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Vladimir79 [104]
2 years ago
11

Use log 3 = .477 and log 6 =.778 to approximate the expression. log 2​

Mathematics
1 answer:
Fed [463]2 years ago
3 0

Answer:

0.301

Step-by-step explanation:

Given that log 3 = .477 and log 6 =.778

Log 2

= log(6/3)

= log 6  - log 3

= 0.778 - 0.477

= 0.301

Hence the value of log 2 is 0.301

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Your task is to build a road joining a ranch to a highway that enables drivers to reach the city in the shortest time. The perpe
lubasha [3.4K]

Answer:

(a)In the attachment

(b)The road of length 35.79 km should be built such that it joins the highway at 19.52km from the perpendicular point P.

Step-by-step explanation:

(a)In the attachment

(b)The distance that enables the driver to reach the city in the shortest time is denoted by the Straight Line RM (from the Ranch to Point M)

First, let us determine length of line RM.

Using Pythagoras theorem

|RM|^{2}=30^2+x^2\\|RM|=\sqrt{30^2+x^2}

The Speed limit on the Road is 60 km/h and 110 km/h on the highway.

Time Taken = Distance/Time

Time taken on the road  =\frac{\sqrt{30^2+x^2}}{60}

Time taken on the highway =\frac{50-x}{110}

Total time taken to travel, T =\frac{\sqrt{30^2+x^2}}{60}+\frac{50-x}{110}

Minimum time taken occurs when the derivative of T equals 0.

T^{'}=\frac{x}{60\sqrt{30^2+x^2}}-\frac{1}{110}\\\frac{x}{60\sqrt{30^2+x^2}}-\frac{1}{110}=0\\\frac{x}{60\sqrt{30^2+x^2}}=\frac{1}{110}\\110x=60\sqrt{30^2+x^2}\\

Square both sides

12100x^2=3600(30^2+x^2)\\12100x^2=3240000+3600x^2\\12100x^2-3600x^2=3240000\\8500x^2=3240000\\x^2=\frac{3240000}{8500} =381.18\\x=\sqrt{381.18} =19.52

The road should be built such that it joins the highway at 19.52km from the point P.

In fact,

|RM|=\sqrt{30^2+19.52^2}=35.79km

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3 years ago
In Texas, the coldest temperature ever recorded is
Molodets [167]
21 degrees Fahrenheit
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Circle e has a radius of 40 inches with m arc ABC=324 degrees. Find the exact length of arc ABC.
creativ13 [48]
The formula to find the Length of the arc = (2r) (θ / 360°)
Substituting the values
Length of the arc = (2) (40) (324° / 360°)
By further calculation
= (80) (0.9)
So we get
= (80) (3.14) (0.9)
= 226.08 cm.
Therefore, the length of the arc is 226.08 cm.

Hope this helps
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2 years ago
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Answer: this is a INVERSE choice C

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You play a game on your phone. For every correct move you make, you receive 50 points. For every second that it takes you to com
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50*25= 1250
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