The percentage of high school students who drink and drive was 17.5% at the beginning of 2001 and declined linearly to 10.3% at the beginning of 2011.† (a) Find a linear function f(t) giving the percentage of high school students who drink and drive in year t, where  t = 0  corresponds to the beginning of 2001.

Q: Find the derivative of the function. 7x-4 y = 6x + 1

A: Giveny=7x-46x+1We know thaty'=ddxf(x)g(x)=f'(x)g(x)-g'(x)f(x)g(x)2

Q: Use the Chain Rule to find the derivative of the function. y = (2x² - 9)3

A:

Q: Suppose that f is a linear function with slope -3.4 and that f (3) = 4. What value of x gives f(x) =…

A:

Q: use the Chain Rule to find the derivative. y = (x4 − x3 − 1)2/3

A: y = (x4 − x3 − 1)2/3 derivative formula ddxxn=nxn-1

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A:

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A: As per our guidelines we are supposed to solve only one question i.e. the first one. For the…

Q: Suppose that f is a linear function with slope -3.2 and that f (3) = 6. What value of x gives f(x) =…

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A:

Q: Determine the derivative of a quadratic function of general form y=ax2+bx+c.

A:

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Q: Hamed own a local gold market that currently has (4693401)subscriber in Instagram at a quarterly…

A: Given: There are 4693401 subscribers when the quarterly charge is R.O. 18 and 4684852 subscribers…

Q: Calculate the derivative of the exercise: y=(4x3+3)4(x+1)-3

A: To find: The derivative of below expression.

Q: Use the Chain Rule to find the derivative of the function. y = (2x2 − 3)3 y' =

A: The chain rule to find the derivation is,

Q: Use the Chain Rule to find the derivative of the function. y = (x3 + 5x2)−1 y' =

A: The function is given by,

Q: Use the Chain Rule to find the derivative. y = (x4 - x3 - 1)2/3

A: To find the derivative y = x4 - x3 - 123.

Q: Find the derivative of the function. g (x) = 6x-3 + 2x Og (x) = 18x + 10x-6 %3D Og (x) = -18x-3…

A:

Q: The average rate of change of the linear function f(x) =3x +5 between any two points is_________ .

A: Given that: The linear function f(x) = 3x + 5.

Q: Does the given equation define an implicit function around the point (y=3, x=1) and why?

A:

Q: Let f and g be linear functions with equations f(x) = m1x + b1 and  g(x ) = m2x +b2. Is f ° g also a…

A: The given linear functions are fx=m1x+b1    and  gx=m2x+b2. This implies that,…

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Q: Suppose that f is a linear function with slope 4 and that f(2) =  4.   Find the equation for f and…

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Q: Use the Chain Rule to find the derivative of the function. y = (3x2 - 7)3

A:

Q: ƒ(x) = (x³ – 4x) 10

A: Solve the derivative

Q: Find the derivative of the function. f(x) = V3x + 2

A:

Q: ATTACHED THANKYOU

A: Given that the first term of the AP is a and common difference is d.And the AP is constructed by the…

Q: uppose that f is a linear function with slope -3.2 and that f (2) = 4. What value of x gives f(x) =…

A: Given that the f is a linear function. Slope = -3.2 f(2) = 4

Q: Find the first and second derivatives of the function. (6t2 - 4)2 (5t2)

A: Given function: f(t) = (6t2 - 4)2 (5t2) = (36t4 - 48t2 + 16) (5t2) = 180t6 - 240t4 + 80t2 Recall the…

Q: 1 y = 8x* + 7x³ + =x² – 14x + 6 %3D -

A:

Q: Use the Chain Rule to find the derivative. y = (x4 − x3 − 1)2/3

A:

Q: Suppose that average annual income (in dollars) for the years 1990 through 1999 is given by the…

A: The general linear equation is fx=y=mx+c Here m is the slope of the curve and c is the y-intercept.…

Q: Assume the number of U.S. dial-up Internet households stood at 39.5 million at the beginning of 2004…

A: Given  The number of U.S. dial-up Internet households at the beginning of 2004 = 39.5 million…

Q: Find the derivative of the function y=3√2x2.

A:

Q: Use the chain rule to find the derivative of f(x) = 2e5a* + 9x³ %3D f' (x) =

A: We have to find

Q: Find the derivative of the function y=(2x+5)^4(3x+1)^-5

A: The given function is y=(2x+5)4(3x+1)-5. The negative property of exponent isa-x is 1ax. The…

Q: Find the derivative of the function y=(4x+1)^5(3x+1)^-4

A: We can find the derivative as below.

Q: What is the output when the input is 4 for a linear function that has a y-intercept of 5 and a rate…

A: Given information: The input of the linear function is 4. The y-intercept of 5 and the rate of…

Q: Find the derivative of the function y=5x3+3−2x3+3√x5.

A: To Find: Derivative of function   y=5x3+3-2x3+3x5.

Q: Find the derivative of the function y=3x2−2√x+1.

A: y=3x2-2x+1Differentiate with respect to xdydx=ddx(-2x+1+3x2)

Q: 3.Find the coordinates of the points on the curves y =x3 -3x2-12x+10 with the gradients -2.

A:

Q: Find the gradient of the graph a) y = 6-3x where x = 5 )y= 12 + x-3x? where x = - 3

A: Find the gradient of the function

Q: y = (x² + 2)(x-3)

A: The objective is to find the derivative.

Q: The idea of a large, stable middle class (defined as those with annual household incomes in 2010…

A:

Q: Assume the number of U.S. dial-up Internet households stood at 38.5 million at the beginning of 2004…

A: The number of U.S. dial-up Internet households at the beginning of 2004 t = 0 year, f0 = 38.5…

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A: Given,The amount of heat H(in joules) required to convert one gram of water into vapor is linearly…

Q: y is a linear function of x with slope −4. If y is −3 when x is −1, what is y when x is 8? You do…

A: Linear Function  Y= mX+c  m= slope of function  c = Y intercept

Q: y=4x

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A:

Q: Find the derivative of the function. 3x-4 %3D 2. X+6x y' = ]

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.