Select the four points that appear on the line with the given slope and y-intercept

anzhelika [568]

12 * 5280 * 2.56 I think would give us the answer of <span>162201.6, unless I did my addition wrong</span>

4 0

3 years ago

When I have walked 20% of the way to school, I have 1200 metres more to walk than when I have 20% of the walk remaining.

Orlov [11]

Given:

I have walked 20% of the way to school.

I have 1200 metres more to walk than when I have 20% of the walk remaining.

To find:

The distance from home to school.

Solution:

Let x be the distance from home to school.

I have already walked 20% of the way to school and i have 1200 metres more to walk than when I have 20% of the walk remaining.

It means 1200 is $100\%-20\%-20\%=60\%$ of the total distance from home to school.

$1200=\dfrac{60}{100}x$

$1200=0.6x$

$\dfrac{1200}{0.6}=x$

$2000=x$

Therefore, the distance from home to school is 2000 metres.

7 0

3 years ago

Use Euler's method with each of the following step sizes to estimate the value of y(0.4), where y is the solution of the initial

sergey [27]

Answer:

h=0.4--> 15

h=0.2 --> 14.06

h=0.1 --> 13.71

Step-by-step explanation:

This is a numerical solution using Euler's method. Euler's method enables us to numerically approch a solution with a suitable step size. As the step size gets smaller, the approximation will be more accurate. Euler's method is as the following.

$y_{i+1}=y_{i}+h*y_{first derivation}$

Here, h is the step size. The reason why first derivation used here is to make an appriximation with using the rate of increase or decrease. As the step size is smaller, the icreases or decreases are followed more accurately. Now, let's solve the question:

for h= 0.4:

y(0.4)=y(0)+0.4*y'

The trick here is y' is equal to y, thus we can write that y'=y(0.4) and our starting point y(0) is given as 9 in the question and the equation becomes:

y(0.4)=9+0.4*y(0.4) and this is easy to solve.By replacing y(0.4) functions to be at the same side of the equation, we get:

0.6*y(0.4)=9 and by solving this equation, y(0.4) is found to be 15.

for h=0.2:

This will be similar to the previous question, but since the step size is 0.2, we will first calculate y(0.2) and then y(0.4).

y(0.2)=y(0)+0.2*y(0.2) and y(0) is 9.

0.8*y(0.2)=9 and y(0.2)=11.25. Now, we will replace this value into the next iteration o the formula istead of y(0). The equation is like:

y(0.4)=y(0.2)+0.2*y(0.4) and y(0.4) is found to be 14.06.

for h=0.1:

This is also similar to the above solutions but will be longer and have 4 iterations.

first iteration: y(0.1)=9+0.1*y(0.1) --> y(0.1)=10

second iteration: y(0.2)=y(0.1)+0.1*y(0.2) --> y(0.2)=11.11

third iteration: y(0.3)=y(0.2)+0.1*y(0.3) --> y(0.3)=12.34

fourth iteration: y(0.4)=y(0.3)+0.1*y(0.4) --> y(0.4)=13.71

As the step size gets smaller, the answer also gets smaller and more accurate. With even smaller step sizes, there will be a better approximation. However, in case you have more complex equations or smaller step sizes, it is recommended to use a computer software to make an approximation.

6 0

3 years ago

Use a given information to create equation for the rational function. The function is written in factored form to help see how t

Mars2501 [29]

Recall that a rational function: