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3 years ago

(a-b) (a+b)?? How do you solve this equation?

2 answers:

5 0

Distribute the first +a to the +a and multiply, then multiply the same +a and the +b and then multiply the -b and the +a and then the -b and the +b.

Hope this helped, if you have any more questions about this, just ask.

gregori [183]3 years ago

5 0

You can use a system called foil.
1. a*a= a^2
2. a*b= ab
3. -b*a= -ab
4. -b*b= -bb
a^2+ ab -ab-bb= a^2-bb
(Positive ab is canceled out by negative ab)

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Solve dis attachment and show all work ( I got it all wrong and I want to know how to solve it )

DedPeter [7]

(a) First find the intersections of $y=e^{2x-x^2}$ and $y=2$ :

$2=e^{2x-x^2}\implies \ln2=2x-x^2\implies x=1\pm\sqrt{1-\ln2}$

So the area of $R$ is given by

$\displaystyle\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}\left(e^{2x-x^2}-2\right)\,\mathrm dx$

If you're not familiar with the error function $\mathrm{erf}(x)$ , then you will not be able to find an exact answer. Fortunately, I see this is a question on a calculator based exam, so you can use whatever built-in function you have on your calculator to evaluate the integral. You should get something around 0.5141.

(b) Find the intersections of the line $y=1$ with $y=e^{2x-x^2}$ .

$1=e^{2x-x^2}\implies 0=2x-x^2\implies x=0,x=2$

So the area of $S$ is given by

$\displaystyle\int_0^{1-\sqrt{1-\ln2}}\left(e^{2x-x^2}-1\right)\,\mathrm dx+\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}(2-1)\,\mathrm dx+\int_{1+\sqrt{1-\ln2}}^2\left(e^{2x-x^2}-1\right)\,\mathrm dx$
$\displaystyle=2\int_0^{1-\sqrt{1-\ln2}}\left(e^{2x-x^2}-1\right)\,\mathrm dx+\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}\mathrm dx$

which is approximately 1.546.

(c) The easiest method for finding the volume of the solid of revolution is via the disk method. Each cross-section of the solid is a circle with radius perpendicular to the x-axis, determined by the vertical distance from the curve $y=e^{2x-x^2}$ and the line $y=1$ , or $e^{2x-x^2}-1$ . The area of any such circle is $\pi$ times the square of its radius. Since the curve intersects the axis of revolution at $x=0$ and $x=2$ , the volume would be given by

$\displaystyle\pi\int_0^2\left(e^{2x-x^2}-1\right)^2\,\mathrm dx$

5 0

3 years ago

What is the distance between 23 and -8 on a number line?

elena55 [62]

Answer: 31

Step-by-step explanation:

To find the distance, find the difference between the number.

23 - (-8) = 31 So the distance is 31 units.

Note: To go from -8 to 23 you will have to add 31 to -8 and to go from 23 to -8 you will have to subtract 31 so the distance is 31

7 0

4 years ago

Jason watched a caterpillar move 16 feet in 8 minutes. Jason says that the caterpillar's unit rate is 0.5 foot per minute. Is Ja

MrRa [10]

Answer:

Jason is incorrect.

The caterpillar's rate is 2 ft/min

Step-by-step explanation:

The rate of motion is defined as the quotient between the distance covered (in our case 16 feet) divided by the time it took to cover that distance (in our case 8 minutes)

Then, the rate is:

$rate=\frac{distance}{time} = \frac{16\,\,ft}{8\,\,min} = 2\,\frac{ft}{min}$

3 0

3 years ago

Hi please help,i really need it and so appreciate it:)

nadya68 [22]

Hey there!

12 ≥ 5f - 18

5f - 18 ≤ 12

ADD 18 to BOTH SIDES

5f - 18 + 18 ≤ 12 + 18

SIMPLIFY IT!

5f ≤ 30

DIVIDE 5 to BOTH SIDES

5f/5 ≤ 30/5

SIMPLIFY IT!

f ≤ 6

Therefore, your answer is: f ≤ 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

7 0

2 years ago

Is this a true statement?<br><br> <br> (-k) - 10k = -11k

marissa [1.9K]

Yes because if you solve it it will become -11k

8 0

3 years ago