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3 years ago

Find the volume of a cone with a

Mathematics

1 answer:

kotegsom [21]3 years ago

7 0

Answer:

Step-by-step explanation:

Volume of a cone formula is

$V=\frac{1}{3}\pi r^2h$ where r is radius and h is height. Filling in:

$V=\frac{1}{3}(3.14)(10)^2(7)$ and doing all the math on that and rounding gives us

V = 733 units cubed

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Determine which values of p the following integrals converge. Give your answer in each case by selecting the appropriate inequal

sashaice [31]

Answer:

Step-by-step explanation:

$\int\limits^2_1 {\frac{1}{x(lnx)^p} } \, dx$

this can be done by substitute lnx = u

dx/x = du

When x =1, u =0 and when x =2, u = ln 2

So integral = $\int\limits^{ln2} _0 {du/u^p} \\\=\frac{u^{-p+1} }{-p+1}$

We find that this integral value is not definid for p =1

Hence for values of p other than 1, this converges.

When we substitute limits

$\frac{1}{1-p} ((ln2)^{1-p} -1)$

and converges for p ≠1

b) $\int\limits^1_0 {lnx}/x^p \, dx \\\int \frac{\ln \left(x\right)}{x^p}dx=\frac{1}{-p+1}x^{-p+1}\ln \left(x\right)-\frac{x^{-p+1}}{\left(-p+1\right)^2}+C$

So not converging for p =1

But ln x is defined only for x >0

So integral 0 to 1 makes this integral not valid and hence not convergent.

7 0

4 years ago

Please answer ASAP what is 7.28 times 6 than that answer + 41.25 = ?

nataly862011 [7]

Answer: 84.93

Step-by-step explanation:

when you multiply 7.28 by 6 you get 43.68 then when you add 43.68+41.25 you get 84.93

8 0

3 years ago

Read 2 more answers

Which symbol is correct ?

ANEK [815]

Answer:

the answer is c i donw the quiz

Step-by-step explanation:

6 0

3 years ago

The plane x + y + z = 12 intersects paraboloid z = x^2 + y^2 in an ellipse.(a) Find the highest and the lowest points on the ell

emmasim [6.3K]

Answer:

Highest (-3,-3)

Lowest (2,2)

Farthest (-3,-3)

Closest (2,2)

Step-by-step explanation:

To solve this problem we will be using Lagrange multipliers.

Let us find out first the restriction, which is the projection of the intersection on the XY-plane.

From x+y+z=12 we get z=12-x-y and replace this in the equation of the paraboloid:

$\bf 12-x-y=x^2+y^2\Rightarrow x^2+y^2+x+y=12$

completing the squares:

$\bf x^2+y^2+x+y=12\Rightarrow (x+1/2)^2-1/4+(y+1/2)^2-1/4=12\Rightarrow\\\\\Rightarrow (x+1/2)^2+(y+1/2)^2=12+1/2\Rightarrow (x+1/2)^2+(y+1/2)^2=25/2$

and we want the maximum and minimum of the paraboloid when (x,y) varies on the circumference we just found. That is, we want the maximum and minimum of

$\bf f(x,y)=x^2+y^2$

subject to the constraint

$\bf g(x,y)=(x+1/2)^2+(y+1/2)^2-25/2=0$

Now we have

$\bf \nabla f=(\displaystyle\frac{\partial f}{\partial x},\displaystyle\frac{\partial f}{\partial y})=(2x,2y)\\\\\nabla g=(\displaystyle\frac{\partial g}{\partial x},\displaystyle\frac{\partial g}{\partial y})=(2x+1,2y+1)$

Let $\bf \lambda$ be the Lagrange multiplier.

The maximum and minimum must occur at points where

$\bf \nabla f=\lambda\nabla g$

that is,

$\bf (2x,2y)=\lambda(2x+1,2y+1)\Rightarrow 2x=\lambda (2x+1)\;,2y=\lambda (2y+1)$

we can assume (x,y)≠ (-1/2, -1/2) since that point is not in the restriction, so

$\bf \lambda=\displaystyle\frac{2x}{(2x+1)} \;,\lambda=\displaystyle\frac{2y}{(2y+1)}\Rightarrow \displaystyle\frac{2x}{(2x+1)}=\displaystyle\frac{2y}{(2y+1)}\Rightarrow\\\\\Rightarrow 2x(2y+1)=2y(2x+1)\Rightarrow 4xy+2x=4xy+2y\Rightarrow\\\\\Rightarrow x=y$

Replacing in the constraint

$\bf (x+1/2)^2+(x+1/2)^2-25/2=0\Rightarrow (x+1/2)^2=25/4\Rightarrow\\\\\Rightarrow |x+1/2|=5/2$

from this we get

x=-1/2 + 5/2 = 2 or x = -1/2 - 5/2 = -3

and the candidates for maximum and minimum are (2,2) and (-3,-3).

Replacing these values in f, we see that

f(-3,-3) = 9+9 = 18 is the maximum and

f(2,2) = 4+4 = 8 is the minimum

Since the square of the distance from any given point (x,y) on the paraboloid to (0,0) is f(x,y) itself, the maximum and minimum of the distance are reached at the points we just found.

We have then,

(-3,-3) is the farthest from the origin

(2,2) is the closest to the origin.

3 0

3 years ago

2x^4y^-4 ————— 8x^7y^3

bazaltina [42]

Answer:

16x11/y (i hope)

Step-by-step explanation:

5 0

3 years ago