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3 years ago

A box of toy cars contains blue, orange, yellow, red, and black

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

5 0

Answer:

Step-by-step explanation:

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It takes layla 2/5 hour to swim 1/2 mile what is the unit rate of miles that layla can swim per hour

Mazyrski [523]

Good Morning!

Distance = rate x time

1/2 mile = R x 2/5 hour

1/2=2/5R

/2/5 /2/5

R=1/2 x 5/2

R=1 1/4

She can swim 1 1/4 per hour.

I hope this helps! :)

4 0

3 years ago

B) Let g(x) =x/2sqrt(36-x^2)+18sin^-1(x/6)<br><br> Find g'(x) =

jolli1 [7]

I suppose you mean

$g(x) = \dfrac x{2\sqrt{36-x^2}} + 18\sin^{-1}\left(\dfrac x6\right)$

Differentiate one term at a time.

Rewrite the first term as

$\dfrac x{2\sqrt{36-x^2}} = \dfrac12 x(36-x^2)^{-1/2}$

Then the product rule says

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 x' (36-x^2)^{-1/2} + \dfrac12 x \left((36-x^2)^{-1/2}\right)'$

Then with the power and chain rules,

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12\left(-\dfrac12\right) x (36-x^2)^{-3/2}(36-x^2)' \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} - \dfrac14 x (36-x^2)^{-3/2} (-2x) \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12 x^2 (36-x^2)^{-3/2}$

Simplify this a bit by factoring out $\frac12 (36-x^2)^{-3/2}$ :

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-3/2} \left((36-x^2) + x^2\right) = 18 (36-x^2)^{-3/2}$

For the second term, recall that

$\left(\sin^{-1}(x)\right)' = \dfrac1{\sqrt{1-x^2}}$

Then by the chain rule,

$\left(18\sin^{-1}\left(\dfrac x6\right)\right)' = 18 \left(\sin^{-1}\left(\dfrac x6\right)\right)' \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac x6\right)'}{\sqrt{1 - \left(\frac x6\right)^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac16\right)}{\sqrt{1 - \frac{x^2}{36}}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{3}{\frac16\sqrt{36 - x^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18}{\sqrt{36 - x^2}} = 18 (36-x^2)^{-1/2}$

So we have

$g'(x) = 18 (36-x^2)^{-3/2} + 18 (36-x^2)^{-1/2}$

and we can simplify this by factoring out $18(36-x^2)^{-3/2}$ to end up with

$g'(x) = 18(36-x^2)^{-3/2} \left(1 + (36-x^2)\right) = \boxed{18 (36 - x^2)^{-3/2} (37-x^2)}$

5 0

2 years ago

The ticket sales for Fist Bump are as follows:

Fed [463]

Notice that the denominators are 3 and 7, which are factors of 21.

So express all the fractions with denominator 21:

On Monday $\frac{1}{7} = \frac{1}{7} * \frac{3}{3} = \frac{3}{21}$ are sold
On Tuesday $\frac{1}{3} = \frac{1}{3} * \frac{7}{7} = \frac{7}{21}$ are sold
On Wednesday $\frac{2}{7} = \frac{2}{7} * \frac{3}{3} = \frac{6}{21}$ are sold

by Thursday $\frac{3}{21}+\frac{7}{21}+\frac{6}{21} = \frac{3+7+6}{21}= \frac{16}{21}$ of the tickets was sold.

Answer: $\frac{16}{21}$

8 0

3 years ago

Which statement best explains why the graphed relation is not a function?

timurjin [86]

C. A function can only have one y value for an x value

5 0

3 years ago

Help please I’ve been looking online for help but couldn’t find any.

alexandr1967 [171]

5 is 33 because the question ends up being 14+3+16

4 0

3 years ago