Is for today, algebrica members

Mathematics

1 answer:

arsen [322]2 years ago

5 0

Answer:

1. 11x + C

4. 5/14 x^2 + C

Step-by-step explanation:

When taking an integral of a one term power function, which means it has one number multiplied by an x t some power, so ax^b you use the power rule for integration.

ax^b becomes $\frac{ax^{b+1}}{b+1}$

So first you identify a and b and just plug in. I will walk you through all of them through the comments if you like, but here I am just going to solve one. Inf act I'll solve one that looks the hardest.

Number 4. We have (5/7)x. so a is 5/7 and b is 1. so just fill in.

$\frac{\frac{5}{7}x^{1+1} }{1+1}\\\frac{\frac{5}{7}x^{2} }{2}$

From here you can actually divide 5/7 by 2 and get 5/14 so the answer is 5/14 x^2 + c. Since these are indefinite integrals NEVER forget the constant C. Go ahead and try taking tis derivative though. Just remember C is a constant.

Also I wanted to mention, if you just have a number, so in number 1 it's ust 11, it is the same as 11x^0 so b is 0 in this case. So bonus, the answer to 11 is 11x + C. Never forget the C.

Let me know if there are any specifically you need help with, or you do want to work through all of them.

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what is the polynomial function of lowest degree with leading coefficient of 1 and roots 2 and 1 + square root2

Marta_Voda [28]

If the roots to such a polynomial are 2 and $1+\sqrt2$ , then we can write it as

$(x-2)(x-(1+\sqrt2))$

courtesy of the fundamental theorem of algebra. Now expanding yields

$(x-2)(x-1-\sqrt2)=x^2-2x-(1+\sqrt2)x+2(1+\sqrt2)=x^2-(3+\sqrt2)x+2+2\sqrt2$

which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.

So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use $1-\sqrt2$ as a root. In this case, that would make our polynomial

$(x-2)(x-(1+\sqrt2))(x-(1-\sqrt2))=x^3-4x^2+3x+2$

so that the answer is (probably) the third choice.

Whoever originally wrote this question should reevaluate their word choice...

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2 years ago

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365,987,784+365,987,784
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2 years ago

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Answer:

The answer is C