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olga2289 [7]
3 years ago
7

Please help me with this question. Thank you so much everyone.

Mathematics
2 answers:
LiRa [457]3 years ago
8 0

Answer:

1159

Step-by-step explanation:

She wants to read 1000 pages per week for five weeks.

So in total she wants to read 1000 * 5 = 5000 pages.

The first three weeks she read 894 pages per week.

So during the first three weeks she read a total of 894 * 3 = 2682 pages.

We want to find how many pages she must read per week for the last two weeks to reach her goal.

Goal: 5000 pages

Pages read so far: 2682

Weeks remaining: 2

To find how many pages she must read for the last two weeks we simply subtract the number of pages she read during the first 3 weeks (2682 ) by her goal ( 5000 )

5000 - 2682 = 2318

So she must read 2318 pages during the last 2 weeks.

If we want to find the amount of pages she must read per week during the last 2 weeks to reach her goal, we simply divide the amount of pages she must read during the last few weeks to reach her goal ( 2318 ) by the number of remaining weeks ( 2 )

2318 / 2 = 1159

So for the last two weeks she must average 1159 pages per week.

Georgia [21]3 years ago
3 0

Answer:

1159 pages

Step-by-step explanation:

According to Briana's goal,

Pages to be read per week = 1000 pages

Number of weeks = 5

So, pages to be read in 5 weeks

= 5×1000 pages

= 5000 pages

But in reality,

Pages read in each first 3 weeks = 894 pages

So, total pages read in all first 3 weeks

= 3×894 pages

= 2682

Pages remained to be read to complete the goal

= Pages to be read in 5 weeks according to her goal - Pages actually read in all first 3 weeks

= 5000 pages - 2682 pages

= 2318 pages

So, pages to be read in each last 2 weeks

= 2318 pages/2

= 1159 pages

So, Briana will have to need to average 1159 pages over the last two weeks to complete her goal.

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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.

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