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Black_prince [1.1K]
3 years ago
14

I'm given that log4=0.602 and log12=1.079

Mathematics
2 answers:
prisoha [69]3 years ago
7 0
(log3) = log(12/4) = (log12) - (log4) = 0.477
Rudiy273 years ago
6 0

log(3) = log(12/4)

Use the quotient rule [ \text{log}_a\frac{x}{y}=log_ax-log_ay ] to simplify.

log(12/4) = log(12) - log(4)

Simplify using the given values for 12 and 4.

1.079 - 0.602

0.477

Therefore, log(12) ≈ 0.477

Best of Luck!

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Valentina made costume crowns for the king and the prince in her school play. She used 5 red gems and 8 purple gems for the king
kobusy [5.1K]

Answer:

The prince's crown had a greater ratio of red gems to purple gems.

Step-by-step explanation:

KING = 5 red / 8 purple

PRINCE = 4 red / 5 purple

Times the ratio for the king by 5

5(5) / 8(5) = 25/40

Times the ratio for the prince by 8

4(8) / 5(8) = 32/40

The prince has a greater ratio of red gems

Hope this is right, and sorry if it is incorrect. Have a good day!

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2 years ago
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Answer:

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A diameter of a circle has endpoints P(-10,-2) and Q(4,6).
Lesechka [4]

Check the picture below.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{-10}~,~\stackrel{y_1}{-2})\qquad Q(\stackrel{x_2}{4}~,~\stackrel{y_2}{6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{4-10}{2}~~,~~\cfrac{6-2}{2} \right)\implies \left( \cfrac{-6}{2}~,~\cfrac{4}{2} \right)\implies \stackrel{\textit{center}}{(-3~,~2)} \\\\[-0.35em] ~\dotfill

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{center}}{(\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})}\qquad Q(\stackrel{x_2}{4}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-3)]^2+[6-2]^2}\implies r=\sqrt{(4+3)^2+(6-2)^2} \\\\\\ r=\sqrt{49+16}\implies r=\sqrt{65} \\\\[-0.35em] ~\dotfill

\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-3}{ h},\stackrel{2}{ k})\qquad \qquad radius=\stackrel{\sqrt{65}}{ r} \\[2em] [x-(-3)]^2+[y-2]^2=(\sqrt{65})^2\implies (x+3)^2+(y-2)^2=65

5 0
3 years ago
Please help me!! its sooo hard!!!!
den301095 [7]
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3 0
3 years ago
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Find the geometric sum: 40 + 20 + 10 + … + 0.078125
sveticcg [70]
S=40+20+10+\cdots+0.078125
S=40\left(1+\dfrac12+\dfrac14+\cdots+\dfrac1{512}\right)
S=40\left(1+2^{-1}+2^{-2}+\cdots+2^{-9}\right)

2^{-1}S=40\left(2^{-1}+2^{-2}+2^{-3}+\cdots+2^{-10}\right)

\implies S-2^{-1}S=40\left(1-2^{-10}\right)
\implies\dfrac12S=40\left(1-\dfrac1{1024}\right)
\implies S=80\left(1-\dfrac1{1024}\right)=\dfrac{5115}{64}=79.921875
4 0
3 years ago
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