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2 years ago

Find five rational numbers between 3/7 and 2/3

Mathematics

1 answer:

Softa [21]2 years ago

4 0

Answer:

First, you get both of them with same denominator:

3/7 and 2/3 => 9/21 and 14/21, however, there are only 4 rational numbers between 9/21 and 14/21.

The solution is that you can raise the denominator 2 times:

9/21 and 14/21 => 18/42 and 28/42

Now you can select : 19/42, 20/42, 21/42, 22/42, 23/42. They are a group of 5 rational numbers you are looking for.

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Please help me :)) algebra 2! what are the real roots?

irina1246 [14]

Answer:

Step-by-step explanation:

So we have the equation:

$3(x-4)^\frac{4}{3}+16=64$

First, let's subtract 16 from both sides:

$3(x-4)^\frac{4}{3}=48$

Now, let's divide both sides by 3:

$(x-4)^\frac{4}{3}=16$

Remember that with fractional exponents, we can move the denominator into the root position. Therefore:

$(\sqrt[3]{x-4})^4=16$

Let's take the fourth root of both sides. Since we're taking an even root, make sure to have the plus-minus symbol!

$\sqrt[3]{x-4} =\pm 2$

Cube both sides. Since we're cubing, the plus-minus stays.

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Add 4 to both sides.

$x=\pm 8+4$

Calculator:

$x=8+4\text{ or } x=-8+4\\x=12\text{ or } x=-4$

So, our answer is A.

And we're done!

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3 years ago

A car wheel has a radius of 16 inches. Through what angle ( to the nearest tenth of a degree ) does the wheel turn when the car

olya-2409 [2.1K]

First of all, let's convert all the measures to the same unit: 4 feet are 48 inches.

Now, as the wheel turns, there is a proportion between the angle and the distance travelled: for example, when the car moves forward a whole circumference, the angle will be 360°. Conversely, if the wheel turns 180°, then the car will move forward a distance which is half the circumference of the wheel, and so on.

Since the radius is 16 inches, the circumference will be

$C=2\pi r = 32\pi$

So, we have the following proportion:

$360\div 32\pi = x \div 48$

that you can read as: "if an angle of 360 corresponds to a distance travelled of $32\pi$ , then the unknown angle x corresponds to a distance travelled of 48 inches.

Solving for x, we have

$x = \dfrac{360\cdot 48}{32\pi} = \dfrac{17280}{32\pi} = 171.887338539\ldots \approx 171.9$

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