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3 years ago

Round 5.05870925358 to 4 decimal places.

Mathematics

1 answer:

aniked [119]3 years ago

4 0

Answer:

5.0587

Step-by-step explanation:

"four decimal places" would be the numerals 0587. Since that 7 is followed by a zero, we round off 5.05870925358 to 5.0587. This is "to 4 decimal places."

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1) Solve the following absolute value equation: 3x + 8) = 9

Andru [333]

Answer:

x = 1/3

Step-by-step explanation:

3x+8=9

3x-8= 9 - 8

3x=1

3x/3 = 1/3

x = 1/3

7 0

2 years ago

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

Are the triangles Similar? (yes or no). If yes, by what

kakasveta [241]

Answer:

The triangles are not similar

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

<em>Triangle X.Y.Z</em>

$\angle X=61^o$

$\angle Z=90^o$

$\angle Y=90^o-61^o=29^o$ ---> angle X and angle Y are complementary angles

<em>Triangle H.G.J</em>

$\angle H=90^o-34^o=56^o$ ---> angle H and angle J are complementary angles

$\angle G=90^o$

$\angle J=34^o$

X.Y.Z is a $61^o-90^o-39^o$ triangle

H.G.J is a $56^o-90^o-34^o$ triangle

The measure of its corresponding angles are not congruent

therefore

The triangles are not similar

8 0

3 years ago

please help 50 points!!!! answer 1-5 please if you can show how you got the answer if you cant its ok at least show how you got

kvasek [131]

Answer:

Step-by-step explanation:

1. D

2. B

3. C

4. C

5. C

Thanks for letting me know.

;)

4 0

2 years ago

Read 2 more answers

The apparent brightness of a star if it were viewed from a distance of 10 parsecs (32.6 light- years) is called ________.

Maru [420]

Answer:

Absolute magnitude

Step-by-step explanation: Astronomy deals with the study of stars and other heavenly bodies. Astronomers use apparent magnitude to define how bright a star appears and shines from the earth.

8 0

3 years ago