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2 years ago

Find the volume of a cone with base area 367 ft2 and a height equal to twice the radius. a

Mathematics

1 answer:

Lostsunrise [7]2 years ago

6 0

Answer:

The volume in terms of π is 144 ft³

The volume rounded to the nearest tenth is 452.4 ft³

Step-by-step explanation:

The formula of the volume of a cone is V = π r² h , where r is its radius and h is its height

The formula of the area of a circle is A = π r²

The area of the base of the cone is 36π ft²

Equate the formula of the area of the circle by 36π to find r

πr² = 36π

Divide both sides by π

r² = 36

Take √ to both sides

r = 6 ft

The height of the cone is equal to twice the radius

The radius of the cone is 6 ft

Multiply 6 by 2 to find the height

h = 2(6) = 12 ft

The height of the cone is 12 ft

Subsitute the values of h and r in the formula of the volume of the cone to find it

V = π(6)²(12)

V = 144 π ft³

V = 452.3893421 ft³

Round it to the nearest tenth

V = 452.4 ft³

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0.325 is _____ 100 percent.

dexar [7]

Answer:

0.00325

Step-by-step explanation:

0.325/100

8 0

3 years ago

At the produce counter, 71⁄5 pounds of seedless grapes cost $12.89. How much would 3 pounds cost? A. $3.58 B. $5.16 C. $1.79 D.

Sonja [21]

Answer:

D. $5.37

Step-by-step explanation:

We need to figure out how much grapes cost per pound

Change the mixed number to an improper fraction

7 1/5 = (5*7+1) /5 = 36/5

$12.89 / 36/5

Copy dot flip

12.89 * 5/36 = 1.79 per lb

If we are purchasing 3 pounds, we will multiply by 3

3 lbs * $1.79 / lb = $5.37

3 0

3 years ago

Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id

Thepotemich [5.8K]

$\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

Explanation

$\frac{1}{a+bi}=c+di$

Step 1

multiplicate by the conjugate

$\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}$

notice that

$\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\ \end{gathered}$ $\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

I hope this helsp you

6 0

1 year ago

The expression (x - 0.35x) represents 35% off the cost of item x. How is this equivalent to multiplying x by 0.65?

myrzilka [38]

Answer:

It is equivalent.

Step-by-step explanation:

(x-0.35x) is (Total price-0.35 × the original price)=0.65×

7 0

3 years ago

The lifetimes of 10,000 watch batteries are normally distributed the mean lifetime is 500 days the standard deviation is 60 days

Lelu [443]

Given:
μ = 500 days, the population mean
σ = 60 days, the population standard deviation

Therefore
μ + σ = 560
μ - σ = 440
μ + 2σ = 620
μ - 2σ = 380
μ + 3σ = 680
μ - 3σ = 320

The figure shown below illustrates the normal distribution
About 68% of the total area lies in x = (μ-σ, μ+σ)
About 95% of the total area lies in x = (μ-2σ, μ+2σ)
About 99.7% of the total area lies in x = (μ-3σ, μ+3σ).

7 0

4 years ago