Find the HCF of 750,630 and 18900

If there are 48 boys and 32 girls in a room, fill out all of the possible ratios of boys to girls that could be made.

kaheart [24]

Answer:

12 to 8, 6 to 4

Step-by-step explanation:

4 0

2 years ago

The ratio of tickets sold to see the incredible musical wicked to tickets sold to see Cats is 11 to 7 if there were 2700 total t

tia_tia [17]

Use algebra to set up 2 equations.

Assign c as number of tickets for CATS and w for number of tickets of WICKED

c + w = 2700

c / w = 7 / 11

Then solve for one of them in the first equation

c = 2700 - w

Then put this value for c into the 2nd equation

(2700 - w) / w = 7 / 11

Now cross multiply the numerator by denominator of both numerator and denominator pairs

7w = 11 x (2700 - w)
7w = 29700 - 11w

Now solve for w

7w = 26700 - 11w

Add +11w to both sides

18w = 29700

Now divide by 18 on both sides

w = 1650

Then c is the remainder of that ... 2700 - 1650 = 1050

You can also check because 7 / 11 = 1050 / 1650

8 0

3 years ago

Use the Newton-Raphson method to find the root of the equation f(x) = In(3x) + 5x2, using an initial guess of x = 0.5 and a stop

xxMikexx [17]

Answer with explanation:

The equation which we have to solve by Newton-Raphson Method is,

f(x)=log (3 x) +5 x²

$f'(x)=\frac{1}{3x}+10 x$

Initial Guess =0.5

Formula to find Iteration by Newton-Raphson method

$x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}\\\\x_{1}=x_{0}-\frac{f(x_{0})}{f'(x_{0})}\\\\ x_{1}=0.5-\frac{\log(1.5)+1.25}{\frac{1}{1.5}+10 \times 0.5}\\\\x_{1}=0.5- \frac{0.1760+1.25}{0.67+5}\\\\x_{1}=0.5-\frac{1.426}{5.67}\\\\x_{1}=0.5-0.25149\\\\x_{1}=0.248$

$x_{2}=0.248-\frac{\log(0.744)+0.30752}{\frac{1}{0.744}+10 \times 0.248}\\\\x_{2}=0.248- \frac{-0.128+0.30752}{1.35+2.48}\\\\x_{2}=0.248-\frac{0.17952}{3.83}\\\\x_{2}=0.248-0.0468\\\\x_{2}=0.2012$

$x_{3}=0.2012-\frac{\log(0.6036)+0.2024072}{\frac{1}{0.6036}+10 \times 0.2012}\\\\x_{3}=0.2012- \frac{-0.2192+0.2025}{1.6567+2.012}\\\\x_{3}=0.2012-\frac{-0.0167}{3.6687}\\\\x_{3}=0.2012+0.0045\\\\x_{3}=0.2057$

$x_{4}=0.2057-\frac{\log(0.6171)+0.21156}{\frac{1}{0.6171}+10 \times 0.2057}\\\\x_{4}=0.2057- \frac{-0.2096+0.21156}{1.6204+2.057}\\\\x_{4}=0.2057-\frac{0.0019}{3.6774}\\\\x_{4}=0.2057-0.0005\\\\x_{4}=0.2052$