• ### Find the value of the constant C such that y = 3/2 X +6 is tangent to y=CX^1/2 Any help...?

y^2 = C^2*x & Y^2 = (3/2 x + 6)^2 C^2 x = 9x^2/4 + 18x + 36 (9/4)x^2 + (18 - c^2)x + 36 = 0 9x^2 + (72 - 4c^2)x + 144 = 0 Use the Discriminent b^2 - 4ac = 0 (72 - 4c^2)^2 - 4(4)(144) = 0 5184 - 576c^2 + 16c^4 - 2304 = 0 16c^4 - 576c^2 + 2880 = 0 c^4 - 36c^2 + 180 = 0 (c^2 - 30)(c^2 - 6) = 0 c^2 = 30 c = +/- sqrt(30) = +/- 5.477.... &... show more
y^2 = C^2*x & Y^2 = (3/2 x + 6)^2 C^2 x = 9x^2/4 + 18x + 36 (9/4)x^2 + (18 - c^2)x + 36 = 0 9x^2 + (72 - 4c^2)x + 144 = 0 Use the Discriminent b^2 - 4ac = 0 (72 - 4c^2)^2 - 4(4)(144) = 0 5184 - 576c^2 + 16c^4 - 2304 = 0 16c^4 - 576c^2 + 2880 = 0 c^4 - 36c^2 + 180 = 0 (c^2 - 30)(c^2 - 6) = 0 c^2 = 30 c = +/- sqrt(30) = +/- 5.477.... & c^2 = 6 c = sqrt(6) = +/- 2.449...
3 answers · Mathematics · 12 hours ago
• ### Solve the triangle using the Law of Sines?

No such thing as the Law of Sines. It is the SINE RULE ,which is a/SinA = b/SinB = c/SinC The SINE FUNCTION is Sin(Angle) = opposite(o) / Hypotenuse(h)
No such thing as the Law of Sines. It is the SINE RULE ,which is a/SinA = b/SinB = c/SinC The SINE FUNCTION is Sin(Angle) = opposite(o) / Hypotenuse(h)
7 answers · Mathematics · 13 hours ago
• ### Can someone help with maths? ive been trying for ages?

x^2 + 12x - 220 = 0 (x + 22)(x - 10) = 0 x = -22 & x = 10 4 x 10 x X = 924 40X = 924 X = 23.1 4, 10, 23.1
x^2 + 12x - 220 = 0 (x + 22)(x - 10) = 0 x = -22 & x = 10 4 x 10 x X = 924 40X = 924 X = 23.1 4, 10, 23.1
3 answers · Mathematics · 2 days ago
• ### Maths related question?

x = 2y + 5 x^2 = )2y + 5)^2 x^2 = 4y^2 + 20y + 25 Substitute 4y^2 + 20y + 25 + y^2 = 5 5y^2 + 20y + 20 = 0 5(y^2 + 4y + 4) = 0 y^2 + 4y + 4 = 0 (y + 2)(y + 2) = 0 (y + 2)^2 = 0 Hence there is only ONE contact point at y = -2
x = 2y + 5 x^2 = )2y + 5)^2 x^2 = 4y^2 + 20y + 25 Substitute 4y^2 + 20y + 25 + y^2 = 5 5y^2 + 20y + 20 = 0 5(y^2 + 4y + 4) = 0 y^2 + 4y + 4 = 0 (y + 2)(y + 2) = 0 (y + 2)^2 = 0 Hence there is only ONE contact point at y = -2
4 answers · Mathematics · 2 days ago
• ### Stuck on this maths question?

Best answer: BD^2 = (2sqrt(5))^2 - (3sqrt(2))^2 BD^2 = (4 x 5) - (9 x 2) BD^2 = 20 - 18 BD^2 = 2 BD = sqrt(2) Hence area = (1/2)(3sqrt(2) + sqrt(2))(sqrt(2) A = (1/2)(4sqrt(2)(sqrt(2)) A = (1/2)(4 x 2) A = 4 cm^2
Best answer: BD^2 = (2sqrt(5))^2 - (3sqrt(2))^2 BD^2 = (4 x 5) - (9 x 2) BD^2 = 20 - 18 BD^2 = 2 BD = sqrt(2) Hence area = (1/2)(3sqrt(2) + sqrt(2))(sqrt(2) A = (1/2)(4sqrt(2)(sqrt(2)) A = (1/2)(4 x 2) A = 4 cm^2
2 answers · Mathematics · 2 days ago
• ### Can someone help with some geometry?

