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3 years ago

Evaluate exactly in radians: arctan(1/sqrt(3)). Show solution w/ explanation.

Mathematics

1 answer:

balandron [24]3 years ago

5 0

Arc tan ( 1/√3 ) = arc tan ( √3/3 ) = 30°
180° = π ( in radians )
30° = 180°/6 = π/6

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PLS HELP

Fiesta28 [93]

Answer:

1. 1/3 x 2/2 = 1/3

2. 1/4 x 5/5 = 1/4

3. 1/6 x 4/4 = 1/6

4. 9/8 x 3/4 = (9x3)/(8x4) = 27/32

4. 4/5 x 2/2 = 4/5

Step-by-step explanation:

n/n = 1

7 0

3 years ago

mary had 1 3/4 pound of blackberries. Mary's friend ate 3/4 of the blackberries. How many pounds of blackberries did Mary friend

OLEGan [10]

Hey there! I'm happy to help!

If Mary's friend at 3/4 of blackberries, we will simply multiply the total number of blackberries by 3/4 to find how many blackberries Mary ate.

3/4×1 3/4= 1 5/16

Therefore, Mary's friend at 1 5/16 pounds of blackberries.

I hope that this helps! Have a wonderful day!

3 0

4 years ago

The sum of three consecutive even integers is -114.

Alika [10]

The sum of three consecutives is b

5 0

3 years ago

If you place a 24-foot ladder against the top of a 20-foot building, how many feet will the bottom of the ladder be from the bot

LenKa [72]

Answer:

13.3 ft

Step-by-step explanation:

24² - 20² = d²

d = √(576 - 400) = √176 = 13.26649... ≈ 13.3 ft.

6 0

3 years ago

Two cars simultaneously left Points A and B and headed towards each other, and met after 2 hours and 45 minutes. The distance be

Oksana_A [137]

<h2>Hello!</h2>

The answers are:

$FirstCarSpeed=41mph\\SecondCarSpeed=55mph$

To calculate the speed of the cars, we need to write two equations, one for each car, in order to create a relation between the two speeds and be able to calculate one in function of the other.

So,

Tet be the first car speed "x" and the second car speed "y", writing the equations we have:

For the first car:

$x_{FirstCar}=x_o+v*t$

For the second car:

We know that the speed of the second car is the speed of the first car plus 14 mph, so:

$x_{SecondCar}=x_o+(v+14mph)*t$

Now, from the statement that both cars met after 2 hours and 45 minutes, and the distance between to cover (between A and B) is 264 miles, so, we can calculate the relative speed between them:

If the cars are moving towards each other the relative speed will be:

$RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph$

Then, since we know that they covered a combined distance equal to 264 miles in 2 hours + 45 minutes, we have:

$2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours$

Writing the equation:

$264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph$

So, the speed of the first car is equal to 41 mph.

Now, for the second car we have that:

$SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph$

We have that the speed of the second car is equal to 55 mph.

Hence, the answers are:

$FirstCarSpeed=41mph\\SecondCarSpeed=55mph$

Have a nice day!

7 0

3 years ago