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2 years ago

Which relationships describe angles 1 and 2?

Mathematics

1 answer:

Vesna [10]2 years ago

7 0

Answer:

angles one and two are supplementary angles and adjacent angles

Step-by-step explanation:

Definitions:

Supplementary angles: two angles that add to 180 deg

Adjacent angles: two angles that have a common side and a common vertex (corner point) and don't overlap

complementary angles: two angles that add up to 90 deg

vertical angles: two angles that are directly opposite from each other, formed by intersecting lines

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There are 100 students at a college who have taken a course in calculus, 110 who have taken a course in discrete mathematics, an

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Answer:

110 students

Step-by-step explanation:

The number of students who have only taken calculus is given by the number of students who have taken calculus minus the students who have taken both classes:

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2 years ago

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

seropon [69]

Answer:

$h'(x)=\frac{3r^{2}}{2\sqrt{r^3+5}}$

Step-by-step explanation:

1) The Fundamental Theorem of Calculus in its first part, shows us a reciprocal relationship between Derivatives and Integration

$g(x)=\int_{a}^{x}f(t)dt \:\:a\leqslant x\leqslant b$

2) In this case, we'll need to find the derivative applying the chain rule. As it follows:

$h(x)=\int_{a}^{x^{2}}\sqrt{5+r^{3}}\therefore h'(x)=\frac{\mathrm{d} }{\mathrm{d} x}\left (\int_{a}^{x^{2}}\sqrt{5+r^{3}}\right )\\h'(x)=\sqrt{5+r^{3}}\\Chain\:Rule:\\F'(x)=f'(g(x))*g'(x)\\h'=\sqrt{5+r^{3}}\Rightarrow h'(x)=\frac{1}{2}*(r^{3}+5)^{-\frac{1}{2}}*(3r^{2}+0)\Rightarrow h'(x)=\frac{3r^{2}}{2\sqrt{r^3+5}}$

3) To test it, just integrate:

$\int \frac{3r^{2}}{2\sqrt{r^3+5}}dr=\sqrt{r^{3}+5}+C$

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2 years ago