Answer:
60, 75
150 165
240 255
330 345
Step-by-step explanation:
csc 4 theta = -2 sqrt(3)/3
Write in terms of sin
1/ sin (4 theta) = -2 sqrt(3)/3
Using cross products
-2 sqrt(3) = 3 sin (4 theta)
Divide each side by 3
-2 sqrt(3)/3 = sin (4 theta)
Take the inverse sin on each side
sin ^ -1(-2 sqrt(3)/3) = sin ^ -1 (sin (4 theta))
240 +360n = 4 theta
and 300 +360n = 4 theta where n is an integer
Dividing each side by 4
240/4 +360n/4 = 4/4 theta and 300/4 +360n/4 = 4/4 theta
60 + 90n = theta and 75 +90n = theta
We want all the values between 0 and 360
Let n=0
60, 75
n=1
60+90=150 and 75+90 =165
n=2
60+180= 240 75+180=255
n=3
60+270 = 330 75+ 270 =345
Answer:
C
Step-by-step explanation:
(2x + 3)^5 = C(5,0)2x^5*3^0 +
C(5,1)2x^4*3^1 + C(5,2)2x^3*3^2 + C(5,3)2x^2*3^3 + C(5,4)2x^1*3^4 + C(5,5)2x^0*3^5
Recall that
C(n,r) = n! / (n-r)! r!
C(5,0) = 1
C(5,1) = 5
C(5,2) = 10
C(5,3) = 10
C(5,4) = 5
C(5,5) = 1
= 1(2x^5)1 + 5(2x^4)3 + 10(2x^3)3^2 + 10(2x^2)3^3 + 5(2x^1)3^4 + 1(2x^0)3^5
= 2x^5 + 15(2x^4) + 90(2x^3) + 270(2x^2) + 405(2x) +243
= 32x^5 + 15(16x^4) + 90(8x^3) + 270(4x^2) + 810x + 243
= 32x^5 + 240x^4 + 720x^3 + 1080x^2 + 810x + 243
Answer:
x = 5.5
y = - 6.5
Step-by-step explanation:
Let one of the numbers = x
Let the other number = y
x + y = - 1
x = y + 12 Put the second equation into the first one
y + 12 + y = - 1 Subtract 12 from both sides
y + y = - 1 - 12 Combine both left and right sides
2y = - 13 Divide by 2
2y/2 = - 13/1
y = - 6.5
x + y = - 1
x - 6.5 = - 1 Add 6.5 to both sides
x = 5.5
Suppose the original price to be x.
62%x=296.4
Divide both sides by 62% to get x=478, which is the original price.
<span>Ishaan is 21, Christopher is 7
No actual question given, but I will assume that the question is "How old are they?". If that's the case, we can create two equations. I'll use I for Ishaan's age and C for Christopher's. I will also assume that there's been some formatting issues here and for some reason, numbers are repeated 3 times without any spaces. So
"Ishaan is 3 times as old as Christopher"
I = 3C
"is also 14 years older than Christopher
I = C + 14
Since both equations are equal to each other, let's set them equal. So
3C = C + 14
2C = 14
C = 7
So Christopher is 7. And we can use the equation I = C + 14 to get Ishaan's age. So
I = C + 14
I = 7 + 14
I = 21</span>
