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Paraphin [41]
4 years ago
14

Write each as a single logarithm using the properties of logarithms.

Mathematics
1 answer:
Afina-wow [57]4 years ago
8 0
3 log x - 2 log y

log x³ - log y²

log x³ / y²

_______________________

1/2 log b 15 + 1/2 log b x

log b √15 + log b √x

log b (√15*√x)

log b √(15x)
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How do you this question (pre-cal)
Novay_Z [31]

The goal to proving identities is to transform one side into the other. We can only pick one side to transform while the other side stays the same the entire time. The general rule of thumb is to transform the more complicated side (though there may be exceptions to this guideline).

So I'll take the left hand side and try to turn it into \csc^2( B )

One way we can do that is through the following steps:

\frac{\tan(B) + \cot(B)}{\tan(B)} = \csc^2(B)\\\\\frac{\tan(B)}{\tan(B)} + \frac{\cot(B)}{\tan(B)} = \csc^2(B)\\\\1 + \cot(B)*\frac{1}{\tan(B)} = \csc^2(B)\\\\1 + \cot(B)*\cot(B) = \csc^2(B)\\\\1 + \cot^2(B) = \csc^2(B)\\\\1 + \frac{cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{sin^2(B)}{\sin^2(B)}+\frac{cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{sin^2(B)+cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{1}{\sin^2(B)} = \csc^2(B)\\\\\csc^2(B)=\csc^2(B) \ \ {\Large \checkmark}\\\\

Since we've shown that the left hand side transforms into the right hand side, this verifies the equation is an identity.

4 0
3 years ago
You inherit $1000, but spends $8 each day at lunch. How many days until you have $768
schepotkina [342]

Answer:

29 days

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
An army base in the desert is located at the origin, O of an x-y coordinate system. A soldier at point P needs to determine his
Nutka1998 [239]

Answer/step-by-step explanation

The soldier at point P lie on a parabola because he determined his position and distances from towns A and B through measurement of the difference in timing (phase) of radio signals received from the two towns.

This analysis of the signal time difference gives the difference in distance of the soldier at P, from the towns.

This process is known as hyperbolic navigation.

These distances of point P from towns A and B is estimated by the soldier at point P, by measuring the delay localizes the receiver to a hyperbolic line on a chart.

Two hyperbolic lines will be drawn by taking timing measurements from the

towns A and B .

Point P will be at the intersection of the lines.

These distances of point P(The soldier's positions) from town A and town B were determined using the timing of the signals received from the two towns, due to the fact that point P was on a certain hyperbola.

8 0
3 years ago
What is the value of (j+3k)(5)?<br><br> j(x) = (x + 4)^2; k(x) = 8 - x<br><br> (j + 3k)(5) =
jeyben [28]

Step-by-step explanation:

J=(x+4)²

K=(8-x)

X=5

=J+3k

=(x+4)(x+4)+3(8-x)

=(x²+8x+16+24-3x)

=25+25+40

=90

Alternatively:

J=(5+4)²

J=81

K=8-5

K=3

J+3k

81+3(3)

81+9

90

3 0
3 years ago
Find the value of the expression
Amiraneli [1.4K]
3m^2+2p^2-15

3(3)^2+2(10)^2-15
3(9)+2(100)-15
21+200-15
206
3 0
3 years ago
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