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2 years ago

(3,4) (3,5) (3,6) y as a function of x

Mathematics

1 answer:

Nezavi [6.7K]2 years ago

6 0

Answer:

Step-by-step explanation:

y is NOT a function of x because there is not a unique y for each x.

The vertical line through these three points is

x = 3

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Marysya12 [62]

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2 years ago

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Carla's Plumbing charges $25 for a service call and $28 per hour, h, for labor for any repair. The total cost, t, for a repair c

MA_775_DIABLO [31]

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2 years ago

A. Evaluate ∫20 tan 2x sec^2 2x dx using the substitution u = tan 2x.

irakobra [83]

Answer:

The integral is equal to $5\sec^2(2x)+C$ for an arbitrary constant C.

Step-by-step explanation:

a) If $u=\tan(2x)$ then $du=2\sec^2(2x)dx$ so the integral becomes $\int 20\tan(2x)\sec^2(2x)dx=\int 10\tan(2x) (2\sec^2(2x))dx=\int 10udu=\frac{u^2}{2}+C=10(\int udu)=10(\frac{u^2}{2}+C)=5\tan^2(2x)+C$ . (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)

b) In this case $u=\sec(2x)$ hence $du=2\tan(2x)\sec(2x)dx$ . We rewrite the integral as $\int 20\tan(2x)\sec^2(2x)dx=\int 10\sec(2x) (2\tan(2x)\sec(2x))dx=\int 10udu=5\frac{u^2}{2}+C=5\sec^2(2x)+C$ .

c) We use the trigonometric identity $\tan(2x)^2+1=\sec(2x)^2$ is part b). The value of the integral is $5\sec^2(2x)+C=5(\tan^2(2x)+1)+C=5\tan^2(2x)+5+C=5\tan^2(2x)+C$ . which coincides with part a)

Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.

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2 years ago

Write five important features. of democratic government

Phantasy [73]

Democracy- The democracy is a government of the people by the people and for the people.

It means the room by the people.

It is a form of government in which the rulers are elected by the people.

Features of Democracy :

a) Major decisions by Elected Leaders :

In a democratic government the major decisions are taken by the leaders who are elected by the people of that country. These elected leaders represent the whole country so in this way the need of all people are satisfied.

b) Free and Fair Electoral Competition :

A democracy is based on a free and fair election where does currently in power have a fair chance of losing.

c) One Person, One Vote , One Value :

In a democratic country each and every adult is provided a single word which is having equal value. It means each what must have one value then that of other.

d) Rule of Law and Respect of Rights :

In democracy a country can be rule only within limits set by constitutional law and citizens' rights.

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2 years ago