A function problem in Higher Mathematics If a company produces a product and can sell it all, the revenue function is r = 36x-x quadratic / 20, where x is the daily production of the company. If the daily production of the company increases from 250 to 260, please estimate the increase of the company's revenue It's necessary to explain the text and the steps, We should use the function method of higher mathematics, not the method of elementary school, complete steps, instructions and results

A function problem in Higher Mathematics If a company produces a product and can sell it all, the revenue function is r = 36x-x quadratic / 20, where x is the daily production of the company. If the daily production of the company increases from 250 to 260, please estimate the increase of the company's revenue It's necessary to explain the text and the steps, We should use the function method of higher mathematics, not the method of elementary school, complete steps, instructions and results

Derivative is defined as f '(x0) = [f (x0 + Δ x) - f (x0)] / Δ x (Δ x tends to 0) = Δ Y / Δ x (Δ x tends to 0), so Δ y = f' (x0) Δ x0 + O (Δ X0), O (Δ x0) is the higher-order infinitesimal of Δ x, which can be ignored in approximate calculation, then Δ y is about equal to f '(x0) Δ x0, Just find the derivative of the function at x = 250 and multiply by 10
R = 36x-x ^ 2 / 20, then R '= 36-x / 10, when x = 250, R' = 36-25 = 11, so Δ y is about 11 * 10 = 110, that is, the increase of the company's revenue is about 110

F (x) is an odd function. When x ∈ (0. + ∞), f (x) = x & sup2; - 1, find the value range of X with F (x) > 0

F (x) is an odd function. When x ∈ (0, + ∞), f (x) = x & sup2; - 1  when x ∈ (- ∞, 0), f (x) = - X & sup2; + 1 x ∈ (0, + ∞), f (x) = x & sup2; - 1 ＞ 0, x ^ 2 ＞ 1, X ＞ 1. When x ∈ (- ∞, 0), f (x) = - X & sup2; + 1 ＞ 0, x ^ 2 ＜ 1, - 1 ＜ x ＜ 0

Cut a circle into several equal parts along the radius, and then put it together into a rectangle. It is known that the length of the rectangle is 4.28 meters more than the width. What is the area of the circle in square centimeter

Radius 4.28 △ 3.14-1 = 2cm
The area of the garden is 2x2x3.14 = 12.56 square centimeters
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Given the power a of 2 = 5 and the power B = 100, find the value of 1 / A + 1 / b
Such as the title

2^a=5^b=100
So a = log (2) 100 = LG100 / LG2 = 2 / LG2
b=log(5)100=lg100/lg5=2/lg5=2/(1-lg2)
1/a+1/b=lg2/2+(1-lg2)/2
=1/2
Predestined relationship. I've just done this. It must be in the new century

A telecom company has set up two kinds of local mobile communication services: A and B. a user needs to pay a monthly rent of 15 yuan, and then pay 0.3 yuan for each minute of the call. B user does not pay the monthly rent, and pays 0.6 yuan for each minute of the call. If the call time is X minutes in a month, the fees of a and B are Y1 and Y2 yuan respectively (1) Try to write the functional relationship between Y1, Y2 and X respectively; (2) draw the image of Y1 and Y2 in the same coordinate system; (3) according to the call time of one month, which communication service do you think is more favorable?

(1) Y1 = 0.3x + 15 (x ≥ 0) (2 points) y2 = 0.6x (x ≥ 0) (4 points) (2) as shown in the figure: (50, 30) (6 points) (3) solution (1) from the image: when a month's talk time is (50 minutes), the two services are equally preferential (7 points). When a month's talk time is less than (50 minutes), the second industry

It is known that in the trapezoidal ABCD, ab ‖ CD, M is the midpoint of AB, and cm = DM

Because cm = DM
So cm and DM have equal angles in the triangle
That is, angle MCD = angle MDC
Because ab ‖ CD,
So AMC = MCD, BMD = MDC
So AMC = BMD
M is the midpoint of ab
Then am = BM
And because cm = DM
So AMC of triangle is equal to BMD (SAS)
So angle a = angle B
So ABCD is isosceles trapezoid

The gravity of an egg is close to (?) The gravity of a middle school student is about (?) A、5N；    B、50N；    C、500N；    D、0.5N．

It may not be easy to estimate the gravity of an object, but if you have a certain understanding of the mass of an object, you can calculate its gravity according to the mass of the object; (1) a kilogram (500g) of eggs can generally be weighed 8-10, so the mass of each egg is about 50g; then the gravity of an egg is about g = mg = 0.05kg × 10N / kg = 0.5N; (2) according to the actual situation of students, the mass of middle school students is generally high According to the calculation formula of gravity, we can get the gravity: g = mg = 50kg × 10N / kg = 500N

Xiaohua's father is a taxi driver. On this day, when his father drove back, Xiaohua helped his father sort out the fare and found 44 pieces of RMB 5 yuan, 10 yuan and 20 yuan
The total is 500 yuan, of which 10 yuan is equal to 20 yuan. How many yuan are there in each of the three kinds of RMB?

Let 5 yuan have X pieces, 10 yuan and 20 yuan each be y pieces, then the following relation is obtained
X + 2Y = 44; 5x + 30y = 500; find x = 44-2y and substitute it into the following formula
44-2y + 6y = 100, then y = 14, then x = 16
Then: 5 yuan altogether has 5x = 80 yuan; 10 yuan altogether has 10Y = 140 yuan; 20 yuan altogether has 20Y = 280 yuan

As shown in the figure, Xiao Hong cuts a 4 cm wide strip from a square, and then cuts a 5 cm wide strip from the remaining rectangular paper along the direction parallel to the short side. If the area of the strips cut twice is exactly the same, what is the area of each strip? What is the area of the original square?

Suppose the side length of the square is xcm, then according to the meaning of the question: 4x = 5 (x-4), the solution is: x = 20. Then 4x = 80 (cm2), 20 × 20 = 400 (cm2). Answer: the area of each strip is 80cm2, the area of the original square is 400cm2

It is known that in △ ABC, a, B and C are the opposite sides of angles a, B and C respectively, C = 7 / 2, ∠ C = π / 3, and the area of △ ABC is 3 √ 3 / 2, then a + B = ()
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C = π / 3, a + B = 2 π / 3 according to sine theorem: A / Sina = B / SINB = C / sinc = 2R = (7 / 2) / sin (π / 3) = 7 / √ 3sina = √ 3A / 7, SINB = √ 3B / 7 according to cosine theorem: C & # 178; = A & # 178; + B & # 178; - 2abcosca & # 178; + B & # 178; - 2abcos π / 3 = 49 / 4A & # 178; + #