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3 years ago

A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.

Mathematics

2 answers:

GrogVix [38]3 years ago

7 0

Using the Pythagorean theorem we can solve for the radius

see attached picture:

nika2105 [10]3 years ago

7 0

Answer:

The correct option is 3.

Step-by-step explanation:

From the given figure it is noticed that the radius of a circle is 11 inches and the centers of two circles are 20 inches apart. The length of the direct common tangent between both circles is 19 inches.

If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is

$l=\sqrt{d^{2}-(r_{1}-r_{2})^{2}}$

$19=\sqrt{20^{2}-(11-r_{2})^{2}}$

Square both sides.

$361=400-(11-r_{2})^{2}$

$(11-r_{2})^{2}=400-361$

$(11-r_{2})^{2}=39$

Tnking square root both sides.

$11-r=\sqrt{39}$

$11-6.245=r$

$4.775=r$

$r\approx 4.8$

Therefore the radius of second circle is 4.8 inches and option 3 is correct.

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A conditional statement is logically equivalent to a biconditional statement. True False pls help i have a test and i was absent

andreyandreev [35.5K]

Answer:

false.

Step-by-step explanation:

A conditional statement is something like:

If P, then Q.

This means that if a given proposition P is true, then another proposition Q is also true.

An example of this is:

P = its raining

Q = there are clouds in the sky.

So the conditional statement is

If its raining, then there are clouds in the sky.

A biconditional statement is:

P if and only if Q.

This means that P is only true if Q is true, and Q is only true if P is true.

So, using the previous propositions we get:

Its raining if and only if there are clouds in the sky.

This statement is false, because is possible to have clouds in the sky and not rain.

(this statement implies that if there are clouds in the sky, there should be rain)

Then we could see that for the same propositions, the conditional statement is true and the biconditional statement is false.

Then these statements are not logically equivalent.

The statement is false.

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3 years ago

How would I go about solving this?

garik1379 [7]

If you draw more of those triangles, there will be 6 that can fit, so find area of 1 triangle and multiply it by 6. Write that number down and then do Pi r squared to find the area of the circle, then do circle area minus triangles area when you get that, divide it by 6. That is the area of the white region so then do Pi R squared again and then subtract the white area from that

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3 years ago

A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y. Corn costs $215 per acre to produce, and cotton costs

tatyana61 [14]

Answer:

The system that represent the scenario is

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