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expeople1 [14]
3 years ago
5

Used use euler's method with step size 0.1 to estimate y(0.5), where y(x) is the solution of the initial-value problem y ' = y +

4xy, y(0) = 1. (round the answer to four decimal places.)
Mathematics
1 answer:
brilliants [131]3 years ago
4 0
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
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In Walmart parking, there are 175 vehicles parked joe figures out that 64% of the vehicles are white. How many vehicles are NOT
aksik [14]

Answer:

63 vehicles are not white

Step-by-step explanation:

Well you know that there are 175 total vehicles, and that 64% of those vehicles are white.  Therefore the remaining percentage of vehicles must not be white.

100%-64%=36%

This means that 36% of the vehicles aren't white.

Now you must find what 36% of 175 is.  The word "of" always signals for multiplication, which is exactly what you need to do here.  First start by converting the percentage into decimal form:

36%=0.36

Now you can multiply

175 x 0.36 = 63

63 Vehicles are not white

5 0
3 years ago
Read 2 more answers
Can someone answer question 2a and b only please
Mice21 [21]

Answer:

2a)  -2

b) 8

Step-by-step explanation:

<u>Equation of a parabola in vertex form</u>

f(x) = a(x - h)² + k

where (h, k) is the vertex and the axis of symmetry is x = h

2 a)

Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):  

f(x) = a(x - 2)² - 6

If one of the x-axis intercepts is 6, then

                 f(6) = 0

⇒ a(6 - 2)² - 6 = 0

⇒         16a - 6 = 0

⇒              16a = 6

⇒                  a = 6/16 = 3/8

So f(x) = 3/8(x - 2)² - 6

To find the other intercept, set f(x) = 0 and solve for x:

                    f(x) = 0

⇒ 3/8(x - 2)² - 6 = 0

⇒      3/8(x - 2)² = 6

⇒           (x - 2)² = 16

⇒              x - 2 = ±4

⇒                   x = 6,  -2

Therefore, the other x-axis intercept is -2

b)

Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):  

f(x) = a(x - 2)² - 6

If one of the x-axis intercepts is -4, then

                 f(-4) = 0

⇒ a(-4 - 2)² - 6 = 0

⇒         36a - 6 = 0

⇒              36a = 6

⇒                  a = 6/36 = 1/6

So f(x) = 1/6(x - 2)² - 6

To find the other intercept, set f(x) = 0 and solve for x:

                    f(x) = 0

⇒  1/6(x - 2)² - 6 = 0

⇒       1/6(x - 2)² = 6

⇒           (x - 2)² = 36

⇒              x - 2 = ±6

⇒                   x = 8,  -4

Therefore, the other x-axis intercept is 8

8 0
2 years ago
Discrete R.V. Assume a student shows up for EGR 280 completely unprepared and the instructor gives a pop quiz. Assume there are
Tom [10]

Answer:

a) p=0.2

b) probability of passing is 0.01696

.

c) The expected value of correct questions is 1.2

Step-by-step explanation:

a) Since each question has 5 options, all of them equally likely, and only one correct answer, then the probability of having a correct answer is 1/5 = 0.2.

b) Let X be the number of correct answers. We will model this situation by considering X as a binomial random variable with a success probability of p=0.2 and having n=6 samples. We have the following for k=0,1,2,3,4,5,6

P(X=k) = \binom{n}{k}p^{k}(1-p)^{n-k} = \binom{6}{k}0.2^{k}(0.8)^{6-k}.

Recall that \binom{n}{k}= \frac{n!}{k!(n-k)!} In this case, the student passes if X is at least four correct questions, then

P(X\geq 4) = P(X=4)+P(X=5)+P(X=6)=\binom{6}{4}0.2^{4}(0.8)^{6-4}+\binom{6}{5}0.2^{5}(0.8)^{6-5}+\binom{6}{6}0.2^{6}(0.8)^{6-6}= 0.01696

c)The expected value of a binomial random variable with parameters n and p is E[X] = np. IN our case, n=6 and p =0.2. Then the expected value of correct answers is 6\cdot 0.2 = 1.2

5 0
3 years ago
A parallelogram is a _____. (Choose all that apply)
Mama L [17]

Answer:

Quadrilateral

Step-by-step explanation:

The definition of a parallelogram is a quadrilateral that has two sets of parallel sides.

3 0
3 years ago
Read 2 more answers
Answer each part below using only mental math, and describe your method. a. If 39 is 1% of a number, what is that number? How di
Leni [432]

Answer:

Step-by-step explanation:

Given:  39 = 0.01n

Move the decimal point on each side two places to the right:  3900 = n

8 0
3 years ago
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