We want to solve the Initial Value Problem y' = y + 4xy, with y(0) = 1.
To use Euler's method, define
y(i+1) = y(i) + hy'(i), for i=0,1,2, ...,
where
h = 0.1, the step size.,
x(i) = i*h
1st step.
y(0) = 1 (given) and x(0) = 0.
y(1) ≡ y(0.1) = y(0) + h*[4*x(0)*y(0)] = 1
2nd step.
x(1) = 0.1
y(2) ≡ y(0.2) = y(1) + h*[4*x(1)*y(1)] = 1 + 0.1*(4*0.1*1) = 1.04
3rd step.
x(2) = 0.2
y(3) ≡ y(0.3) = y(2) + h*[4*x(2)*y(2)] = 1.04 + 0.1*(4*0.2*1.04) = 1.1232
4th step.
x(3) = 0.3
y(4) ≡ y(0.4) = y(3) + h*[4*x(3)*y(3)] = 1.1232 + 0.1*(4*0.3*1.1232) = 1.258
5th step.
x(4) = 0.4
y(5) ≡ y(0.5) = y(4) + h*[4*x(4)*y(4)] = 1.258 + 0.1*(4*0.4*1.258) = 1.4593
Answer: y(0.5) = 1.4593
Answer:
<em><u>1/4 of his income.</u></em>
Step-by-step explanation:
If Wilbur spends 2/3 of his income, 1/3 or 4/12 of it is left for other purposes (It is easier if everything has a common denominator of 12). And if he shares 1/12 of that remaining amount, there is 3/12 left. And when we simplify 3/12, we get <u>1/4</u>.
*Mark me brainliest!*
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .<span>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 30/5 = 6.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 30/-3 = -10.Slope is -5/-3 = 1.66666666666667.<span> Equation in slope-intercept form: y=1.66666666666667*x+-10.</span></span>
Answer:
it is
Step-by-step explanation:
Answer: the smallest number of people required for the sample to meet the conditions for performing inference is 100
Step-by-step explanation:
Given that;
36% of US population has never been married
32% are divorced
27% are married
5% are widowed
Taking a simple random sample of individuals to test this claim;
we need expected count in each cell to be at least 5, here the smallest proportion is 5% = 0.05
so we only need to satisfy condition for its expected count;
n × 0.05 ≥ 5
n = 5 / 0.05 = 100
Therefore the smallest number of people required for the sample to meet the conditions for performing inference is 100
