y = 7x - 3
Note the gradient of the tangent is the derivative of y at x = 1
Differentiate using the power rule
(a
) = na
y = 3x³ - x² + 2
= 9x² - 2x
x = 1 :
= 9 - 2 = 7 ← gradient of tangent
equation in point- slope form, using m = 7 and (a, b) = (1, 4)
y - 4 = 7(x - 1) ← point-slope form
y - 4 = 7x - 7
y = 7x - 3 ← in slope-intercept form
Answer:
a) 7x words
b) 1000/x days
c) 15000 + 10x words
Step-by-step explanation:
The best way to do this would be to plug in real numbers to see how each situation would play out. For example, for part a, let's say he learns 20 new words each day. One week has seven days, so that would be 20 x 7, which is 140 words. You multiply the # of days by the # of words, which is x.
For part b, if he tried to reach 1000 new words by doing 20 new words a day, you would find how long that would take by doing 1000 / 20, which would give you 500 days. You divide the # of new words he's trying to reach by the # of words a day.
For part c, he already has a set # of new words that he's learned, and now he's just continuing the progress, so you start out with 15000, then add that to 10 new words a day multiplied by # of days (x).
Answer:
2 miles per day
Step-by-step explanation:
The length of the road built is 1/3 miles, so let's call L = 1/3
The time spent to build this length is 1/6 days, so let's call D = 1/6
To find the unit rate in miles per day, that is, the speed that this length of the road was built, we just need to divide L by D (speed is distance over time). Let's call the speed S:
S = D/T
S = (1/3) / (1/6)
S = (1/3) * 6
S = 2 miles per day