Question: What is the measure of angle 2?

Mathematics

1 answer:

ad-work [718]3 years ago

8 0

Answer:

56 degrees

Step-by-step explanation:

We know that the angle TWR must be 90 degrees because TWK is 90 degrees and the two angles msut add up to 180. Since we know that TWR=90 degrees and since LWR=34 degrees we do 90-34 so angle 2=56 degrees.

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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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3 years ago

How does the distributive property relate to the factoring expression ?

Elena L [17]

Factoring – Using the Distributive Property. A factor is a number that can be divided into another number evenly. For example, the factors of 6 are 1, 2, 3, and 6. ... It means that a number outside the parentheses of an addition problem can be multiplied by each number inside the parentheses.

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3 years ago

Sarah has a brother who is 5 years younger than herself and another brother who is 8 years younger than herself. She observes th

ELEN [110]

Answer:

Sarah is 13 years old

Step-by-step explanation:

Represent Sarah's age with S

Her first brother's age with F

Her second brother's age with B

So, we have:

From the first statement, we have: