Answer:
Step-by-step explanation:
![\\ \int\limits^{a}_{0} \int\limits^{x}_{0} \int\limits^{x+y}_{0} {e^{x+y+z}} \, dzdydx \\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [\int\limits^{x+y}_{0} {e^{x+y}e^z} \, dz]dydx \\\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [e^{x+y}\int\limits^{x+y}_{0} {e^z} \, dz]dydx\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [e^{x+y}e^z\Big|_0^{x+y}]dydx \\\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [e^{x+y}e^{x+y}-e^{x+y}]dydx \\\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} e^{2x+2y}-e^{x+y}dydx \\\\\\](https://tex.z-dn.net/?f=%5C%5C%20%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5Cint%5Climits%5E%7Bx%7D_%7B0%7D%20%5Cint%5Climits%5E%7Bx%2By%7D_%7B0%7D%20%7Be%5E%7Bx%2By%2Bz%7D%7D%20%5C%2C%20dzdydx%20%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5Cint%5Climits%5E%7Bx%7D_%7B0%7D%20%5B%5Cint%5Climits%5E%7Bx%2By%7D_%7B0%7D%20%7Be%5E%7Bx%2By%7De%5Ez%7D%20%5C%2C%20dz%5Ddydx%20%5C%5C%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5Cint%5Climits%5E%7Bx%7D_%7B0%7D%20%5Be%5E%7Bx%2By%7D%5Cint%5Climits%5E%7Bx%2By%7D_%7B0%7D%20%7Be%5Ez%7D%20%5C%2C%20dz%5Ddydx%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5Cint%5Climits%5E%7Bx%7D_%7B0%7D%20%5Be%5E%7Bx%2By%7De%5Ez%5CBig%7C_0%5E%7Bx%2By%7D%5Ddydx%20%5C%5C%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5Cint%5Climits%5E%7Bx%7D_%7B0%7D%20%5Be%5E%7Bx%2By%7De%5E%7Bx%2By%7D-e%5E%7Bx%2By%7D%5Ddydx%20%5C%5C%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5Cint%5Climits%5E%7Bx%7D_%7B0%7D%20e%5E%7B2x%2B2y%7D-e%5E%7Bx%2By%7Ddydx%20%5C%5C%5C%5C%5C%5C)
![\\=\int\limits^{a}_{0} [\int\limits^{x}_{0} e^{2x}e^{2y}-e^{x+y}dy]dx \\\\\\=\int\limits^{a}_{0} [\int\limits^{x}_{0} e^{2x}e^{2y}dy- \int\limits^{x}_{0}e^{x}e^{y}dy]dx \\\\\\u=2y\\du=2dy\\dy=\frac{1}{2}du\\\\\\=\int\limits^{a}_{0} [\frac{e^{2x}}{2}\int e^{u}du- e^x\int\limits^{x}_{0}e^{y}dy]dx \\\\\\=\int\limits^{a}_{0} [\frac{e^{2x}}{2}\cdot e^{2y}\Big|_0^x- e^xe^{y}\Big|_0^x]dx \\\\\\=\int\limits^{a}_{0} [\frac{e^{2x+2y}}{2} - e^{x+y}\Big|_0^x]dx \\\\](https://tex.z-dn.net/?f=%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5B%5Cint%5Climits%5E%7Bx%7D_%7B0%7D%20e%5E%7B2x%7De%5E%7B2y%7D-e%5E%7Bx%2By%7Ddy%5Ddx%20%5C%5C%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5B%5Cint%5Climits%5E%7Bx%7D_%7B0%7D%20e%5E%7B2x%7De%5E%7B2y%7Ddy-%20%5Cint%5Climits%5E%7Bx%7D_%7B0%7De%5E%7Bx%7De%5E%7By%7Ddy%5Ddx%20%5C%5C%5C%5C%5C%5Cu%3D2y%5C%5Cdu%3D2dy%5C%5Cdy%3D%5Cfrac%7B1%7D%7B2%7Ddu%5C%5C%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5B%5Cfrac%7Be%5E%7B2x%7D%7D%7B2%7D%5Cint%20e%5E%7Bu%7Ddu-%20e%5Ex%5Cint%5Climits%5E%7Bx%7D_%7B0%7De%5E%7By%7Ddy%5Ddx%20%5C%5C%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5B%5Cfrac%7Be%5E%7B2x%7D%7D%7B2%7D%5Ccdot%20e%5E%7B2y%7D%5CBig%7C_0%5Ex-%20e%5Exe%5E%7By%7D%5CBig%7C_0%5Ex%5Ddx%20%5C%5C%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5B%5Cfrac%7Be%5E%7B2x%2B2y%7D%7D%7B2%7D%20-%20e%5E%7Bx%2By%7D%5CBig%7C_0%5Ex%5Ddx%20%5C%5C%5C%5C)
