Answer:
1. slope
2. slope
3. slope
4. y intercept
5. slope
6. it crosses the x axis
7. when the value of y is zero
8. when the form is y = something
9. when the form is x = something
10. Positive slope
11. Negative slope
12. y=x
13. Slope Intercept form
14. Standard form
The function is (-x+3)/ (3x-2) and we get f(1)=1 and differentiation is f'(x)=-7/ (9x²- 12x+4).
Given that,
The function is (-x+3)/ (3x-2)
We have to find f(1) and f'(x).
Take the function expression
f(x)= (-x+3)/ (3x-2)
Taking x as 1 value
f(1)= (-1+3)/(3(1)-2)
f(1)=2/1
f(1)=1
Now, to get f'(x)
With regard to x, we must differentiate.
f(x) is in u/v
We know
u/v=(vu'-uv')/ v² (formula)
f'(x)= ((3x-2)(-1)- (-x+3)(3))/ (3x-2)²
f'(x)= ((-3x+2)-(-3x+9))/ 9x²- 12x+4
f'(x)=(-3x+2+3x-9)/ 9x²- 12x+4
f'(x)=2-9/ (9x²- 12x+4)
f'(x)=-7/ (9x²- 12x+4)
Therefore, The function is (-x+3)/ (3x-2) and we get f(1)=1 and differentiation is f'(x)=-7/ (9x²- 12x+4).
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Answer:
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Step-by-step explanation:
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It will take them 3 hours to meet
Step-by-step explanation:
The given is:
- Jack and Jill live 345 miles apart from one another
- They want to meet for lunch and agree to leave the same time, drive toward each other, and meet somewhere along the route
- Jack's average rates 60 mph
- Jill's average rate is 55 mph
We need to find how long it will take them to meet
Distance = Speed × Time
∵ They will drive toward each other at the same time and meet
each other somewhere
- That means they will drive for the same time
∵ Jack's average rates 60 mph for t hours
∴ Jack will drive a distance = 60 × t = 60 t miles
∵ Jill's average rate is 55 mph for t hours
∴ Jill will drive a distance = 55 × t = 55 t miles
∵ The distance between Jack and Jill is 345 miles apart
- Add their distance above and equate the sum by 345
∴ 60 t + 55 t = 345
∴ 115 t = 345
- Divide both sides by 115
∴ t = 3 hours
It will take them 3 hours to meet
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