Answer:
The heights are the same after 4 hours.
Step-by-step explanation:
The red candle burns at a rate of 7/10 inches per hour. In t hours, (7/10)t inches have burned. The height of the candle after t hours is 8 - (7/10)t.
The blue candle burns at a rate of 1/5 inch per hour. In t hours, (1/5)t inches have burned. The height of the candle after t hours is 6 - (1/5)t.
You need to find the time, t, when their heights are equal.
8 - (7/10)t = 6 - (1/5)t
Multiply both sides by 10 (the LCD).
80 - 7t = 60 - 2t
-5t = -20
t = 4
The heights are the same after 4 hours.
Let's calculate the value of angle A and B
sin(A) =-4/5 → sin⁻¹(- 4/5) = A → A = - 53.13
cos(B) = -5/13 → cos⁻¹ (- 5/13) = B → B = 112.62
tan (A+B) = sin(A+B)/cos(A+B) with A+B = -53.13 + 112.62 = 59.49
tan (A+B) = sin(59.49)/cos(59.49) = 0.86154/0.507688 = 1.6969.
(Answer H = 56/33 = 1.6969)
(2x+3y)⁴
1) let 2x = a and 3y = b
(a+b)⁴ = a⁴ + a³b + a²b² + ab³ + b⁴
Now let's find the coefficient of each factor using Pascal Triangle
0 | 1
1 | 1 1
2 | 1 2 1
3 | 1 3 3 1
4 | 1 4 6 4 1
0,1,2,3,4,.. represent the exponents of binomials
Since our binomial has a 4th exponents, the coefficients are respectively:
(1)a⁴ + (4)a³b + (6)a²b² + (4)ab³ + (1)b⁴
Now replace a and b by their real values in (1):
2⁴x⁴ +(4)8x³(3y) + (6)(2²x²)(3²y²) + (4)(2x)(3³y³) + (1)(3⁴)(y⁴)
16x⁴ + 96x³y + 216x²y² + 216xy³ + 81y⁴
Remember
xyz=(x)(y)(z)
if x and y and z are all perfect cubes, xyz is also a perfect cube
remmeber
(x^n)^m=x^(mn)
so if it is perfect cube it can be factored into
(x^n)^3, such taht n is a whole number
basiclaly, see if the expoent is divisble by 3
all of them should be perfect cubes
215x^18y^3z^21
split them up to see which ones need changing
215=5*43, not a perfect cube
could be changed to 6^3, which is 216
x^18=(x^6)^3
y^3=y^3
z^21=(z^7)^3
the 215 needs to be changed
Answer:
Step-by-step explanation:
Suppose the time required for an auto shop to do a tune-up is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - u)/s
Where
x = points scored by students
u = mean time
s = standard deviation
From the information given,
u = 102 minutes
s = 18 minutes
1) We want to find the probability that a tune-up will take more than 2hrs. It is expressed as
P(x > 120 minutes) = 1 - P(x ≤ 120)
For x = 120
z = (120 - 102)/18 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.8413
P(x > 120) = 1 - 0.8413 = 0.1587
2) We want to find the probability that a tune-up will take lesser than 66 minutes. It is expressed as
P(x < 66 minutes)
For x = 66
z = (66 - 102)/18 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.02275
P(x < 66 minutes) = 0.02275
