All Answers 352880 Answers

N=5*12; R=0.048/12;PV=500; FV=PV*(1 + R)^N; print"FV =$",FV

1 - Balance after 5 years =$635.32 + $500 deposit.
2 - Balance after 10 years=$1,442.58 + $500 deposit.
3 - Balance after 15 years =$2,468.32 + $500 deposit.
4 - Balance after 18 years =$3,427.08 - on her 18th birthday.

Call a positive integer kinda-prime if it has a prime number of positive integer divisors. If there are 168 prime numbers less than 1000, how many kinda-prime positive integers are there less than 1000?

Mmm

Prime numbers between 1 and 500  (from quora.com)

1–100 -> 25 numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97)

101–200 -> 21 numbers (101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 183, 193, 197, 199)

201–300 -> 16 numbers (211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293)

301–400 -> 16 numbers (307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397)

401–500 -> 17 numbers (401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499)

Beats me...

1. The space diagonal of a rectangular prism with integer unit dimensions is 13 units. What is the volume of the rectangular prism in cubic units?

2. Elliott Farms has a silo for storage. The silo is a right circular cylinder topped by a right circular cone, both having the same radius. The height of the cone is half the height of the cylinder. The diameter of the base of the silo is 10 meters and the height of the entire silo is 27 meters. What is the volume, in cubic meters, of the silo?

3. A  3 cm x 4cm x 5cm rectangular metal block was put into a well that took the shape of a right circular cylinder. When the block was submerged, the water level in the container had increased by 0.5 centimeters. What is the base area of the well in square centimeters?

4. The base of a right circular cone has area  9pi square yards. The lateral surface of the cone has area  15pi square yards. What is the volume of the cone in cubic yards?

5. Prism A has 9 edges and each of its faces is a regular polygon with side length 18. Prism B has 18 edges and each of its faces is a regular polygon with side length 9. What is the ratio of the volume of Prism A to that of Prism B?

6. A right square pyramid with base edges of length 8 sqrt 2 units each and slant edges of length 10 units each is cut by a plane that is parallel to its base and which sits 3 units above its base. What is the volume, in cubic units, of the new pyramid that is cut off by this plane?

1 + rt2 is a root => 1 - rt 2 is also a root

1 + rt3 is a root => 1 - rt 3 is also a root

P(x) = \(((x-1)^2 - 2)((x-1)^2 - 3) \)

P(x) = \((x-1)^4 - 5(x-1)^2 + 6\)

P(x) = \(x^4-4x^3+6x^2-4x+1-5x^2+10x-5+6\)

P(x) = \(x^4-4x^3+x^2+6x+2\)

Q: Solve cos x = 0.4 for 0 rad < x < 60 (rad?)

\(\cos x = 0.4\\ x = 2n\pi + \arccos \left(0.4\right)\text{ or }x = 2n\pi - \arccos(0.4)\)

Just find out how many of these general solutions fit inside the range.

\(\text{When }ax^2 + bx + c = 0\text{ has only 1 solution, }b^2 = 4ac\)

So 

\(\left(b+\dfrac 1 b\right)^2 = 4c\\ b^2 + \dfrac 1 {b^2} - 4c + 2 = 0\\ \left(b^2\right)^2 - (4c - 2)b^2 +1 = 0\\ \)

And there is only 1 positive value for b, so there are only 1 possible value for b.

Use that again and you get: 

\(\left(-(4c-2)\right)^2 = 4\\ 2c - 1 = 1\\ c = 1\)

I am not sure about what the question is talking about, but I guess you meant that. 

\(3x + \dfrac{2}{x} - 4 = 2(x+9) - (7-\dfrac 1 x)\\ 3x + \dfrac{2}{x} - 4 = 2x+18-7+\dfrac{1}{x}\\ x + \dfrac{1}{x} = 15\)

\(V = 150\pi\\ \pi r^2 h = 150\pi\\ \pi \left(\dfrac{5h}{6}\right)^2 h = 150\pi\\ \dfrac{25h^3}{36} = 150\\ h = \sqrt[3]{\dfrac{150\cdot 36}{25}} = 6\\ r = \dfrac{5h}{6} = 5\\ \text{Total surface area} = 2\pi r (r + h) = 2\pi (5)(5+6) = 110\pi\)

When a = 1 1/2 = 3/2,

\(2a = 3\\ 2a - 3 = 0\)

\((5a^2-13a+4)(2a - 3) = (5a^2-13a+4)(0) = 0\)

\(y=\sqrt x\\ y=x^{0.5}\\ \frac{dy}{dt}=0.5x^{-0.5}\cdot \frac{dx}{dt}\\ \frac{dy}{dt}=\frac{1}{2\sqrt x}\cdot \frac{dx}{dt}\\ When\;\;x=4\\ \frac{dy}{dt}=\frac{1}{4}\cdot \frac{dx}{dt}\\\)

I could have done that more simply . Oh well, too bad.

a)      

\(Since\;\; \frac{dx}{dt}=3\;\;then\\ \frac{dy}{dt}=\frac{3}{4}\\~\\ \text {that is when x=4} \)

You can do the other one.  :)

Note that     (1/8)^(-1)   =  8

So

(x - 4)^3  = 8         take the cube root of each side

x - 4  =  (8)^(1/3)

x - 4   =  2         add 4 to both sides

x  =  6

Thank you! I was debating between that answer! 

THX, Hypotenuisance.....!!!!!

EP's answer for (b) is correct.....we know the hypotenuse.....and an angle....and we are looking for the side opposite the angle

The sine  relates the   opp side  / hypotenuse

[ y + z ] / z    =    y/z  + z/z    =  y/z + 1  =   3/4 + 1   =  7/4 

Hi thanks for the reply! But I'm super confused at your answer for b. Shouldn't it be 11*tan(20) instead of sinus?