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Elan Coil [88]
3 years ago
6

David drops a ball from a bridge at an initial height of 100 meters.

Mathematics
1 answer:
KonstantinChe [14]3 years ago
6 0
h(t) = \frac{1}{2}gt^{2} + v0t + h0

this equation is the given equation that will determine the high of an object using the time. This equation comes from physic though, so if you have a chance to study physic classes, you would have more understanding of this formula
g represents the gravity, -9.8 m/s^2 is the acceleration.
t represents the second. 
you just let t = 3, plug them into the equation, v0: initial speed is 0 because the ball was dropping, not throwing down. 
h(3) = \frac{1}{2}(-9.8)(3)^{2} + (0)(3) + 100
h(3) = 55.9 m is the height of the ball at 3 second. 
The second question asks you how many seconds will the ball hit the ground. When the ball touches the ground, that means the height is 0, but you don't how long was the dropping down.

Still, we use the equation h(t) = \frac{1}{2}gt^{2} + v0t + h0
Note: v0 is always 0 in this situation as I mentioned above. This equation does not involve the speed of ball during the dropping time, so no need to worry about it

0 = \frac{1}{2}(-9.8)t^{2} + (0)t + 100
Now we solve this equation to find t.
0 = -4.9t^{2} + 100
-4.9t^{2} = - 100
\sqrt{t^{2}} =  \sqrt{ \frac{-100}{-4.9} } ==\ \textgreater \  t = 4.5s is the total time for the ball to hit the ground
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21 + (-21) + (-4) please help me out with this question
max2010maxim [7]

Answer:

-4

Step-by-step explanation:

Adding 21 and -21 cancel each other out so you're left with -4

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3 years ago
Zack plans to borrow $7,300 to buy a car.
Neko [114]
I believe the second one, double check
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3 years ago
You play two games against the same opponent. The probability you win the first game is 0.4. If you win the first game, the prob
koban [17]

Answer:

a) No, because the probabilities of winning the 2nd game are dependant on the result of the 1st game. The probabilities are different if you win or lose the first game.

b) P=0.42

c) P=0.08

d)

X    |    P(X)

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

0    |    0.42

1     |    0.50

2    |    0.08

e) E(x)=0.66

s.d.=0.62

Step-by-step explanation:

a) No, because the probabilities of winning the 2nd game are dependant on the result of the 1st game. The probabilities are different if you win or lose the first game.

b) The probability of losing the first game is

P(G_1=L)=1-P(G_1=W)=1-0.4=0.6

The probability of losing the second game, given that the first game was lost is:

P(G_2=L|G_1=L)=1-P(G_2=W|G_1=L)=1-0.3=0.7

So the probability of losing both games is:

P(G_2=L\&G_1=L)=P(G_1=L)*P(G_2=L|G_1=L)=0.6*0.7=0.42

c) The probability of winning both games is:

P(G_2=W\&G_1=W)=P(G_1=W)*P(G_2=W|G_1=W)=0.4*0.2=0.08

d) The variable X can take values 0, 1 and 2.

X=0 is when both games are lost. This happens with probability P=0.42.

X=2 is when both games are won. This happens with probability P=0.08.

X=1 is when one game is won and the other is lost. This happens with probability P=1-0.42-0.08=0.50.

Then the table of probabilities become:

X    |    P(X)

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

0    |    0.42

1     |    0.50

2    |    0.08

e) The expected value is:

E(x)=\sum p_ix_i=0.42*0+0.50*1+0.08*2=0.00+0.50+0.16=0.66

The variance and standard deviation of x are:

V(x)=\sum p_i(x_i-E(x))^2\\\\V(x)=0.42(0-0.66)^2+0.50(1-0.66)^2+0.08(2-0.66)^2\\\\V(x)=0.42*0.4356+0.50*0.1156+0.08*1.7956\\\\V(x)=0.183+0.058+0.144=0.385\\\\\\\sigma=\sqrt{V(x)}=\sqrt{0.385}=0.62

The standard deviation can

5 0
3 years ago
Solve the equation 3(x-4)=12x
sineoko [7]

Answer:

X= -4/3

Step-by-step explanation:

3 0
2 years ago
The number is even. It is nit divisible by 3. It is not divisible by 5. It is not greater than 9^2. Is it not less than 8^2. Wha
TEA [102]

Answer:

64, 68, 74, 76

Step-by-step explanation:

Ok so in a confusing way, the last two statements are telling you that the number is greater than 8^2, which is 64, and the number is less that 9^2, which is 81.

The number has to be even, so I will list the even numbers between those two numbers:

64, 66, 68, 70, 72, 74, 76, 78, 80.

It cannot be divisible by 3, which rules out 66, 72, 78

64, 68, 70, 74, 76, 80 remains

It cannot be divisible by 5, which rules out 70 and 80

64, 68, 74, 76  are the possible answers,

*Note: I believe I did this right, but because of the tricky wording of the last two statements, 64 may not be included.

4 0
3 years ago
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