Mathematics, 01.08.2019 21:00 val4218

Sydney drives 10 mi at a certain rate and then drives 20 mi at a rate 5 mi/h faster than the initial rate. write expressions for the time along each part of the trip. add these times to write an equation for the total time in terms of the initial rate, t total (r).

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From the given we know that Sydney drives 10 mi at a certain rate. Let us call this initial rate as r. We also know that Sydney then drives 20 mi at a rate 5 mi/h faster than the initial rate.

We know that the relationship between time, distance and rate is:

$t=\frac{d}{r}$

where t is the time, d is the distance and r is the rate. We also know that the distances given to us in the question are constants at 10 mi/h and 20 mi/h, thus, the time, t is a dependent of the rate variable, r only and this will make the above equation to be:

$t(r)=\frac{d}{r}$

Thus, for the first part of the trip, the time, $t_{1}$ can be expressed as : $t_{1}(r)=\frac{10}{r}$

Likewise, for the next part of the trip, the time $t_{2}$ can be expressed by: $t_{2}(r)=\frac{20}{r+5}$

The above two equations represent the expressions for the time along each part of the trip.

Adding both these times to write an equation for the total time in terms of the initial rate, $t_{total}(r)$ , we will get:

$t_{total}(r)=\frac{10}{r}+\frac{20}{r+5}$

$t_{total}(r)=\frac{10r+50+20r}{r(r+5)} =\frac{30r+50}{r(r+5)}$

The above is the total time in terms of the initial rate.

Answer from: Quest

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step-by-step explanation:

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Answer from: Quest

Answer: f(x) = -2x^3 +3x^2 +11x -6see attachedan infinite number. since the magnitude of the leading coefficient is not specified, it may be any negative number. (we have chosen the smallest magnitude integer that makes all coefficients be integers.)step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

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Sydney drives 10 mi at a certain rate and then drives 20 mi at a rate 5 mi/h faster than the initial...