Tim's phone service charges $26.39 plus an additional $0.21 for each text message sent per month. If Tim's phone bill was $31.64
1 answer:
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Option A
The new price is $
Given that, a stock was priced at $ per share.
It rose in price by $ per share.
New price = old price + rise in price
Thus to find out the new price, we have to add old price and rise in price
On solving we get,
On converting to mixed fraction,
Hence, the new price is , so option A is correct.
Answer:
Check attachment for necessary information
Step-by-step explanation:
At point B. Check attachment for free body diagram.
Where an is the centripetal acceleration and it is given as
an = Vb²/r
Fn = m•Vb²/r
Fn = 6 × Vb²/1.2
Fn = 5Vb²
Applying Newton's second law along the y direction
ΣF = m•ay
ay = 0, since the body is not moving in y direction
N —W = 0
N — WCosβ = 0
N = Fn = 5Vb²
5Vb²—58.86Cosβ = 0
Divide through by 5
Vb² — 11.772Cosβ = 0
Vb² = 11.772Cosβ, equation 1
Applying conservation of energy.
∆K.E(A) + ∆P.E(A) = ∆K.E(B) +∆P.E(B)
½m•Va²— 0+ mg•Ha — 0 = ½m•Vb² — 0 + mg•Hb — 0
½m•Va²+mg•Ha = ½m•Vb² + mg•Hb
From attachment
Ha = 1.13m
Hb = 1.2Cosβ.
Va = 2m/s²
½m•Va²+mg•Ha = ½m•Vb² + mg•Hb
½×6×2² + 6×9.81×1.13 = ½×6×Vb²+6×9.81×1.2Cosβ
12 + 66.512 = 3Vb² + 70.632Cosβ
From equation,.Vb² = 11.772Cosβ
78.512 = 3×11.772Cosβ+70.632Cosβ
78.512 = 35.316Cosβ+70.632Cosβ
78.512 = 105.948Cosβ
Cosβ = 78.512/105.948
Cosβ = 0.7410
β = ArcCos(0.7410)
β = 42.18 °
β = 42.2°
From the attachment, it is notice that,
θ + 20° = β
θ = β — 20°
θ = 42.2 — 20°
θ = 22.2°
The angle θ at which the box
left the smooth circular ramp is 22.2°
b. Using equation free fall motion
∆y = Vby•t + ½gt²
Let get Vb first, from equation 1
Vb² = 11.772Cosβ
Vb² = 11.772Cos42.2
Vb² = 8.721
Vb = √8.722
Vb = 2.95m/s
Now, to get Vby
Vby = VbSinβ
Vby = 2.95Sin42.2
Vby = 1.984 m/s
Then, applying free fall equation at point B
∆y = Vby•t + ½gt²
Hb - 0 = 1.984t + ½ × 9.81t²
1.2Cosβ = 1.984t + 4.905t²
1.2Cos42.2 = 1.984t + 4.905t²
4.905t² + 1.984t —0.889 = 0
Using formula method
t = [-b±√(b²-4ac)]/2a
a = 4.905 b = 1.984 and c = -0.889
t =[-1.984±√(1.984²-4×4.905×-0.889)] / 2×4.905
t = (-1.984±√21.378)/9.81
t = (-1.984± 4.624)/9.81
So,
t = (—1.984 — 4.624)/9.81
t = -0.674s
Or
t = (-1.984 + 4.624)/9.81
t = 2.64/9.81
t = 0.269s
Since time cannot negative, then,
t = 0.269s
Now, we can find the distance "s" by applying range formula, the part of motion is parabola this allow us to use projectile motion
R = Ux • t
s= Vbx × t
s= VbCosβ × t
s= 2.95Cos42.2 × 0.269
s= 0.588m
So, the distance "s" where the box fall into the cart is 0.588m
