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Rasek [7]
3 years ago
13

Find the terminal point on the unit circle determined by 7pi//6 radians?

Mathematics
1 answer:
Anit [1.1K]3 years ago
4 0
\frac{7 \pi}{6} =  \frac{7*180}{6} = 7*30 = 210

210 we can write it as 210 = 180 + 30.
So 210 has a reference angle  of 30 degree in third quadrant.

So x co-ordinate of terminal point is cos(210) = \frac{- \sqrt{3} }{2}

y co-ordinate of terminal point is sin(210) = \frac{-1}{2}

So the terminal point is ( \frac{- \sqrt{3} }{2} ,  \frac{-1}{2} )
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Find the acute angles between the curves at their points of intersection. (the angle between two curves is the angle between the
amm1812
At point of intersection the two equations are equal,
hence, 6x³ =6x²
           6x³-6x²=0
           6x²(x-1)=0 , the values of x are 0 and 1
The points of intersection are therefore, (0,0) and (1,6)
To find the slopes of the tangents at the points of intersection we find dy/dx
for curve 1, dy/dx=12x, and the other curve dy/dx=18x²
At x=0, dy/dx=12x =0, dy/dx=18x² = 0, hence the angle between the tangents is 0, because the tangents to the two curves have the same slope which is 0 and pass the same point (0,0) origin.
At x=1, dy/dx =12x = 12, dy/dx= 18x² =18, Hence the angle between the two tangents will be given by arctan 18 -arctan 12 
                                      = 86.8202 - 85.2364 ≈ 1.5838, because the slope of the lines is equal to tan α where α is the angle of inclination of the line.


5 0
3 years ago
Simplify &cm-4) - :m+5)-(m - 6)-(n+7)
Mekhanik [1.2K]

Answer:

m-1-n

Step-by-step explanation:

7 0
3 years ago
Using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true:
spin [16.1K]

Answer:

(4+5-2+1)- (7+3-8+6) = 0

Step-by-step explanation:

you look for what numbers when subtracted equal zero (in this case each of the parentheses is 8) in each of the parentheses and combine them at the end to form the final equation.  

8 0
3 years ago
Anna, Boris, and Clara thought of 1 number each Ana's number increased by 20 is 21 greater than boris's number decreased by 22.
sleet_krkn [62]

Answer:

Clara's number is 42 less than Anna's number

Step-by-step explanation:

We can start this problem out by setting our variables up:

A= Anna's number

B= Boris's number

C= Clara's number

so we can use them to build our equations. We can sepparate the problem into little more understandable pieces of information, let's start with the first piece of information:

- "Ana's number increased by 20"

A+20

- "boris's number decreased by 22"

B-22

- "21 greater than boris's number decreased by 22."

(B-22)+21

- "Ana's number increased by 20 is 21 greater than boris's number decreased by 22."

A+20=(B-22)+21

This is our first important equation here. Let's go with the second part of the problem:

- "Boris's number decreased by 20"

B-20

- "claras number increased by 22"

C+22

- "21 greater than claras number increased by 22"

(C+22)+21

Now the whole thing:

"Boris's number decreased by 20 is 21 greater than claras number increased by 22."

B-20=(C+22)+21

This is our second important equation.

So now we have the following system of equations:

A+20=(B-22)+21

B-20=(C+22)+21

We can now simplify the equations by combining like terms so we get:

Equation 1:

A+20=(B-22)+21

we can get rid of the parenthesis so we get:

A+20=B-22+21

We can subtract a 20 from both sides of the equation so we get:

A=B-22+21-20

We perform the subtractions so we get:

A=B-21

Equation 2:

B-20=(C+22)+21

We get rid of the parenthesis:

B-20=C+22+21

We add a 20 to both sides so we get:

B=C+22+21+20

We can now perform the additions so we get:

B=C+63

And now we can combine the equations. In this case we can substitute equation 2 into equation 1 to get:

A=C+63-21

We combine like terms to get:

A=C+42

We can subtract 42 from both sides to get:

C=A-42

which reads:

Clara's number is 42 less than Anna's number.

3 0
3 years ago
p is a polynomial of degree 5. p has roots of multiplicity 2 at t=4 and t=0, a root of multiplicity 1 at t=-4, and p(1)=2025. Fi
DENIUS [597]
P(x) = (x^2)(x - 4)^2(x + 4) + some constant(b)
2025 = (1^2)(1 - 4)^2(1 + 4) + b
2025 = 45 + b
b = 1980

Complete Equation:

p(x) = (x^2)(x - 4)^2(x +4) + 1980

or expanded form

p(x) = x^5 - 4x^4 - 16x^3 + 64x^2 + 1980
5 0
2 years ago
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