How do you find the x and y intercepts of the equation 3x-6y=18 ?

Given: Circle O with diameter LN and inscribed angle LMN Prove: is a right angle. What is the missing reason in step 5? Statemen

ZanzabumX [31]

Answer:

Inscribed angle theorem

Step-by-step explanation:

This theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

In this case, the angle is ∠LMN and the arc is arc LN. Arc LN measures 180°, because segment LN is the diameter of the circle. Then, by the theorem:

∠LMN = (1/2)*arc LN = (1/2)*180° = 90°

3 0

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

Factor completely. 2x^4+4x^3-30x^2

kramer

Answer:

Step-by-step explanation:

2x⁴ + 4x³ - 30x² = 2x²*(x² + 2x - 15)

x² + 2x - 15

Sum = 2

Product = -15

Factors = 5 ; (-3)

x² + 2x - 15 = x² + 5x - 3x - 3 *5