The population of a slowly growing bacterial colony after t hours is given by p(t) = 5t² + 20t + 150. Find the growth rate after 4 hours. bacteria/hour

Q: Find all x-intercepts of the following function. Write your answer or answers as coordinate points.…

A: f(x)=(x2+11x-12)

Q: Find the indicated angle 8. (Use either the Law of Sines or the Law of Cosines, as appropriate.…

A:

Q: 2 3 If f(x) = 7+ + x x2¹ Find f'(5). find f'(x).

A:

Q: what is the addition or subtraction on formula used to write the expressions.

A:

Q: 25. f(x) = 2x³/5 - x6/5; c= 0.

A:

Q: Solve each equation for x by converting to exponential form. In part (b), give two forms for the…

A:

Q: The system dx/dt = x + y, dy/dt = x + 2y + 1 has a constant solution. true or false?

A: dx/dt = x + y,dy/dt = x + 2y + 1

Q: Use the graph below to answer the question. B no E Oyes H Is vertex H adjacent to vertex A? F

A: The graph is given as,

Q: Given the curve تن 2³ + 2xy + y³ = 3 3 Find an equation of the tangent line to the curve at the…

A:

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it…

A: The given integral is

Q: An icosahedron is a Platonic solid with a surface that consists of 20 equilateral triangles. By what…

A: An icosahedron consists 20 equilateral triangle.Side length of the equilateral triangle is 16.2The…

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: If exists for every  then,provided that limit exist and finite. Then it is convergent.Given…

Q: Find the standard equation of the circle with center(2,-5) and radius 2.

A:

Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Remember the…

A: To find the following integral.

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: Find the derivative of the function. f(x) = 8x² In(x) f'(x) = 16x ln(x) + 8x

A: The objective of the question is to find the derivative of the function f(x) = 8x^2 ln(x).

Q: Consider the parabola p(x) −9.7x² + 13.7x + 4.7. For which interval [A, B] is O a. [0.7062, -0.7062]…

A:

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A:

Q: 33. Let f(x) = ax²+bx+c, a ‡0. Show that f has a local maximum at x = -b/(2a) if a 0.

A: The objective of this question is to prove that the function f(x) = ax^2 + bx + c, where a ≠ 0, has…

Q: Find all horizontal asymptotes of the following function. f(x) = 3x² 33x + 84 5x² – 39x + 28

A:

Q: Which of the following expressions can be differentiated using the product rule? B arcsin (cos x)…

A: To find the correct option which can be differentiated using product rule

Q: A particle moves along the y-axis so that at time t≥ 0 its position is given by y(t) = 3³-5t² +8t.…

A: The given position function is

Q: Find the area of the region. y = 81 - x4 -4 -2 y 80 60 40 20 2 4 X

A:

Q: 1. Find dy/dx: 5x² 10X (a) y = 3√x - 5x² 3x (d) y = xe³x - ln(x² + 1)

A: As per your demand we solve question 1 part dThe given function is

Q: Given f(x, y) =−x5 + 6xy² + 4yº, find fxx(x, y): g) fay(x, y) =

A:

Q: If f(x) = cos(x)²x, find f'(π/4)

A: f(x)=cos(x)2x

Q: Two six sided dice are rolled, and the numbers are observed. What is the probability that the two…

A:

Q: $5000 is invested in an account that pays interest of 5% compounded daily. What will the account be…

A:

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A:

Q: The constant solution y ≡ π/2 of the equation y' = cos(y) is stable , true or false ?

A:

Q: Identify the inflection points and local maxima and minima of the function graphed to the right.…

A:

Q: Question Find the volume of the solid obtained by rotating the region bounded by y=3x^2, x=1,…

A: The objective of this question is to find the volume of the solid obtained by rotating the region…

Q: s sec² x /1+tanx dx.

A: I=∫sec2⁡x1+tan⁡xdx

Q: fx = a(0-sin0) and y = a(1- cos 0), find d and d²y/dx².

A:

Q: - Find a polynomial function of degree 4 with the zeros – 1 (multiplicity 2) and 1 (multiplicity 2),…

A: A polynomial has zeros of multiplicity  and  of multiplicity  and the graph passes through the…

Q: The graph of f(x) is shown below. Estimate and list the value of x where f(x) has a horizontal…

A:

Q: Use the substitution formula to evaluate the integral. T 1² √ cos ² (0³/2) de T √0 cos ² (0³/2) de=…

A: The given integral is .The aim is to find the value of the integral.

Q: (e) ¹/4 sin (27x) dx

A: 2.(e)

Q: Find the average rate of change of the function over the given intervals. h(t) = cott 3 5T a. b. 5…

A: Average rate of change of f(x) over [a,b] is given by average rate of change of f(x) =

Q: 37. So x + 3 √x+1 dx.

A:

Q: 5 If cos(0) = in quadrant I, what is sin(0)? 13

A: This is question of trigonometric ratioHere cosine function value is given  We have to find sine…

Q: Use the Fundamental Theorem of Calculus to find the derivative of the function Paragraph V R F(2) =…

A:

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A:

Q: A coin is tossed 9 times. What is the probability of getting heads exactly one time? Round your…

A:

Q: 3. f(x) = x³, 3x-2, x < 1 x ≥ 1.

A: The given function if

Q: How many cycles are in this graph: a 02 3 01 2 1 3 5 b 1 1 d

A: We find the number of cycles in the following graph:

Q: A solid is bounded below by the cone z = √x² + y² and above by the plane z = 1. Find the center of…

A:

Q: If b 3 4 -2 [° f(x) dx = [² f(x) dx + [ f(x) dx - [² f(x) dx; f(x)dx, a 3 -9 what are the bounds of…

A:

Q: Suppose that the total cost (in dollars) for a product is given by C(x) = 1400 + 150 ln(2x + 1)…

A:

Q: Directions: Use the digits 1 to 9, at most one time each, to fill in the boxes so that the line is…

A: