what is the remainder when 2^20+3^30+4^40+5^50 is divided by 7?

請問倒數第二行的根號三為何到了最後一行變成3了？x 代入u 也不會影響到他才對啊

32. Let u = x, u = x, 2u du 2u du = dx. 1 2u du 2 1 ) ma dx = 5 x√3 - √x) u? (V3 – u) - S du ( 03 - art) A B. (3-2) = u( V3 – u) 13 - u 2 = A(V3 – u) + Bu When u = 0,2 = V3A > A = 1 - 23. I 3 2 When u = V3, 2 - BV3 B 23 > = 3 2 S I du = 1 13 du u( 3 – u) 23 (+ v6 - .) die Cat 2013 (1n|u|- In|u - v3) + 243 (In Vos - In|V8 - 3) + C 2、3 C 1 S dx = = - . x(V3 - Vx

拜託救我 arcsec(4/3)怎麼代入tan裡？

4 (b) When x = 4,8 = arcsec When x = 6,8 = arcsec(2) | |m 3 12 Si dx 2 -9 (3) {[sec - 12. v3+ 1/2+13) - (16+) In- sec Ô tan + In sec 0 + tan o 1/3 8 8 arcsec(4/3) 011 13 9 4 x In 2. 3 3 3 3 9 6 + 3/3 04 ||| = 9/3 - 2/7 + In 12.644 2 4 +

求救第55題 完全看不懂他要我幹嘛

Year slenue Req) = 1932 1958 +1000 q R 9)=-1000q =74 1963 1968 COM If the price in dollars of a stereo system is given by 1000 p(q) + 1000, 1000 ² q where q represents the demand for the product, find the mar- ginal revenue when the demand is 10. 54. Profit Suppose that for the situation in Exercise 53 the cost in dollars of producing a stereo systems is given by C(q) = 0.2q2 + 69 + 50. Find the marginal profit when the demand is 10. 59. Marginal Product of Labor The output y of a manufacturing y process is a function of the size of the labor force n using the function 1990 +1000 1971 1974 = 990 197 197 19 19 1 y = kVn. The marginal product of labor, defined as dy/dn, measures the rate that output increases with the size of the labor force, and is a measure of labor productivity. (a) Show that (c) Using the a cubic f respond the rate and 200 (d) Discus descri part ( the y (e) Exp data calc ful x C(x) = 58. Money 1955-7 dy k dn an (b) How can you tell from your answer to part (a) that as the size of the labor force increases, the marginal product of labor gets smaller? This is a phenomenon known as the law of diminishing returns, discussed more in the next chapter. 56. Profit An analyst has found that a company's costs and rev- enues in dollars for a product are given by x2 C and R(x) 2x 2 5000' respectively, where x is the number of items produced. (a) Find the marginal cost function. (b) Find the marginal revenue function. (c) Using the fact that profit is the difference between revenue and costs, find the marginal profit function. (d) What value of x makes the marginal profit equal O? (e) Find the profit when the marginal profit is 0. (As we shall see in the next chapter, this process is used to find marimum profit.) A wher in bi find year (a) (C) (e) nad since

教教5、6、9

*/ *y *** 15 x xx * 一 7+13 2x+y X-7 .xy =-1 2 = 2 + 三 > } } - X y x=1 y 5.有一工作,由A、B兩部機器同時運作,帶 12 小時完成;若先讓A運作4小時後,再讓B單獨運作 24 小時也可完成。若此工作單獨由A運作,需要x小時,而單獨由B運作,需要y小時,試求(x,y) = (A)(30, 20) (B)(20, 30) (C)(15, 20) (D)(20, 15) (2x + ay=4 甲、乙兩人同解: |bx+4y=5 若甲看錯a得(x,y)=(3,-1);乙看錯得(x,y) = (5,-2),試求正確的 F(x, y) = (A)(2, -1) (B)(-2,1) (C)(1,-2) (D)(-1,2) 7 A 13.-1) 2:6 (5,-2) 6-a=4 2X+24.4 56-8.5 - a=-2 > X + 2 y = 5 56:13 a=2 X+2 =4 1- / 3X + 104 y 10 24.16 944= 30 b. 12 Wol. -

［高二 正餘弦疊合］ 請問為什麼這一題是化成cos？請問什麼時候要化成cos什麼時候是sin？

1-4 正餘弦函數的疊合 67 題1 E B A O 100 如右圖,一半徑為100公尺的圓形水池上建有一「工」字型木橋, AB=CD, 試問: (1) AB+CD+EF 之總長最長為 公尺。 (2)承(1),當總長最長時,此時AB= 公尺, EF= 公尺。 素養題 D D C F (1) (2)白 - 中 2 = 200 x # S0015 8.500 + È cose [03 中 400 cose + 2006 =300 (2006 e sont 20ocos 6=200 cas & 左 I sino EF= sino x 200=200sind 二 soofs (cos(0-0)) cos & = 2 2 2 # when &=ope cos=0=10=0 → 20055 ( cos 0°) 20055 I 二00 x Is Jo = 4055 D 二 #, X X 90-IX :

