Which of the following is equal to m

Mathematics

1 answer:

Snowcat [4.5K]2 years ago

7 0

Answer: tan^-1 (c/a)

Step-by-step explanation: An angle C ∈ ℝ such that angle C > 0 can be defined by the trigonometric ratio Arctangent (or rather tan^-1) where side "c" divided by side "a" ≠ 0.

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1. A tortoise is running on a long, moving sidewalk. Her pedometer doesn't report her speed, but she knows that—since she got on

Burka [1]

Answer:

the sidewalk speed q = 3km/hr

the tortoise speed p is 1.5 km/hr

Step-by-step explanation:

From the given information:

let the speed of the tortoise be p & the speed of the sidewalk be q

she's been running for 40 minutes (40/60 = 2/3) and that she's travelled 3 kilometres

Thus,

p + q = $\dfrac{3}{\dfrac{2}{3}}$

p + q = 9/2

p + q = 4.5 ----- (1)

when returning, she travelled 3km in 2 hours

i.e. -p + q = 3/2

-p + q = 1.5 ----- (2)

Thus, by using the elimination method for equation (1) and (2)

p + q = 4.5 ----- (1)

q = 6/2

q = 3 km/hr

From equation (1)

p + q = 4.5

p + 3 = 4.5

p = 4.5 - 3

p = 1.5 km/hr

Therefore, the sidewalk speed q = 3km/hr and the tortoise speed p is 1.5 km/hr

8 0

3 years ago

Find the inverse laplace transform of: (2 s + 4) / (s - 3)^3

Serhud [2]

Answer:

$e^{3t}(2t+5t^{2})$

Step-by-step explanation:

$L^{-1}[\frac{2s+4}{(s-3)^{3}} ]=$

Using the Translation theorem to transform the s-3 to s, that means multiplying by and change s to s+3

Translation theorem: $L^{1} [F(s-a)=L^{-1}[F(s)|_{s \to s-a}\\ L^{1} [F(s-a)=e^{at} f(t)$

$L^{-1}[\frac{2s+4}{(s-3)^{3}} ]=e^{3t} L^{-1}[\frac{2(s+3)+4}{s^{3}} ]$

Separate the fraction in a sum:

$e^{3t} L^{-1}[\frac{2s+10}{s^{3}} ]=e^{3t} L^{-1}[\frac{2s}{s^{3}}+\frac{10}{s^{3}} ]=e^{3t} (L^{-1}[\frac{2}{s^{2}}]+ L^{-1}[\frac{10}{s^{3}}])$