Answer:
f(0) = 12
Step-by-step explanation:
You want to substitute 0 for x
f(0) = 5(0) + 12
f(0) = 12
Taking x as the number to be found,
x=32a+30=58b+44 where a and b are the quotients you get on dividing x by 32 and 58.
Simplifying this equation you get 16a+15=29b+22
16a= (16+13)b+22-15 or 16a=16b+13b+7
16(a-b)=13b+7
Now I have to find a value for b where 13b+7 is divisible by 16. The least common multiple of these numbers can be found by
going through the multiplication tables of 13 and 16 and 13x13+7=176,
while 16x11 is also 176.
Now that the value of b is found to be 13, we can substitute it in our first equation, x=58b+44=58x13+44=798.
Now find the least common multiple of 58 and 32
LCM (n,m)=nm/GCD (n,m) where GCD is the greatest common divisor of n and m
LCM (58, 32)=58x32/2 as 2 is the GCD of 58 and 32
LCM (58, 32)= 1856/2= <em>928</em>
Add this LCM to the previous answer, ie, 798 to get the next answer in the series. 798+928=1726
Add the LCM again to the last answer to get the final answer, that is less than 3000=1726+928=2654
Answer:
Step-by-step explanation:
We are given that differential equation
Taking integration on both sides
Using identity:
Substitute
Differentiate w.r.t x
Substitute
Differentiate w.r.t y
Substitute the values then we get
Using identity:
By using formula :
Substitute the values then we get
Answer:
x = no. of quarters
3x = no. of dimes
3x + 11 = no. of nickels
2(3x + 11) = no. of pennies
340 quarters
1020 dimes
1031 nickels
2062 pennies
Step-by-step explanation:
x = no. of quarters
3x = no. of dimes
3x + 11 = no. of nickels
2(3x + 11) = no. of pennies
x + 3x + 3x + 11 + 2(3x + 11) = 4453
x + 3x + 3x + 11 + 6x + 22 = 4453
13x + 33 = 4453
13x = 4420
x = 340 quarters
3x = 1020 dimes
3x + 11 = 1031 nickels
2(3x + 11) = 2062 pennies
Check: 340 + 1020 + 1031 + 2062 = 4453