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charle [14.2K]
3 years ago
12

Is the difference of two polynomials always a polynomial? Explain..

Mathematics
1 answer:
gregori [183]3 years ago
8 0
No, most of the time yes unless the difference contains a negative exponent.

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Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25-cent coins that he can use to pay her. Wha
kykrilka [37]
So, what is the case in which he uses the least coins? can he use 1 coin? no, there isn't a 35 cent coin. can he use 2 coins? yes! he can use 25+10 cent coins!

now, the largest number of coins means the coins of the smallest value: so using only 5 cent coins. How many would this be?

we have to divide:

35/5=7

so we would use 7 coins.

And the difference is 5: 7-2 is 5.
6 0
3 years ago
Simplify the expression. tan(sin^−1 x)
Blizzard [7]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2799412

_______________


Let  \mathsf{\theta=sin^{-1}(x)\qquad\qquad-\dfrac{\pi}{2}\ \textless \ \theta\ \textless \ \dfrac{\pi}{2}.}

(that is the range of the inverse sine function).


So,

\mathsf{sin\,\theta=sin\!\left[sin^{-1}(x)\right]}\\\\ \mathsf{sin\,\theta=x\qquad\quad(i)}


Square both sides:

\mathsf{sin^2\,\theta=x^2\qquad\qquad(but~sin^2\,\theta=1-cos^2\,\theta)}\\\\ \mathsf{1-cos^2\,\theta=x^2}\\\\ \mathsf{1-x^2=cos^2\,\theta}\\\\ \mathsf{cos^2\,\theta=1-x^2}


Since \mathsf{-\,\dfrac{\pi}{2}\ \textless \ \theta\ \textless \ \dfrac{\pi}{2},} then \mathsf{cos\,\theta} is positive. So take the positive square root and you get

\mathsf{cos\,\theta=\sqrt{1-x^2}\qquad\quad(ii)}


Then,

\mathsf{tan\,\theta=\dfrac{sin\,\theta}{cos\,\theta}}\\\\\\ \mathsf{tan\,\theta=\dfrac{x}{\sqrt{1-x^2}}}\\\\\\\\ \therefore~~\mathsf{tan\!\left[sin^{-1}(x)\right]=\dfrac{x}{\sqrt{1-x^2}}\qquad\qquad -1\ \textless \ x\ \textless \ 1.}


I hope this helps. =)


Tags:  <em>inverse trigonometric function sin tan arcsin trigonometry</em>

3 0
3 years ago
Read 2 more answers
Need help on this ASAP
vodomira [7]
76 granola bars
to solve this, you need to multiply 15 by 5 for the big boxes and 8 by 2 for the small boxes. 15 x 2 = 60 and 8 x 2 = 16, therefore adding them together gets you 76.
8 0
3 years ago
Help on number 20 please?​
adell [148]

Answer:

1/8

Step-by-step explanation:

P(-3, 0) and Y(5,-1)

If PLAY is reflected over x-axis, then P-->P'(-3,0) and Y-->Y'(5,1)

Slope of P'Y' = (1 - 0)/(5+3) = 1/8

8 0
3 years ago
Why is the square root of 144 rational
Vitek1552 [10]
The square root of 144= 12. 12 is an integer, integers are always rational since they can be written into a fraction.
7 0
3 years ago
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