d<em>y</em>/d<em>x</em> = 4 + √(<em>y</em> - 4<em>x</em> + 6)
Make a substitution of <em>v(x)</em> = <em>y(x)</em> - 4<em>x</em> + 6, so that d<em>v</em>/d<em>x</em> = d<em>y</em>/d<em>x</em> - 4. Then the DE becomes
d<em>v</em>/d<em>x</em> + 4 = 4 + √<em>v</em>
d<em>v</em>/d<em>x</em> = √<em>v</em>
which is separable as
d<em>v</em>/√<em>v</em> = d<em>x</em>
Integrating both sides gives
2√<em>v</em> = <em>x</em> + <em>C</em>
Get the solution back in terms of <em>y</em> :
2√(<em>y</em> - 4<em>x</em> + 6) = <em>x</em> + <em>C</em>
You can go on to solve for <em>y</em> explicitly if you want.
√(<em>y</em> - 4<em>x</em> + 6) = <em>x</em>/2 + <em>C</em>
<em>y</em> - 4<em>x</em> + 6 = (<em>x</em>/2 + <em>C </em>)²
<em>y</em> = 4<em>x</em> - 6 + (<em>x</em>/2 + <em>C </em>)²
Answer:
22 feet in centimeters is 670.56
22 inch in centimeters is 55.88
Step-by-step explanation:
Answer:
I don't know that answer will come back to you
Answer:
x = log(33)/(3·log(2))
Step-by-step explanation:
The relevant logarithm relation is ...
log(a^b) = b·log(a)
__
Taking the logarithm of both sides of your equation gives ...
2^(3x) = 33
log(2^(3x)) = log(33)
(3x)·log(2) = log(33)
The coefficient of x is 3·log(2). Dividing by that gives the value of x:
x = log(33)/(3·log(2))
x ≈ 1.51851/(3·0.301030) ≈ 1.6814647
PEMDAS ( Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)
4(2.53(207))
Since there are no equations in the parentheses, or exponents, we skip these, and head straight for multiplication:
4(523.7)
Then, do multiplication again:
2094.8
So that means, 4(2.53(207)) = 2094.8
I assume the brackets mean parentheses, since the absolute value of 523.7 does not mean anything in this equation.
