Answer:
Step-by-step explanation:
We use these three methods
1. Generalized cylinder method
2. Surface of revolution method
3. Method of slices general quadratic
1. For A = x² = 4z + 8
We use the method of slices for general quadratic
2. X²-4y²-4z² = 16
We use the generalized cylinder method
3. Y² = z² + 2z²
We use surface of revolution
Please check attachment for answers
The density of a substance is the ratio of its mass and its volume. The mass of the rod is 10,666.67 grams or 10.67 kgs.
<h3>What is the density of a substance?</h3>
The density of a substance is the ratio of its mass and its volume. Therefore we can write,

mass of substance = m kg
density of substance = d kg/m³
volume of that substance = v m³
The length of the rod is 4 meters, therefore, the length of the rod in centimeters will be 400 centimeters. Thus, The mass in terms of density can be written as,

![= [2\cdot \dfrac{2x^{\frac32}}{3}]_0^{400}\\\\= [\dfrac{4x^{\frac32}}{3}]_0^{400}\\\\=[\dfrac{4(400)^{\frac32}}{3}]-[\dfrac{4(0)^{\frac32}}{3}]\\\\= 10,666.\bar6\rm\ grams](https://tex.z-dn.net/?f=%3D%20%5B2%5Ccdot%20%5Cdfrac%7B2x%5E%7B%5Cfrac32%7D%7D%7B3%7D%5D_0%5E%7B400%7D%5C%5C%5C%5C%3D%20%5B%5Cdfrac%7B4x%5E%7B%5Cfrac32%7D%7D%7B3%7D%5D_0%5E%7B400%7D%5C%5C%5C%5C%3D%5B%5Cdfrac%7B4%28400%29%5E%7B%5Cfrac32%7D%7D%7B3%7D%5D-%5B%5Cdfrac%7B4%280%29%5E%7B%5Cfrac32%7D%7D%7B3%7D%5D%5C%5C%5C%5C%3D%2010%2C666.%5Cbar6%5Crm%5C%20grams)
Hence, the mass of the rod is 10,666.67 grams or 10.67 kgs.
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Answer:
Step-by-step explanation:
Given that an automatic machine is set to fill bags of dog food with exactly 25 pounds on average with a standard deviation of 0.5 pounds.
Sample size = n =100
x bar = 24.85 pounds
Sample std error = 
Hypotheses:

(Two tailed test at 5% level)
Mean difference =0.15
Test statistic = mean diff/se = 3
Since population std dev is known z test can be used
p value =0.0000
Since p <0.05 we find that the bag does not contain exactly 25 pounds.
Answer:
38
Step-by-step explanation:
Answer: segment KH
Explanation:
The altitude of a triangle is defined as a segment connecting one of the vertex of the triangle with the opposite side of the triangle (or with an external prolongation of it), forming a right angle with it.
Note that the altitude of a triangle can also be outside the area of the triangle.
If we look at the picture, we see that:
- IH is a side, so it is not an altitude of the triangle
- KH is an altitude of the triangle, since it connects the vertex H with the external prolongation of IG, and it makes a right angle with it
- GJ: we don't know if it is an altitude, since we don't know if it forms a right angle or not
- GH: it is a side of the triangle, so it is not an altitude
So, the correct answer is segment KH.