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3 years ago

Explain the error in the following factorization. (20 Points)

Mathematics

1 answer:

juin [17]3 years ago

6 0

Answer:

It would not be x^2 -9^2. It would be x^2-9. That way you can facto it to make (x+3) and (x-3)

Step-by-step explanation:

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How do I solve the equation in an interval from 0 to 2π ? 9 cos 2t = 6

Ivahew [28]

$9\cos(2t)=6\implies\cos(2t)=\dfrac23$

Using the fact that cos is 2π-periodic, we have

$\cos(2t)=\dfrac23\implies2t=\cos^{-1}\left(\dfrac23\right)+2n\pi$

That is, $\cos(\theta+2n\pi)=\cos\theta$ for any $\theta$ and integer $n$ .

$\implies t=\dfrac12\cos^{-1}\left(\dfrac23\right)+n\pi$

We get 2 solutions in the interval [0, 2π] for $n=0$ and $n=1$ ,

$t=\dfrac12\cos^{-1}\left(\dfrac23\right)\text{ and }t=\dfrac12\cos^{-1}\left(\dfrac23\right)+\pi$

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3 years ago

Solving Multi-Step Equations

KengaRu [80]

$1.\\2n+3n+7=-41\\5n=-41-7\\5n=-48\\n=-48:5\\\boxed{n=-9.6}\\------------------\\2.\\2x-5x+6.3=-14.4\\-3x=-14.4-6.3\\-3x=-20.7\\x=(-20.7):(-3)\\\boxed{x=6.9}\\------------------$

$3.\\2z+9.75-7z=5.15\\-5z=5.15-9.75\\-5z=-4.6\\z=(-4.6):(-5)\\\boxed{z=0.92}\\------------------\\4.\\3h-5h+11=17\\-2h=17-11\\-2h=6\\h=6:(-2)\\\boxed{h=-3}\\------------------$

$5.\\2t+8-t=-3\\t=-3-8\\\boxed{t=-11}\\------------------\\6.\\6a-2a=-36\\4a=-36\\a=-36:4\\\boxed{a=-9}\\------------------$

$7.\\3c-8c+7=-18\\-5c=-18-7\\-5c=-25\\c=(-25):(-5)\\\boxed{c=5}\\------------------\\8.\\7g+14-5g=-8\\2g=-8-14\\2g=-22\\g=-22:2\\\boxed{g=-11}\\------------------$

$9.\\2b-6+3b=14\\5b=14+6\\5b=20\\b=20:5\\\boxed{b=4}\\------------------\\10.\\2(a-4)+15=13\\2a-8=13-15\\2a=-2+8\\2a=6\\a=6:2\\\boxed{a=3}\\------------------$

$11.\\7+2(a-3)=-9\\2a-6=-9-7\\2a=-16+6\\2a=-10\\a=-10:2\\\boxed{a=-5}\\------------------\\12.\\13+2(5c-2)=29\\10c-4=29-13\\10c=16+4\\10c=20\\c=20:10\\\boced{c=2}$

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3 years ago

What is the solution of n^2 - 49 = 0

Jlenok [28]

N² - 49 = 0
<u>   + 49 + 49</u>
      n² = 49
   n = <u>+</u>7

The solution to the problem is {7, -7}.

5 0

4 years ago

Read 2 more answers

CALCULUS EXPERT WANTED

Vlad [161]

a. Use the mean value theorem. 16 falls between 12 and 20, so

$v'(16)\approx\dfrac{v(20)-v(12)}{20-12}=\dfrac{240-200}8=5$

(Don't forget your units - 5 m/min^2)

b. $v(t)$ gives the Johanna's velocity at time $t$ . The magnitude of her velocity, or speed, is $|v(t)|$ . Integrating this would tell us the total distance she has traveled whilst jogging.

The Riemann sum approximates the integral as

$\displaystyle\int_0^{40}|v(t)|\,\mathrm dt=12\cdot200+8\cdot240+4\cdot220+16\cdot150=7600$

If you're not sure how this is derived: we're given 5 sample points, so we can cut the interval [0, 40] into 4 subintervals. The lengths of each subinterval are 12, 8, 4, and 16 (the distances between each sample point), and the height of the rectangle approximating the area under the plot of $|v(t)|$ is determined by the value of $v(t)$ at each sample point, 200, 240, |-220| = 220, and 150.

c. Bob's velocity is given by $B(t)$ , so his acceleration is given by $B'(t)$ . We have