Answer:
see explanation
Step-by-step explanation:
given
f'(x) = 12cos x - 4sin x, then
f'(
) = 12cos(
) - 4sin(
)
[ cos(
) = -cos(
), sin(
= - sin(
) ]
= -12cos(
) + 4sin(
)
= - 12 ×
+ 4 × ![\frac{\sqrt{3} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D)
= - 6 + 2
≈ - 2.536 ( 3 dec. places )
Answer:
Explained below.
Step-by-step explanation:
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normal.
Then, the mean of the sampling distribution of sample means is given by,
![\mu_{\bar x}=\mu](https://tex.z-dn.net/?f=%5Cmu_%7B%5Cbar%20x%7D%3D%5Cmu)
And the standard deviation of the sampling distribution of sample means is given by,
![\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Csigma_%7B%5Cbar%20x%7D%3D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
So, if the sample of daily calcium intake of Americans collected is more than 30, then the sampling distribution of
will be approximately normal.
Let's call the width
. Since the length is three more than the width, it is
.
The area (which we know to be 70) is given by the multiplication of width and length:
![x(x+3) = 70 \iff x^2+3x = 70 \iff x^2+3x-70 = 0](https://tex.z-dn.net/?f=%20x%28x%2B3%29%20%3D%2070%20%5Ciff%20x%5E2%2B3x%20%3D%2070%20%5Ciff%20x%5E2%2B3x-70%20%3D%200%20)
To solve this equation, you can use the usual quadratic formula: given an equation
, the two solutions are
![x_{1,2} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%20x_%7B1%2C2%7D%20%3D%20%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%20)
which in your case becomes
![x_{1,2} = \frac{-3\pm\sqrt{9+280}}{2} = \frac{-3\pm 17}{2}](https://tex.z-dn.net/?f=%20x_%7B1%2C2%7D%20%3D%20%5Cfrac%7B-3%5Cpm%5Csqrt%7B9%2B280%7D%7D%7B2%7D%20%20%3D%20%5Cfrac%7B-3%5Cpm%2017%7D%7B2%7D)
So, two solutions are
![\frac{-3-17}{20} = -10,\qquad \frac{-3+17}{2} = 7](https://tex.z-dn.net/?f=%20%5Cfrac%7B-3-17%7D%7B20%7D%20%3D%20-10%2C%5Cqquad%20%5Cfrac%7B-3%2B17%7D%7B2%7D%20%3D%207%20)
Since we can't accept a negative length, we only accept the second solution.
So, the dimensions are 7 and 10
It’s gonna be in quadrant III because the rule for x-axis is -> (x,-y).