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Zigmanuir [339]
3 years ago
14

Hannah invested $540 in an account paying an interest rate of 4.7% compounded continuously. Assuming no deposits or withdrawals

are made, how much money, to the nearest hundred dollars, would be in the account after 18 years?
Mathematics
2 answers:
kumpel [21]3 years ago
3 0
I got $1,234 by the 18th year
alekssr [168]3 years ago
3 0

Answer:

1300

Step-by-step explanation:

did it on usatestprep

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16 boxes

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94+37=131

131/8=16.375

This means that the most possible boxes that they can fill is 16 boxes

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X-4 in word form <br> Please help!
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Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +
slava [35]
\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx

Taking x=7\tan\theta gives \mathrm dx=7\sec^2\theta\,\mathrm d\theta, so that the integral becomes

\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta
=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta
=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta
=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta
=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta

When \sec\theta>0, we have

=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta
=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta

and from here we can substitute u=\tan\theta to proceed from here.

Quick note: When we set x=7\tan\theta, we are implicitly enforcing -\dfrac\pi2 just so that the substitution can be undone later via \theta=\tan^{-1}\dfrac x7. But note that over this domain, we automatically guarantee that \sec\theta>0, so the absolute value bars can be dropped immediately.
6 0
3 years ago
Given the function f(x)=-8x2+8x+9,state whether the vertex represents a maximum or minimum point for the function.
Lelechka [254]
8x2+8x+9
=16x+8x+9
=24x+9
Are that right
5 0
3 years ago
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