We have divided by two this is because you know the are of a rectangle is base + height but a triangle is like cut rectangle into two half pieces of you look carefully than to make any traingle a rectangle you will have to take another on opposite side so that's why we divide it by two

If you need further help plz ask

8 0

3 years ago

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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

A baker has 5 1/4 pies in her shop. She cut the pies in pieces that are each 1/8 of a whole pie.

Inessa05 [86]

Knowing that 1 = 8/8
this means 5 = 40/8
1/4 = 2/8

add 40/8 + 2/8 to get 42/8

this means she will have 42 pieces of pie

8 0

2 years ago

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