Identify this pair of angles

Evaluate rq2 + 3qr + r2 for r = 5 and q = 2

abruzzese [7]

Answer is 60 U need to calculate carefully with brackets involving multiplication

7 0

3 years ago

Find the average value of f over region

SVETLANKA909090 [29]

$D$ is a right triangle with base length 1 and height 8, so the area of $D$ is $\dfrac12(1)(8)=4$ .

The average value of $f(x,y)$ over $D$ is given by the ratio

$\dfrac{\displaystyle\iint_Df(x,y)\,\mathrm dA}{\displaystyle\iint_D\mathrm dA}$

The denominator is just the area of $D$ , which we already know. The average value is then simplified to

$\displaystyle\frac74\iint_Dxy\,\mathrm dA$

In the $x,y$ -plane, we can describe the region $D$ as all points $(x,y)$ that lie between the lines $y=0$ and $y=8x$ (the lines which coincide with the triangle's base and hypotenuse, respectively), taking $0\le x\le1$ . So, the integral is given by, and evaluates to,

$\displaystyle\frac74\int_{x=0}^{x=1}\int_{y=0}^{y=8x}xy\,\mathrm dy\,\mathrm dx=\frac78\int_{x=0}^{x=1}xy^2\bigg|_{y=0}^{y=8x}\,\mathrm dx$
$=\displaystyle56\int_{x=0}^{x=1}x^3\,\mathrm dx$
$=14x^4\bigg|_{x=0}^{x=1}$
$=14$

3 0

2 years ago

I need help with this work

Anton [14]

Answer:

Please find the answer in the image attached

Step-by-step explanation:

Here we are asked to solve a pair of linear inequalities.

In order to do so , we are first required to plot the two lines with inequalities taking into considerations.

Hence let us plot

x+2y=-4 and 5x+2y=4

let us first plot x+2y=-4

$y=\frac{-4-x}{2}$

let us plot a table for the same for two random values of x and putting them into above equation

x y

0 -2

2 -3

Let us now plot these points and join the line .

Let us check whether (0,0) satisfies the in equation or not

0+2(0)≤-4

0≤-4

Which is not true , Hence we shade the portion divided by our line which does not contain (0,0)

Now let us plot the second line 5x+2y=4

$y = \frac{4-5x}{2}$

let us plot a table for the same for two random values of x and putting them into above equation

x y

0 2

1 -0.5

Let us now plot these points and join the line .

Let us check whether (0,0) satisfies the in equation or not

5(0)+2(0)≤4

0≤4

Which is true , Hence we shade the portion divided by our line which does contain (0,0)

Please refer to the image attached with this answer.

now the commonly shaded area as shown in the image will be our solution to the above pair of in equations.

3 0

3 years ago

1,5,25,61.....<br>What's following number?

Lana71 [14]

Given:

1,5,25,61.....

To find:

The following number.

Solution:

We can see a pattern in the given sequence.

$(-1)^2+(0)^2=1+0=1$

$(1)^2+(2)^2=1+4=5$

$(3)^2+(4)^2=9+16=25$

$(5)^2+(6)^2=25+36=61$

Using this pattern the next term is the sum of squares of 7 and 8.

$(7)^2+(8)^2=49+64=113$

Therefore, the next number is 113.

3 0

2 years ago

Thea has a key on her calculator marked $\textcolor{blue}{\bf\circledast}$. If an integer is displayed, pressing the $\textcolor

ch4aika [34]

Answer:

$9$

Step-by-step explanation:

Given: Thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again such that the calculator displays final number as $243$.

To find: number that Thea originally entered

Solution:

The final number is $243$.

As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,

the number before $243$ must be $324$.

As previously the number was squared, so the number before $324$ must be $18$.

As previously the $\textcolor{blue}{\bf\circledast}$ key was pressed,

the number before $18$ must be $81$

As previously the number was squared, so the number before $81$ must be $9$.

4 0

3 years ago

Identify this pair of angles ​

Identify this pair of angles