03/11/25

reference angle to find the exact value of the expression
Use reference angle to find the exact value of the expression. Show your work. sin (-300°) cos 1200°
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03/11/25

Find the exact values of the remaining trigonometric functions
Find the exact values of the remaining trigonometric functions of θ from the given information.tan θ = - 5/12, θ in quadrant IIcot θ = - 12/5, θ in quadrant IV
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02/07/25

Use calculus to find the area A of the triangle with the given vertices. (0, 0), (5, 3), (1, 4)
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02/06/25

Solve this equation for R
4R3-499R-1575=0I came across this equation as part of the solution of another problem elsewhere.It is an example of casus irreducibilis. However, it has a rational solution which can be obtained... more
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02/06/25

Order of operations HELP
/I'm confused on how to handle this operation, as the answer says 9/4The question: Simplify using order of operations. Write the answer as a mixed number, if possible. Here's the example.(2-1/2) ... more
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11/22/24

I need help with this problem. It is a differential equation.
The following differential equation is used to model population growth in an environment with limited resources. y' = 0.2y (1- y/85)Find the values of y at which the population is in... more
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10/30/24

solve the equation
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.The freshman and sophomore classes at Fairview High School are decorating floats for... more
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10/30/24

\sum_(n=1 )^(\infty ) ((-1)^(n)ln(n))/(n)
(a) Determine whether the series is absolutely convergent, conditionally convergent, or divergent.b) Summarize your work and conclusions from part (a) in 5–7 complete sentences. Make sure to... more
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10/22/24

Implicitly Defined Functions
Consider the implicitly defined function 1+x=sin(xy2). Find dy/dx.
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10/22/24

Calculus in Polar coordinates
Find the area of the region that lies inside the first curve and outside the second curve.r = 5 − 5 sin(𝜃),    r = 5
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10/21/24

Integration with fraction like equations...
Integrate ∫ (10x^2 -45x +6) / (2x^2 - 9x + 4 ) dx
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10/08/24

Integration with partial fractions

Use the substitution t = tan (x/2) to transform the integrand into a rational function of t and then evaluate the integral.∫ (from 0 to pi/2) (8sin(2x))/(2+cos(x)) dx
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10/08/24

Integration with partial fractions
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember the constant of integration.)∫ dx/(x√x-1)
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09/07/24

Geometry Problem
Determine the value of y:
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09/04/24

Did Jenni write the converse statement properly? Determine if it's true or false, then give a counterexample if it's false.
Jenni wrote a conditional statement, and the converse statement to accompany it.The conditional statement Jenni wrote: "If angles are right angles, then they have the same measure."The converse... more
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08/29/24

Identify the x-intercepts, vertex, and axis of symmetry of the graph of F(x)=-0.25 (x+4)(x+8)
Identify the x-intercepts, vertex, and axis of symmetry of the graph of F(x)=-0.25 (x+4)(x+8)
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08/28/24

Find the area of the region bounded by the three lines below. [Hint: You will have to split up the integral into two parts.]
y=4/3x, y=7x, y=3/2x +17/2
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08/16/24

Use Newton's method to approximate a root of the equation 4sin(x)=x as follows
Use Newton's method to approximate a root of the equation 4sin(x)=x as follows. Let x1=1 be the initial approximation.
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08/14/24

FInding feet of a wall
A fence 6 feet tall runs parallel to a tall building at a distance of 5 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall... more
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08/08/24

Linear Approximations and Applications
Use linear approximation, i.e. the tangent line, to approximate 1.7^7 as follows:Let 𝑓(𝑥) = 𝑥^7. Find the equation of the tangent line to 𝑓 (𝑥) at 𝑥 = 2𝐿(𝑥) =   Using this, we find our... more
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08/02/24

Finding the Area of a given Enclosed Region
How would I find the area of the region enclosed by f(x) = 2x2 and y = 12-2x, and also how would I sketch the graphs?
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07/18/24

When does object A overtake object B?

Two objects at t=0t = 0t=0 start moving along a straight path. Object A starts at 8 miles per hour. The velocity of object A changes according to the function Va(t)= (t+8)/(e^t) for t>0. The... more
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07/10/24

The ratio and root tests

Use the ratio tests to determine the ak of this series below.∞∑ (n𝜋^n)/(-4)^(n-1)n = 1 I know that it is convergent but I was not able to figure out the ak specifically.
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07/10/24

Find the amount of oil that the field can be expected to yield during the first 6 years of production, assuming that the projection holds true
Based on a preliminary report by a geological survey team, it is estimated that a newly discovered oil field can be expected to produce oil at the rate of R(t)=((600t^2)/(t^3+32))+5... more
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06/12/24

Law of Logarithms 4.4 (1)
The logarithm of a product of two numbers is the same as the sum  of the logarithms of these numbers. So log4(16 · 64) = log4(16) +  __________
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