The formula d = 16t gives the distance d, in feet, that an object has fallen t seconds after it is

Arte-miy333 [17]

$208:2=104\\104:2=52\\52:2=26\\26:2=13\\13:13=1\\\\208=2\cdot2\cdot2\cdot2\cdot13=2^2\cdot2^2\cdot13\\\\\sqrt{208}=\sqrt{2^2\cdot2^2\cdot13}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{13}=2\cdot2\cdot\sqrt{13}=4\sqrt{13}\\\\Answer:\ \sqrt{208}=4\sqrt{13}\\\\Used:\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a$

6 0

3 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:

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

5 0

2 years ago

In the diagram below, xy and yz are tangent to O. What is the measure of angle y

Tatiana [17]

If we draw in OX, OY, OZ we have two congruent right triangles, right angles at the tangent points.

We know XOZ is 132 degrees, which is the meaning of the arc measure

So YOX is half that, 66 degrees.

That leaves 180 - 90 - 66 = 24 degrees for OYX

Angle Y aka XYZ is double that, 48 degrees.

Answer: C

4 0

3 years ago

Read 2 more answers

How to learn the ratio of standard angles of right angled triangle [ like sin 90=?, cos 30=?]....??

lawyer [7]

Answer:

just learn the sin value of all the degrees

the cos values are opposite to the sin values example sin 30 degree = cos 60 degrees. and sin 45 and cos 45 remains same . use the same logic for tan and cot and also for sec and cosec . tan values are sin degrees / cos degrees

3 0

3 years ago

Juan's 3 math quizzes this week took him 1/3 hour, 4/6 hour, and 1/5 hour to complete. Which list shows the lengths of time from

Marysya12 [62]

The order from least to greatest would be 1/5, 1/3, then 4/6.

To solve, multiply the fractions so that they all have the same denominator. I multiplied the 1/3 by 10, 1/5 by 6, and 4/6 by 5. After they all have a common denominator, you can easily order them from the numerator.

10(1/3) = 10 / 30
6(1/5) = 6 / 30
5(4/6) = 20 / 30
6/30, 10/30, 20/30

Hope this helps! :)

7 0

2 years ago