find exact value using reference angles

cot -53pi/6

Answers

Answer 1
Answer:

Answer:

cot(-53π/6) = cot(7π/6) = √(3)

Step-by-step explanation:

Remember that a trig function repeats itself every 2π, so you can add any multiple of 2π to your angle and it'll give you the same answer.

cot(-53π/6) = cot(-53π/6 + 2πk)

= cot(-53π/6 + 2π·5)

= cot(-53π/6 + 10π)

= cot(7π/6)

= [-√(3)/2] / [-1/2]

= √(3)

Answer 2
Answer: It's the same as cot (-150 or -5pi/6) and that's a reference angle of 30 so cot 30 or pi/6 is sqrt (3) and since it's in the 3rd quadrant, it's positive.

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Express each ratio as a fraction in simplest form. Hint: 1 yard = 3 feet.9 yards to 48 feet

Answers

9 yards are the same as 27 (9·3) feet, and 48 feet are equal to 16 (48:3) yards.

To express a ratio we've to convert these figures into the simplest available ones, so, let's simplify using the smallest numbers, 9 yards to 16 yards.

9 is divisible by 3 only, and 16 can be divided by 2, 4, and 8. That means we cannot use a common denominator, so the simplest ratio will be the one we already have: 9/16.

Final answer:

To convert the ratio 9 yards to 48 feet into a fraction in simplest form, we need to first convert 9 yards into feet, which is 27 feet. Then, we express this ratio as a fraction, 27/48. To simplify this fraction, we divide both numerator and denominator by their GCD, which is 3, resulting in 9/16.

Explanation:

The student has asked to express the ratio 9 yards to 48 feet as a fraction in simplest form. Given that 1 yard equals 3 feet, we first need to convert 9 yards to feet. So, 9 yards * 3 feet/1 yard = 27 feet.

Now, let's express 27 feet to 48 feet as a fraction. The ratio is 27:48, and we can write this as the fraction 27/48. However, this is not the simplest form. We simplify a fraction by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). The GCD of 27 and 48 is 3. Therefore, we divide 27 and 48 by 3 to get 9/16. So, the fraction in simplest form is 9/16.

Learn more about Fraction Simplification here:

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(2((x+1) ^3 – (x+1) ^2 + (x+1)) )+3

Answers

( x + 1 )^3 = x^3 + 3x^2 +3x + 1;
(x + 1 )^2 = x^2 + 2x + 1;
=> (2((x+1) ^3 – (x+1) ^2 + (x+1)) )+3 =2( x^3 + 3x^2 +3x + 1 - x^2 -2x - 1 + x + 1 ) + 3 = 2( x^3 + 2x^2 + 2x + 1 ) + 3 =
= 2x^3 +4x^2 +4x + 5.

What is the least common multiple of 3 and 8?

Answers

the lowest common multiple is 24
Just do 8 x 3 = 24
LCM = 24

Hope This Helps You!
Good Luck Studying :)

0.3(y+2)=1.7+(8-y) solve the following equation​

Answers

Answer:

y = 7

Step-by-step explanation:

0.3y+0.6 = 9.7 - y

0.3y+y = 9.7 -0.6

1.3y = 9.1

y= 7

sorry it had an error

What is 2x3x6x4x7x5x0x4x5

Answers


I followed the numbers across, thinking to myself "this won't be
too hard to multiply, because they're all small numbers".  And then
when I got to the zero, I burst out laughing !  It doesn't matter at all
what all the other numbers are.  Once there's a zero in there, the whole
product will be zero, no matter what else gets multiplied along the way.
There could be millions and billions in there.  You wouldn't need to do
any calculating at all.  With zero as a factor, you know right away that
the product is zero.


So your question is 
\sf{2*3*6*4*7*5*} \bf{0} \sf{*4*5=}

We need to use this property:
\sf{a * 0=0}

So then your problem has one number that is a 0. And all these numbers are getting multiplied. That means you could have like a million numbers, but if you multiply it by 0 even once, your final answer will be 0.

So your final answer is 

\boxed{\bf{0}}

In a right triangle, the length of the hypotenuse is 20 inches and the length of one leg is 15 inches. What is the length of the other leg in inches?

Answers

Solutions 

To solve this problem we have to use the Pythagorean theorem. You can only use the Pythagorean theorem in Right Triangles. The longest side of the triangle is called the "hypotenuse". C² is the longest side so it is the hypotenuse . To calculate c² we have to do α² + β² = c². 

Given 

In a right triangle, the length of the hypotenuse is 20 inches and the length of one leg is 15 inches. 

c^2 = 20 in

a^2 = 15 in

b^2 = Unknown 

------------ Calculations 

b^2 = c^2 - a^2  

b^2 = c^2(20) - a^2(15) 

b^2 = 400 - 225 

b^2 = 175 

b = √(175) 

b = 13.2287565553