Solve the following initial value problems (ivp) using the modified euler’s method with a) the average derivative and b) the derivative at midpoint: 1. dy dx = 4y x , subject to: y(1) = 2 → y(x) = 2x 4 2. dy dx = −2y − x, subject to: y(0) = −1 → y(x) = 2 − 3e −x − 2x integrate over the interval x = [1, 3] for the first ivp and over x = [0, 3] for the second ivp using 4 and 5 intervals. you will use the given true solution to determine the absolute error of the methods.

Use addition and subtraction to simplify the following polynomials. a. add polynomials: (3 – 4x + 8x^2) + (–6 + 2x – 5x^2) step 1: rewrite the polynomials without the parentheses. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial. b. subtract polynomials: (3x – 5 – 7x^2) – (–2 + 6x^2 – 5x) step 1: rewrite the polynomials without the parentheses. remember to multiply each term in the second parentheses by –1. show your work. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial.

This is so hard and it’s for a test

Arecipe calls for 2 2/4 cups of raisins, but julie only has a 1/4 measuring cup. how many 1/4 cups is needed to measure out 2 2/4 cups of raisins?