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3 years ago

Solve the equation using the Quadratic Formula. 2x(5x + 1) = 3

Mathematics

1 answer:

fomenos3 years ago

7 0

Answer:

2x(5x +1)=3

Step-by-step explanation:

2x(5x + 1) = 3

3 is the answer because 2x-5x=3 and 3*1=3

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I need help it’s hard

Reika [66]

9514 1404 393

Answer:

f^-1(x) = (x +4)/3

Step-by-step explanation:

The inverse function is found by swapping x and y, then solving for y.

y = 3x -4 . . . . . function y = f(x)

x = 3y -4 . . . . . inverse relation

x +4 = 3y . . . . add 4

(x +4)/3 = y . . . divide by 3. This is the inverse function

f^-1(x) = (x +4)/3

6 0

3 years ago

Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

4 0

3 years ago

which has a greater effect on the volume - changing the radius by a given amount or changing the height by the same amount/ why?

AURORKA [14]

Assuming we’re talking about a cylinder, whose volume formula is V = pi r^2 h…

It will have a greater effect to change a variable’s value that has a greater power on it.

Changing h from 1 to 2 doubles the volume.
Changing r from 1 to 4 quadruples the volume, because 1^2 = 1 and 2^2 = 4. The effect of the change on r is amplified by the power.

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horrorfan [7]

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3 years ago

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Factorize completely the following algebra expression : 81x^4-16y^8

ohaa [14]

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