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ankoles [38]
3 years ago
14

Sal was tired of waiting for Amir to show up at their meeting place, so he started running at an average speed of 4.5 mph withou

t him. Ten minutes later, Amir still had 0.25 of a mile to go before he reached the meeting place, but Sal was 0.75 of a mile beyond it. If Amir is running at a faster pace, 6.7 mph, to the nearest hundredth of an hour, after how much time will Amir catch up to Sal?
A0.04 hours

B0.09 hours

C0.23 hours

D0.45 hours
Mathematics
1 answer:
strojnjashka [21]3 years ago
4 0

27 minutes (0.45 hours)

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Find the vector equation of the line through the points (1, 2, −1) and (2, 4, 5). Is the point (−5, −10, −37) on this line?
pav-90 [236]

Answer:

(1+t, 2+2t, -1+6t); C is on this line.

Step-by-step explanation:

Let's find the vector equation of the line.

Given information:

Point A is (1, 2, -1)

Point B is (2, 4, 5)

Point C is (-5, -10, -37)

The difference between the two first given points (A, B) is:

B-A=(2, 4, 5)-(1, 2, -1)=(2-1, 4-2, 5-(-1))=(1, 2, 6) which is called the direction vector, so the equation is:

(x, y, z)=(1, 2, -1) + t*(1, 2, 6)=(1+t, 2+2t, -1+6t)

Now let's find if point C is on the line:

(x, y, z)=(1, 2, -1) + t*(1, 2, 6)

(-5, -10, -37)=(1, 2, -1) + t*(1, 2, 6)

(-5, -10, -37)-(1, 2, -1)=t*(1, 2, 6)

(-5-1, -10-2, -37+1)=t*(1, 2, 6)

(-6, -12, -36)=t*(1, 2, 6) from where we can obtain:

1*t=-6 --> t=-6

2*t=-12 --> t=-6

6*t=-36 --> t=-6

In conclusion, because from all the equations we obtained t=-6, then point C is on this line.

7 0
3 years ago
Help me find the asnswer
lyudmila [28]
The first one tehehe :)
7 0
3 years ago
How many solutions does tan^-1 3 have?
Ivahew [28]

<span>y = arctan(3) </span>

<span>Since the inverse tangent is a function, there is only one y-value. However, there are infinitely many solutions to tan(y) = 3 (they are arctan(3) + kπ where k is an integer). The approximate value of y here is y = arctan(3) ≈ 1.24905 (in radians). 
</span>
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
6 0
3 years ago
Do not scam or u get a report i need help so please
ser-zykov [4K]

Answer:

0.35 each

Step-by-step explanation:

6 0
3 years ago
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Emilio bought an ant farm that had 15 ants in it already. He read somewhere that
Nina [5.8K]

The number of ants in his farm after 12 weeks is 218.

Step-by-step explanation:

Step 1:

It is given that there are 15 ants initially and the ant population increases by 25% each week.

This is an exponential rate of increase that can be modeled by the following equation:

Number of ants after n weeks = Initial number of ants * (1 + rate of increase) ^{n}

Step 2:

Rate of increase = 25% = 25 / 100 = 0.25

Number of weeks = 12

Number of ants  after 12 weeks = 15* (1 + 0.25 )^{12} = 218.27 (rounded off to 218)

Step 3:

Answer:

The number of ants in his farm after 12 weeks is 218.

6 0
3 years ago
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