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Natasha_Volkova [10]
3 years ago
12

Jack invests $500 at a certain annual Interest rate, and he invests another $2000 at an annual rate that is one-half percent hig

her. If he receives a total of $210 Interest in 1 year, at what
rate is the $500 Invested?
Mathematics
1 answer:
MrRa [10]3 years ago
3 0

Answer:

8%

Step-by-step explanation:

So we have two investments.  The first is 500 with an interest rate of x while 2000 has an interest rate of x+.005 (.005 is .5 %),

annual interest means it gets interest once a year, it then says in total, after one year, so one time getting interest he gets 210 total, so in total the money is 500 + 2000 + 210.  So let's set up an equation with all this

500x + 2000(x+.005) = 2710

500x + 2000x + 10 = 2710

2500x = 2700

x = 1.08

So that means we multiply 500 by 1.08, which represents 8% and 2000 by 1.085.  But the question is just asking for the interest rate for 500 so the answer is 8%

If you don't understand how I did anything let me know.

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3 years ago
(I've been trying to figure this out for 3 days and I really need help)
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Check the picture below.

since the diameter of the cone is 6", then its radius is half that or 3", so getting the volume of only the cone, not the top.

1)

\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\cfrac{\pi (3)^2(4)}{3}\implies V=12\pi \implies V\approx 37.7

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\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=3 \end{cases}\implies V=\cfrac{4\pi (3)^3}{3}\implies V=36\pi \\\\\\ \stackrel{\textit{half of that for a semisphere}}{V=18\pi }\implies V\approx 56.55

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pretty much the same thing, we get the volume of the cone and its top, add them up.

\bf \stackrel{\textit{cone's volume}}{\cfrac{\pi (3)^2(8)}{3}}~~~~+~~~~\stackrel{\stackrel{\textit{half a sphere}}{\textit{top's volume}}}{\cfrac{4\pi 3^3}{3}\div 2}\implies 24\pi +18\pi \implies 42\pi ~~\approx~~131.95~in^

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