07/27/25

Solve the system of 3 equations by elimination. State as an ordered triple

Solve the system by eliminationx+y+2z=23x+4y-z=254x-y+3z=-7
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05/09/25

Linear Algebra-Linear Transformations
Find the associated matrix (i.e. matrix with respect to the standard basis ) for the linear transformation on R2 representing reflection about the line 3y=4x followed by rotation by 3π ⁄2 radians... more
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04/21/25

verify for all points (x1,y1) on circle x^2+y^2=r^2, that all points (x2,y2) on tangent line to circle at (x1,y1) satisfy x1x2+y1y2=r^2
assume (x1,y1) is a point on the circle x2+y2=r2the tangent line will be -x1/y1=(y-y1)/(x-x1)-x(x1)+x12=y(y1)-y12x(x1)+y(y1)=r2this means all points (x2,y2) on the tangent line for point (x1,y1) on... more
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02/20/25

Evaluate the integral. (Use C for the constant of integration.)
\int (dx)/((x^(2)+4)^((5)/(2)))
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01/30/25

Exercise from Calculus 'Separation of Variables'
At any time t, the rate of growth of the population N of deer in a state park is proportional to the product of N and L-N, where L=500 is the maximum number of deer the park can sustain. When t=0,... more
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01/22/25

How to explain this to a 3rd grader???
Trying to explain this to my 3rd grader without algebra. No teacher help- so frustrated. This is a test question (we are reviewing what she got wrong) from Math Expressions unit 6. Do I just say... more
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12/21/24

what is juxtaposition, how does it factor into order of operations and what is the correct answer?
Hi, my name is Matthew and I stopped at algebra in high school and was never able to really go beyond that and have recently seen one of the popular facebook posts on a math equation that is 50/50... more
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11/11/24

determine the two tangent line points (x1,y1) and (x2,y2) on circle (x-h)^2+(y-k)^2=r^2 drawn from point (m,n)
determine the two tangent line points (x1,y1) and (x2,y2) on circle (x-h)2+(y-k)2=r2 drawn from point (m,n), where (m,n) is outside circle, that is,... more
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09/22/24

Why AC factoring works?
AC factoring can be used to factor quadratic equations. Why does it work?
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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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07/19/24

Green's Theorem
Compute the flux of the vector field ⟨x5, −xy4⟩, out of the rectangle with vertices (0,0), (4,0), (4,1) and (0,1)
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07/18/24

Find the radius of convergence, R, of the series.
∑(from n=2 to ∞) ((x+7)^n)/(7^n ln (n)) Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)
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07/18/24

Pre-Calculus Question
25x2 − 120xy + 144y2 − 156x − 65y = 0(b) Use a rotation of axes to eliminate the xy-term. (Write an equation in XY-coordinates. Use a rotation angle that satisfies 0 ≤ 𝜑 ≤ 𝜋/2.)
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05/27/24

Triangle with Difference of Two Angles Given
About triangle ABC, we know b = 7 inches, c = 6 inches, and β-γ = 15° [where α = ∠A, β = ∠B, and γ = ∠C]. Calculate α, β, and γ.
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05/07/24

Geometry+trigonometry exercise
I can't get ahead with it. Could you possibly give me some help on how to get started?So this is the task:The side lengths of a triangle are a, b, and c. We know this a+b=3c. Let us prove that... more
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03/21/24

Suppose we want to integrate
Sometimes we switch coordinates because it makes the integrand easier. Let D� denote the triangular region with vertices at (0,0),(1,0) and (0,1). This region is not round. However, suppose we want... more
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05/10/23

Describe three methods you can use to find the value of ∫∫s curlF•ndσ
Let S be the hemisphere of equation x2 + (y -2) +z2 = 9; z ≥ 0, with positive (outward) orientation, and let F(x,y,z) = xy i + yz j + xz k.Describe three methods you can use to find the value of... more
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12/27/22

Is there a specific formula to reflect a point over ANY linear line?
I know how to reflect (-5, 0) over y = 2x manually by algebra, but is there a formula for all? I remember there was. It had to do with absolute values and some stuff like that. Any you know of?... more
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