Cot(theta -pi/2) = cos(theta - pi/2)/sin(theta - pi/2)
using cosine and sin law
= [cos(theta)*cos(pi/2)+sin(theta)*sin(pi/2)] / [sin(theta)*cos(pi/2) - cos(theta) * sin(pi/2)]
by simplify it :
= sin(theta) / -cos(theta)
= -tan(theta)
Answer:
Lulu has 14 quarters and 6 dimes
Step-by-step explanation:
Let x be the number of dimes and y the number of quarters. The sum of quarters and dime is 20 coins. Then:
x + y = 20
We also know that the value of each dime is $ 0.10 and the value of each quarter is $0.25. The total value of the coins is $4.10. Then, the number of dimes times 0.10 plus the number of quarters times 0.25 will be 4.10:
0.10x + 0.25y = 4.10
So, we have a system of 2 equations and 2 unknowns:
x + y = 20
0.10x + 0.25y = 4.10
Let´s solve the first equation for y:
x + y = 20
subtract x from both sides
y = 20 - x
And now let´s replace y in the second equation:
0.10x + 0.25(20 - x) = 4.10
Apply distributive property
0.10x + 5 - 0.25x = 4.10
subtract 5 from both sides of the equation
-0.15x = -0.9
Divide by -0.15 both sides of the equation
x = 6
Now let´s calculate y:
y = 20 - x
y = 20 - 6 = 14
Lulu has 14 quarters and 6 dimes
Y=-3
X=0
(0,-3)
To solve,
Distribute 5 to the whole first equation.
You will get -10x+25y=-75
Then distribute 2 across second equation
You will get 10x+4y=-12
X will cance out and you will have 29y=-87
Y=-3
And just plug -3 into one of the equation and you get X=0
Final answer :
(0,-3)
120 square inches because a circle is 360 degrees so there will be 6 60 degree sections in it and each 60 degree section needs 20 square inches to cover it so 6 x 20= 120
Answer:
I'm not totally sure this is a VERY tricky question but I do know that 3 people did not say yes.
Step-by-step explanation:
Well if 70% of people said that they order toppings on pizza, then 30% don't order toppings. Therefore out of 10 people, 7 order toppings and 3 don't.