Where would the line go??? Please help asap!!
2 answers:
Answer: Draw a line through (0,5) and (1,2)
The graph is shown below.
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Reason:
The equation y = -3x+5 is in the form y = mx+b
m = -3 = slope
b = 5 = y intercept
The y intercept is where the graph crosses the y axis. In this case, it's at (0,5). This is one point needed.
Another point can be found by going down 3 and to the right 1 to arrive at (1,2). The motion "down 3, right 1" is from the slope of -3/1.
Therefore, this line goes through (0,5) and (1,2)
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Another approach:
Plug in x = 0 to get...
y = -3x+5
y = -3(0) + 5
y = 5
The input x = 0 leads to the output y = 5
This tells us the point (x,y) = (0,5) is on the line.
Repeat for x = 1
y = -3x+5
y = -3(1)+5
y = 2
So (1,2) is another point on the line.
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Check out the graph below.
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Answer:
a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)
Step-by-step explanation:
Let's solve by separating variables:
a) x’=t–sin(t), x(0)=1
Apply integral both sides:
where k is a constant due to integration. With x(0)=1, substitute:
Finally:
b) x’+2x=4; x(0)=5
Completing the integral:
Solving the operator:
Using algebra, it becomes explicit:
With x(0)=5, substitute:
Finally:
c) x’’+4x=0; x(0)=0; x’(0)=1
Let be the solution for the equation, then:
Substituting these equations in <em>c)</em>
This becomes the solution <em>m=α±βi</em> where <em>α=0</em> and <em>β=2</em>
Where <em>A</em> and <em>B</em> are constants. With x(0)=0; x’(0)=1:
Finally:
<u>Solution-</u>
From the figure,
AE = 2.4
EB = 2.8
BC = 11.7
Area of rectangle 1 = 8.68 sq.in
(∵ sides of the rectangle 2)
Area of Triangle 1 = 6.48 sq.in
(∵ sides of the rectangle 1)
(∵ sides of the rectangle 2)
The area of Rectangle 2,
The area of Triangle 2,
The area of the whole figure = Area of Triangle 1 + Area of rectangle 1 + Area of Triangle 2 + Area of rectangle 2
= 6.48+8.68+8.82+6.44=30.42 sq.in
