剛開始學隱函數，想問框起來的部分是用什麼rule呢？課程裡面是說用chain rule，但我看不太懂是怎麼寫成那樣的

Example 1: Let x² + y² = 25, , find dy == dx , dx dy and the equation of the tangent at (3, 4). Solution: 2x+2y 33 dy dx = 0 dx 2x dy |+ 2y = 0 X dy m = dx dy dx\(3,4) 3 -¾³½⇒(y−4) = −²/√(x − 3). =- 4 dx dy X

右下角是解答，但我一直算不出來，請幫我解答一下，還有過程

Apply elementary row operations to transform the following matrix first into echelon form and then into reduced echelon form. 64-5 3 -6 3 -7 -7 8-589 3-9 12-96 15 1 0-2 3 0 -24 0 1 -2 2 0 -7 000014 62 62

想問這題怎麼算

28. A trough is 6 m long and its ends have the shape of isos- celes triangles that are 1 m across at the top and have a height of 50 cm. If the trough is being filled with water at a rate of 1.2 m³/min, how fast is the water level rising when the water is 30 centimeters deep? goal: dh dt

想問這題要怎麼算🙇‍♀️

37. Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev's theorem to determine the percentage of the data within each of the ranges which follow. LO 5 a. 20 to 40 b. 15 to 45 c. 22 to 38 d. 18 to 42 e. 12 to 48

感覺這題要用反函數

Finding Values In Exercises 28-30, find f-1(a) for the function f and real number a. Function 30. f(x) = x³ - Real Number 4 x > 0 a = 6 X

怎麼解？

2. For what value of a and t does the equation |t-a-a-t hold?

請問綠色框起來的是什麼意思

example.o A,B: sets, |A|-|B|=n<∞ A function f : A → B is one to one Proof (F) Suppose 39, #az & fears = fiaz) : 充分必要 if and only if it is onto. 7-1-4 3 | { bib = fca, for a EA & 979, 192}|≤n-2 =|f(A)| = h-1 < |B| 7 f is not onto Proof

這題的解答給的是C, 該怎麼求出，感謝！

6. Find the volume of the solid whose region is the intersection of the cube {(x, y, z) : |x| ≤ 1, |y| ≤ 1, || ≤ 1} and the ball {(x, y, z) = x² + y²+ z² < 2}. 16 (A) 32(√2-1). (B) (8-√2). 3 16 (C) (10- √2)TT. (D) √√2π. 3 32 3

想知道這個的原理

29,8 1, a(0,0)=2024 2₁a (2₁-113) = 0 B SM + GRE at á (1, 2) = 8² a(-2₁-1)=12 109287 11 3 1 6 12 3-4 5 13 14 15 16 17 BESIL ANDRIA LO CH

大二統計學 請問畫黃色的部分要怎麼算

268 CHAPTER 6 The Normal Distribution and Other Continuous 6.5 Given a normal distribution with = 70 and o = 20, what is the probability that a. X > 110. b. X < 10. c. X< 70 or X > 130. d. Between what two X values (symmetrically distributed around the mean) are 70% of the values. 8 6.6 Given a normal distribution with μ = 30 and σ = 4, what is the probability that a. X > 38. b. X < 25. c. Find the X value such that the area to the left of X is 5% of the total area under the normal curve. d. Between what two X values (symmetrically distributed around the mean) are 40% of the values? P(Z > 2) = (1-0,9094 = 00228 P(25-1.2²) 011056 27:25-30 4 1125 5x1165 Z=30+4 1-905=0.95 (₁28-1 46.64 = 3