Answer:
See attachment
Step-by-step explanation:
The given inequality is
![- \frac{1}{2}p \: < \: - 16](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B1%7D%7B2%7Dp%20%5C%3A%20%3C%20%20%5C%3A%20%20-%2016)
We multiply both sides by -2 and reverse the inequality sign to get:
![- 2 \times - \frac{1}{2} p \: > \: - 2 \: \times - 16](https://tex.z-dn.net/?f=%20%20-%202%20%5Ctimes%20%20-%20%20%5Cfrac%7B1%7D%7B2%7D%20p%20%5C%3A%20%20%20%3E%20%20%5C%3A%20%20-%202%20%5C%3A%20%20%5Ctimes%20%20-%2016)
![p \: > \: 32](https://tex.z-dn.net/?f=p%20%5C%3A%20%20%3E%20%20%5C%3A%2032)
We draw an open circle at 32 and draw an arrow to the right as shown in attachment.
The area of the region bounded above by y= eˣ bounded by y = x, and bounded on the sides; x =0; and x = 1 is given as e¹ - 1.5.
<h3>What is the significance of "Area under the curve"?</h3>
This is the condition in which one process increases a quantity at a certain rate and another process decreases the same quantity at the same rate, and the "area" (actually the integral of the difference between those two rates integrated over a given period of time) is the accumulated effect of those two processes.
<h3>What is the justification for the above answer?</h3>
Area = ![\int\limits^1_0 {(e^x-x)} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E1_0%20%7B%28e%5Ex-x%29%7D%20%5C%2C%20dx)
= ![\int\limits^1_0 {e^x-x} \, dx - \int\limits^1_0 {(x)} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E1_0%20%7Be%5Ex-x%7D%20%5C%2C%20dx%20-%20%5Cint%5Climits%5E1_0%20%7B%28x%29%7D%20%5C%2C%20dx)
= e¹-(1/2-0); or
Area = e -1.5 Squared Unit
The related Graph is attached accordingly.
Learn more about area bounded by curve:
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Answer:
![A=22.5\ \text{feet}^2](https://tex.z-dn.net/?f=A%3D22.5%5C%20%5Ctext%7Bfeet%7D%5E2)
Step-by-step explanation:
We have,
Height of a cone is 12 feet
Volume of the cone is 90 feet
It is required to find the area of the base of the cone.
The base of a cone is circular in shape.
The formula used to find the volume of a cone is given by :
![V=\dfrac{1}{3}\pi r^2 h](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h)
here,
(area of base of cone)
![V=\dfrac{1}{3}\times Ah\\\\A=\dfrac{3V}{h}\\\\A=\dfrac{3\times 90}{12}\\\\A=22.5\ \text{feet}^2](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%5Ctimes%20Ah%5C%5C%5C%5CA%3D%5Cdfrac%7B3V%7D%7Bh%7D%5C%5C%5C%5CA%3D%5Cdfrac%7B3%5Ctimes%2090%7D%7B12%7D%5C%5C%5C%5CA%3D22.5%5C%20%5Ctext%7Bfeet%7D%5E2)
So, the area of the base of the cone is
.
For this case we have the following system of equations:
5x + 3y = 17
-8x - 3y = 9
We can rewrite the system like:
Ax = b
Where,
A = [5 3; -8 -3]
b = [17; 9]
x = [x; y]
The determinant of matrix A is given by:
lAl = ((5) * (- 3)) - ((3) * (- 8))
lAl = (-15) - (-24)
lAl = -15 + 24
lAl = 9
Answer:
The determinant for solving this linear system is:
lAl = 9
Answer:
3.83333333333
Step-by-step explanation: