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Bad White [126]
3 years ago
8

Is my answer correct?

Mathematics
1 answer:
adell [148]3 years ago
6 0
Actually, it's the bottom one.  
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The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope
NARA [144]

Answer:

a) (i) m = 2.22, (ii) m = 2, (iii) m = 2, (iv) m = 2, (v) m = 1.82, (vi) m = 2, (vii) m = 2, (viii) m = 2; b) m \approx 2; c) The equation of the tangent line to curve at P (7, -2) is y = 2\cdot x + 12.

Step-by-step explanation:

a) The slope of the secant line PQ is represented by the following definition of slope:

m = \frac{\Delta y}{\Delta x} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}

(i) x_{Q} = 6.9:

y_{Q} =\frac{2}{6-6.9}

y_{Q} = -2.222

m = \frac{-2.222 + 2}{6.9-7}

m = 2.22

(ii) x_{Q} = 6.99

y_{Q} =\frac{2}{6-6.99}

y_{Q} = -2.020

m = \frac{-2.020 + 2}{6.99-7}

m = 2

(iii) x_{Q} = 6.999

y_{Q} =\frac{2}{6-6.999}

y_{Q} = -2.002

m = \frac{-2.002 + 2}{6.999-7}

m = 2

(iv) x_{Q} = 6.9999

y_{Q} =\frac{2}{6-6.9999}

y_{Q} = -2.0002

m = \frac{-2.0002 + 2}{6.9999-7}

m = 2

(v) x_{Q} = 7.1

y_{Q} =\frac{2}{6-7.1}

y_{Q} = -1.818

m = \frac{-1.818 + 2}{7.1-7}

m = 1.82

(vi) x_{Q} = 7.01

y_{Q} =\frac{2}{6-7.01}

y_{Q} = -1.980

m = \frac{-1.980 + 2}{7.01-7}

m = 2

(vii) x_{Q} = 7.001

y_{Q} =\frac{2}{6-7.001}

y_{Q} = -1.998

m = \frac{-1.998 + 2}{7.001-7}

m = 2

(viii)  x_{Q} = 7.0001

y_{Q} =\frac{2}{6-7.0001}

y_{Q} = -1.9998

m = \frac{-1.9998 + 2}{7.0001-7}

m = 2

b) The slope at P (7,-2) can be estimated by using the following average:

m \approx \frac{f(6.9999)+f(7.0001)}{2}

m \approx \frac{2+2}{2}

m \approx 2

The slope of the tangent line to the curve at P(7, -2) is 2.

c) The equation of the tangent line is a first-order polynomial with the following characteristics:

y = m\cdot x + b

Where:

x - Independent variable.

y - Depedent variable.

m - Slope.

b - x-Intercept.

The slope was found in point (b) (m = 2). Besides, the point of tangency (7,-2) is known and value of x-Intercept can be obtained after clearing the respective variable:

-2 = 2 \cdot 7 + b

b = -2 + 14

b = 12

The equation of the tangent line to curve at P (7, -2) is y = 2\cdot x + 12.

7 0
2 years ago
What is the difference in elevation between a plane flying 14,200 feet above sea level and a submarine traveling 890 feet below
marissa [1.9K]

maths is gud to us 151617128




5 0
2 years ago
Read 2 more answers
Put in slope intercept form
LiRa [457]
These require you solve for y. Do that by subtracting the x-term, then dividing by the y-coefficient.

5. 3y = 7x -9
  y = (7/3)x -3

6. 6y = -2x -3
  y = (-2/6)x -3/6
  y = (-1/3)x -1/2

7. 8y = 2x + 12
  y = (1/4)x +3/2
3 0
3 years ago
A rectangular turf of size 20 feet by 34 feet is surrounded by a flower bed of uniform width
BaLLatris [955]

Answer:

9.18 feet

Step-by-step explanation:

dimensions of whole area = (20 + x)(34 + x)

= 680 + 54x + x^2

where x is the width of the flower bed.

we know that x^2 + 54x + 680 = 1200

x^2 + 54x - 520 = 0

x = 9.18 or x = -63.18

width of flower bed cannot be negative therefore it is width 9.18 feet

6 0
3 years ago
Round 63.796 to the nearest tenth
Scrat [10]

Answer:

63.8

Step-by-step explanation:

to the tenth

4 0
3 years ago
Read 2 more answers
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