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3 years ago

Find the equation of the circle centre (3-2)radius 2 unit

Mathematics

1 answer:

il63 [147K]3 years ago

3 0

Answer:

(x - 3)^2 + (x + 2)^2 = 4

Step-by-step explanation:

Equation of circle:

(x - h)^2 + (x - k)^2 = r^2

(h, k) = (3, -2)

r = 2

(x - 3)^2 + (x - (-2))^2 = 2^2

(x - 3)^2 + (x + 2)^2 = 4

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What is the diameter of a hemisphere with a volume of 2233\text{ cm}^3,2233 cm 3 , to the nearest tenth of a centimeter?

Agata [3.3K]

Answer:

The diameter of the hemisphere is 20.4 centimeters.

Step-by-step explanation:

The volume of an hemisphere is given by:

$V = \frac{2 \pi r^{3}}{3}$

In this problem, we have that:

$V = 2233$

$\frac{2 \pi r^{3}}{3} = 2233$

$2\pi r^{3} = 3*2233$

$r^{3} = \frac{3*2233}{2\pi}$

$r = \sqrt[3]{\frac{3*2233}{2\pi}}$

$r = 10.2$

The radius is 10.2 centimeters.

The diameter is double the radius. So:

2*10.2 = 20.4

The diameter of the hemisphere is 20.4 centimeters.

5 0

4 years ago

Why is the answer to this integral's denominator have 1+pi^2

ss7ja [257]

It comes from integrating by parts twice. Let

$I = \displaystyle \int e^n \sin(\pi n) \, dn$

Recall the IBP formula,

$\displaystyle \int u \, dv = uv - \int v \, du$

Let

$u = \sin(\pi n) \implies du = \pi \cos(\pi n) \, dn$

$dv = e^n \, dn \implies v = e^n$

Then

$\displaystyle I = e^n \sin(\pi n) - \pi \int e^n \cos(\pi n) \, dn$

Apply IBP once more, with

$u = \cos(\pi n) \implies du = -\pi \sin(\pi n) \, dn$

$dv = e^n \, dn \implies v = e^n$

Notice that the ∫ v du term contains the original integral, so that

$\displaystyle I = e^n \sin(\pi n) - \pi \left(e^n \cos(\pi n) + \pi \int e^n \sin(\pi n) \, dn\right)$

$\displaystyle I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n - \pi^2 I$

$\displaystyle (1 + \pi^2) I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n$

$\implies \displaystyle I = \frac{\left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n}{1+\pi^2} + C$

6 0

2 years ago

Need HELP ASAP WITH THISSS!!

givi [52]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the area of the shaded part in the given diagram

enyata [817]

Answer:

30cm^2

Step-by-step explanation:

area of large rectangle = length x width

= 5 X 9 = 45 cm^2

area of small rectangle = length x width

= 3 X 5 = 15 cm ^2

45 - 15 = 30cm^2

5 0

2 years ago

Write the equation of the line that passes through (0, 1) and has a slope of 0

Inessa [10]

Answer:

y = 1

Step-by-step explanation:

The slope is 0.

y = (0)x + b

y = b

The line passes through (0, 1).

(x, y)

Put y as 1.

1 = b

The y-intercept is 1.

y = 1

7 0

3 years ago

Find the equation of the circle centre (3-2)radius 2 unit​

Find the equation of the circle centre (3-2)radius 2 unit