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12345 [234]
3 years ago
12

how much would $100 invested at 6% interest compounded mothly be worth after 20 years? round answer to the nearest cent

Mathematics
2 answers:
murzikaleks [220]3 years ago
7 0

Answer:

He's right. It's 331.02

Step-by-step explanation:

Soloha48 [4]3 years ago
6 0
Alright, so in order to solve this problem, you need to know the formula for compound interest, which is 
A= P(1+r/n)^nt
A is the final amount, P is the beginning amount, r is the rate it is being compounded at, n is the number of compounds per year, and t is obviously the time or number of years

Since it is compounded monthly, n will equal 12, as there are 12 months in a year.

Plug in what you have and you get A= 100 (1 + .06/12)^(12)(20)
A=331.02
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A vector with magnitude 9 points in a direction 190 degrees counterclockwise from the positive x axis. Write in component form
Over [174]

Answer:

\vec{v}= \text{ or } \approx

Step-by-step explanation:

Component form of a vector is given by \vec{v}=, where i represents change in x-value and j represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector \vec{v}=, the magnitude is ||v||=\sqrt{i^2+j^2.

190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being i, one leg being j, and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.

In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.

Therefore, we have:

\sin 10^{\circ}=\frac{j}{9},\\j=9\sin 10^{\circ}

To find the other leg, i, we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:

\cos 10^{\circ}=\frac{i}{9},\\i=9\cos 10^{\circ}

Verify that (9\sin 10^{\circ})^2+(9\cos 10^{\circ})^2=9^2\:\checkmark

Therefore, the component form of this vector is \vec{v}=\boxed{}\approx \boxed{}

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