What is the equation of the line that crosses the y-axis at 2 and h. a unit rate of ?

Q: Find the rate of change. Cube root 3√x with respect to x when x = 1, 8, 27

A: Consider the given: fx=x3ddxfx=ddxx3ddxfx=ddxx13ddxfx=13x13-1ddxfx=13x23

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm²/min, find the decreasing…

A: To find- Radius is decreasing at the rate of

Q: consider the equation f(x) = 2x2 - x find the average rate of change between x=3 and x=6

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Q: Find the slope of the tangent line to the curve - 2a? – 2ry – 2y = - 38 at the point (- 4, - 1).

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Q: Q 6. The rate at which ice melts is proportional to the amount of ice at any instant. Find the…

A: ice melts is proportional to the amount of ice, so dm/dt ~ m so dm/dt = km ; k is constant so after…

Q: (a) Find the point at y = x³ + x, if the slope is equal to 4. Then find the equation of tangent…

A: Slope is derivative of y with respect to x. And equation of tangent is (y-y1) =m(x-x1).

Q: Find the slope of the line Express the slope as a rate of change with the popular unit attached

A: We know that slope is the ratio of vertical and horizontal change between two points. Slope of the…

Q: Find an equation of the line tangent to the graph of y = at the point (16, 4/4). Answer: y =

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Q: Q4 if xy-yx=6 is the equation of a curve, find the slope and the equation of the tangent line at the…

A: As per our guidelines we can solve only first question. Please repost the other questions that need…

Q: The side of a cube increases at the rate of 3 m/s, when side of the cube is 8m . Then the rate of…

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Q: Suppose that a particle has been shot into the air in such a way that the rate at which its height…

A: v = 320 - 32tIf h represents the height of the particle at any time t, then:v = dh / dt = 320 - 2t

Q: Suppose you drive your car on a perfectly flat road at a constant speed with no wind. In this case,…

A: As given in the question, The amount of fuel is directly proportional to the distance Travelled. ⇒y…

Q: If x + y represents a motorboat's rate with the current, in miles per hour, its distance after 4…

A: If x+y represents a motorboat’s average velocity with the current, in miles per hour, its distance…

Q: If f(x) = 12x2 - x', what is the rate of change of f'(x) at (2, 40)? %3D Need Help? Watch It

A: Rate of change of f'(x)

Q: If y = 42x2 – 7x³ + x, what is the rate of change of y' at (1, 36)? Need Help? Read It

A: Rate of change of the function

Q: Find the average rate of change of h (x) = 2x² – 7x from x = 3 to r = 6. Simplify your answer as…

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Q: Where k is constant. If the temperature is increasing at 4 kelvins per hour, what is the rate of…

A: We need to find the rate of change of pressure  when temperature is 150K and pressure is 450…

Q: 4. The weight, M, of an astronaut on the moon is directly proportional to the weight, E, on Earth.…

A: Explanation and solutions is given below......

Q: The velocity v of a falling object is directly proportional to the time t of the fall. If, after 2…

A: What will its velocity be after 3 seconds?

Q: In the equation, x² + y² = 45, what is the value of the rate of change in y with respect to time t…

A: To solve this problem we have to first differentiate the given function with respect to 't' and then…

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

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Q: Find an equation for the line tangent to the graph of f(x)=4xe^x at the point (a,f (a)) for a=3…

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Q: If the demand for q units of a product priced at $p per unit is described by the equation 200 V29 +…

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Q: Suppose the constant rate of change y with respect to x is -2.5 and we know that y=-6.75 when x=1.5…

A: Given,The constant rate of change of y with respect to x = -2.5.We know that,Slope = rate of change…

Q: Find the slope and equation of the line tangent to f (x) = x2 +9 at the point (1, 10).

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Q: Consider the ordered pair of points below. (X1, V1) = (-8, -7) (x2, Y2) = (-5, 2) Find the average…

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Q: Find the equation of the straight line described below. At right angles to y = e* at the point where…

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Q: Solve Find the values of x where the tangent line is horizontal. fめ =(x^-q)? 2. 9

A: To find the points at which the tangent line is horizontal we need to find at which point the slope…

Q: a. What is the slope of the constant function y = k?b. What is the rate of change of a constant…

A: If function is given as y=fx Then the slope of the function is given as the first derivative of the…

Q: Find the rate of change of the given equation y = (2x-1)/(x^2+1) at (1,1).  Select correct answer:…

A: We can find the rate of change of the given equation at the indicated point as below

Q: hamster wheel has a point on the wheel with height modelled by the equation, where h is in cm and t…

A: In this question, the concept of the average rate of change is applied. The average rate of change…

Q: For the curve y = 5x – 2x3, if x .6 increases at the rate of 2 units/s, then find the rate of change…

A: We are given the curve: y=5x-2x3 Slope (m)=dydx=5-6x2 Rate of change of slope  = dmdt=0-12xdxdt Now…

Q: A square with side x cm, is changing with time where x(t) = 4t – 2. What is the rate of change of…

A: Given: A square with side x. changing with time is given as, xt=4t-2. The objective is to find the…

Q: If V(t) is the volume of water in a reservoir at time t (seconds), v(t) is the rate of change,  then…

A: Rate Change: Rate change is defined as the change in one quantity with respect to any other quantity…

Q: S(x) = 3r2 - 5r + 10 %3D What is the rate of change as x goes from r=2 to r = 4? SUBMIT

A: Given: f(x)=3x2-5x+10 a=2 b=4

Q: rate of change

A: It is given that an increase of 3 units change in t corresponds to 4 unit change in d. We have to…

Q: Find the slope of the tangent line to the curve y 5x at the point (-7, 245). A 70 25 -7 -70 E) 7

A: As we know that; The slope of the tangent line to the curve at a given point Px,y is equal to the…

Q: Find the slope of the tangent line to the curve - 6y3 – 42?y? = 2 at the point (1, – 1)

A: We have to find slope of the tangent line to the curve -6y3-4x2y2=2 at the point 1,-1

Q: A5.5-foot-tall woman walks at 4 ft/s toward a street light that is 16,5 ft above the ground, What is…

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Q: Given the model y=3.2(2.4)^x, what is its rate of change?

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Q: If f(x) = 5x2 − x3, what is the rate of change of f '(x) at (2, 12)?

A: To calculate the rate at which the given function changes at the given point

Q: What is the rate of change for h(x) = 2x2 + 7 on the interval [2, 9]?

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Q: For the given curve y = 5x – 2x', when x increases at the rate of 2 units / sec, then how fast is…

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Q: a drug concentration curve is given by C(t)= 20te^-0.2t, which C in mg/ml and t in minutes. What is…

A: A drug cocentration curve isC(t)=20te-0.2tTo find the rate of concentration. We have to…

Q: Which pairs of points would result in a line with a rate of change of 2:1?

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Q: As y increases by 10,x Jncreases by 5. Which equation represents this rate of change? (7.1B, 7.1D,…

A: Rate of change = change in y /change in x

Q: In the equation, r + y² = 45, what is the value of the rate of change in y with respect to time t…

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