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Gelneren [198K]

2 years ago

8

Twenty cars pass through Intersection X in 4 minutes, 35 cars pass through Intersection Y in 5 minutes, and 36 cars pass through

Intersection Z in 6 minutes. Which intersection has the least number of cars passing through it every minute?

1 answer:

Sidana [21]2 years ago

3 0

Answer:

intersection x

Step-by-step explanation:

divide the number of cars by the minutes

x= 5 per

y= 7 per

z = 6 per

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Divide the number 20 into two parts (not necessarily integers) in a way that makes the product of one part with the square of th

Ilya [14]

Answer:

13 1/3 and 6 2/3.

Step-by-step explanation:

Let the 2 parts be x and (20 - x).

So x^2(20 - x) must be a maximum.

y = x^2(20 - x)

y = 20x^2 - x^3

Finding the derivative):

y' = 40x - 3x^2 = 0 for maxm/minm value.

x( 40 - 3x) = 0

40 - 3x = 0

3x = 40

x = 40/3.

This is a maximum because the second derivative y" = 40 - 6x = 40 - 6(40/3)) is negative.

So the 2 numbers are 13 1/3 and 6 2/3.

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2 years ago

Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation

Vaselesa [24]

Answer:

$\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}$

Step-by-step explanation:

The circumference of a circle with radius $r$ is given by $C=2\pi r$ . The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle $\theta^{\circ}$ is equal to $2\pi r\cdot \frac{\theta}{360}$ .

Formulas at a glance:

Circumference of a circle with radius $r$ : $C=2\pi r$
Length of an arc with central angle $\theta^{\circ}$ : $\ell_{arc}=2\pi r\cdot \frac{\theta}{360}$

<u>Question 1:</u>

The radius of the circle is 12 m. Therefore, the circumference is:

$C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}$

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

$\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}$

<u>Question 2:</u>

In the circle shown, the radius is marked as 2 miles. Substituting $r=2$ into our circumference formula, we get:

$C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}$

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

$\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}$

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2 years ago

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Alexeev081 [22]

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Step-by-step explanation:

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2 years ago

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