Answer:
The expression 6x should be 6x²
Step-by-step-explanation:
The chart being referred to showing the multiplication of the binomial by the trinomial is given in the attached picture below.
To find out where Chin made an error in his multiplication, and also determine the right expression, let's take a look at each multiplication done. Thus we have:
3x*x² = 3x³
3x*2x = 6x² (here is where the error was made, in the chart, Chin wrote 6x)
3x*4 = 12x
2*x²=2x²
2*2x = 4x
2*4 = 8
Therefore, the expression 6x should be 6x²
17.09 has 2 decimal places, so we put the decimal digits of 17.09, 09, over 1 followed by the number of zeroes equal to the number of decimal places, 2: 09 = 09/100. We add 17 as 1700/100 and get: 17.09 as decimal fraction = 1709/100
We are given the parametric equations:
x = 6 cos θ
y = 6 sin θ
We know that the derivative of cos a = - sin a and the
derivative of sin a = cos a, therefore taking the 1st and 2nd
derivates of x and y:
d x = 6 (-sin θ) = - 6 sin θ
d^2 x = -6 (cos θ) = - 6 cos θ
d y = 6 (cos θ) = 6 cos θ
d^2 y = 6 (-sin θ) = - 6 sin θ
Therefore the values we are asked to find are:
dy / dx = 6 cos θ / - 6 sin θ = - cos θ / sin θ = - cot θ
d^2 y / d^2 x = - 6 sin θ / - 6 cos θ = sin θ / tan θ =
tan θ
We can find the value of the slope at θ = π/4 by using
the dy/dx:
dy/dx = slope = - cot θ
dy/dx = - cot (π/4) = - 1 / tan (π/4)
dy/dx = -1 = slope
We can find the concavity at θ = π/4 by using the d^2 y/d^2
x:
d^2 y / d^2 x = tan θ
d^2 y / d^2 x = tan (π/4)
d^2 y / d^2 x = 1
Since the value of the 2nd derivative is
positive, hence the concavity is going up or the function is concaved upward.
Summary of Answers:
dy/dx = - cot θ
d^2 y/d^2 x = tan θ
slope = -1
concaved upward
He receives 8.5% <span>commission on sales from $70,000 to $100,000, therefore the commission is:
comission = 8.5%($82000) = (85/1000)(82000)
= 6979
that is his commission</span>
Answer:
The mean is given by:
And the deviation:
Step-by-step explanation:
For this case we assume that the true population proportion of Americans do not know that GOP stands for Grand Old Party is 0.55 and we select a random sample of n = 953 americans
For this case we assume that we satisfy the conditions to use the normal approximation for 
1) np >10 , n(1-p)>10
2) Independence
3) Random sample
4) The sample size is less than 10% of the population size
We assume that all the conditions are satisfied and the distribution for would be:
The mean is given by:
And the deviation:
