Answer:
0.73 N to 2 dp.
Step-by-step explanation:
F = k/d^2 where k is a constant , F = force and d = distance.
Substituting:
0.36 = k / (6)^2
k = 36*0.36 = 12.96 s the equation is F = 12.96 / d^2.
When d = 4.2 :
F = 12.96 / 4.2^2
F = 0.73 Newtons to 2 dp.
Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
Answer:
The original price is 337.50
Step-by-step explanation:
If we get 20% off, we still have to pay 100-20 =80%
Let x be the original price
x *80% = 270
.80x = 270
Divide each side by .80
.80x/.80 = 270/.80
x =337.50
The original price is 337.50
Answer:
Option A is correct.
Solution for the given equation is, 
Step-by-step explanation:
Given that : 
Let 
then our equation become;
.....[1]
A quadratic equation is of the form:
.....[2] where a, b and c are coefficient and the solution is given by;
Comparing equation [1] and [2] we get;
a = 2 b = -1 and c =-1
then;
Simplify:
or
or
and 
Simplify:
y = 1 and 
Substitute y = cos x we have;
⇒
and
⇒ 
The solution set: 
Therefore, the solution for the given equation is, 
Answer:
Use the cross technique if it’s name like that in English but , I wish you can understand it from what I‘ve written .
