08/14/24

Width and height

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola 𝑦 = 11 - 𝑥^2. What are the dimensions of such a rectangle with the greatest possible area?Width =   Height... more
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08/12/24

How Derivatives Affect the Shape of a Graph 6
Consider the function 𝑓(𝑥)=7(𝑥-2)2/3. For this function there are two important intervals: (-∞,𝐴) and (𝐴,∞) where 𝐴 is a critical number.𝐴 is   For each of the following intervals, tell... more
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08/09/24

Simplify the following expression: (3 + 2i) + (1 + i)(1-i)
Simplify the following expression: (3 + 2i) + (1 + i)(1-i)
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08/07/24

At the beginning of an environmental study
At the beginning of an environmental study, a forest covered an area of 1500km^2 . Since then, this area has decreased by 6.75% each year. Let t be the number of years since the start of the study.... more
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08/06/24

related rates Problem 15
The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the triangle is increasing at a rate of 5 square centimeters/minute. At what rate is the base of the... more
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08/06/24

find the derivative of the function
g(x) = (4x^2 + 3x +4) e^x g'(x) = ?? leave answer in ( 4x^2 + ?x + ?)
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08/05/24

Trigonometry question
To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. Enter your answer as a number; your answer should be... more
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08/04/24

ACT question equations of circles and finding x-intercepts
A circle with the equation x2 + y2 = 16 is graphed in the standard (x,y) coordinate plane. At what pointsdoes the circle intersect the x-axis?F. (−2,0) and (2,0)G. (−4,0) and (4,0)H. (−8,0) and... more
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08/04/24

Word problem using the law of sines
The law of sines. A 150-ft antenna is on top of a building. From a point on the ground, the angle of elevation to the top of the antenna is 28.5 degrees, while the angle of elevation to the bottom... more
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08/03/24

How to use implicit differentiation on a trignometric and natural logarithm equation to find dy/dx
For sin xy + cos y + x2 = e^(x2) + ln x, how can I use implicit differentiation to find dy/dx ?
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08/03/24

Solving a trigonometric equation
How can I solve the equation 4 sin2x + 8 cos x - 7 =0 for 0° ≤ x ≤ 360° ?
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08/01/24

Separable equations

Find the solution of the differential equation that satisfies the given initial condition.dy/dx =  5xey,    y(0) = 0 .
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08/01/24

Separable equations
Find the solution of the differential equation that satisfies the given initial condition.x ln(x) = y(1 +  √(15 + y2)y',    y(1) = 1 .
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07/31/24

Use implicit differentiation to find the slope of the tangent line to the curve
Use implicit differentiation to find the slope of the tangent line to the curve y/(x-9y) = x^8 -3 at the point (1, 2/17) find the slope.
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07/31/24

Use implicit differentiation to find the slope of the tangent line to the curve.
Use implicit differentiation to find the slope of the tangent line to the curve y/(x+8y) = x^6 - 4 at the point (1, -3/25) what is the slope?
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07/31/24

Separable Equations
Find an equation of the curve that passes through the point (0, 2) and whose slope at (x, y) is x/y..
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07/30/24

How can you determine the equation of a plane given three non-collinear points in space?
This question encourages discussion about fundamental concepts in geometry and can lead to an exploration of how planes are mathematically defined.
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07/26/24

Taylor and Maclaurin series

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 8xf(x) = ∑ (from n=0 to ∞) ( ? ... more
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07/26/24

Representations of functions as power series

Find a power series representation for the function.f(x) = (8+x)/ (1-x)2f(x) = ∑(from n=0 to ∞) ( ? )I got the answer ∑ (from n=0 to ∞) (9n-1)x^n but the professor marked my answer wrong! What... more
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07/26/24

Representations of functions as power series

Find a power series representation for the function.f(x) = (8+x)/ (1-x)2f(x) = ∑(from n=0 to ∞) ( ? )
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07/26/24

Representation of functions as a power series

Find a power series representation for the function. (Give your power series representation centered at x = 0.)f(x)= x2 / (x4+16) f(x)= ∑(from n=0 to ∞) ( ? )
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07/25/24

Partial Fraction Decomposition (cont'd)
Find the P.F.D. of the following function.
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07/24/24

Please walk me through how to do this problem (CALC 3) I'm confused what a Unit disc is.

Compute the double integral R (region) of (x^2+y^2)^2dA where R is the unit disc. I know I have to set up d-theta and dr, but does the bounds of a unit disc (which I'm assuming is 0 to 2pi)? Apply... more
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07/21/24

The intergel (3x^2 -4x+10)^6 (12x-8)

It should not be a fourteen-degree polynomial but thats what i keep getting
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07/21/24

Solve 7 sin (2a) + 10 cos (a) = 0 for all solutions 0 ≤ a < 2π. Give your answers separted by commas. Round answers to at least two decimal places. a=?
Would someone be able to explain this process? Thank you so much!
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