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3 years ago

Tangent segments from a common external point are

Mathematics

1 answer:

n200080 [17]3 years ago

7 0

Answer:

Tangent segments from a common external point are congruent

Explanation:

A tangent line to a circle is a line that touches the circle in only one point of the cirfumference, and, hence, the tangent is perpendicular to (forms a right angle with) the radius of the circle.

There are many thorems relative fo the tangent lines of a cirle.

One of those theorems states that if two tangent lines to a circle are drawn from a same external point, the two segments formed from the coomon external point to the tangency points have the same length.

Also, you must know that, from the definition, two segments of the same length are known as congruent segments.

Therefore, calling P the common external point, A one point of tangency in the circle, and B the other point of tangency, then:

length segment PA = length segment PB.

So, the two tangent segments from an common enternal point are congruent.

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Determine the values of the constants B and C so that the function given below is differentiable.

laila [671]

For the function to be differentiable, its derivative has to exist everywhere, which means the derivative itself must be continuous. Differentiating gives

$f'(x)=\begin{cases}24x^2&\text{for }x1\end{cases}$

The question mark is a placeholder, and if the derivative is to be continuous, then the question mark will have the same value as the limit as $x\to1$ from either side.

$\displaystyle\lim_{x\to1^-}f'(x)=\lim_{x\to1}24x^2=24$
$\displaystyle\lim_{x\to1^+}f'(x)=\lim_{x\to1}B=B$

So the derivative will be continuous as long as $B=24$

For the function to be differentiable everywhere, we need to require that $f(x)$ is itself continuous, which means the following limits should be the same:

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}8x^3=8$
$\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}Bx+C=24+C$

$24+C=8\implies C=-16$

So, the function should be

$f(x)=\begin{cases}8x^3&\text{for }x\le1\\24x-16&\text{for }x>1\end{cases}$

with derivative

$f'(x)=\begin{cases}24x^2&\text{for }x$

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4 years ago

Which expression is equivalent to (4x^3)(3x^5y)^2

Anettt [7]

Answer:

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Step-by-step explanation:

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2 years ago

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chubhunter [2.5K]

If the truck can carry 1000 apples at a time, Bananaville is 1000 miles away from Appleland and you pay one apple per mile, then it's impossible to deliver any apple to Bananaville, because on 1000 miles you'll pay 1 apple * 1000 miles = 1000 apples as a tax. So no matter if you go once, twice, three times or a hundred times there - you'll be never able to deliver any apple.

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4 years ago

How do you find line e?

jolli1 [7]

Answer:

The answer to your question is the slope of line e is $\frac{4}{5}$

Step-by-step explanation:

If two lines are parallel they have the same slope.

If two lines are perpendicular their slopes are reciprocals and of different signs.

In this question, line d is parallel to line e, which means that they have the same slope.

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3 years ago

Which conditional statement has the same truth value as its converse

hodyreva [135]

In other words, you are looking for which one is the biconditional statement.

A: This is true. Both the Conditional and Converse Statements are true. The Biconditional Statement would be this: The angles are bisected if and only if the angles have two congruent parts. This is true.

B: This is false. It is true as a conditional statement, but if you flip the p and q, it says that ALL acute angles are 60 degrees. This isn't true because a 35 degree angle or a 89 degree angle is also acute.

C: This is False. The conditional statement isn't true. The Converse statement is true but because the conditional statement is not then it is false. You can have two angles the aren't touching and they would be supplementary.

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Therefore, your answer is A.

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3 years ago