Answer:
12.57 km
Step-by-step explanation:
Radius = 4 / 2 = 2 km
Circumference = 2πr = 2π(2) = 4π = 12.57 km
Answer:
3x+5=5x-9(llgram oppositesides are equal)
3x-5x= -9-5
-2x=-14
x= -14/-2
x=7
Answer:
a.
b.
Step-by-step explanation:
We have a differential equation
y''-2 y'-35 y=0
Auxillary equation

By factorization method we are finding the solution


Substitute each factor equal to zero
D-7=0 and D+5=0
D=7 and D=-5
Therefore ,
General solution is

Let 
We have to find Wronskian

Substitute values then we get



a.
We are given that y(0)=-7 and y'(0)=23
Substitute the value in general solution the we get

....(equation I)


......(equation II)
Equation I is multiply by 5 then we subtract equation II from equation I
Using elimination method we eliminate
Then we get 
Substitute the value of
in I equation then we get


Hence, the general solution is
b.
Answer:
Ivan gets £90 more than Tanya
Step-by-step explanation:
Given that
Total amount = £150
Ratio: 4:1
First of all we have to find the sum of ratio: 4+1 = 5
Now,
Ivan's Share:

Tanya's Share:

Ivan gets £120 and Tanya gets £30
The difference between their shares is the answer.
So,

Hence,
Ivan gets £90 more than Tanya
Total number of oz of honey = 12 oz.
Cost of 12 oz of honey = $5.40.
Cost per oz of honey = 5.40 divided 12 = $0.45 per oz.
Therefore,
a) Cost per ounce of honey = $0.45.
b) Number of ounces we can buy for one dollar = 12 divided by 5.40 = 2.22 oz approximatly.
c)
h = 2.22c, wherr h is the number of ounces of honey for c dollars.
c=0.45h, where c is the total cost of h number of ounces of honey.
d) Let us take c=0.45h equation for graph the situation.
x-axis would be for h number of ounces of honey and y-axis is the total cost c of h ounces of honey.
Let us find some values of h and c for the graph.
For equation: c=0.45h for h=1,we get c=$0.45.
If we plug h=2, we get c= 0.45*2 = $0.90.
If we plug h=3, we get c= 0.45*3 = $1.35.
Therefore, we would plot (1,0.45), (2,0.90) and (3,1.35) on the graph and draw a straight line.