求解1. b

B 3 Investigation 1 When a curve is increasing, we say that it has a positive gradient, and when it is decreasing we say that it has a negative gradient. Consider the curve y=xº shown in the diagram. 1 a Give the range of x values for which the gradient of the curve is i negative I ii positive iii equal to zero. b At which point is the gradient of the curve greater. A or B? The tangent to a curve at a point is the straight line that just touches but does not cross the curve at that point. N 1 y=p 1 2. 3 2 2 a On your GDC or other software, plot the curve y=x' and draw the tangent at the point (1, 1), as shown in the second diagram. b Zoom in to the point (1, 1). Factual What do you notice about the gradient of the tangent and the gradient of the curve at the point of contact? c Use your GDC or online software to draw tangents to y=x' at the points listed below and in each case write down the gradient of the tangent. 0 -1 1 2 X -1 0 2 2. 3 Gradient of tangent at x 2 d Conjecture a function for the gradient of y = x2 at the point on the curve with coordinates (x,x).

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五、綜合測驗:10% When we think of sleepi Jaying our heads ori big ftuffy pillows and lying under niee warm bl ,SjJeep in very different places. Sea otters, for instan' 2. don't drown. When giraffes get their forty Winks, tbey are water and _2. use fheir hips as a pillow. And some creatures, like the Alpine swWift, can even doze 0 | while in 各ght! These every year On these extremely 1ong 和ights, they stay in the Sky _5 , We prob: migratory birds trayel thousand ably picture a nice comtortable bed. We imagine ankets. Most antmals, ce, sleep on their backs in the | 蟬 人G | js of kilometers between continents Weeks and even months at a time. One Swiss study in 2013 showed that Alpine sSWitts remain in the air for even 1onger than we imagined. Special sensors w be measured at all timmes. The research team found that tte Jocafion and speed _6. swifts could cover up to 10,000 km and go as long as 200 days 和hatAlpine swWifts don't sleep atall during these flights Tecently. 9. Some 8 many ag nakes fhem some Of the coolest sleepers Juffier一piows Or clouds? ( ) 1L.(A) therefore ( ) 2.(A) otherwise )訪3(0a9l ) 4.(A)amazZe ) 5.(A) Within 0 must ree that they are capable oF getting 所 least some Shut- ere_ attached to SiX birds so that their Vanding! eye up in the Sky. This 10._. It also makes you Wonder which 3 (B) however (0C) fortunately (D) miraculousiy (B) thus (C) theretore (D)yet (B) sure (C) about (D) goimg (B) amazes (C) amazg (D) amazew (B) during (C) for (D) on (B) might (C) should (D)wil

求解。句子我不太會(;´༎ຶД༎ຶ`)

(和 上Lesson 3 -、詞類變化:10% 一六弛 The children stared at the mag gieian in took arabbit from his hat suddenly. 影 (amaziangy When he The wonderful scene i 和 scenery in the countryside G y 5 Ympressivey S me so much thatI will never forget it 3. It takes some 一(seientist knowledge and crYeattviy to Invent something like an electronie pet 4. Wendy likes to go to the ice cream store, for there are (variety) flavors of ice cream to choose from.- 1 5. The (average) age of the workers in this company is about 2 thirty-five, so you are probably the youngestone here. 句型練習 :20% +fYV+wh- (+ S$)+V”句型來改寫以下句衛。 (3) 9 2 Why did Rachel leave Eric Without saying a Word? Eric was Wondering, (3%9) 今 When will Peter's birthday party be held? His friends are not sure (40%) 3 -光2 ) 用“im order (mo0 6 V句型來合併以人二 ]. Tom works day and night. He can support his family. (3%) 當 0, 2. Jane spends some time exercising. She Wants to Stay fit. (3%6) the tratn. (406) tim1ss 3. You had better get Out ofthe house early. You Wontim 信 翻譯:15% (1至3一格1分)4至5是人多 dam 討厭某些蔬菜 ; 例如, 1 _gXQp he hates lettt 9 Y dam hates certaln vegetables; 0

請問第4題該怎麼算？

呈 宮 < 2 交 Ki sald the plzza in this restaurant Was the best he had ever had hen (B) X (0C) place (D) what 2006 work miracles, and one high school teacher did something to prove this point.”Wh teacher, she was having a hard time _27. her students. Then she came up With an re about his or her classmates. “When Students 4. 擲甲、乙兩個骰子, 令點數和為的事件為 4, 甲骰子點數為1的事件為2 看 獨立, 則= : 5. 袋中有3個白色球和。 Ariaom硬間了品