11/08/23
What rate is the plate's area increasing?
when a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm / min. At what rateis the plate's area increasing when the radius is 50 cm?
11/07/23
Verify the identity by converting the left side into sines and cosines. (Simplify at each step.
7 sec(x) − 7 cos(x) = 7 sin(x) tan(x)
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11/07/23
Conveyor belt at a rate
Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast...
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11/05/23
What are the x and y intercepts and slopes of this equation?
In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. Write an equation in slope intercept form that models this situation.
11/05/23
The apparent magnitude (how bright an object appears to the observer) is given by
The apparent magnitude (how bright an object appears to the observer) is given by M=(5/2)log(b0/b) where b is the brightness of the object and b0 is a positive constant. A particular telescope is...
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Calculus 1: f(x) = ln(2 + sin(x)), 0 ≤ x ≤ 2𝜋
f(x) = ln(2 + sin(x)), 0 ≤ x ≤ 2𝜋Find the interval(s) on which f is concave up. (Enter your answer using interval notation.)Find the interval(s) on which f is concave down. (Enter your answer using...
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11/03/23
Solve using variable separable
(y + 1) dx - (xy + x - 3y - 3) dy = 0, when x = 5, y = ln 4a. y = (x - 3)^2b. y = ln (2x - 6)c. y = ln (x - 3)^2d. y = (2 - cos t)^-3
11/03/23
Solve DE using variable separable
e^(y-2x) (1 + x²) dx + cos y dy = 0 when x = 0 and y = 0a. 2e^2x (cos y - sin y) + e^y (2x^2 + 2x + 3) = 5e^(2x+y)b. 2e^y (cos y - sin y) + e^2x (2x^2 + 2x + 3) = 5e^(y-2x)c. e^2x (sin y - cos y) +...
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11/03/23
Find all real solutions.
Find all real solutions to the equation log4(3x^2) - log4(4x+8) = -1Be sure to check any potential solutions in the original equation.
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11/02/23
find the following questions
Consider the function f(x) = e^x /4+e^x . compute the derivative of this function f'(x) = a) f(x) is increasing on b) f(x) is decreasing on c) f(x) has a local minimum d) f(x) has a local maximum...
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11/02/23
Fill in the table so it represents a linear function.
X:5,10,15,20,25Y:-1, blank, blank, blank, 11
Fina power series representation for the function
Fina power series representation for the functionf(x) = ln(1-3x)Could you walk me step by step how to solve this problem? I'm struggling trying to get the right answer.
10/31/23
i need help sol.ving this
Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers using the appropriate multiplicities.)P(x) = 1/7(2x4 + 3x3 − 16x...
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10/31/23
Compute the requested derivative. Do not simplify your answer after applying the differentiation rules.
b) y=(x-3)/(x+4); Find d2y/dx2 c) y3+x3-5x(y-1)=2; Find dy/dx at (1,1)For b, I tried to do implicit differentiation by first using the quotient rule on d2y/dx2, but I got stuck there.For c, I got...
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10/31/23
let f(x) = 5xˆ2. Determine the value of x such that the average rate of change of f(x) from 3 to x is 55
let f(x) = 5xˆ2. Determine the value of x such that the average rate of change of f(x) from 3 to x is 55
10/31/23
Evaluate the following limit: the limit as θ approaches 0, of sin(3θ)/(θ^2-2θ). DO NOT USE L'HOSPITAL'S RULE
The limit as θ approaches 0, of sin(3θ)/θ2-2θ. Without using L'Hospital's rule.After applying the derivative using the quotient rule, I got (3cos(3θ))(θ2-2θ)-(2θ-2)(sin(3θ))/(θ2-2θ)2Do I distribute...
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10/30/23
When the base is 3 feet from the wall, how fast is the bottom of the ladder moving away from the wall?
A 5 foot ladder is sliding down a wall with the top of the ladder moving down the wall at the rate of 1/2 foot per second. When the base is 3 feet from the wall, how fast is the bottom of the...
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10/30/23
absolute maximum
Consider the function f(x) = x^3e^6x -2< x< 2 The absolute maximum value is ... and this occurs at x equals ..... The absolute minimum value is .... and this occurs at x equals .
10/30/23
INTERMEDIATE ALGEBRA
The concentration C(t)�(�) of a certain drug in the bloodstream after t minutes is given by the formula C(t)=0.06(1−e−0.2t)�(�)=0.06(1−�−0.2�). What is the concentration after 44 minutes? Round to...
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10/29/23
Write an equation, in slope-intercept form, for the line that passes through the point (-8, 7) and is parallel to the line y=− 2/3x−6
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10/28/23
A researcher believes that if x thousand individuals among a susceptible population are inoculated
A researcher believes that if x thousand individuals among a susceptible population are inoculated (made no longer susceptible to a disease), then a function of formI(x)=a⋅R^x−bfor constants a, b,...
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10/28/23
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.
The graph below shows how the volume of the box in cubic inches, V, is related to the length of the side of the square cutout in inches, x.The graph of the function V equals x times the quantity 7...
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