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6 hours ago

Consider the following function. f(x) = 2/x, a = 1, n = 2, 0.6 ≤ x ≤ 1.4 (a) Approximate f by a Taylor polynomial with degree n

at the number a. T2(x) = 2−2(x−1)+(x−1)2 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R2(x)| ≤

Mathematics

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Rachel found this rate of change for the scenario represented in the table.

babunello [11817]

THE FUNCTION IS CONTINUOUS - True
The table indicates that for every hour indicated, there is a corresponding amount of juice (cups) provided. The graph would represent a linear progression between the hours of 4 and 8 without any discontinuities.

TIME IS THE DEPENDENT VARIABLE - False
Time acts as the independent variable since it remains unaffected by any other factors. Conversely, the number of cups is contingent upon the hours, categorizing it as a dependent variable.

THE SCENARIO IS CHARACTERIZED BY
A LINEAR FUNCTION AS THE RATE OF CHANGE IS CONSTANT - True
The rate of change is a steady 53 cups per hour, indicating a linear function.

AS TIME INCREASES, THERE ARE FEWER CUPS OF JUICE POURED EACH HOUR - False
Since the rate of change is positive, the cups poured each hour will actually increase.

FOR EACH EXTRA HOUR, 53 CUPS OF JUICE ARE POURED - True
The hourly difference in cups poured is consistently 53.

8 0

1 month ago

Read 2 more answers

Assume that the cheetah travels an average of 40 mph to go from its resting place to a rock near a river. On the return trip to

AnnZ [12381]

Response:

9.55 minutes

Step-by-step breakdown:

x hours to reach the river

0.25-x hours for the return trip, as 15 minutes equals 0.25 hr.

to the river 40 mph * x hours =40x miles

from the river 70 mph (0.25-x) hours=17.5-70x

these two equations are equivalent

40x=17.5-70x

110x=17.5

x=17.5/110=0.159 hours

9.55 minutes

3 0

2 months ago

Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. x2 + y2 = 25 (a) Fin

Zina [12379]

Answer:

(a) $\frac{dy}{dt}=-3\frac{3}{4}$

(b) $\frac{dx}{dt}=3\frac{3}{4}$

Step-by-step explanation:

$x^{2} +y^{2}=25$

Calculate $\frac{d}{dt}$ for each term.

$\frac{d}{dt}(x^{2})+\frac{d}{dt}(y^{2})=\frac{d}{dt}(25)\\\\(\frac{d}{dx}(x^{2})*\frac{dx}{dt}) +(\frac{d}{dy}(y^{2})*\frac{dy}{dt})=\frac{d}{dt}(25)\\\\2x\frac{dx}{dt} +2y\frac{dy}{dt} = 0\\\\$

For Question a

$2y\frac{dy}{dt}=-2x\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{-2x\frac{dx}{dt}}{2y} \\\\\frac{dy}{dt}=-\frac{x}{y}\frac{dx}{dt}$

With x = 3, y = 4, and dx/dt = 5.

$\frac{dy}{dt}=-\frac{3}{4}*5=-\frac{15}{4}\\ \\\frac{dy}{dt}=-3\frac{3}{4}$

For Question b

$2x\frac{dx}{dt}=-2y\frac{dy}{dt}\\\\\frac{dx}{dt}=\frac{-2y\frac{dy}{dt}}{2x} \\\\\frac{dx}{dt}=-\frac{y}{x}\frac{dy}{dt}$

Given x = 4, y = 3, and dx/dt = -5.

$\frac{dx}{dt}=-\frac{3}{4}*-5=\frac{15}{4}\\ \\\frac{dx}{dt}=3\frac{3}{4}$

5 0

2 months ago

Lee has a bag with 500 quarters. Some are the older eagle quarters, and others are the newer state quarters. She pulls out 10 qu

tester [12383]

I couldn't write it out in detail, so the solution is 200. The work is visible in the image below if you need clarification. I hope this is useful to you!

7 0

3 months ago

The area of a square picture frame is 55 square inches. Find the length of one side of the frame. Explain to the nearest whole i

Inessa [12570]

We know that the area of a square picture frame measures 55 square inches. We need to calculate the length of one side of the frame. Let's denote the side length as x inches. The formula for the area of a square is x squared, and we can conclude that the area equals 55. Taking the square root of both sides, we see that 55 is nearer to 49, so x is approximately 7 inches.

7 0

2 months ago