Step-by-step explanation: You are trying to isolate the variable, x, so you have to subtract 1 on both sides of the inequality. Then, you are left with x < 4.

4 0

3 years ago

Show Work Please Thank You

Misha Larkins [42]

Answer:

$\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}$

Step-by-step explanation:

We are given the trigonometric equation of:

$\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}$

Let u = 4x then:

$\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}$

Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).

$\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}$

Convert u-term back to 4x:

$\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}$

Divide both sides by 4:

$\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}$

The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.

Therefore:

$\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}$

8 0

2 years ago

boxes of a whole wheat linguine are on sale this week for 30% off the original price. they cost $1.50 when they are not on sale.

allochka39001 [22]

30% of $1.50 is 0.45 and if it's on sale you subtract from original price
so 1.50 - 0.45
and your answer would be $1.05

4 0

3 years ago

4) Solve for x: 2x=8.

MatroZZZ [7]

4) x=4 -> divide by 2
5) y=9 -> add 2
6) z=2 -> multiply 2 times 1
7) a=10 -> add 7 then divide by 3
8) b=3 -> distributive property, add 1 to other side, and then divide by 8
9) c= -d +4 -> subtract +d+1 and put on other side to solve
10) m= 10/p+2 -> distrubutive property, subtract 2m on both sides to solve

8 0

3 years ago