Investigation Circles: Investigation 2

I need help with the worksheet

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Answer 1

Answer:

Explanation:

1. In order for the idea of "perpendicular distance" to make any sense in this context, the number of sides of the polygon must be even. Then the "diameter" is the diameter of the inscribed circle. As the number of sides increases, the polygon differs less and less from a circle, so the relationship of perimeter and "diameter" becomes closer to the relationship in a circle.

"As the number of sides in a regular polygon increases, the ratio of perimeter to diameter for that polygon approaches pi."

2. We know from the first question that ...

circumference/diameter = π

And we know that ...

diameter = 2·radius

Then the following are true:

A. circumference = π · diameter

B. circumference = (2·radius) · π

3. The expressions in order evaluate to approximately ...

4.0, 3.45, 3.31, 3.24

Of these, the last is closest to pi (3.14....). The appropriate choice is ...

D. (10·5)/15.4

4. Pi cannot be expressed as a rational number, because pi is irrational. A number of lengthy proofs have been offered to demonstrate this fact. One of them makes use of the fact that the tangent of any rational number is irrational, and the tangent of π/4 is 1. Since 1 is a rational number, π/4 cannot be, so π cannot be expressed as a rational number.

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A hypothesis must be testable and falsifiable to be scientifically valid. Being testable and falsifiable means that __________.

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Final answer:

A scientifically valid hypothesis must be testable and falsifiable. Testable means that it can be evaluated through observations or experimentation. Falsifiable means that it's possible to design an experiment whose results would prove the hypothesis to be incorrect.

Explanation:

Within the scientific community, a hypothesis is considered to be scientifically valid only if it is testable and falsifiable. When we say a hypothesis is testable, it means that it can be evaluated through observations or experimentation, using the scientific method. An example of this could be the hypothesis 'If I water my plants more, they will grow faster.' This hypothesis is testable because we can carry out an experiment to confirm or refute it.

On the other hand, a hypothesis is said to be falsifiable if it is possible to design an experiment whose outcome could prove the hypothesis to be incorrect. For example, the hypothesis 'All swans are white' is falsifiable because finding just a single swan of a different color would falsify the hypothesis. However, it's important to note that falsifiable doesn't mean the hypothesis is incorrect, rather it means that it's possible to prove it's incorrect through testing.

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Final answer:

A hypothesis must be testable and falsifiable in order to be considered scientifically valid. This means that it can be tested through experimentation or observation, and can be proven false if the experimental results contradict it.

Explanation:

A hypothesis must be testable and falsifiable to be scientifically valid. Being testable and falsifiable means that it can be tested through experimentation or observation and can be proven false if the experimental results contradict it. Testability and falsifiability are key requirements in scientific research as they allow for the advancement of knowledge and the development of more accurate explanations of natural phenomena.

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A 135 degree angle is classified as what

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An Acute angle is an angle is under 90 degrees, a right angle is 90 degrees, and obtuse angle is greater than 90 degrees but less than 180 degrees.... which out of these angles you would choose an Obtuse angle.

Use the Pythagorean identity sin^2 Θ + cos^2 Θ = 1 to derive the other Pythagorean identities, 1 + tan^2 Θ = sec^2 Θ and 1 + cot^2 Θ = csc^2 Θ. Discuss how to remember these identities and other fundamental identities.

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1 ) 1 + tan² t = sec² t
1 + sin² t / cos² t = 1 / cos² t
( This is because we know that tan x = sin x / cos x and csc x = 1 / cos x )
Then we will multiply both sides of an equation by cos² t
1 * cos² t + sin² t * cos² t / cos² t = 1
cos² t + sin² t = 1 ( and we know that it is the identity - true )
2 ) 1 + cot ² t = csc² t
1 + cos² t / sin² t = 1 / sin² t / · sin² t ( multiply both sides by sin² t )
sin² t + cos² t = 1 ( true )

Convert to exponential equation log9 1/81= 2

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log₉ $(1)/(81)$ = - 2
$(1)/(81)= 9^(-2)$

If an object is dropped from a height of 85 feet, the function h(t)=-16t^2+85 gives the height of the object after t seconds. Approximately, when will the object hit the ground?a. 85.00 seconds
b. 69.00 seconds
c. 0.33 seconds
d. 2.30 seconds

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We are given the function of the situation. The function is given as h(t) = -16t^2 + 85 where h(t) signifies that height is a function of time. For this case, our height would be zero and we find the time it hits the ground. Thus,

0 = -16t^2 + 85
t = 2.30 seconds

The answer is d.

Explain your answerSimplify the difference.

(4w2 - 7w - 6) - (8w2 + 2w - 3)
Choose one answer.
a. -4w2 - 9w - 3
b. 12w2 + 9w + 3
c. -4w2 - 5w - 9
d. 12w2 - 5w - 9

Answers

$(4w^2-7w-6)-(8w^2+2w-3)\n -(a\pm b)=-1(a\pm b)\ \ \ \ |use\ a\ distributive\ property: a(b\pm c)=ab\pm ac\n\n\=4w^2-7w-6-8w^2-2w-(-3)\n\n = 4w^2-7w-6-8w^2-2w-(-3)\n\n=(4w^2-8w^2)+(-7w-2w)+(-6+3)\n\n=\boxed{-4w^2-9w-3}$