Answer:
1) x= -36.
2) x = 0.
Step-by-step explanation:
1) Taking the 3rd power to both sides and using the following exponent law:
we get:
So this tells us that x = -36.
2) We can distribute the power inside every term. So the left side becomes:
Now, the trick here is to remember that , so replacing 1 with
, which then gives us:
, telling us that 3x = 0 and thus, x = 0.
The decimal representation of any number is a linear combination of powers of 10. In other words, given a number like 123.456, we can expand it as
for any
, so the above is the same as
Similarly, we can write
Now it's a question of reducing the fraction as much as possible. We have so
Answer:
.894
Step-by-step explanation:
First thing to do is to solve for the height of the triangle, BD. That's easy. We have the length of the hypotenuse and the base, so Pythagorean's Theorem gives us that the height is 8.003255588 which rounds nicely to 8. Now you have to call on the fond memories you have of the geometric mean in right triangles to solve the rest. For the sin of x you need the hypotenuse of that smaller right triangle on the left, side AB. First let's use geometric mean to find AD. The formula for that, now that we know the height, is
Filling that in with numbers we have
and
64 = 16(AD). Solve for AD to get that AD has a length of 4. Now we know two of the three sides in that smaller triangle on the left and can solve for the hypotenuse.
and
so
c=√80 which simplifies to 4√5. That means that the sin ratio for x is
which divides out to .894