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4 years ago

With a quick explanation please

Mathematics

1 answer:

Tju [1.3M]4 years ago

6 0

$\dfrac{40}{5x-2}=\dfrac{55}{6x+6}\ \ \ |\text{cross multiply}\\\\40(6x+6)=55(5x-2)\\\\240x+240=275x-110\ \ \ |-240\\\\240x=275x-350\ \ \ \ |-275x\\\\-35x=-350\ \ \ \ \ |:(-35)\\\\\boxed{x=10}$

Look at the picture.

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Karolina [17]

Answer:

15m^3n + 1

Step-by-step explanation:

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3 years ago

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Kiley had a piece of bamboo skewer that measured 14Three-fifths inches long. She wanted to cut it into toothpicks that were each

forsale [732]

Answer:

4 toothpicks.

Step-by-step explanation:

We have been given that Kiley had a piece of bamboo skewer that measured 14 3/5 inches long. She wanted to cut it into toothpicks that were each 3 1/5 inches long.

To find the number of toothpicks that Kiley can make from bamboo skewer, we need to divide the length of skewer by length of each toothpick.

Total number of toothpicks = 14 3/5 ÷ 3 1/5

First of all, we will convert our given mixed fractions into improper fractions as:

Total number of toothpicks = 73/5 ÷ 16/5

Dividing a fraction by another fraction is same as multiplying the 1st fraction by the reciprocal of 2nd fraction.

Total number of toothpicks = 73/5 x 5/16

Total number of toothpicks = 73/16

Total number of toothpicks = 4.5625

Therefore, Kiley can make 4 toothpicks.

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3 years ago

If x = a cosθ and y = b sinθ , find second derivative

Olin [163]

I'm guessing the second derivative is for y with respect to x, i.e.

$\dfrac{\mathrm d^2y}{\mathrm dx^2}$

Compute the first derivative. By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

We have

$y=b\sin\theta\implies\dfrac{\mathrm dy}{\mathrm d\theta}=b\cos\theta$

$x=a\cos\theta\implies\dfrac{\mathrm dx}{\mathrm d\theta}=-a\sin\theta$

and so

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{b\cos\theta}{-a\sin\theta}=-\dfrac ba\cot\theta$

Now compute the second derivative. Notice that $\frac{\mathrm dy}{\mathrm dx}$ is a function of $\theta$ ; so denote it by $f(\theta)$ . Then

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm dx}$

By the chain rule,

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$