The calc-alkaline magma series is one of two main subdivisions of the subalkaline magma series, the other subalkaline magma series being the tholeiitic series. A magma series is a series of compositions that describes the evolution of a mafic magma, which is high in magnesium and iron and produces basalt or gabbro, as it fractionally crystallizes to become a felsic magma, which is low in magnesium and iron and produces rhyolite or granite. Calc-alkaline rocks are rich in alkaline earths (magnesia and calcium oxide) and alkali metals and make up a major part of the crust of the continents.
The diverse rock types in the calc-alkaline series include volcanic types such as basalt, andesite, dacite, rhyolite, and also their coarser-grained intrusive equivalents (gabbro, diorite, granodiorite, and granite). They do not include silica-undersaturated, alkalic, or peralkaline rocks.
My work so far:
I am stuck because when I inputted the two possible values of t and k, neither solution worked. Where did I go wrong? Pointers would be appreciated! :)
1. Fold in half the long way
2. Fold in half the short way
3. Unfold paper, grasping the left side horizontal crease, bend the paper as shown by making the left crease flush with the bottom vertical crease and crease along the -45 degree bend (not shown)
4. This is the visualization for...
I am looking for a (practice)book that has problems on definite and indefinite integration from easy to intermediate.
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Homework Statement
Find the points on the surface xy^2z^3=2 that are closest to the origin
Homework EquationsThe Attempt at a Solution
x,y,z=/= 0, as when x,y,z = 0 it is untrue. Right?? Otherwise, I am very unsure as to how to approach this problem. Should I be taking partial derivatives to...
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Homework Statement
Trying to help a friend with a problem. We are supposed to solve the below using polar coordinates. The actual answer is supposed to be π/16. Solving the integral is not the issue, just converting it.
2. The attempt at a solution
What I got sort of worked, but it is only...
Homework Statement
Given g(x,y)=x2 - xy + 2y2, find the equation of the line normal to the contour that passes through the point (1,2).
Homework Equations
Not 100% positive, but the equation to a plane tangent to a function of 3 variables g(x,y,z) is (partial of x)(x - x0) + (partial of y)(y -...
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Homework Statement
Suppose an infinitely long wire carrying current ##I=sin_0(\omega t)## is a distance ##a## away from a equilateral triangular circuit with resistance ##R## in the same plane as shown in the figure. Each side of the circuit is length ##b##. I need to find the induced voltage...
I am having trouble with this proof. I just need a step in the right direction. Let u and v be vectors.
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Homework Statement
https://ibb.co/g6iKDQ
Calculate the magnitude of the force on cables 1 and 2 in the figure below if θ_1 = 55° and θ_2 = 35°.
(Round your answers to two decimal places.)
Homework Equations
Is my method incorrect or did I go wrong somewhere in my calculations??
The...
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Homework Statement
Find the volume of the given solid:
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Homework Equations
Double Integral
The Attempt at a Solution
I drew the triangle, and found the the equations of the lines to be:
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Homework Statement
Match the parametric equations with the graphs.
In this case, I am stuck on this equation:
x = cos t
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Homework EquationsThe Attempt at a Solution
So far I have:
x^2 + y^2 = cos ^2 t + sin ^2 t = 1
I know this is a circle in the xy-plane, and thus...
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Homework Statement :
[/B]
Find two elevation angles that will enable a shell, fired from
ground level with a muzzle speed of 800 ft/s, to hit a groundlevel
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Homework Equations
Look at attached picture
The Attempt at a Solution
Look at attached picture
***I get to...
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Homework Statement
Find a vector in the direction opposite to <-4,1,2>, that has a magnitude of 3.
Homework Equations
I think that I did the first part of the problem correctly:
<-4,1,2>
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Homework Statement
Find the arc length of:
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from 0 to ln(2)
Homework Equations
L=integral from a to b of the magnitude of r'(t)
The Attempt at a Solution
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Homework Statement
verify that |T ' (s)| = |T ' (t)| / |r ' (t)|
Homework Equations
K = |dT / ds|
K = |r'(t) x r''(t)| / |r'(t)|^3 the x is a cross product
The Attempt at a Solution
I don't know how to start this problem because one side of the verification is in terms of arc length...
Homework Statement
Imagine a 50kg vehicle located at the origin. We wish to navigate this vehicle by means of applying directed force.
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Homework Statement
Attached below
Homework Equations
The Attempt at a Solution
So I cannot figure this out. Would this be integration by parts? or by substitution.. It provides me with an answer but no reasoning behind it and I cannot figure it out =/
Homework Statement
See attached image
Homework Equations
they are provided in the image. I see the domain is used
The Attempt at a Solution
I can't figure out how they went from step one to step 2. where does the -81 come from and the 9 multiplied to the function in the middle. I...
Homework Statement
Apologies for the attachment.
Homework Equations
Limit definition of the divergence as seen in attachment
Volume of a sphere: \frac{4}{3}\pi r^{3}The Attempt at a Solution
The first thing I did was parameterize the vector function F(x,y,z) = <xy,x,y+z>
My parameterization is...
I'm trying to do this homework problem but I keep getting an answer that is not given. Can someone tell me what I am doing wrong please. This is for University level calc 3.
Homework Statement
Homework Equations
A vector U=<x,y>
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Homework Statement
Find the maximum value of f(x,y)=xy+1 on the triangular region: x ≥ 0, y ≥ 0, x+y ≤ 1
The Attempt at a Solution
Partial derivatives of f(x,y) with respect to both x and y are positive within the given bounds, so the maxima will be found on the boundary where y=1-x...
Homework Statement
Find the mass of a wire in the shape of the parabola y=x2 for 1 \leq x\leq2 and with density p(x,y)=x.
Homework Equations
The Attempt at a Solution
I just want to make sure I am setting this integral up right. Here is what I did:
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Normal semesters here are 15 weeks. The summer sessions here are 10 weeks; there's a 10 week session and they can be split into two 5 week sessions.
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Homework Statement
Locate all relative max,min,and saddle points if any.
f(x,y)=x2+xy+y2-3x
fx=2x+y-3
fy=x+2y
Skipping some algebra I get the critical points (2,-1)
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fyy=2
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Homework Statement
Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.
Homework Equations
∫∫ (f(x,y) dA
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Homework Statement
A person is standing 80 ft from a tall cliff. She throws a rock at 80 ft/sec at an angle of 45 degrees from the horizontal. Neglecting air resistance and discounting the height of the person, how far up the cliff does it hit?
Homework Equations
r = ((xo + vo*cos(~))t) i...
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Homework Statement
Can you check if this is right?
Let f(x,y) x^(2)y-3x^2-2y^2+11y+5
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crits at (0,11/4), (-1/3),(1/3)
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D(-1,3) saddle
D(0,11/4) max
D(1,3) saddle
3...
Homework Statement
V.Field F(x,y,z)=<x^2 z, xy^2, z^2> where S is part of the plane x+y+z=1 inside cylinder x2 + y2 =9
Homework Equations
Line integrals, Stokes Theorem, Parametrizing intersections...
The Attempt at a Solution
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