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3 years ago

Express 20cm as a percentage of 3m. give your answer as a mixed number

Mathematics

1 answer:

Ludmilka [50]3 years ago

8 0

Answer:

$6\frac{2}{3}$ %

Step-by-step explanation:

First, convert 3 meters into centimeters.

1m = 100cm

3m = 100 × 3 = 300cm

Now, form the fraction by putting the given value, 20cm, over the total measurement, 300cm.

$\frac{20}{300}$ = $\frac{2}{30}$ = $\frac{1}{15}$ ⇒ Simplify your fraction to its simplest terms.

Next, multiply your simplified fraction by 100 to get your percentage.

$\frac{1}{15}$ × $100$ = $\frac{100}{15}$ = $6\frac{10}{15}$ = $6\frac{2}{3}$ % ⇒ Simplify your percentage to its simplest terms.

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The temperature is changing at a constant rate of –0.75ºC per half hour. At 6:45 PM, the temperature was –4.6ºC. At what time wa

tino4ka555 [31]

Answer:

11:15PM

Step-by-step explanation:

The difference between 4.6°C and -2.1°C is 6.7

0.75×?=6.7

?=9

This is 9 half hours, which is equal to 4 1/2 hours.

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3 0

3 years ago

Help with 30 please. thanks.

Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

$\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}$

And we want to show that:

$\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}$

Instead of differentiating directly, we can first square both sides:

$\displaystyle y^2 = 3e^{2x} -4x + 1$

We can find the first derivative through implicit differentiation:

$\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4$

Hence:

$\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}$

And we can find the second derivative by using the quotient rule:

$\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}$