Use order of operations to solve the equation

Which is true about the completely simplified difference of the polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5?

Galina-37 [17]

<span>Let be A= 6x6 − x3y4 − 5xy5 and B= 4x5y + 2x3y4 + 5xy5 and when we do their difference, it is A - B = 6x6 − x3y4 − 5xy5 -( 4x5y + 2x3y4 + 5xy5)=6x6 − x3y4 − 5xy5 - 4x5y - 2x3y4 - 5xy5 = 6x6 - x3y4 - 2x3y4 - 5xy5 -4xy5 -5xy5=6x6 - 3x3y4 -14xy5, so the final solution is A - B =6x6 - 3x3y4 -14xy5, the degree of this is equal to the degree of - 3x3y4, and it is 3+4=7, the answer is The difference has 3 terms and a degree of 7.</span>

8 0

2 years ago

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Y is between X and Z on a line. XZ = 15 and XY = 10. What is the length of YZ?

Mariulka [41]

Answer:

5

Step-by-step explanation:

if xz is 15 and xy is 10 then we can infer that z is 10 and x is 5

3 0

2 years ago

Using Cramer's Rule, what are the values of x and y in the solutio

olya-2409 [2.1K]

Answer:

x = -3, y = 1

Step-by-step explanation:

To find the value of x and y, find the determinant of original matrix, which would be 21.

Then, substitute the value of x with the solutions to the equations and find the determinant of that matrix, which is -63.

Cramer's rule says that Dx ÷ D is the value of x. So, -63 ÷ 21 = -3.

So, the x-value is -3.

You can find the determinant of the y-value in the same way, and you'll find out that y = 1.

Hope this helped! :)

8 0

2 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$