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DaniilM [7]
3 years ago
10

Condense to a single logarithm : log 12 18+3 log 12 2

Mathematics
1 answer:
Over [174]3 years ago
8 0

Answer:

2 or \log_{12} 144

Step-by-step explanation:

I assume 12 is the base.

\log_{12} 18 + 3 \log_{12} 2 =

= \log_{12} 18 + \log_{12} 2^3

= \log_{12} (18 \times 8)

= \log_{12} 144

= \log_{12} 12^2

= 2\log_{12} 12

= 2

The entire expression simplifies to 2, but if you need the simplest log expression, then you can use

\log_{12} 144

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An airplane has its auto pilot set to fly in a direction of 40 degrees at a speed of 320 mph. The wind is blowing the airplane t
Effectus [21]

Answer:

distance: 320.624 miles

direction: 43.576°

Step-by-step explanation:

The speed and direction can be found by adding the given vectors.

... 320∠40° + 20∠130°

... = (320·cos(40°), 320·sin(40°)) + (20·cos(130°), 20·sin(130°))

... = (245.134, 205.692) +(-12.856, 15.321) = (232.278, 221.013)

The magnitude of the vector with these components is found using the Pythagorean theorem. The direction is found using the arctangent function.

... = √(232.278² +221.013²)∠arctan(221.013/232.278)

... = 320.624∠43.576°

_____

A suitable vector or graphing calculator can do this easily. In the screenshot of a TI-84 app below, the variable D has the value π/180. The display mode is set to degrees.

_____

<em>Comment on coordinate systems</em>

Navigation directions are generally measured clockwise from North. Angles in the usual x-y coordinate plane are measured counterclockwise from +x (effectively, East). You can consider the geometry of the navigation coordinate system to be a reflection across the line y=x of the geometry of the usual x-y coordinate system.

Reflection does not change lengths or angles within a given geometry. Hence, we can use all the usual tools of vector calculation using navigation coordinates, without bothering to translate them back and forth to x-y coordinates.

_____

Problems like this generally can be worked using the Law of Cosines and the Law of Sines, too. It generally helps to draw a diagram so you can find the values of the angles betwee the various vectors more easily.

8 0
3 years ago
1. Line that crosses through (6,4) with a slope of -23
navik [9.2K]

Answer:

y= -23x+142

Step-by-step explanation:

we know that our equation has to look likethis

y=mx+b

where m is the slope and b is the y intercept

we're given that m = -23 so we have

y= -23x+b

we also know that when x=6 y=4 so we can just plug those values in and solve for b

4= -23(6)+b

142=b

Which means our equation is

y= -23x+142

5 0
3 years ago
Read 2 more answers
PLEASE HELP
Virty [35]

Answer:

86

Step-by-step explanation:

4 0
3 years ago
A polynomial function has a root of -3 with multiplicity 2, a root of 0 with multiplicity 1, a root og 1 woth multiplicity 1 and
damaskus [11]

25 is the answer hurry hurry

5 0
3 years ago
Express 1 m as a percentage of 56 mm
hichkok12 [17]

Answer:

2

Step-by-step explanation:

use your head

7 0
2 years ago
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