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匿名使用者
匿名使用者 發問時間: 科學數學 · 3 年前

請問有人會這個嗎?(急)?

1.設兩向量a.b的夾角為θ,且|a|向量=|b|向量,向量|a+b|=4 , 向量|a-b|=3,則cosθ=?

2.方程式(81x平方)=27分之根號3之解為何?

3.設向量a=(cos60度, sin30度),向量b=(tan315度, sec120度),則向量a+b=?

4已知三角形ABC之三邊長為8,9,14,則向量AB+BC+CA=?

5.設0小於等於x<2π,則函數f(x)=cos2平方x-3sinx+2之最大值為?

6函數y=tan3分之x的週期為?

7設θ為銳角,若sinθ+cosθ=5分之7,則tanθ+cotθ之值為?

8若a2分之3平方乘a6分之5平方乘a3分之2平方=ax平方,其中a>0,則?

9設a>0且a不等於1,若loga3+loga7=3,則a=?

10若log2=a , log7=b,則log35等於下列何者?(a) 1+a-b (b)1+a-b (c)1-a-b (d) 1-a+b

11已知θ=755度,則θ為第幾象限?

12.f(x)=3sinx-2的最大值為?

13設A(-1.4) . B(2,3) , 則線段AB之垂直平方程式為?

14在座標平面上,若兩平行線x+2y=k與-x-2y=4的距離為根號20且k>0 , 則 k=?

1 個解答

評分
  • 麻辣
    Lv 7
    3 年前
    最佳解答

    1.設兩向量a.b的夾角為θ,且|a|向量=|b|向量,向量|a+b|=4 , 向量|a-b|=3,則cosθ=?

    Set { } = 向量, c = cosθ, s = sinθ

    Let {a} = (k, 0), {b} = (k*c, k*s) where k = waiting for determined

    then {a} + {b} = (k(1+c), k*s)

    and {a} - {b} = (k(1-c), -k*s)

    |{a} + {b}| = k√[(1+2c+c^2)+s^2] = k√2(1+c) = 4

    |{a} - {b}| = k√[(1-2c+c^2)+s^2] = k√2(1-c) = 3

    divided:

    4/3 = √(1+c)/√(1-c)

    => 16/9 = (1 + c)/(1 - c)

    => 9 + 9c = 16 - 16c

    => 25c = 7

    => c = 7/25 =answer

    2.方程式(81x平方)=27分之根號3之解為何?

    81x^2 = √3/27

    x^2 = √3/(81*27)

    x = +- ∜3/(9*3√3)

    = +- ∜3*√3/(27*3)

    = +- ∜3*∜9 / 81

    = +- ∜27 / 81

    = answer

    3.設向量a=(cos60度, sin30度),向量b=(tan315度, sec120度),則向量a+b=?

    {a} = (1/2, 1/2)

    {b} = (-tan45, -sec60) = (-1, -2)

    {a} + {b} = (-1/2, -3/2)

    4.已知三角形ABC之三邊長為8,9,14,則向量

    AB + BC + CA = 0 for a closed loop

    5.設 0 <= X < 2π,則函數f(X) = cos²X - 3sinX + 2之最大值為?

    We find max at point X = 270 deg by using of graphic method.

    max = f(270 deg)

    = cos²270 - 3sin270 + 2

    = 0 + 3 + 2

    = 5

    = answer

    6.y(x) = tan(x/3) 的週期為?

    x/3 = π

    => x = 3π

    => Period = 3π = answer

    7.設X為銳角,若sinX + cosX = 7/5,w = tanX + cotX = ?

    7/5 = √2(sinX/√2 + cosX/√2)

    = √2*sin(x + 45)

    = √2*cos(X - 45)

    => sin(X + 45) = 7√2/10 & cos(X - 45) = 7√2/10

    => X = asin(7√2/10) - π/4 & X = acos(7√2/10) + π/4

    Add:

    2X = asin(7√2/10) + acos(7√2/10) = A + B

    sin(2X) = sinAcosB + sinBcosA

    = (7√2)^2/100 + [√(1-98/100)]^2

    = 98/100 + 2/100

    = 1

    = sin90

    => 2X = 90

    => X = 45 deg

    w = 1 + 1 = 2 = answer

    8.若a2分之3平方乘a6分之5平方乘a3分之2平方=ax平方,其中a>0,則?

    題意不明.無法演算

    9.設 a > 0 且a不等於1,若 log<a>3 + log<a>7 = 3, 則 a = ?

    3 = log3/loga + log7/loga

    3*log(a) = log(a^3)

    = log3 + log7

    = log21

    => a^3 = 21

    => a = ∛21 = answer

    10.若 log2 = a, log7 = b, 則log35等於下列何者?

    (a) 1+a-b (b)1+a-b (c)1-a-b (d) 1-a+b

    log35 = log5 + log7

    = log(10/2) + log7

    = log10 - log2 + log7

    = 1 - a + b

    = (d)

    11.已知 x = 755度,則 x = 第幾象限?

    x = 755 - 360*2

    = 755- 720

    = 35

    = IQ

    12.f(X) = 3sinX-2的最大值為?

    -1 <= sinX <= 1

    => max = f(90 deg)

    = 3 - 2

    = 1

    = answer

    13.設A(-1, 4), B(2, 3), 則線段AB之垂直平分方程式為?

    (x + 1)^2 + (y - 4)^2 = (x - 2)^2 + (y - 3)^2

    2x + 1 - 8y + 16 = -4x + 4 - 6y + 9

    answer: 6x - 2y + 4 = 0

    14.在座標平面上,若兩平行線 L1: x + 2y = k 與 L2: x + 2y + 4 = 0

    距離為根號√20且 k > 0, 則 k = ?

    Point A = (0, -2) on L2

    distance(A to L1) = |x + 2y - k|/√5

    = |0 - 4 - k|/√5

    = |k + 4|/√5

    = √20

    |k + 5| = 10

    k + 5 = +-10

    k = 10 - 5 = 5 = answer

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