How can knowing the greatest common factor and least common multiple help when adding subtracting and multiplying fractions

Sin(x2 y2 da r , where r is the region in the first quadrant between the circles with center the origin and radii 1 and 5

Rudik [331]

I assume there's a plus sign missing above...

Convert to polar coordinates, using

$\begin{cases}x(r,\theta)=r\cos\theta\\y(r,\theta)=r\sin\theta\end{cases}$

Then the Jacobian is

$\dfrac{\partial(x,y)}{\partial(r,\theta)}=\begin{vmatrix}x_r&y_r\\x_\theta&y_\theta\end{vmatrix}=\begin{vmatrix}\cos\theta&\sin\theta\\r\sin\theta&-r\cos\theta\end{vmatrix}=-r$

Then

$\mathrm dA=\mathrm dx\,\mathrm dy=|-r|\,\mathrm dr\,\mathrm d\theta=r\,\mathrm dr\,\mathrm d\theta$

so the integral can be written as

$\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^5r\sin(r^2)\,\mathrm dr\,\mathrm d\theta$

Let $s=r^2$ , so that $\dfrac{\mathrm ds}2=r\,\mathrm dr$ .

$\displaystyle\frac12\int_0^{\pi/2}\int_1^{25}\sin s\,\mathrm ds\,\mathrm d\theta=-\frac12(\cos25-\cos1)\int_0^{\pi/2}\mathrm d\theta=\frac\pi4(\cos1-\cos25)$

3 0

2 years ago

Find the unit rate. Enter your answer as a mixed number.

lesya [120]

The unit rate is the change of a quantity over one unit of another thus the unit rate of fertilizer covers is (30/8) foot per hour.

<h3>What is the rate of change?</h3>

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

As per the given,

A fertilizer covers 5/8 square feet in 1/6 hour.

5/8 square feet ⇒ 1/6 hour

Multiply both sides by 6

6 × 5/8 square feet ⇒ 6/6 hour

30/8 square feet ⇒ 1 hour.

Hence "The unit rate is the change of a quantity over one unit of another thus the unit rate of fertilizer covers is (30/8) foot per hour".

To learn more about the rate of change here,

brainly.com/question/12786410

#SPJ1

5 0

1 year ago

Olivia baked 16 mini-loaves of banana bread to be sliced for snacks at a craft fair. She will place an equal number of loaves in

lukranit [14]

Answer:

The number of whole loaves at each location = 5 loaves

Step-by-step explanation:

This problem is essentially testing your ability to use simple division within remainders, and the number of whole loaves is calculated as follows:

Numer of loaves of bread = 16

number of locations = 3

next, we will divide the number of loaves by the number of locations since Olivia placed an equal number of loaves in 3 different locations:

$= \frac{16}{3} = 5\frac{1}{3}$

This means that there will be 5 whole loaves and 1 loaf that will be divided equally into the three places.

Therefore, the number of whole loaves at each location = 5 loaves

<em>but remember that there will be a remainder of 1 loaf.</em>

4 0

3 years ago

NO LINKS!! Please help me with these graphs

Stella [2.4K]

Answer:

square: 9 square units
triangle: 24 square units

Step-by-step explanation:

Using a suitable formula the area of a polygon can be computed from the coordinates of its vertices. You want the areas of the given square and triangle.

<h3>Square</h3>

The spreadsheet in the first attachment uses a formula for the area based on the given vertices. It computes half the absolute value of the sum of products of the x-coordinate and the difference of y-coordinates of the next and previous points going around the figure.

For this figure, going to that trouble isn't needed, as a graph quickly reveals the figure to be a 3×3 square.

The area of the square is 9 square units.

<h3>Triangle</h3>

The same formula can be applied to the coordinates of the vertices of a triangle. The spreadsheet in the second attachment calculates the area of the 8×6 triangle.

The area of the triangle is 24 square units.

__

<em>Additional comment</em>

We have called the triangle an "8×6 triangle." The intention here is to note that it has a base of 8 units and a height of 6 units. Its area is half that of a rectangle with the same dimensions. These dimensions are readily observed in the graph of the vertices.

7 0

11 months ago

150 is 25% of what number? Four students solved this problem using equivalent ratios. Choose the student whose work is correct.

jenyasd209 [6]

Answer:

liam's answer is correct

Step-by-step explanation:

6 0

3 years ago

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