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Ludmilka [50]
3 years ago
6

Question 3 (4 MARKS) Find the equation of the tangents to the curve of the function with rule y = x^2 at the points where x = a

and x =-a and find the coordinates of the point of intersection of these two tangents.​
Mathematics
1 answer:
Arte-miy333 [17]3 years ago
3 0

Answer:

(0 , -a²)

Step-by-step explanation:

tangent at x = a and x = -a

y = x²     (a , a²) and (-a , a²) must be on the curve and tangent to curve

gradient dy/dx = 2x

slope (m) at x = a is <u>2a</u>     and slope (m') at x=-a is<u> -2a</u>

line1: (y - a²) / (x - a) = 2a

        y - a² = 2a (x - a)                           y = 2ax - a²   ... (1)

line2: (y - a²) / (x + a) = - 2a                   y = -2ax- a²   ... (2)

(1) - (2): 4ax = 0       a≠0    x = 0

y = - a²

I wish I did it right, or ....

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Let g represent video games. The equation you can use to solve for the amount of video games and CDs Jasmine can buy with her savings is:
43g+72=1128

The 43g part is because it costs 43 dollars for every video game, so you need to multiply 43 by the amount of games she buys to get the total for g games.
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Now, solving:
43g+72=1128 ...subtract 72 from both sides
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The answer: Jasmine can buy 24 games with her savings after spending $72 on CDs.
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