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2 years ago

A cone has a diameter of 8ft and height of 3ft. What’s the volume?

Mathematics

2 answers:

stepladder [879]2 years ago

7 0

Step-by-step explanation:

1/3 πr²h

Given

diameter (d) = 8ft

radius (r) = d/2 = 8/2 = 4 ft

height (h) = 3 ft

Volume of cone

$\frac{1}{3} \times \pi {r}^{2} h$

$\frac{1}{3} \times 3.14 \times {4}^{2} \times 3$

$\frac{150.72}{3}$

=50.24 ft³

Gennadij [26K]2 years ago

5 0

The cone formula is V=1/3(pi*r^2)h, plug in what you know 150pi=1/3(pi*r^2)8.

Multiply both sides by 3: 450pi=(pi*r^2)8

Divide by 8: 56.25pi=pi*r^2

Divide by pi: 56.25=r^2

Square root both sides: 7.5=r

Multiply by 2 to find diameter: d=15

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natita [175]

Answer:

f(-2) = +2

Step-by-step explanation:

Let x = -2

So,

f(x) = 4x + 10

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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2 years ago

Solve the following differential equation: y" + y' = 8x^2

PtichkaEL [24]

Answer:

$y=y_p+y_h = \frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$

Step-by-step explanation:

Let's find a particular solution. We need a function of the form $y= ax^3+bx^2+cx+d$ such that

$y'= 3ax^2+2bx+c$ and

$y''= 6ax+2b$

$y'+y''= 3ax^2+2bx+c+6ax+2b = 3ax^2+x(2b+6a)+(c+2b) = 8x^2$

then, 3a= 8, 2b+6a =0 and c+2b = 0. With the first equation we obtain

a = 8/3 and replacing in the second equation 2b+6(8/3) = 2b + 16 = 0. Then, b = -8. Finally, c = -2(-8) = 16.

So, our particular solution is $y_p= \frac{8}{3}x^3-8x^2+16x$ .

Now, let's find the solution $y_p$ of the homogeneus equation $y''+y'=0$ with the method of constants coefficients. Let $y=e^{\lambda x}$

$y'=\lambda e^{\lambda x}$

$y''=\lambda^2e^{\lambda x}$

then $\lambda e^{\lambda x}+\lambda^2 e^{\lambda x} = 0$

$e^{\lambda x}(\lambda +\lambda^2)= 0$

$(\lambda +\lambda^2)= 0$

$\lambda (1+\lambda)= 0$

$\lambda =0$ and $\lambda)= -1$ .

So, $y_h = C_1 + C_2e^{-x}$ and the solution is

$y=y_p+y_h =\frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$ .

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2 years ago

An athlete takes 10 rounds of a rectangular park, 60 m long and 35 m wide. Find the total distance covered by him

serious [3.7K]

Answer:

1900M

Step-by-step explanation:

If the athlete runs round a rectangular park, the distance covered can be determined by calculating the perimeter of the park

Perimeter of a rectangle = 2 x (length + width)

2 x (60 + 35) = 190m

Since he run rounds 10 times, the total distance covered = 190m x 10 = 1900m

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2 years ago