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3 years ago

Rearrange the formula to make h the subject: V = pr^2h

Mathematics

1 answer:

mario62 [17]3 years ago

3 0

Step-by-step explanation:

$V = p {r}^{2} h$

$h = \frac{V}{p {r}^{2} }$

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Lannie ordered 12 copies of the same book for his book club members. The book cost $19 each and the order has a$15 shipping char

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$(12*19)+15=228+15=243$

The total cost is $243.

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3 years ago

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a sketch of a fashion designer's shirt is 9cm long. the actual shirt is 1 meter long. What is the scale of the drawing?

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Step-by-step explanation:

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3 years ago

1. (a) Solve the differential equation (x + 1)Dy/dx= xy, = given that y = 2 when x = 0. (b) Find the area between the two curves

erastova [34]

(a) The differential equation is separable, so we separate the variables and integrate:

$(x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx$

$\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx$

$\ln|y| = x - \ln|x+1| + C$

When x = 0, we have y = 2, so we solve for the constant C :

$\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)$

Then the particular solution to the DE is

$\ln|y| = x - \ln|x+1| + \ln(2)$

We can go on to solve explicitly for y in terms of x :

$e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}$

(b) The curves y = x² and y = 2x - x² intersect for

$x^2 = 2x - x^2 \implies 2x^2 - 2x = 2x (x - 1) = 0 \implies x = 0 \text{ or } x = 1$

and the bounded region is the set

$\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}$

The area of this region is

$\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}$

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2 years ago

Help me solve this problem

Gennadij [26K]

The value of GK = 18.6, GM = 14.5 AND JZ = 19.9.

From the figure:

MZ is a perpendicular bisector of ∆GHJ.

GM = MJ

GM = 14.5

KZ is a perpendicular bisector of ∆GHJ.

GK = KH

GK = 18.6

Z is the circumcenter of ∆GHJ.

JZ = GZ

JZ = 19.9

Therefore the value of GK = 18.6, GM = 14.5 AND JZ = 19.9.

Learn more about the perpendicular bisector here:

brainly.com/question/24753075

#SPJ1

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1 year ago