Since Sydney has planted 5/9 of her flowers and there were 63 flowers that are left unplanted, the first thing we are going to determine is the number of flowers that were planted. To do this, we just have to do the cross multiplication process.
So 5/9 x ?/63 = 35. Therefore, the number of plants planted were 35. To start, Sydney has a total of 100 flowers to be planted. That would be 35 + 65 is 100.

6 0

3 years ago

Y=x.arctan(x)^1/2. find dy/dx. pls show steps

Whitepunk [10]

$y=x(\arctan x)^{1/2}$

Use the product rule first:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dx}{\mathrm dx}(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

Use the chain rule to compute the derivative of $(\arctan x)^{1/2}$ . Let $z=(\arctan x)^{1/2}$ and take $u=\arctan x$ , so that by the chain rule

$\dfrac{\mathrm dz}{\mathrm dx}=\dfrac{\mathrm dz}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx}$

$\dfrac{\mathrm dz}{\mathrm du}=\dfrac{\mathrm du^{1/2}}{\mathrm du}=\dfrac12u^{-1/2}$

$\dfrac{\mathrm du}{\mathrm dx}=\dfrac{\mathrm d\arctan x}{\mathrm dx}=\dfrac1{1+x^2}$

$\implies\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}(1+x^2)}$

So we have

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+\dfrac x{2(\arctan x)^{1/2}(1+x^2)}$

You can rewrite this a bit by factoring $(\arctan x)^{-1/2}$ , just to make it look neater:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}}\left(2\arctan x+\dfrac x{1+x^2}\right)$

3 0

3 years ago

What two numbers multiplied together equal -36 but then added together equal 16

larisa86 [58]

18 and -2! 18(-2)= -36 and 18-2=16

8 0

3 years ago

Read 2 more answers

A small tree was planted at a height of 10 feet. The tree has been planted for 14 months, and is now 56.2 feet tall. Which equat

Natali5045456 [20]

The equation that could be used to find x, the average number of feet the tree grew each month is; 14x + 10 = 56.2

<h3>Algebra Word Problems</h3>

We are told that the tree was planted at a height of 10 ft.

Period for which tree was planted = 14 months

Height of tree after 14 months = 56.2 ft.

Thus, if x is the average number of feet the tree grew each month, then the equation to find x is;

14x + 10 = 56.2

Read more about algebra word problems at; brainly.com/question/21405634

8 0

3 years ago