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shusha [124]
3 years ago
7

Find the LCM of the pair of numbers. 6 and 12. The lcm is

Mathematics
2 answers:
MArishka [77]3 years ago
5 0
The LCM is 12:

6 - 6, <u>12</u>, 18, 24
12 - <u>12</u>, 24, 36, 48
romanna [79]3 years ago
3 0
Least common multiple is 12
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Evaluate triple integral ​
kaheart [24]

Answer:

\\ \frac{1}{8} e^{4a}-\frac{3}{4}e^{2a}+e^{a} -\frac{3}{8} \\\\or\\\\ \frac{e^{4a}-6e^{2a}+8e^{a}-3}{8}

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 \\\\\\

\\=\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 \\\\

\\=\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 \\\\\\

\\=\frac{1}{8}e^{u_1}\Big| -\frac{3}{4}e^{u_2}\Big| + e^{x}\Big|_0^a \\\\\\=\frac{1}{8}e^{4x}\Big|_{0}^a -\frac{3}{4}e^{2x}\Big|_{0}^a + e^{x}\Big|_0^a \\\\\\=\frac{1}{8}e^{4x} -\frac{3}{4}e^{2x} + e^{x}\Big|_0^a \\\\\\=\frac{1}{8}e^{4a} -\frac{3}{4}e^{2a} + e^{a}-\frac{1}{8} +\frac{3}{4} -1\\\\\\=\frac{1}{8}e^{4a} -\frac{3}{4}e^{2a} + e^{a}-\frac{3}{8}\\\\\\

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.

6 0
2 years ago
I have no idea on how to do this using calculus. I know how to do it on a calculator but my teacher wants some sort of actual wo
Cerrena [4.2K]

you can use integration

I could have done It by typing it here is hectic. you can inbox you email so that I send you scanned answer

6 0
2 years ago
The probability that a traffic light will be green is 40%. If you pass through 3 lights on your way to the store, what is the pr
larisa [96]

Answer:

0.216

Step-by-step explanation:

If the probability of green, P(green) is 40%, the probability of red, P(red) is 60%.

The probability of a light being red is not affected by the colour of the previous light, so at each of the 3 lights, the probability of red is always 60%.

To find the probability that all three lights will be red, multiply the three probabilities together. (Convert them to decimals first).

0.6 x 0.6 x 0.6 = 0.216

7 0
3 years ago
Charlie drove 864 miles in 12 hours. at the same rate, how long would it take him to drive 504 miles?
katrin2010 [14]
We can solve this by setting up a proportion where 864/12 = 504/x. We cross multiply and get 864x = 504 * 12. So 864x = 6048. Divide by 864 on both sides, x = 7.

It would take Charlie 7 hours to drive 504 miles. 
5 0
3 years ago
Read 2 more answers
What is the vertical asymptote of f(x)=3/x+5
Rudiy27

Answer:

X = -5

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
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