Answer:
11. 4400
Step-by-step explanation:
11.
solution :
MP = RS 5500
Discount = 20%
SP = MP - D % of MP
= 5500 - 20 % × 5500
= 5500 - 1100
= Rs 4400
2006 x 5.75 = 11534.5 .....
Answer with explanation:
The equation using trigonometric function are whose value we have to evaluate in the interval [0, 2π].
1.→
cos²x +2 cos x=3
→cos²x +2 cos x-3=0
→cos²x +3 cos x-cos x-3=0
→cos x ( cos x +3) -1×(cos x +3)=0
→ (cos x -1)(cos x +3)=0
→cos x -1= 0 ∧ →cos x+3=0
→cos x =1 ∧ → cos x = -3
⇒-1 ≤ cos x ≤ 1
→cos x=1
where, n is any integer.
→Solution in the Interval [0, 2π] is , x=0, 2 π
2.
2 sin² Ф +7 sin Ф =4
→2 sin² Ф +7 sin Ф -4=0
→2 sin² Ф +8 sin Ф- sin Ф -4=0
→2 sin Ф × (sin Ф +4) -1 × (sin Ф +4)=0
→ (2 sin Ф -1)(sin Ф +4)=0
→ 2 sin Ф -1=0 ∧ →sin Ф +4=0
→sin Ф ≠ -4≡→ ∵ -1 ≤ sin Ф ≤ 1
Where , n is any Integer.
3.
→tan² x+4=2 sec² x+tan x
→tan² x+4=2(1+tan²x)+tan x
→2 tan²x -tan²x +tan x +2-4=0
→tan²x +tan x -2=0
→tan²x +2 tan x -tan x -2=0
→tan x (tan x +2) -1×(tan x +2)=0
→(tan x-1)(tan x +2)=0
→tan x-1 =0 ∧ tan x +2=0
→tan x=1 ∧ tan x = -2
→tan x=1
→tan x= -2
where, k and n are integer.
Using the quadratic formula, you can solve this quite easily.,,,,
a b c
x² - 12x + 59 = 0 a(1)...b(-12).....c(59)
(-b +/- √b² - 4ac) / (2a) (substitute the values for a, b, and c)
(-(-12) +/- √ (-12)² - 4 (1) (59)) / 2(1)
(12 +/- √-92) / 2 ( √-92 can be written as √-1√4√23)
(12 +/- √-1√4√23) / 2 (√-1 = i and √4 = 2)
6 +/- 23i