#6 Find Value of X . Round answer to nearest tenth.

Mathematics

1 answer:

MaRussiya [10]3 years ago

6 0

This is a right triangle. We know that

$\tan x = \frac{\text{opposite side}}{\text{adjacent side}}$

Therefore,

$\tan x = \frac{18}{21} = \frac{6}{7} = 0.857$

Now we have:

$x=\tan^{-1}0.86$

$x=40.6$

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A line segment has endpoints (-5, 10) and (a,b) . If the midpoint of the segment is (13, -2), what is the absolute difference be

AlexFokin [52]

If the line segment point is D(-5, 10) and E(a,b) and the midpoint of the segment is F(13, -2) that mean
DE= 2*DF

You can directly find the distance of AC
Xdf= Xf-Xd= 13 - (-5)= 18
Ydf= Yf - Yd= -2 - 10= -12

Then add the distance of AB( which is 2*AC) to point D
Xe= a = Xd + 2*Xdf
a= -5 +2*18= 31

Ye= b = Yd + 2Yf
b= 10+ 2*-12= -14

<span>absolute difference between a and b:
|b-a|= </span>|-14-31|= 45

7 0

3 years ago

If θ=0rad at t=0s, what is the blade's angular position at t=20s

babunello [35]

The attached figure represents the relation between ω (rpm) and t (seconds)
To find the blade's angular position in radians ⇒ ω will be converted from (rpm) to (rad/s)
              ω = 250 (rpm) = 250 * (2π/60) = (25/3)π    rad/s
              ω = 100 (rpm) = 100 * (2π/60) = (10/3)π    rad/s

and from the figure it is clear that the operation is at constant speed but with variable levels
            ⇒   ω = dθ/dt   ⇒   dθ = ω dt

            ∴    θ = ∫₀²⁰ ω dt

while ω is not fixed from (t = 0) to (t =20)
the integral will divided to 3 integrals as follow;
       ω = 0                                          from t = 0 to t = 5
       ω = 250 (rpm) = (25/3)π            from t = 5   to t = 15
       ω = 100 (rpm) = (10/3)π            from t = 15 to t = 20

∴ θ = ∫₀⁵ (0) dt   + ∫₅¹⁵ (25/3)π dt + ∫₁₅²⁰ (10/3)π dt

the first integral = 0
the second integral = (25/3)π t = (25/3)π (15-5) = (250/3)π
the third integral = (10/3)π t = (25/3)π (20-15) = (50/3)π

∴ θ = 0 + (250/3)π + (50/3)π = 100 π

while the complete revolution = 2π
so instantaneously at t = 20
∴ θ = 100 π - 50 * 2 π = 0 rad

Which mean:
the blade will be at zero position making no of revolution = (100π)/(2π) = 50