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2 years ago

7-3x = -x+1 Simplify this equation

Mathematics

2 answers:

MatroZZZ [7]2 years ago

5 0

Answer: X=3

Step-by-step explanation:

<em>Rearrange terms</em> = −3

frozen [14]2 years ago

4 0

Answer:

x=11

Hope this helps :)

Step-by-step explanation:

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A frog is climbing out of a well that is 12-feet deep. The frog can climb 3 feet per hour but then it rests for an hour, during

vovangra [49]

Answer:

7 hours and 20 minutes.

Step-by-step explanation:

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3 years ago

Which function has an inverse that is a function?

Fudgin [204]

Answer:

Its going to be C on 2020 edg

Step-by-step explanation:

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3 years ago

Given that the measurement is in centimeters, find the area of the circle to the nearest tenth. (Use 3.14 for π)

kvv77 [185]

Answer:

Option D) 254.3 cm2

Step-by-step explanation:

we know that

The area of a circle is equal to

$A=\pi r^{2}$

we have

$r=9\ cm$

substitute

$A=(3.14)(9)^{2}=254.3\ cm^2$

7 0

3 years ago

Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.

Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
$f_x=5yz=0\implies y=0\text{ or }z=0$
$f_y=5xz=0\implies x=0\text{ or }z=0$
$f_z=5xy=0\implies x=0\text{ or }y=0$

Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

$L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)$

with partial derivatives (set to 0)

$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
$L_z=5xy+2\lambda z=0$
$L_\lambda=x^2+y^2+z^2-1=0$

We then observe that

$xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2$

So, ignoring the critical point we've already found at (0, 0, 0),

$5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}$
$5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}$
$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

5 0

3 years ago

A pump fills a pool at the rate of 20 cubic meters in an hour. If each cubic meter of water costs $10, how many minutes will the

fomenos

The first thing any good mathematician does is convert the measurements to the same unit as what the question is asking. In this problem, it states that the pool fills at a rate of 20 cubic meters per hour. Just keep in mind that an hour is 60 minutes.

The next step is to see how many cubic meters will cost $300. This can be done by dividing 300 by 10. This gets you 30 cubic meters of water.

You already know that 60 minutes is 20 cubic meters of water. That leaves the remaining 10 cubic meters of water. By dividing the rate given, you get that 30 minutes is 10 cubic meters of water. Add the 60 and 30 together to get 90 minutes.

It will take 90 minutes for the pump to use $300.

7 0

3 years ago