11/05/20

Please help ? Determine, with support, a rational function of the form f(x) = g(x)/h(x) that has the following features. Justify your thinking for full marks.
x − intercept: x =2/3y − intercept: y = −4point discontinuity (a hole) at (4, 4)a horizontal asymptote at y = 6a vertical asymptote at x = −1
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11/04/20

Hello. I am seeking help solving the problem below. I think I know how to solve it, but I'm hoping I can get a second set of eyes. Thanks.
Given f(x) = ( sin (5x) ) x , find f ' (x) .I believe I would use this rule: e ^ ( ln(x) ) = x . Is this correct?If so, would I then do this: e ^ ( ln(sin (5x) ) ) ? What... more
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11/03/20

How to find intervals
F(x)= x^4 -2x^3-4x^2+8x(A)Determine the intervals where the second derivative is positive and where the secondderivative is negative.(B) Use a graphing utility to make a plots of f and f00 for −4 ≤... more
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11/02/20

Use the given information to find the area of the sector. Round to four decimal places. a sector of a circle has a central angle of 30° and a radius 8 cm.
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11/02/20

Use the Second Derivative Test to classify the relative extrema, for (x^3)+(-6√x)-3 .if the test applies, otherwise use the First Derivative Test.

Hi I have been having trouble with this question because when I try to calculate the second derivative extrema i get imaginary numbers and I dont understand if those count as greater or less than... more
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11/02/20

Calculus Applied Optimization sec 4.7
Consider a wire of length 11ft. The wire is to be cut into two pieces of length x and 11-x. Suppose the length x is used to form a circle of radius r and the length 11-x is used to form a square... more
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10/29/20

Item 16 Use the Distance Formula to write an equation of the parabola with focus F(0,4) and directrix y=−4.
an equation is y= I need to find the equation of y=
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10/29/20

2. Consider the function 𝑑/𝑑𝑥 (𝑥 ^4 − 𝑎) ∙ (𝑏 − 𝑐𝑥)

A. State the product rule. B. Use the product rule to find and simplify the following derivative: 𝑑/𝑑𝑥 (𝑥 ^4 − 𝑎) ∙ (𝑏 − 𝑐𝑥) C. Find the equation of the tangent line at the point where 𝑥 = 0. D.... more
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10/28/20

Let g(x) = x2/3(6-x)1/3, (A) Use log differentiation to verify that g '(x) = 4-x/x1/3(6-x)2/3 ...
Let g(x) = x2/3(6-x)1/3(A) Use log differentiation to verify that g '(x) = 4-x/x1/3(6-x)2/3(C) Find critical points of g(x). (D) Draw the sign graph of g '(x). (E) Find the intervals of increase... more
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10/28/20

I don’t understand how to do this
Find the value of 3 consecutive integers such that the sum of the first and the second is 20 less than three times the third.
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10/28/20

A student 6 feet tall stands a few feet in front of a 12 feet tall lamppost and starts to walk in a straight path away from the lamppost.
A student 6 feet tall stands a few feet in front of a 12 feet tall lamppost and starts to walk in a straight path away from the lamppost. When the tip of his shadow is moving 5 feet per second from... more
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10/24/20

URGENT SERIOUS HELP NEEDED
A model rocket is shot out of a building and into the sky. The path of the rocket can be modelled by the equation ℎ = −2(𝑡 − 4)^2 + 50, where h is the height above ground in metres and t is the... more
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10/23/20

Write rational equation based on given properties
Suppose we have a rational function r(x) with the properties below. x-intercepts at (2, 0), (-1, 0), and (6, 0) A hole at (1, r(1)) and a vertical asymptote at x = 5and at x = 3. End behavior... more
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10/23/20

Integration Application
Use the slicing method to find the volume of a cone with radius 8 units and height 10 units. Use a sketch to assist in the explanation.
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10/23/20

rotating around y axis
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.y=0,y=cos(2x),x=π/4,x=0 about the axis y=−1
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10/22/20

Use a straightedge and compass to construct an angle bisector for . ∠Q

In , ∠Q name the bisected angles 1 and 2.If m 1∠ is 4x + 3y, can m∠Q bedetermined in terms of x and y? If so,state m∠Q in terms of x and y andexplain your reasoning. If not, explainwhy not.hope... more
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10/22/20

The point P(1, 1/9) lies on the curve y = x/(8 + x). If Q is the point (x, x/(8 + x)), use a scientific calculator to find the slope of the secant line PQ

The point P(1, 1/9) lies on the curve y = x/(8 + x). If Q is the point (x, x/(8 + x)), use a scientific calculator to find the slope of the secant line PQ (correct to six decimal places) for the... more
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10/20/20

First derivative test and curve sketch analysis
y= (x-5)/(x^2)sketch the curve using a first derivative test, second derivative test, and a curve sketch analysis.I thought I had found that the critical values from finding the derivative and... more
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10/16/20

Locate the critical points of the given function
Do the following:a) Locate the critical points of the given functionf(x)=x^2/3 (x-4)b) Use the first derivative test to locate the local maximum and minimum valuesc) Identify the absolute minimum... more
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10/13/20

Rational Exponents
Based on what I have told you √a2 b4=ab2, but I have made a mistake. Find a counterexample where this is not true. How do you propose we fix the mistake?
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10/13/20

pre-calc question
The count in a bacteria culture was 500 after 15 minutes and 1700 after 40 minutes. Assuming the count grows exponentially, answer each of the following. Round populations to the nearest whole... more
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10/13/20

Find an equation of the tangent line at the given point.
(a) xy+x^2y^2 =5, (2,1).and(b) x^2e^y +ye^x =4, (2,0).can someone help me solve these problems by showing the work. I am having trouble understanding. thank you in advance.
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10/13/20

Find derivative of...
A. Suppose[g(x)^]2 + 12x = x^2 g(x) and g(4) = 12. Find g'(4). If y = 2x^3 + 5x and dx/dt = 3, find dy/dt when x = 1.
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10/12/20

Find where increasing and decreasing

For f(θ)=sinθcosθ+cosθfor0≤θ≤2πFind where f (θ) is increasing and decreasing, and where it has local max and min values.
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10/12/20

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 25 ft/s.
A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 25 ft/s.(a) At what rate is his distance from second base decreasing when he is... more
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