Answer:
y = 3sin2t/2 - 3cos2t/4t + C/t
Step-by-step explanation:
The differential equation y' + 1/t y = 3 cos(2t) is a first order differential equation in the form y'+p(t)y = q(t) with integrating factor I = e^∫p(t)dt
Comparing the standard form with the given differential equation.
p(t) = 1/t and q(t) = 3cos(2t)
I = e^∫1/tdt
I = e^ln(t)
I = t
The general solution for first a first order DE is expressed as;
y×I = ∫q(t)Idt + C where I is the integrating factor and C is the constant of integration.
yt = ∫t(3cos2t)dt
yt = 3∫t(cos2t)dt ...... 1
Integrating ∫t(cos2t)dt using integration by part.
Let u = t, dv = cos2tdt
du/dt = 1; du = dt
v = ∫(cos2t)dt
v = sin2t/2
∫t(cos2t)dt = t(sin2t/2) + ∫(sin2t)/2dt
= tsin2t/2 - cos2t/4 ..... 2
Substituting equation 2 into 1
yt = 3(tsin2t/2 - cos2t/4) + C
Divide through by t
y = 3sin2t/2 - 3cos2t/4t + C/t
Hence the general solution to the ODE is y = 3sin2t/2 - 3cos2t/4t + C/t
Answer:
Step-by-step explanation:
A way to make your grades go higher is by asking your teacher for extra credits. If you fail some quizzes ask your teacher to re-take it to get a better grade, another way is ask your teacher for assistance on assignments.
Greatest Common Factors (GCF) can help you in real life problems with fractions and measuring things. Below is a real life example.
Let's say you want to send cookies into one of two classes and want to make sure you have an even number per student. You know that one class has 8 students and the other has 10 students. How many cookies do you make?
Answer: All you have to do is figure out the biggest number that goes into each number equally (division). In this case the answer would be 2.
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Answer:
see below for a graph
Step-by-step explanation:
To draw a graph on a grid, locate the point (4, -2) and use the slope to find another point. One such point will be 1 to the left and up 3*, at (3, 1). With two points, you can draw the line through them to complete the graph.
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For a graphing tool that requires an equation, the point-slope form of the equation can be used:
y -k = m(x -h) . . . . . a line of slope m through point (h, k)
For the given slope and point, the equation of the line is ...
y +2 = -3(x -4)
y = -3x +10
_____
* The slope is "rise" over "run". The slope of -3 means that a <em>run</em> of +1 will result in a <em>rise</em> of -3. The given point is already below the x-axis, so we don't really want to find more points farther down. In order to go up on a line with negative slope, we must choose a point to the left of the given one.
Answer:
The correct option is;
An isosceles trapezoid with legs of length 8
Step-by-step explanation:
The correct option is an isosceles trapezoid with legs of length 8
The given properties of the quadrilateral are;
1) One pair of equal opposite sides
2) One pair of parallel opposite sides
From the given options, the two options which are not parallelograms are the kite and the trapezoid
However given that the option of the kite has a pair of adjacent side of length 8, with the given pair of equal length opposite side of length 8, we have that all the sides of the quadrilateral will be of length 8, and the figure cannot be a kite
An isosceles trapezoid of leg length 8 has one pair of equal length opposite sides of length 8 and one pair of parallel sides of unequal length
Given that the length of the lines that make up the pair of opposite parallel sides in the figure are not specified, the figure can be described by as being an isosceles trapezoid.
