What is the solution set of the inequality x5 + x4 - 6x3 + x2 + x

What is 1-2sin^2x=sinx Please show steps and find all solutions in interval [0,2pi)

Svetlanka [38]

Answer:

$\large\boxed{x=\dfrac{3\pi}{2}\ \vee\ x=\dfrac{\pi}{6}\ \vee\ x=\dfrac{5\pi}{6}}$

Step-by-step explanation:

$1-2\sin^2x=\sin x\\\\\text{substitute}\ t=\sin x,\ t\in[-1,\ 1]\\\\1-2t^2=t\qquad\text{subtract t from both sides}\\\\-2t^2-t+1=0\qquad\text{change the signs}\\\\2t^2+t-1=0\\\\2t^2+2t-t-1=0\\\\2t(t+1)-1(t+1)=0\\\\(t+1)(2t-1)=0\iff t+1=0\ \vee\ 2t-1=0\\\\t+1=0\qquad\text{subtract 1 from both sides}\\\boxed{t=-1}\\\\2t-1=0\qquad\text{add 1 to both sides}\\2t=1\qquad\text{divide both sides by 2}\\\boxed{t=\dfrac{1}{2}}$

$\sin x=-1\to x=-\dfrac{\pi}{2}+2k\pi,\ k\in\mathbb{Z}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}\\\\x\in[0,\ 2\pi)$

$x=-\dfrac{\pi}{2}\notin[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+2\pi=\dfrac{3\pi}{2}\in[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+4\pi=\dfrac{7\pi}{2}\notin[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}+2\pi=\dfrac{13\pi}{6}\notin[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}+2\pi=\dfrac{17\pi}{6}\notin[0,\ 2\pi)$

4 0

4 years ago

PLS HELP ASAP WILL GIVE BRAINLEAST

Ymorist [56]

Answer:

32

Step-by-step explanation:

8 0

3 years ago

What is the lateral area of the pyramid

Mkey [24]

Answer:

43.75 ft²

Step-by-step explanation:

$s_l$ = (l√(w/2)² + h²) + (w√(l/2)² + h²)

l & w become 3.5, and h becomes 6.

$s_l$ = (3.5√(3.5/2)² + 6²) + (3.5√(3.5/2)² + 6²)

Step 1:Because this is a square pyramid, what you see above essentially becomes what you see below.

$s_l$ = 2(3.5√(3.5/2)² + 6²)

Step 2: Divide 3.5 by 2 to get 1.75.

$s_l$ = 2(3.5√1.75² + 6²)

Step 3: Square both 1.75 and 6 to get 3.0625 and 36 respectively.

$s_l$ = 2(3.5√3.0625 + 36)

Step 4: Add 3.0625 and 36 to get 39.0625.

$s_l$ = 2(3.5√39.0625)

Step 5: The square root of 39.0625 is 6.25.

$s_l$ = 2(3.5 * 6.25)

Step 6: Multiply 3.5 by 6.25 to get 21.875.

$s_l$ = 2(21.875)

Step 7: Multiply 2 by 21.875 to get 43.75.

$s_l$ = 43.75 ft²

The lateral area of this pyramid is 43.75 ft².

3 0

3 years ago

For which of the inequalities below is v = 4 a solution? A v + 5 ≥ 9 B v + 5 > 9 C v + 5 < 8 D v + 5 ≤ 8

Setler79 [48]

B. 9-5=4. That's it.

5 0

3 years ago

In this figure triangle BAE is congruent to triangle DEA. Which statement is true by CPCTC?

Vsevolod [243]

The correct answer is the last option

5 0

3 years ago

Read 2 more answers

What is the solution set of the inequality x5 + x4 - 6x3 + x2 + x - 6 ≥ 0?