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Pani-rosa [81]
4 years ago
11

A tennis ball, starting from rest, rolls down the hill in the drawing. At the end of the hill the ball becomes airborne, leaving

at an angle of 35° with respect to the ground. Treat the ball as a thin-walled spherical shell, and determine the range x.
Mathematics
1 answer:
seraphim [82]4 years ago
7 0

Answer:

3.61metres

Step-by-step explanation:

The first thing to do is that as the ball rolls down the hill, its initial potential echanged into rotational and linear

Assuming the height is 3.2 meters

kinetic energy.

Initial Potential Energy = m * 9.8 * 3.20 = m * 31.36

For a thin walled spherical shell, the moment of inertia is ⅔ * m * r^2

Rotational KE = ½ * I * ω^2 = ⅓ * m * r^2 * ω^2

ω = v/r, ω^2 = v^2/r^2

Rotational KE = ⅓ * m * v^2

Linear KE = ½ * m * v^2

Total KE = 5/6 * m * v^2

5/6 * m * v^2 = m * 31.36

v^2 = 37.632

v = √37.362

The ball’s velocity at the bottom of the hill is approximately 6.134 m/s. To determine he range, use the following equation.

Let R be equal to the range

R = v^2/g * sin 2 θ

R = 37.632/9.8 * sin 70 = 3.84 * sin 70

Which is equal to 3.61 meters.

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nalin [4]

Ans(1):

Given equation is f(x)=-1.5x+6

we can plug any number like x=0 and x=2 to find the f(x) also called y-value

plug x=0

f(x)=-1.5x+6 =-1.5*0+6 =0+6 =6

Hence first point is (0,6)

plug x=2

f(x)=-1.5x+6 =-1.5*2+6 =-3+6 =3

Hence first point is (2,3)

now we can graph both points then join them to get final graph of f(x)=-1.5x+6

---------------------

Ans(2):

We can repeat exactly same process for f(x) = -1/2x-5.

So the final graph will look like attached picture:


5 0
3 years ago
2. Jacob deposited $6,000 into an account that offers 4.5% interest compounded annually.
Llana [10]

Answer: a

Step-by-step explanation:

3 0
4 years ago
Read 2 more answers
Memory module consists of 9 chips. The device is designed with redundancy so that it works even if one of its chips is defective
soldier1979 [14.2K]

Answer:

a) P[C]=p^n

b) P[M]=p^{8n}(9-8p^n)

c) n=62

d) n=138

Step-by-step explanation:

Note: "Each chip contains n transistors"

a) A chip needs all n transistor working to function correctly. If p is the probability that a transistor is working ok, then:

P[C]=p^n

b) The memory module works with when even one of the chips is defective. It means it works either if 8 chips or 9 chips are ok. The probability of the chips failing is independent of each other.

We can calculate this as a binomial distribution problem, with n=9 and k≥8:

P[M]=P[C_9]+P[C_8]\\\\P[M]=\binom{9}{9}P[C]^9(1-P[C])^0+\binom{9}{8}P[C]^8(1-P[C])^1\\\\P[M]=P[C]^9+9P[C]^8(1-P[C])\\\\P[M]=p^{9n}+9p^{8n}(1-p^n)\\\\P[M]=p^{8n}(p^{n}+9(1-p^n))\\\\P[M]=p^{8n}(9-8p^n)

c)

P[M]=(0.999)^{8n}(9-8(0.999)^n)=0.9

This equation was solved graphically and the result is that the maximum number of chips to have a reliability of the memory module equal or bigger than 0.9 is 62 transistors per chip. See picture attached.

d) If the memoty module tolerates 2 defective chips:

P[M]=P[C_9]+P[C_8]+P[C_7]\\\\P[M]=\binom{9}{9}P[C]^9(1-P[C])^0+\binom{9}{8}P[C]^8(1-P[C])^1+\binom{9}{7}P[C]^7(1-P[C])^2\\\\P[M]=P[C]^9+9P[C]^8(1-P[C])+36P[C]^7(1-P[C])^2\\\\P[M]=p^{9n}+9p^{8n}(1-p^n)+36p^{7n}(1-p^n)^2

We again calculate numerically and graphically and determine that the maximum number of transistor per chip in this conditions is n=138. See graph attached.

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4 years ago
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pashok25 [27]

Answer:

20 weeks

Step-by-step explanation:

35+5=40

40/2=20

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Answer:

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Step-by-step explanation:

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