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The acceleration y, in meters per second squared, of an object after x seconds is given by y = 7 sin (pi/4 x). During the first

Nataly_w [17]

Answer: (0, 2) and (6, 10)

Step-by-step explanation:

The acceleration is:

y = 7*sin( x*pi/4).

Over which interval is the acceleration increasing?

First, let's study the sin function:

Sin(θ) increases between -pi/2 and pi/2

Sin(θ) decreases between pi/2 and (3/2)*pi.

And so on.

Here we have:

θ = x*(pi/2)

When x = 0, θ = 0.

And sin(θ) is increasing in θ = 0.

Then we must choose one of the options that start with x = 0.

now it will stop increasing when:

θ = pi/2 = x*(pi/4)

x = 2.

So the acceleration is increasing in the segment (0,2)

And it will start increase again when:

θ = (3/2)*pi = x*(pi/4)

(3/2)*pi*(4/pi) = 6 = x.

So at x= 6 the acceleration starts increasing again, and the acceleration is only deffined until x = 10, then

the correct option is: (0, 2) and (6, 10)

6 0

3 years ago

What is the value of x, when 5+x+(−2)=−8?

nasty-shy [4]

5+x+(−2)=−8
5 + x - 2 = -8
x + 3 = -8
x = -11

3 0

3 years ago

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Alex and bob are playing 5 chess games. Alex is 3 times more likely to win than bob. What is the probability that both of them w

givi [52]

Answer:

12.2%

Step-by-step explanation:

Lets firstly find out the probabilities for Alex and Bob. We know that the prb that Alex wins is 3 times the prob for Bob, so:

P(A) = 3P(B)

And, as these values are probabilities they must sum 1:

P(A) + P(B) = 1

Replacing the first equation in the second:

3P(B) + P(B) = 1

4P(B) = 1

Dividing both sided by 4:

4P(B)/4 = 1/4

P(B) =1/4

So, the probability for Bob is 1/4. Then the probability for Alex is 3*1/4 = 3/4

Now we have to find the probability that both win at least two games. Lets think about the possible combination of cases. As they play 5 games and both have to win at least to there is a remaining game that cane variate, this is, can be won by Alex or Bob. So, we can have:

AABBB

AABBA

Where A is "Alex win" and B is "Bob win" (here we do not pay attention to the order).

Thus, we have to find the probability that Alex wins 3 games and Bob 2 games, and the probability that Alex wins 2 games and Bob 3 games. As the games are independent, i.e., the result of one games does not affect the followings we can just multiply the probabilities:

P(3A and 2B) = (3/4)*(3/4)*(3/4)*(1/4)*(1/4) = 0.42*0.06 = 0.026

P(2A and 3B) = (3/4)*(3/4)*(1/4)*(1/4)*(1/4) = 0.56*0.016 = 0.096

So,

P (at least 2) = P(3A and 2B) + P(2A and 3B) = 0.026 + 0.096 = 0.122 = 12.2%

7 0

3 years ago

What is the factor of 28/88

Llana [10]

The factors are:
4, 2, 1

6 0

3 years ago

17_2_3_8=3 insert + - × or ÷ symbols to make each statement true

erastova [34]

Answer:

17-2*3-8=3

Step-by-step explanation:

We have given:

17_2_3_8=3 insert + - × or ÷ symbols to make each statement true?

Solution:

We will insert multiplication sign between 2 and 3 and then subtract all the terms

17-2*3-8=3

We will solve it according to the DMAS rule:

DMAS rule is followed when multiple arithmetic operations are there in a given problem like addition, subtraction, multiplication and division. It tells they should be performed in order of Division, Multiplication, Addition and Subtraction. Without DMAS rule all mathematical equations will come up with different answers.

Lets solve the expression and check whether the L.H.S = R.H.S

17-2*3-8=3

17-6-8=3

11-8=3

3 =3

Be sure to multiply first and then subtract

⇒You can also insert addition sign in place of multiplication. It will give the same answer

3 0

3 years ago

Read 2 more answers