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3 years ago

123.456 RONDED TO THE NEAREST HUNDREDTH.

Mathematics

2 answers:

anzhelika [568]3 years ago

8 0

123.456 RONDED TO THE NEAREST HUNDREDTH.

Answer:

123.46

Rus_ich [418]3 years ago

8 0

Answer:

123.46 is probably the answer

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<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B8%7D%20x%20%20%2B%2012%20%3D%20x%20-%209" id="TexFormula1" title=" \frac{1

elixir [45]

Answer: X = 24

Explanation:

1/8x + 12 = x - 9
12 = 7/8x - 9
21 = 7/8x
X = 24

6 0

3 years ago

Read 2 more answers

Determine whether the integral converges.

Kryger [21]

You have one mistake which occurs when you integrate $\dfrac1{1-p^2}$ . The antiderivative of this is not in terms of $\tan^{-1}p$ . Instead, letting $p=\sin r$ (or $\cos r$ , if you want to bother with more signs) gives $\mathrm dp=\cos r\,\mathrm dr$ , making the indefinite integral equality

$\displaystyle-\frac12\int\frac{\mathrm dp}{1-p^2}=-\frac12\int\frac{\cos r}{1-\sin^2r}\,\mathrm dr=-\frac12\int\sec r\,\mathrm dr=\ln|\sec r+\tan r|+C$

and then compute the definite integral from there.

$-\dfrac12\ln|\sec r+\tan r|\stackrel{r=\sin^{-1}p}=-\dfrac12\ln\left|\dfrac{1+p}{\sqrt{1-p^2}}=\ln\left|\sqrt{\dfrac{1+p}{1-p}}\right|$
$\stackrel{p=u/2}=-\dfrac12\ln\left|\sqrt{\dfrac{1+\frac u2}{1-\frac u2}}\right|=-\dfrac12\ln\left|\sqrt{\dfrac{2+u}{2-u}}\right|$
$\stackrel{u=x+1}=-\dfrac12\ln\left|\sqrt{\dfrac{3+x}{1-x}}\right|$
$\implies-\dfrac12\displaystyle\lim_{t\to\infty}\ln\left|\sqrt{\dfrac{3+x}{1-x}}\right|\bigg|_{x=2}^{x=t}=-\frac12\left(\ln|-1|-\ln\left|\sqrt{\frac5{-1}}\right|\right)=\dfrac{\ln\sqrt5}2=\dfrac{\ln5}4$

Or, starting from the beginning, you could also have found it slightly more convenient to combine the substitutions in one fell swoop by letting $x+1=2\sec y$ . Then $\mathrm dx=2\sec y\tan y\,\mathrm dy$ , and the integral becomes

$\displaystyle\int_2^\infty\frac{\mathrm dx}{(x+1)^2-4}=\int_{\sec^{-1}(3/2)}^{\pi/2}\frac{2\sec y\tan y}{4\sec^2y-4}\,\mathrm dy$
$\displaystyle=\frac12\int_{\sec^{-1}(3/2)}^{\pi/2}\csc y\,\mathrm dy$
$\displaystyle=-\frac12\ln|\csc y+\cot y|\bigg|_{y=\sec^{-1}(3/2}}^{y=\pi/2}$
$\displaystyle=-\frac12\lim_{t\to\pi/2^-}\ln|\csc y+\cot y|\bigg|_{y=\sec^{-1}(3/2)}^{y=t}$
$\displaystyle=-\frac12\left(\lim_{t\to\pi/2^-}\ln|\csc t+\cot t|-\ln\frac5{\sqrt5}\right)$
$=\dfrac{\ln\sqrt5}2-\dfrac{\ln|1|}2$
$=\dfrac{\ln5}4$

Another way to do this is to notice that the integrand's denominator can be factorized.

$x^2+2x-3=(x+3)(x-1)$

So,

$\dfrac1{x^2+2x-3}=\dfrac1{(x+3)(x-1)}=\dfrac14\left(\dfrac1{x-1}-\dfrac1{x+3}\right)$

There are no discontinuities to worry about since you're integrate over $[2,\infty)$ , so you can proceed with integrating straightaway.

$\displaystyle\int_2^\infty\frac{\mathrm dx}{x^2+2x-3}=\frac14\lim_{t\to\infty}\int_2^t\left(\frac1{x-1}-\frac1{x+3}\right)\,\mathrm dx$
$=\displaystyle\frac14\lim_{t\to\infty}(\ln|x-1|-\ln|x+3|)\bigg|_{x=2}^{x=t}$
$=\displaystyle\frac14\lim_{t\to\infty}\ln\left|\frac{x-1}{x+3}\right|\bigg|_{x=2}^{x=t}$
$=\displaystyle\frac14\left(\lim_{t\to\infty}\ln\left|\frac{t-1}{t+3}\right|-\ln\frac15\right)$
$=\displaystyle\frac14\left(\ln1-\ln\frac15\right)$
$=-\dfrac14\ln\dfrac15=\dfrac{\ln5}4$

Just goes to show there's often more than one way to skin a cat...

7 0

3 years ago

Solve for y <br> 5y-x=10<br><br> Is it 2?

svet-max [94.6K]

5y-x=10
Isolate the variable
add x to both sides
5y-x+x=10+x
5y=10+x
Divide both sides by 5
5y/5=10+x/5
y=2+1/5x
So y is equal to 2+1/5x

5 0

3 years ago

Triangles Q R S and T U V are shown. Triangle Q R S is translated across S Q and then is shifted down and to the right to form t

makkiz [27]

Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV.

<h3>What is translation?</h3>

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Given:

△QRS and △TUV is translated across SQ and then is shifted down and to the right to form △TUV.

So, translation mapping vertex Q to vertex T is done and a reflection across the line containing QS will map △QRS to △TUV.

Learn more about this translation here:

brainly.com/question/17485121

#SPJ1

8 0

2 years ago

Joanne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months there is $300 in the

Dimas [21]

The constant rate is 50 dollars per month. I hope this helps!

6 0

3 years ago

Read 2 more answers