In each of the following problrmes, our goal is to determine the area of the region described. for each region, (i) determine the intersection points of the curves, (ii) sketch the region whose area is being found, (iii) draw and label a representative slice, and (iv) state the area of the representative slice. then, state a definite integral whose value is the exact area of the region, and evaluate the integral to find the numeric value of the region's area.
(a) the finite region bounded by y = √(x) and y = (1/4)x.
(b) the finite region bounded by y = 12 - 2x^2 and y = (x^2) - 8.
(c) the area bounded by the y-axis, f(x) = cos(x), and g(x) = sin(x), where we consider the region formed by the first positive value of x for which f and g intersect.
(d) the finite regions between the curves y = (x^3) - x and y = x^2.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

according to this law, when unemployment goes up by 1%, gdp drops by 2%. in the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the gdp drops by 6%. thus the effect is a drop in gdp by 6%.

step-by-step explanation: