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3 years ago

Given that the values in the table represent the graph of a continuous function, y has at least how many zeros?

Mathematics

1 answer:

garri49 [273]3 years ago

7 0

Line segments joining these points cross the x-axis 5 times. The continuous function y has
at least 5 zeros.

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With the drain open, a pool loses water at a rate of 9 gallons per minute. At that rate, how long will it take to drain 486 gall

Snezhnost [94]

divide 486 by 9 = 54

it would take about 54 minutes

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3 years ago

A new company started with 12 founding members. It is quadrupling its membership base every year. Write an equation to model thi

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3 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.

3 0

3 years ago

I need help with this one I know I posted this pic on science sorry please help

Alex

Answer=Order of operations

The order of operations (which we use PEMDAS to help us remember) tells you which operation to do first.

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3 years ago

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The level of the top of the water in the ocean is considered to be at an altitude of zero (0) feet.

Andrew [12]

C because people wasn’t allowed to get a lot of the things they wanted

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3 years ago