Answer:


Step-by-step explanation:
a.
![[\because \int \dfrac{dx}{x}=\log |x|+C]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cint%20%5Cdfrac%7Bdx%7D%7Bx%7D%3D%5Clog%20%7Cx%7C%2BC%5D)
b.
![[\because \int x^n dx=\dfrac{x^{n+1}}{n+1}+C]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cint%20x%5En%20dx%3D%5Cdfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D%2BC%5D)
c.
![[\because \dfrac{adx}{x\sqrt{x^2-a^2}}=\csc^{-1}(\dfrac{x}{a})+C]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cdfrac%7Badx%7D%7Bx%5Csqrt%7Bx%5E2-a%5E2%7D%7D%3D%5Ccsc%5E%7B-1%7D%28%5Cdfrac%7Bx%7D%7Ba%7D%29%2BC%5D)
Step-by-step explanation:
count the slope, 5 up in 2.5 horizontal steps, slope = 5/2.5 or 2
x intercept is on the graph, 2.5
y intercept is also on the graph, -5
Answer:
The correct options are;
1) ΔBCD is similar to ΔBSR
2) BR/RD = BS/SC
3) (BR)(SC) = (RD)(BS)
Step-by-step explanation:
1) Given that RS is parallel to DC, we have;
∠BDC = ∠BRS (Angles on the same side of transversal)
Similarly;
∠BCD = ∠BSR (Angles on the same side of transversal)
∠CBD = ∠CBD = (Reflexive property)
Therefore;
ΔBCD ~ ΔBSR Angle, Angle Angle (AAA) rule of congruency
2) Whereby ΔBCD ~ ΔBSR, we therefore have;
BC/BS = BD/BR → (BS + SC)/BS = (BR + RD)/BR = 1 + SC/BS = RD/BR + 1
1 + SC/BS = 1 + RD/BR = SC/BS = 1 + BR/RD - 1
SC/BS = RD/BR
Inverting both sides
BR/RD = BS/SC
3) From BR/RD = BS/SC the above we have by cross multiplication;
BR/RD = BS/SC gives;
BR × SC = RD × BR → (BR)(SC) = (RD)(BR).
In 1 second it beats about 53 times
In 5 seconds it will beat about (53/1*5) times
= 265 times