# Math Help - Multiple random questions with answers, need explaination?

1. ## Multiple random questions with answers, need explaination?

Please explain how these questions will be solved to get these answers.

Q: Solve for z: e^2z-1 =3
A: (In3+1)/2

Q: A student's test score was 650 on a scale of 200-800. Convert this score to a scale of 0-100.
A: 75

Q:If f(x) = 4-x^2 and g(x)=1-x, find f[g(-2)]
A: -5

Q: Find x: 3^2x-3x= 72
A: 2

Q:Simplify (a^-2 - b^-2) / (a-b)
A: - (a+b) / (a^2b^2)

Q:Find an equation of the circle having center (4, -3) and radius 5.
A: x^2+y^2-8x+6y=0

Q: What is the solutions for the equation ^3√x^2 - ^3√x - 6 = 0
A: (-8, 27)

Q: Find the number of consecutive odd integers beginning with 23 which are necessary to make a sum of 608.
A: 16

Q: Find the vertex of the parabola 4x=y^2-4y
A: (-1,2)

Q: A cube has a diagonal of length 5√3. Find its surface area in sq. units.
A: 150

I really need to know this ASAP

Thanks

2. Originally Posted by Hi888
Please explain how these questions will be solved to get these answers.

Q: Solve for z: e^2z-1 =3
A: (In3+1)/2

Q: A student's test score was 650 on a scale of 200-800. Convert this score to a scale of 0-100.
A: 75

Q:If f(x) = 4-x^2 and g(x)=1-x, find f[g(-2)]
A: -5

Q: Find x: 3^2x-3x= 72
A: 2

Q:Simplify (a^-2 - b^-2) / (a-b)
A: - (a+b) / (a^2b^2)

Q:Find an equation of the circle having center (4, -3) and radius 5.
A: x^2+y^2-8x+6y=0

Q: What is the solutions for the equation ^3√x^2 - ^3√x - 6 = 0
A: (-8, 27)

Q: Find the number of consecutive odd integers beginning with 23 which are necessary to make a sum of 608.
A: 16

Q: Find the vertex of the parabola 4x=y^2-4y
A: (-1,2)

Q: A cube has a diagonal of length 5√3. Find its surface area in sq. units.
A: 150

I really need to know this ASAP

Thanks
Hi

$e^{2z-1} =3 \implies 2z-1 = \ln(3) \implies z = \frac{\ln(3)+1}{2}$

$\frac{650-200}{800-200} = \frac{x-0}{100-0} \implies \frac{450}{600} = \frac{x}{100} \implies x = 75$

$g(x) = 1-x \implies g(-2) = 1-(-2) = 3 \implies f[g(-2)] = f(3) = 4-3^2 = 4-9 = -5$

$3^{2x} - 3^x = 72 \implies \left(3^x\right)^2 - 3^x - 72 = 0 \implies X = 3^x \:and\: X^2 - X - 72 = 0$ $\implies X = 3^x \:and \X = -8 \r\: X = 9) \implies X = 3^x \:and \:X = 9 \implies 3^x = 9 \implies x = 2" alt=" \implies X = 3^x \:and \X = -8 \r\: X = 9) \implies X = 3^x \:and \:X = 9 \implies 3^x = 9 \implies x = 2" />

$\frac{a^{-2} - b^{-2}}{a-b} = \frac{\frac{1}{a^2} - \frac{1}{b^2}}{a-b} = \frac{\frac{b^2-a^2}{a^2b^2}}{a-b} = \frac{(b-a)(b+a)}{a^2b^2(a-b)} = -\frac{a+b}{a^2b^2}$

$(x-4)^2 + (y-(-3))^2 = 25 \implies x^2-8x+16+y^2+6y+9 = 25 \implies x^2+y^2-8x+6y=0$

$23 + (23+2) + (23+4) + \cdots + (23+2n) = 608 \implies 23(n+1) + (2 + 4 + \cdots + n) = 608$ $\implies 23(n+1) + 2(1+2+\cdots+n)=608$ $\implies 23(n+1) + n(n+1) = 608 \implies n^2+24n-585=0 \implies n=15 \implies (n+1)=16$

Diagonal of the cube (length of the sides = a) is $a\sqrt{3}$ (apply twice Pythagorean). Therefore a = 5.
Surface area is 6 (number of faces) x 5 x 5 (surface of each face) = 150

3. Q: A student's test score was 650 on a scale of 200-800. Convert this score to a scale of 0-100.
A: 75

Q:If f(x) = 4-x^2 and g(x)=1-x, find f[g(-2)]
A: -5

Q:Find an equation of the circle having center (4, -3) and radius 5.
A: x^2+y^2-8x+6y=0

Q: Find the vertex of the parabola 4x=y^2-4y
A: (-1,2)

Q: A cube has a diagonal of length 5√3. Find its surface area in sq. units.
A: 150