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faust18 [17]
3 years ago
7

Evaluate Dx / ^ 9-8x - x2^

Mathematics
1 answer:
Solnce55 [7]3 years ago
4 0
It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for \sqrt x.

In that case, you want to find the antiderivative,

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}

Complete the square in the denominator:

9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2

Now substitute x+4=5\sin y, so that \mathrm dx=5\cos y\,\mathrm dy. Then

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy

which simplifies to

\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy

Now, recall that \sqrt{x^2}=|x|. But we want the substitution we made to be reversible, so that

x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)

which implies that -\dfrac\pi2\le y\le\dfrac\pi2. (This is the range of the inverse sine function.)

Under these conditions, we have \cos y\ge0, which lets us reduce \sqrt{\cos^2y}=|\cos y|=\cos y. Finally,

\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C

and back-substituting to get this in terms of x yields

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C
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What equation is solved by the graphed systems of equations? Two linear equations that intersect at the point negative 1, negati
GuDViN [60]

To solve this problem, we have to manually solve for the value of x for each choices or equations. The correct equation will give a value of -1 since the linear equations intersects at point (-1, -4).

<span>1st: 7x + 3 = x + 3</span>

7x – x = 3 – 3

6x = 0

<span>x = 0                (FALSE)</span>

 

<span>2nd: 7x − 3 = x – 3</span>

7x – x = 3 – 3

6x = 0

<span>x = 0                (FALSE)</span>

           

<span>3rd: 7x + 3 = x − 3</span>

7x – x = - 3 – 3

6x = -6

<span>x = -1               (TRUE)</span>

 

<span>4th: 7x − 3 = x + 3</span>

7x – x = 3 + 3

6x = 6

<span>x = 1                (FALSE)</span>

 

Therefore the answer is:

<span>7x + 3 = x − 3</span>

6 0
3 years ago
The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standar
Serggg [28]

Answer:

The 95% confidence interval is given by:

3.30<σ<8.76

Step-by-step explanation:

1) Data given and notation

s=4.798 represent the sample standard deviation

\bar x represent the sample mean

n=10 the sample size

Confidence=95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=10-1=9

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.025,9)" "=CHISQ.INV(0.975,9)". so for this case the critical values are:

\chi^2_{\alpha/2}=19.022

\chi^2_{1- \alpha/2}=2.700

And replacing into the formula for the interval we got:

\frac{(9)(4.798)^2}{19.022} \leq \sigma \frac{(9)(4.798)^2}{2.700}

10.892 \leq \sigma^2 \leq 76.736

Now we just take square root on both sides of the interval and we got:

3.30 \leq \sigma \leq 8.76

So the best option would be:

3.30<σ<8.76

7 0
3 years ago
I need help on this question
Flura [38]

Answer:

you are adding a dollar and 50 cents each time

Step-by-step explanation:

then find your y and x and plot it

6 0
3 years ago
Name the property used in: (5 + 2) + n = 7 + n
rjkz [21]
Additive indentity
(5 + 2) + n
n = 1
a variable is always a number itself remember 7+n
5+2 = 7
5 0
3 years ago
A survey found that 78% of students do their homework before 10:00 predict how many students out 975 do their homework before 10
GenaCL600 [577]
Hi Zahra, I've found a very simple and effective way of calculating percentages. 78% refers to 78 out of every 100, which can also be written as "0.78". Now, we can simply multiply 0.78 by your number (975) to get 760.5 students. Obviously, there isn't a half a student, so we round that number up to 761. So 761 out of 975 students do their homework before 10:00.
4 0
3 years ago
Read 2 more answers
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