For slope, people sometimes use the description 'rise divided by run'. We know that the y axis describes rise, and the x axis describes run. So rise divided by run written numerically is 
. Now let's look at the line above. We can see that every time the y value goes up one unit, the x value goes right two units. This means that [tex]\frac{y}{x} --> \frac{y + 1}{x + 2}
This can be rewritten as 1/2, so the is 1/2. Hope this helped.
Answer:
Step-by-step explanation:
Hello
Match the points on the number line with the rational numbers.
a __ -6/8 = -(2 x 3)/(2 x 4) = -3/4
b __ -2/8 = -2/(2 x 4) = -1/4
c __ -4/8 = -4/(4 x 2) = -1/2
d __ 8/8 = 1
e __ 13/8
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:
6/13
Step-by-step explanation:
We know that
angle (3x) and angle (9x) are supplementary angles
so
3x+9x=180°------> 12x=180°------> x=180°/12-----> x=15°
angle (9x) and angle (1) are supplementary angles
so
9x+∡1=180---------> 9*15+∡1=180
∡1=180-9*15---------> ∡1=180-135------> ∡1=45°
the answer is
∡1 is 45°
alternative method
angle 1 = angle 3x----------> vertical angles
∡1=3x-----> 3*15-----> 45°