![\\=\int\limits^{a}_{0} [\frac{e^{4x}}{2} - e^{2x}-\frac{e^{2x}}{2} + e^{x}]dx \\\\\\=\int\limits^{a}_{0} \frac{e^{4x}}{2} -\frac{3e^{2x}}{2} + e^{x}dx \\\\\\=\int\limits^{a}_{0} \frac{e^{4x}}{2}dx -\int\limits^{a}_{0}\frac{3e^{2x}}{2}dx + \int\limits^{a}_{0}e^{x}dx \\\\\\u_1=4x\\du_1=4dx\\dx=\frac{1}{4}du_1\\\\\u_2=2x\\du_2=2dx\\dx=\frac{1}{2}du_2\\\\\\=\frac{1}{8}\int e^{u_1}du_1 -\frac{3}{4}\int e^{u_2}du_2 + \int\limits^{a}_{0}e^{x}dx \\\\\\](https://tex.z-dn.net/?f=%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5B%5Cfrac%7Be%5E%7B4x%7D%7D%7B2%7D%20-%20e%5E%7B2x%7D-%5Cfrac%7Be%5E%7B2x%7D%7D%7B2%7D%20%2B%20e%5E%7Bx%7D%5Ddx%20%5C%5C%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5Cfrac%7Be%5E%7B4x%7D%7D%7B2%7D%20-%5Cfrac%7B3e%5E%7B2x%7D%7D%7B2%7D%20%2B%20e%5E%7Bx%7Ddx%20%5C%5C%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%20%5Cfrac%7Be%5E%7B4x%7D%7D%7B2%7Ddx%20-%5Cint%5Climits%5E%7Ba%7D_%7B0%7D%5Cfrac%7B3e%5E%7B2x%7D%7D%7B2%7Ddx%20%2B%20%5Cint%5Climits%5E%7Ba%7D_%7B0%7De%5E%7Bx%7Ddx%20%5C%5C%5C%5C%5C%5Cu_1%3D4x%5C%5Cdu_1%3D4dx%5C%5Cdx%3D%5Cfrac%7B1%7D%7B4%7Ddu_1%5C%5C%5C%5C%5Cu_2%3D2x%5C%5Cdu_2%3D2dx%5C%5Cdx%3D%5Cfrac%7B1%7D%7B2%7Ddu_2%5C%5C%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B8%7D%5Cint%20e%5E%7Bu_1%7Ddu_1%20-%5Cfrac%7B3%7D%7B4%7D%5Cint%20e%5E%7Bu_2%7Ddu_2%20%2B%20%5Cint%5Climits%5E%7Ba%7D_%7B0%7De%5E%7Bx%7Ddx%20%5C%5C%5C%5C%5C%5C)
Sorry if that took a while to finish. I am in AP Calculus BC and that was my first time evaluating a triple integral. You will see some integrals and evaluation signs with blank upper and lower boundaries. I just had my equation in terms of u and didn't want to get any variables confused. Hope this helps you. If you have any questions let me know. Have a nice night.
Qualitative data describes the data analyzed through quantitative analysis. Qualitative data refers to the color, texture, olfactory and sensory attributes. These are attributes that are rather described than calculated. In this case, the answer is A. I<span>t cannot be represented by numbers.</span>
Answer:
AEB =43
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
AED + AEB = 180
137+AEB = 180
AEB = 180-137
AEB =43
Answer: r = 7
Step-by-step explanation:
Subtract 12 from both sides to isolate the r variable. You have -42 = -6r. Divide both sides by -6 to get r by itself and you get r = 7. Verify by substituting 7 as the r value and solving the equation.
7 1/2÷ 1 9/10 = 15/2 ÷19/10 = 15/2x10/19 = 159/38 = 4 7/38
4 7/38 (Answer)
_____
38 )159
152
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