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3 years ago

Select the most precise name of quadrilateral MNOP given the coordinates of M, N, O, and P.

Mathematics

2 answers:

ryzh [129]3 years ago

4 0

Answer:

Parallelogram

Step-by-step explanation:

That dude above doesn't know what his talking about its parallelogram my teacher confirmed it too

Harman [31]3 years ago

3 0

Answer:

Square

Step-by-step explanation:

It has four coordinates which means four vertices which is four sides. Can also be a rectangle or parallelogram.

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Consider two circular swimming pools. Pool A has a radius of 22 feet, and Pool B has a diameter of 13.6 meters. Complete the des

Black_prince [1.1K]

Answer:

See below.

Step-by-step explanation:

Diameter of pool A = 2 * radius = 2 * 22

= 44 feet

= 44 * 0.305 = 13.42 meters.

The diameter of Pool B ( 13. 6 m) is greater than the diameter of Pool A.

The circumference of Pool A is 13.42 * pi = 42.16 m and that of B is 42.73 m, so that the circumference of Pool B is greater than that of Pool A by

0.57 m.

4 0

3 years ago

(6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Use an iterated integral to compute the vo

kipiarov [429]

Let $R$ be the ellipsoid with equation

$\left(\dfrac xa\right)^2+\left(\dfrac yb\right)^2+\left(\dfrac zc\right)^2=1$

so that the volume of $R$ is given by the triple integral

$\displaystyle\iiint_R\mathrm dV$

Consider the augmented spherical coordinates given by the identities

$\begin{cases}x=ar\cos u\sin v\\y=br\sin u\sin v\\z=cr\cos v\end{cases}$

Computing the Jacobian, we find that the volume element is given by

$\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=abcr^2\sin v\,\mathrm dr\,\mathrm du\,\mathrm dv$

so that the volume integral can be written as

$\displaystyle\iiint_R\mathrm dV=abc\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\int_{r=0}^{r=1}r^2\sin v\,\mathrm dr\,\mathrm du\,\mathrm dv=\frac{4abc\pi}3$

8 0

3 years ago

Find the polynomial function

laiz [17]

Answer:

y = 2x³ +x² -3x +6

Step-by-step explanation:

The polynomial correlation function of a graphing calculator can work with the table of function values to give you the equation. (See attached)

_____

If you want to solve this by hand, you can write the equations for the unknown coefficients in the polynomial function, then solve those. First of all, notice that you are given the y-intercept, (0, 6), so you know one of the coefficients already. That leaves a system of 3 equations in 3 unknowns that need to be solved.

___

<em>Writing the equations</em>

... ax³ +bx² +cx +6 = y . . . . the generic linear equation in a, b, c that you're writing

For x = -1:

... -a +b -c +6 = 8

For x = 1

... a + b + c + 6 = 6

For x = 2

... 8a +4b +2c +6 = 20

In augmented matrix terms, this set of linear equations looks like ...

$\left[\begin{array}{ccc|c}-1&1&-1&2\\1&1&1&0\\8&4&2&14\end{array}\right]$

___

<em>Solving the equations</em>

There are a number of ways to solve these. Again, a graphing calculator often has solution functions, such as reducing a matrix to row-echelon form, that will solve this in a keystroke or two.

If you add the first two equations, you get ...

... 2b = 2 ⇒ b = 1

Substituting that into the first equation allows you to simplify it to ...

... -a -c = 1

Dividing the third equation by 2 (and substituting for b) makes it ...

... 4a +c = 5

Adding these equations gives ...

... 3a = 6 ⇒ a = 2

Then ...

... c = -a -1 = -2 -1 = -3

And our polynomial function is ...

... y = 2x³ +x² -3x +6