Needed help with this question!

Mathematics

1 answer:

In-s [12.5K]3 years ago

5 0

A) is 2x
b) is $x^{3}$
c) is -2x

I think these are correct.
$log_{10}1000^{x] = log_{10}10^{2x}=2x$
I did similar things to get other answers
$1000^{log_{10}x} = 10^{3log_{10}x}=10^{log_{10}x^{3}}=x^{3}$

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4 0

3 years ago

Find all solutions to the equation:

crimeas [40]

Let z = sin(x). This means z^2 = (sin(x))^2 = sin^2(x). This allows us to go from the equation you're given to this equation: 7z^2 - 14z + 2 = -5

That turns into 7z^2 - 14z + 7 = 0 after adding 5 to both sides. Use the quadratic formula to solve for z. The only solution is z = 1 (see attached image). Since we made z = sin(x), this means sin(x) = 1. All solutions to this equation will be in the form x = (pi/2) + 2pi*n, which is the radian form of the solution set. If you need the degree form, then it would be x = 90 + 360*n

The 2pi*n (or 360*n) part ensures we get every angle coterminal to pi/2 radians (90 degrees), which captures the entire solution set.

Note: The variable n can be any integer.