The point p(7, 1) lies on the curve y = x − 6 . (a) if q is the point (x, x − 6 ), use your calculator to find the slope of the secant line pq (correct to six decimal places) for the following values of x. (i) 6.5 (ii) 6.9 (iii) 6.99 (iv) 6.999 (v) 7.5 (vi) 7.1 (vii) 7.01 (viii) 7.001 (b) using the results of part (a), guess the value of the slope of the tangent line to the curve at p(7, 1). (c) using the slope from part (b), find an equation of the tangent line to the curve at p(7, 1). y =

yes because there is exactly one y value for every x value

for function there can't be more than one value for every x value

.19875994384

step-by-step explanation:

1699/ 8548

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9