Answer:
i)
ii) n = 33
Step-by-step explanation:
For this question you can actually focus on the sine, and forget about the e power. The x-coordinates of the extremes of the curve will be the same as for y=sin(4x)
i) equivalent to solving sin(4x) = -1, so 4x = 3/2 pi, x=3/8 pi
ii) The Tn values are at x = (n·π - π/2)/4
solving (n·π - π/2)/4 > 25 gives:
n > 1/2 + 100/π, so n > 32.331, but n must be integer, so we get n=33
Answer:
1.5 liters = 1500 Milliliters
Answer: 0.12
x is the number which is chosen
The number of ways to choose x from 1 to 100 is 100 (ways)
because x is divisible by 8 => x ∈ {8; 16;...; 96}
=> the number of terms divisible by 8 from 1 to 100 is (96 - 8)/8 + 1 = 12
the number of ways to choose x which is divisible by 8 is 12 (ways)
=> the probability that x is divisible by 8 is 12/100 = 0.12
Step-by-step explanation:
0.12r=1.8
Divide both sides by 0.12
r = 15
Answer:
length = 4 cm
Width = 5 cm
Step-by-step explanation:
<h2>Area of rectangle:</h2>
Area of rectangle = length * width
length = (x - 3) meters
Width = (x - 2) meter
Area = 20 square meters
(x - 3)*(x - 2) = 20
Use FOIL method.
x*x + (x)(-2) + (-3)*x + (-3)*(-2) = 20
x² -2x - 3x + 6 =20
Combine like terms
x² - 5x + 6 = 20
Now subtract 20 from both side
x² - 5x + 6 - 20 = 0
x² - 5x - 14 = 0
Factorize the equation and find the roots
Sum = -5
Product = -14
Factors = (-7) , 2
When we add (-7) + 2 = -5 and when we multiply (-7)*2 = -14
x² + 2x - 7x - 14 = 0
x(x + 2) -7(x + 2) = 0
(x + 2)(x - 7) = 0
x - 7 = 0 {Ignore (x + 2 = 0) as measurements wont't be in negative}
x = 7
length = x - 3
= 7 - 3
width = x - 2
= 7 - 2