Find the equation of the Tangent line by Differentiation. 2x + 2ydy/dx - 4 +6dy/dx = 0 (2y + 6)dy/dx = 4 - 2x dy/dx = 2(2 - x)/ (2(y + 3)) dy/dx = (2 - x)/(y + 3) Hence slope is (2 - 4)/(1 + 3) = -2/4 = -1/2 The tangent line is y - 1)= (-1/2)(x - 4) y = -x/2 + 2 + 1 y = (-x/2) + 3 At A y = 0 Hence x/2 = 3 x = 6 A = ( 6 , 0) At B x =... show more
Find the equation of the Tangent line by Differentiation. 2x + 2ydy/dx - 4 +6dy/dx = 0 (2y + 6)dy/dx = 4 - 2x dy/dx = 2(2 - x)/ (2(y + 3)) dy/dx = (2 - x)/(y + 3) Hence slope is (2 - 4)/(1 + 3) = -2/4 = -1/2 The tangent line is y - 1)= (-1/2)(x - 4) y = -x/2 + 2 + 1 y = (-x/2) + 3 At A y = 0 Hence x/2 = 3 x = 6 A = ( 6 , 0) At B x = 0 y = 3 B = (0,3) A(AOB) = (1/2)(6)(3) A(AOB) = 9 units^2
4 answers · Mathematics · 2 days ago
• ### Work this out please?

What is 'S' Is the Sequence Geometric or Arithmetric; it makes a difference.
What is 'S' Is the Sequence Geometric or Arithmetric; it makes a difference.
4 answers · Mathematics · 2 days ago
• ### Write as a single fraction?

5mn / 3 x 2/n Cancel down by 'n' 5m / 3 x 2/1 10m / 3
5mn / 3 x 2/n Cancel down by 'n' 5m / 3 x 2/1 10m / 3
2 answers · Mathematics · 3 days ago
• ### Find the two positive integers?

7a / 42 + 2b / 42 = 17/42 7a + 2b = 17 a = 1 b = 5
7a / 42 + 2b / 42 = 17/42 7a + 2b = 17 a = 1 b = 5
4 answers · Mathematics · 3 days ago
• ### X squared - 22x + 121 = 100?

x^2 - 22x + 21 = 0 (x - 21)(x - 1) = 0 x = 21 & x = 1
x^2 - 22x + 21 = 0 (x - 21)(x - 1) = 0 x = 21 & x = 1
4 answers · Mathematics · 3 days ago
• ### What is the atlas mountain?

The ATLAS Mountains are located in North West Africa, specifically the country of Morocco. The are real mountains.
The ATLAS Mountains are located in North West Africa, specifically the country of Morocco. The are real mountains.
11 answers · Geography · 4 days ago
• ### Chem help?

c = f *l 3.0 x 10^8 m/s = l * 7,2 x 10^14 s^-1 l = 3.0 x 10^8 m/s/ 7.2 x 10 ^14 s^-1 l = 4.1666... x 10^-7 m l = 4.1666.... x 10^-7 /1.0 x 10^-9 l = 416 nm .
c = f *l 3.0 x 10^8 m/s = l * 7,2 x 10^14 s^-1 l = 3.0 x 10^8 m/s/ 7.2 x 10 ^14 s^-1 l = 4.1666... x 10^-7 m l = 4.1666.... x 10^-7 /1.0 x 10^-9 l = 416 nm .
3 answers · Chemistry · 4 days ago
• ### How do you factor y=x^2-6x-9? Values of x- and y- intercepts?

x^2 - 6x = 9 (x - 3)^2 - 3^2 = 9 (x - 3)^2 = 18 (x - 3) = +/- sqrt(18) x = 3 +/- sqrt(18) The quadratic equation does NOT factor The values of the x-intercepts are 3 + sqrt(18) & 3 - sqrt(18) The values of the y-intercept is '-9' ; The constant.
x^2 - 6x = 9 (x - 3)^2 - 3^2 = 9 (x - 3)^2 = 18 (x - 3) = +/- sqrt(18) x = 3 +/- sqrt(18) The quadratic equation does NOT factor The values of the x-intercepts are 3 + sqrt(18) & 3 - sqrt(18) The values of the y-intercept is '-9' ; The constant.
4 answers · Mathematics · 4 days ago
• ### A circle passes through (3, -1) , (-2, 4) , and (6, 8)?

