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Naddik [55]
2 years ago
13

Need help finding intervals where the function is decreasing.

Mathematics
1 answer:
umka21 [38]2 years ago
8 0

f(x)=-5x-5\sin x\implies f'(x)=-5-5\cos x

f is decreasing on some interval (a,b) if f'(x) for all x\in(a,b). Similarly, f is increasing on (a,b) if f'(x)>0 for all x\in(a,b).

On the domain 0\le x\le2\pi, we have

-5-5\cos x=0\implies\cos x=-1\implies x=\pi

as the only critical point. So we need to check the sign of f' on two intervals, (0,\pi) and (\pi,2\pi).

On (0,\pi), pick any test value. Suppose we take x=\dfrac\pi2. Then f'\left(\dfrac\pi2\right)=-5, so f is decreasing on this interval.

On (\pi,2\pi), you'd find that f'>0, so f is increasing on this interval.

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A. y = 4x - 8
This equation is the only equation out of these that make a linear graph.
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2 years ago
List all possible rational roots. Then use synthetic division to confirm which rational roots exist:
Kisachek [45]

Answer:

\boxed{(1) \, x = \, \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10; (2) \, x = -2}

Step-by-step explanation:

2x³+ 6x² - x - 10 = 0

(1) Possible roots

The Rational Roots Theorem states that, if a polynomial has any rational roots, they will have the form p/q, where p is a factor of the constant term  and q is a factor of the leading coefficient.

\text{Possible rational root} = \dfrac{ p }{ q } = \dfrac{\text{factor of constant term}}{\text{factor of leading coefficient}}

In your function, the constant term is -10 and the leading coefficient is 2, so

\text{Possible root} = \dfrac{\text{factor of 10}}{\text{factor of 2}}

Factors of 10 = ±1, ±2, ±5, ±10

Factors of 2 = ±1, ±2

\text{Possible roots are } \large \boxed{\mathbf{x = \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10}}

(2) Synthetic division

Rather than work through all 12 possibilities, I will do one that works.

\begin{array}{r|rrrr}-2 & 2 & 6 & -1 & -10\\& & -4& -4 & 10\\& 2 & 2& -5 & 0\\\end{array}

So, x = -2 is a root, and the quotient is 2x² + 2x - 5.

(3) Check for other rational roots

2x² + 2x - 5 = 0

D = b² - 4ac =2²- 4(2)(-5) = 4 + 40 = 44

√44 = 2√11, which is irrational.

Since irrational roots come in pairs, the cubic equation has two real, irrational roots and one rational root at x = -2.

6 0
3 years ago
What's the answer to this​
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The answer is, y=-1x+9
4 0
3 years ago
Lauren bought a jacket that was on sale. She paid
Citrus2011 [14]

Answer:

$45

Step-by-step explanation:

40% of 75 is= 30

subtract 30-75=

45!!!

$45 is you answer

5 0
2 years ago
Read 2 more answers
A rectangle has a length of (6x+1) units and a width of (3x+1 units. Express the area of the rectangle as trinomial. Please I re
dimulka [17.4K]

whenever you have say a multiplication of a binomial or any polynomial, you can simply multiply each term of one by the other's terms, namely

(a+b)*(c+d+e)  => a(c+d+e) + b(c+d+e), and then add like-terms.

\bf \stackrel{length}{(6x+1)}\stackrel{width}{(3x+1)}\implies 6x(3x+1)+1(3x+1)\implies (18x^2+6x)~~+~~(3x+1) \\\\\\ 18x^2+6x+3x+1\implies \stackrel{\textit{adding like-terms}}{18x^2+9x+1}

8 0
3 years ago
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