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julia-pushkina [17]
3 years ago
5

Two bikers rode at a constant speed on a 150-meter track. The data here show each biker's distance for a certain part of the rac

e. Who won the race and by how much?
Mathematics
1 answer:
Luda [366]3 years ago
4 0

Answer: 2 then 1

Step-by-step explanation:

Just did it

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Vectors: Find the vector from the point A=(−1,−7,3) to the point B=(3,−2,9).
devlian [24]

Answer:

\overrightarrow {AB} = (4,5,6)

1. 〈x,y,z〉=〈−1,−7,3〉+t〈−4,−5,−6〉 F

2. 〈x,y,z〉=〈−1,−7,3〉+t〈3,−2,9〉 F

3. 〈x,y,z〉=〈−1,−7,3〉+t〈4,5,6〉 T

4. 〈x,y,z〉=〈3,−2,9〉+t〈−1,−7,3〉 F

5. 〈x,y,z〉=〈3,−2,9〉+t〈4,5,6〉 F

Step-by-step explanation:

The vector AB is the vectorial difference between point A and B, that is:

\overrightarrow {AB} = \vec B - \vec A

Given that \vec A = (-1,-7,3) and \vec B = (3,-2,9), the vector AB is:

\overrightarrow {AB} = (3,-2,9)-(-1,-7,3)

\overrightarrow{AB} = (3-(-1),-2-(-7),9-3)

\overrightarrow {AB} = (4,5,6)

The vectorial equation of the line is represented by:

\langle x, y, z\rangle = \vec A + t \cdot \overrightarrow {AB}

Where t is the parametric variable, dimensionless. Given that \vec A = (-1,-7,3) and \overrightarrow {AB} = (4,5,6)

\langle x,y,z \rangle = \langle -1,-7,3 \rangle + t\cdot \langle 4,5,6 \rangle

Finally, the list of questions are now checked:

1. 〈x,y,z〉=〈−1,−7,3〉+t〈−4,−5,−6〉 F

2. 〈x,y,z〉=〈−1,−7,3〉+t〈3,−2,9〉 F

3. 〈x,y,z〉=〈−1,−7,3〉+t〈4,5,6〉 T

4. 〈x,y,z〉=〈3,−2,9〉+t〈−1,−7,3〉 F

5. 〈x,y,z〉=〈3,−2,9〉+t〈4,5,6〉 F

4 0
2 years ago
I don't understand this ​
Mamont248 [21]

Answer:

you have to use graph to make it bro

Step-by-step explanation:

hope it will help you

4 0
3 years ago
A community theater sells about 150 tickets to a play each week when it charges $20 per ticket.
Marta_Voda [28]

Answer:

  • r = 12.5p(32 -p)
  • $16 per ticket
  • $3200 maximum revenue

Step-by-step explanation:

The number of tickets sold (q) at some price p is apparently ...

  q = 150 + 25(20 -p)/2 = 150 +250 -12.5p

  q = 12.5(32 -p)

The revenue is the product of the price and the number of tickets sold:

  r = pq

  r = 12.5p(32 -p) . . . . revenue equation

__

The maximum of revenue will be on the line of symmetry of this quadratic function, which is halfway between the zeros at p=0 and p=32. Revenue will be maximized when ...

  p = (0 +32)/2 = 16

The theater should charge $16 per ticket.

__

Maximum revenue will be found by using the above revenue function with p=16.

  r = 12.5(16)(32 -16) = $3200 . . . . maximum revenue

_____

<em>Additional comment</em>

The number of tickets sold at $16 will be ...

  q = 12.5(32 -16) = 200

It might also be noted that if there are variable costs involved, maximum revenue may not correspond to maximum profit.

5 0
2 years ago
An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. What is the probability that the
mezya [45]
Well there is a total of 20 different outcomes and you can only get a sum of 7 four times and 11 once so in total 5 times out of 20 so that is 5 to the twentieth place beyond the decimal but you can round that up to 0.5%.
4 0
3 years ago
Read 2 more answers
For the function f(x) = (5-6x)^2, fine f^-1
Scorpion4ik [409]

Answer:

f(-1) = 121

Step-by-step explanation:

f(x) = (5-6x)^2 (First we will substitute x for -1)

f(-1) = (5-6(-1))^2 (Then we will combine like terms)

f(-1) = (11)^2 (Then we will square it)

f(-1) = 121 (You are done)

8 0
2 years ago
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