Answer:
The numbers he picked are 11, 17 and 24
Step-by-step explanation:
To solve this, we will work with the information we are given, interpreting it properly.
From the information given , we can already decode that the first of the three numbers is 11. We can write that number down.
The next piece of information we are given is that the range is 13.
The range of a data set is the difference between the highest and lowest numbers in the data set.
Let us say that our highest number is x
Now, we know that the highest number of the data set is 24
Finally, from the information given, we can see that the median number is 17. This is the middle number of the data set. we can simply write that down since the number of figures in our data set is an odd number.
Hence the numbers picked are
11, 17 and 24 arranging them in an ascending order
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:
5 g
Step-by-step explanation:
Answer:
Step-by-step explanation:
48 + 14 / 2 = 31
Answer:
52 units.
Step-by-step explanation:
If we drop a perpendicular line from point C to AD and call the point ( on AD) E we have a right triangle CED.
Now CE = 6 and as the whole figure is symmetrical about the dashed line,
ED = (26 - 10)/2
= 8.
So by Pythagoras:
CD^2 = 6^2 + 8^2 = 100
CD = 10.
So, as AB = CD,
the perimeter = 10 + 26 + 2(8)
= 52.
