

So, we can utilize the surface area formulas.

The surface area of a cylinder is given by:

$SA=2\pi r^2+2\pi r h$

The first term is the two circular bases, and the second term is the lateral surface area.

Notice that the circular base has a diameter of 6. So, its radius is 3.

Also, the height of the cylinder is 50.

However, notice that one of the circular bases is not included in our surface area as it’s connected to the cone. So, we will remove that from our surface area. This gives us:

$SA=\pi r^2+2\pi rh$

Therefore, by substituting 3 for r, the radius, and 50 for the height h we can see that:

$\begin{aligned}SA&=\pi(3)^2+2\pi(3)(50)\\&=9\pi+300\pi\\&=309\pi\end{aligned}$

Now, we can determine the SA of the cone.

Again, we will only need to lateral surface area, since the circular base is connected to the cylinder.

The lateral surface area of a cone is given by the formula:

$SA=\pi r\ell$

Where r is the radius and l is the slant height.

The radius is 3 and the slant height is 5. Therefore:

$SA=\pi(3)(5)=15\pi$

So, our total surface area is:

$SA_{\text{Total}}=309\pi+15\pi$

Simplify:

$SA_{\text{Total}}=324\pi\\$

Approximate:

$SA_{\text{Total}}\approx1017.9\text{ units}^2$

Hence, our answer is A.

Answer from: Quest

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2 = -20

divide by -2 on each side

-2x^2 /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

Answer from: Quest

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

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