Best answer: x^2 + y^2 + 2fx + 2gy + c = 0 Hence 3^2 + (-1)^2 + 2f(3) + 2g(-1) + c = 0 9 + 1 + 6f - 2g + c = 0 10 + 6f - 2g + c = 0 (-2)^2 + 4^2 + 2f(-2) + 2g(4) + c = 0 4 + 16 - 4f + 8g + c = 0 20 - 4f + 8g + c = 0 6^2 + 8^2 + 2f(6) + 2g(8) + c = 0 36 + 64 + 12f + 16g + c = 0 100 + 12f + 16g + c = 0 Hence we have 10 + 6f - 2g + c =... show more
Best answer: x^2 + y^2 + 2fx + 2gy + c = 0 Hence 3^2 + (-1)^2 + 2f(3) + 2g(-1) + c = 0 9 + 1 + 6f - 2g + c = 0 10 + 6f - 2g + c = 0 (-2)^2 + 4^2 + 2f(-2) + 2g(4) + c = 0 4 + 16 - 4f + 8g + c = 0 20 - 4f + 8g + c = 0 6^2 + 8^2 + 2f(6) + 2g(8) + c = 0 36 + 64 + 12f + 16g + c = 0 100 + 12f + 16g + c = 0 Hence we have 10 + 6f - 2g + c = 0 20 - 4f + 8g + c = 0 100 +12f + 16g + c = 0 c = -10 - 6f + 2g Substitute 20 - 4f + 8g - 10 - 6f + 2g = 0 100 + 12f + 16g - 10 - 6f + 2g = 0 10 -10f +10g = 0 90 + 6f + 18g = 0 Factor f - g = 1 -f - 3g = 15 Add -4g = 16 g = -4 f - 4 = 1 f = 5 Hence x^2 + y^2 + 5x - 4y + c = 0 Substitute any point for 'c' 3^2 + (-1)^2 + 5(3) -4(-1) + c = 0 9 + 1 + 15 + 4 + c = 0 29 + c = 0 c = -29 Hence the equation becomes x^2 + y^2 + 5x - 4y - 29 = 0
3 answers · Mathematics · 4 days ago
• ### A square of side x and a quarter-circle of radius r have the same area. Express r in terms of x.?

x^2 = pir^2/4 4x^2 = pi r^2 r^2 = 4x^2/pi r = sqrt(4x^2/pi)
x^2 = pir^2/4 4x^2 = pi r^2 r^2 = 4x^2/pi r = sqrt(4x^2/pi)
3 answers · Mathematics · 4 days ago
• ### How do you factor x^2 + 18x - 648 without using the quadratic formula and without completing the square?

Write down the factors of 648 . They are, First find the common factors 2)648 2)324 2)162 3)81 3)27 3)9 3)3 3)= 1 Hence 2^3 & 3^4 Hence 2 ,4,8,3,9,27,81,6,18,54,36,107,324,,72,216,648 From this list of number you select tw o number that have a difference of '18' They are .36. & .54/ Hence Factor (x + 54)(x - 36) show more
Write down the factors of 648 . They are, First find the common factors 2)648 2)324 2)162 3)81 3)27 3)9 3)3 3)= 1 Hence 2^3 & 3^4 Hence 2 ,4,8,3,9,27,81,6,18,54,36,107,324,,72,21... From this list of number you select tw o number that have a difference of '18' They are .36. & .54/ Hence Factor (x + 54)(x - 36)
6 answers · Mathematics · 5 days ago
• ### If two thirds of a sum of money has been spent, leaving £24, how much money was there originally?

Best answer: If 2/3 rds spent , then you are left with '1/3'. 1/3 is equivalent £24. Multiply both sides by '3' 3(1/3) = £24 x 3 1 is equivalent £72 £72 is the original anount of money .
Best answer: If 2/3 rds spent , then you are left with '1/3'. 1/3 is equivalent £24. Multiply both sides by '3' 3(1/3) = £24 x 3 1 is equivalent £72 £72 is the original anount of money .
8 answers · Mathematics · 5 days ago
• ### How would I solve 1-3cos3x=0 in the interval: 0 ⩽ x ⩽ π?

1 = 3Cos(3x) Cos(3x) = 1/3 3x = Cos^-1(1/3) 3x = Cos^-1(0.33333.....) 3x = 1.23095.... radians. x = 1.23095... / 3 x = 0.4103195,,,, radians & x = pi - 0.4103195... x = 3.141592... - 0.4103195.... = 2.7312728.... radians.
1 = 3Cos(3x) Cos(3x) = 1/3 3x = Cos^-1(1/3) 3x = Cos^-1(0.33333.....) 3x = 1.23095.... radians. x = 1.23095... / 3 x = 0.4103195,,,, radians & x = pi - 0.4103195... x = 3.141592... - 0.4103195.... = 2.7312728.... radians.
2 answers · Homework Help · 5 days ago
• ### A rectangle has a perimeter P,length l and width w.What is the equation when solving for l in terms or P and w?

P = 2(l + w) l + w = P/2 l = (P/2) - w
P = 2(l + w) l + w = P/2 l = (P/2) - w
4 answers · Homework Help · 6 days ago
• ### If the log of x is 4.2 x 10^-3 what is x answer to 3 significant figures?

log(10) x = 4.2 x 10^-3 log(10) x = 0.0042 x = 10^(0.0042) x = 1.0097 x = 1.01 (3 s.f.)
log(10) x = 4.2 x 10^-3 log(10) x = 0.0042 x = 10^(0.0042) x = 1.0097 x = 1.01 (3 s.f.)
2 answers · Mathematics · 6 days ago