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This is not an official document of UTAR. The University is not responsible for any errors found in the solutions.

Solutions to FHMM1014 Mathematics I (April 2013)

2 FHMM1014 MATHEMATICS I Q1. (a) (i) a + bi = +i 1 (a − 2) + bi ⇒ a + bi = a − 2) + bi )(1 + i ) (( a + bi = (a − 2 − b) + (a − 2 + b)i

a a = − 2 − b So   b = a−2+b

⇒ ⇒

− b=2 a= 2

z= 2 − 2i

(ii) (iii)


4+4 = 2 2
⇒ −π θ= 4

−2 = tan θ =−1 2 = arg( z ) θ= −π 4



3log x x log 3 =
3log x =81

2 × 3log x 162 =
3log x =34

log x = 4

x = 104


= log10 x + log(1 + 2 x ) log 5x + log 6 log10 x (1 + 2 x )= log 5 x × 6 10 x (1 + 2 x ) = x × 6 5 Let ⇒ 2 x (1 + 2 x ) = 6

y = 2 x then y 2 + y − 6 = 0

( y − 2)( y + 3) = 0

y − 2 = 0 ⇒ y = 2 ⇒ 2x = 2 ⇒ x = 1 y + 3 = ⇒ y = 3 ⇒ 2 x = 3 impossible − − 0

Solutions to FHMM1014 Mathematics I (April 2013)

3 FHMM1014 MATHEMATICS I Q1. (Continued) (c)
P ( x)= A( x − 2)( x − (2 − i ))( x − (2 + i ))

P( x) = A( x − 2)( x 2 − 4 x + 5) P( x) = A( x3 − 6 x 2 + 13 x − 10)
P(0) = −5 P( x) = ⇒ 1 A= 2

1 3 ( x − 6 x 2 + 13 x − 10) 2


A(B  ( A − ( B  C ) )′ = C )′



= A′  ( B  C )
= ( A′  B )  ( A′  C )
= ( A  B′ )′  ( A  C ′ )′

=B )′  ( A − C )′ (A−



x3 − 2 x 2 + 3x − 4 − x2 + 2x − 3 = 1+ 3 x3 − x 2 + x − 1 x − x2 + x −1

− x2 + 2x − 3 − x2 + 2x − 3 A Bx + C = = + 2 3 2 2 x − x + x − 1 ( x − 1)( x + 1) ( x − 1) ( x + 1)
− x 2 + 2 x −= A( x 2 + 1) + ( Bx + C )( x − 1) 3

x= 1 x= 0

−1 + 2 − 3 =2 A ⇒
−3 = A − C ⇒

A =−1
C= 2
⇒ B= 0

x =1 ⇒ −

2 −1 − 2 − 3 = A − 2(− B + C )

Solutions to FHMM1014 Mathematics I (April…...

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...支付報酬單據*(範本) 名 稱 : _____________________________ 聯 絡 電 話 : __________________________ 僱主資料 辦 公 地 址 : ___________________________________________________________________ 姓 名 : _____________________________ 僱員資料 職 位 : ________________________________ 社 會 保 障 基 金 受 益 人 編 號 : _______________________________________________ 法 律 規 定 給 予 僱 員 的 其 他 編 號 1 : ________________________________________ 與所獲報酬 相應的期間 年 2 月 日 至 名稱 4 名稱 報酬 年 7 月 日 金額 5 (1) (2) (3) 3 總報酬: 扣除 金額 (1) (2) (3) 6 總扣除: 總收入 * 總扣除 淨收入 填寫本單據時,請留意後頁的“注意事項"。 ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ 1 注意事項 1. 倘有法律規定給予僱員的其他編號,則僱主亦可選擇一併填寫該編號。 2. 此欄位填寫僱主計算報酬所對應的具體日期。 3. 報酬包括基本報酬及浮動報酬,故此,不論是基本報酬或是浮動報酬,均須填寫在本 單 據 內 ( 見 第 58 條 第 1 款 及 第 63 條 第 6 款 第 5 項 的 規 定 ) 。 4. 此 欄 位 填 寫 僱 主 向 僱 員 支 付 該 項 報 酬 的 名 稱( 例 如 : 基 本 工 資 、 超 時 工 作 報 酬 (須 列 明 超 時 工 作 時 數 )及 年 終 雙 糧 等 ) 。 5. 此 欄 位 填 寫 該 項 報 酬 所 涉 及 的 金 額 數 目,同 時,須 注 意 的 是,報 酬 須 以 澳 門 元 支 付( 見 第 63 條 第 4 款 的 規 定 ) 。 6. 法 律 容 許 僱 主 從 僱 員 的 報 酬 中 作 出 扣 除 的 情 況 如 下 ( 見 第 64 條 第 1 款 的 規 定 ) : (1) 社 會 保 障 基 金 的 供 款 ; (2) 由 法 律 規 定 或 經 法 院 裁 判 確 定 執 行 的 扣 除 ( 如 職 業 稅 的 每 月 扣 款 ) ; (3) 因 法 院 確 定 裁 判 而 結 算 出 的 僱 員 對 僱 主 所 欠 的 賠 償 ; (4) 因 第 72 條 第 5 款 規 定 的 解 除 合 同 而 結 算 出 的 僱 員 對 僱 主 所 欠 的 賠 償 ; (5) 私 人 退 休 基 金 的 供 款 , 但 須 經 僱 員 同 意 ; (6) 因 缺 勤 而 喪 失 的 報 酬 ; (7) 因 僱 員...

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... Somanabolic Supplementation By: Kyle Leon Being a supplement sponsored athlete you might think I would be promoting supplements and making claims like all of the other supplement sponsored athletes get paid to do. Well, that’s not the case at all. I will cut through all the crap and tell it like it is. In fact, I only signed a contract with Blue Star Nutraceuticals with the mutual understanding that I will only talk about products that I have actually used with measurable results. If I take something and it does nothing, that’s exactly what I’ll say. I don’t want anyone to go through the frustrating cycle of wasting money on crap like I did. If the owner of Blue Star wasn’t the most straight up CEO in the industry with the quality of his products being the most important thing to him, I wouldn’t have signed because of how I feel about supplement companies. I’ll say this- It takes a hell of a confident, stand up guy to sign me to a contract knowing where I stand with my brutal honesty about the industry. Without further ado, here is my straight talking report for you. Enjoy, and make use of it. Supplements are used by millions of people every year in the hopes of losing fat, building muscle and improving overall health. For our purpose, we will be talking about supplements that are being marketed to guys looking to build lean muscle mass. Supplements are a multi-billion dollar industry that is highly unregulated in comparison to other industries...

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Сами Буажила | Maya and Miguel | Kingdom Season 1 Episode 33 English Dubbed