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3 years ago

Latonya swims 50 meters in 1/2 minute

Mathematics

2 answers:

ipn [44]3 years ago

6 0

S = Speed
D = Distance
T = Time
S = D/T
S = 50m/1/2
50 divided by 1/2 = 25
25 = 50/1/2
S = 25 m/min.

Citrus2011 [14]3 years ago

3 0

Answer:don’t understand

Step-by-step explanation:

Explain steps please

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taurus [48]

Answer:

85%

Step-by-step explanation:

If she got 3 wrong then it means she got 20-3 right, so she got 17 questions right.

From there we get the fraction: 17/20

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By doing that we get 17x5/20x5

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3 years ago

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nirvana33 [79]

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Step-by-step explanation:

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7 months 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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