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spin [16.1K]
3 years ago
14

How to find (a) and (b)?​

Mathematics
1 answer:
rodikova [14]3 years ago
3 0

Answer:

A) Gradient = -3

B) 3y - x = 7

Step-by-step explanation:

The curve has the equation;

y = x³ - 6x² + 9x + 1

We are given the pints it passes through as;

A(2,3) and P(3, 1)

A) to find the gradient, we will find the derivative of the given equation.

Thus;

Gradient = y' = 3x² - 12x + 9

At point A, x = 2. Thus;

Gradient = 3(2²) - 12(2) + 9

Gradient = 12 - 24 + 9

Gradient = -3

B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3

Thus, equation of the normal to the curve at point A will be;

(y - 3) = ⅓(x - 2)

Multiply both sides by 3 to get;

3y - 9 = x - 2

3y - x = 9 - 2

3y - x = 7

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Taya2010 [7]

Answer:

top row on 9 page; 9) 53/5 10) 26/4 11) 37/4

bottom row on 9 page; 9) 8 and 1/7 10) 6 and 3/4 11) 1 and 1/3

top row on 3 page; 3) 2 and 2/7 4) 5 and 3/4 5) 8 and 1/10

bottom row on 3 page; 3) 4/3 4) 3/2 5) 12/5

top row on 12 page; 12) 21/10 13) 62/6 14) 57/6

bottom row on 12 page; 12) 1 and 9/10 13) 10 and 1/2 14) 3 and 3/8

Step-by-step explanation:

You never specified if these had to be simplified or turned into a fraction, so I just simplified them. That's about it.

I hope this helps :)

7 0
3 years ago
The results of a car race are shown. How much faster did Evans drive per lap than loza?
Lelechka [254]
Evans finishes 42 laps in 96,6 mins and Loza finished 38 laps in 102,6 mins

Evans. 96,6÷42= 2,30 mins
Loza . 102,6÷38= 2,70 mins

2,70 mins - 2,30 mins
= 40 secs and Evan is faster with 40secs in each lap.
8 0
4 years ago
Write a sine function that has an amplitude of 5, a midline of 3 and a period of 1/8.
vodomira [7]

Answer:

y=5sin(16pix)+3

Step-by-step explanation:

Amp=5 means our curve is either y=5sin(bx+c)+d or y=-5sin(bx+c)+d.

y=sin(x) has period 2pi.

So y=sin(bx) has period 2pi/b.

We want 2pi/b=1/8.

Cross multiplying gives: 16pi=b

y=5sin(16pix+c)+d

d=3 since we want midline y=3.

y=5sin(16pix+c)+3

We can choose c=0 since we aren't required to have a certain phase shift.

y=5sin(16pix)+3

6 0
3 years ago
I need help on iready
kicyunya [14]

Answer:

the answer is 3

Step-by-step explanation:

because if you do the methoes method you know that it rules out 1 and 2 after you do that its just between 3 and 4, for the caunususicon there has to be one, that is why i think its 3. hope this helps!

7 0
3 years ago
9x + 3y = 4<br> 7x + 3y = 20
xeze [42]

Answer:

x=-8, y=76/3

Step-by-step explanation:

I solved for substitution since I didn't know exactly what you're solving for.

5 0
4 years ago
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