In preparation for a conference, Toby is setting up some stations where people can create

Find the area bounded by the curve y = x1/2 + 2 the x - axis, and the lines x = 1 and x = 4?

Serggg [28]

The area is given by

$\displaystyle\int_1^4(x^{1/2}+2)\,\mathrm dx=\left(\frac23x^{3/2}+2x\right)\bigg|_{x=1}^{x=4}=\dfrac{40}3-\dfrac83=\dfrac{32}3=10+\dfrac23$

so the answer is B

8 0

3 years ago

Write the following numbers used in these statements in scientific notation. (Note: Some of these numbers have been rounded.)

lutik1710 [3]

Answer:

So in scientific form 4000 miles will be equal to $4\times 10^3miles$

Step-by-step explanation:

We have given that radius of earth is 4000 miles

4000 miles can be written as 4×1000

We have to written 4000 miles in scientific form

We know that 1000 can be written in scientific form as $1000=10^3$

So $4000miles =4\times 1000=4\times 10^3miles$

So in scientific form 4000 miles will be equal to $4\times 10^3miles$

5 0

3 years ago

The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent

stiks02 [169]

Answer:

The fraction of the area of ACIG represented by the shaped region is 7/18

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the square ABED find the length side of the square

we know that

AB=BE=ED=AD

The area of s square is

$A=b^{2}$

where b is the length side of the square

we have

$A=49\ units^2$

substitute

$49=b^{2}$

$b=7\ units$

therefore

$AB=BE=ED=AD=7\ units$

step 2

Find the area of ACIG

The area of rectangle ACIG is equal to

$A=(AC)(AG)$

substitute the given values

$A=(9)(10)=90\ units^2$

step 3

Find the area of shaded rectangle DEHG

The area of rectangle DEHG is equal to

$A=(DE)(DG)$

we have

$DE=7\ units$

$DG=AG-AD=9-7=2\ units$

substitute

$A=(7)(2)=14\ units^2$

step 4

Find the area of shaded rectangle BCFE

The area of rectangle BCFE is equal to

$A=(EF)(CF)$

we have

$EF=AC-AB=10-7=3\ units$

$CF=BE=7\ units$

substitute

$A=(3)(7)=21\ units^2$

step 5

sum the shaded areas

$14+21=35\ units^2$

step 6

Divide the area of of the shaded region by the area of ACIG

$\frac{35}{90}$

Simplify

Divide by 5 both numerator and denominator

$\frac{7}{18}$

therefore

The fraction of the area of ACIG represented by the shaped region is 7/18

5 0

3 years ago

How do i find the slope

Elodia [21]

Hi, I'm happy to help!

To find the slope, you need to use the slope formula, where m is the slope:

m= $\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }$

Slope means rise over run, or how much the line rises per the amount the line moves forward. This equation shows the movement from the y points to show rise, over the difference in the x points to show run.

Now, to find the slope we insert our values, starting with our second y point:

m= $\frac{2-y_{1 } }{x_{2} -x_{1} }$

Now insert our first y point:

m= $\frac{2-4 }{x_{2} -x_{1} }$

Now we insert our second x point:

m= $\frac{2-4 }{-3 -x_{1} }$

And finally our first x point:

m= $\frac{2-4 }{-3 -3 }$

Now, we solve:

m= $\frac{-2 }{-6}$

So, our slope is -2/-6, to simplify it, we remove both negatives because they cancel each other out.

m= $\frac{2 }{6}$

Now, we simplify our fraction by dividing the top and bottom by 2:

m= $\frac{1}{3}$

So, our slope is 1/3. This means that for every 1 unit the line rises, it goes to the right 3 units. The y-intercept is where the line hits the y axis.

If the question is asking for slope intercept form for the equation, you use y=mx+b

y represents any y coordinate on your line, m represents your slope (1/3), x represents any x coordinate on your line, and b represents your y-intercept (3).

If you were to insert these values, you would get:

y= $\frac{1}{3}$ x+3

You use this to find what a y coordinate would be so you can draw your line.

For the next equation we do the same thing:

m= $\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }$

Insert our values:

m= $\frac{4-1}{2-(-4)}$

Get rid of the double negative:

m= $\frac{4-1}{2+4}$

Solve:

m= $\frac{3}{6}$

Simplify:

m= $\frac{1}{2}$

Now that we know our slope, let's plug it in to our slope intercept form equation.

y= $\frac{1}{2}$ x+3

I hope this was helpful! Keep learning! :D

5 0

3 years ago

If sin A = 6 over 13, then which of the following is correct?

Inessa [10]

Answer is B. CSC A= 13 over 6
You need to learn these basic rules:
Sin is opposite csc
Cos is opposite sec
Tan is opposite Cot
In saying this, CsC is the reciprocal for Sin. You would have to switch the numerator and denominatior to get your answer

4 0

3 years ago