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2 years ago

In circle D with mZCDE = 112 and CD = 9 units, find the length of arc CE.

Mathematics

1 answer:

Lady bird [3.3K]2 years ago

5 0

Answer:

CE= 17.59

Step-by-step explanation:

Arc Length=central angle/ 360 (circumference)

CE= 112/ 360 (2π9)

CE= 17.59

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Find the value of x

Maurinko [17]

Answer:

x=2

Step-by-step explanation:

3 0

2 years ago

67000 dollars is placed in an account with an annual interest rate of 8.25%. how much will be in the account after 28 years, to

anastassius [24]

Answer:

The Amount of money in the account after 28 years is $616,674.5

Step-by-step explanation:

Given as :

The principal amount placed in the account = p = $67,000

The rate of interest = r = 8.25%

The time period of amount in the account = t = 28

Let the Amount of money in the account = $A

Now<u>, From Compound Interest method</u>

Amount = Principal × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

A = p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, A = $67,000 × $(1+\dfrac{\textrm 8.25}{100})^{\textrm 28}$

Or, A = $67,000 × $(1.0825)^{28}$

Or, A = $67,000 × 9.2041

∴ A = $616,674.7

So, The Amount of money in the account = A = $616,674.5

Hence, The Amount of money in the account after 28 years is $616,674.5 Answer

5 0

2 years ago

3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round

Mariana [72]

The volume of the prop is calculated to be 2,712.96 cubic inches.

<u>Step-by-step explanation:</u>

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone : $V=\pi r^{2} \frac{h}{3}$ = $3.14 \times 9^{2} \times \frac{14}{3}$ = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).