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choli [55]
2 years ago
9

A concrete mixing tub contains 34 liters of water and 22 liters of sand. Starting at the same time, water is added to the tub at

a rate of 5 liters per minute,
while sand is also added to the tub at a rate of 7 liters per minute.
Part A
In how many minutes will the tub contain equal amounts of water and sand?
2 minutes
6 minutes
12 minutes
24 minutes
Mathematics
1 answer:
lubasha [3.4K]2 years ago
3 0

Answer:

6 minutes

6

6 minutes

6 minutes

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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
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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}}

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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}

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(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

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

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

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

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

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(viii)  x_{Q} = 7.0001

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

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

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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:

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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

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