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lianna [129]
3 years ago
10

Please help with question 15 and 16!!!

Mathematics
1 answer:
kykrilka [37]3 years ago
6 0
15. [4] insufficient information. only given SA
16. There are 3 right triangles, 3 Pythagorean theorem equations 
x²+b²= 16²
12²+a² = x²
a²+4² = b²

combine equations using substitution to get in terms of only x
substitute b² for (a² +x²) in first equation
x²+a²+4²=16²
substitute a² for (x² - 12²)
x²+x²-12²+4² = 16²
solve for x
2x² - 144 + 16 = 256
2x² = 256 + 144 - 16
2x² = 384
x² = 384/2
x² = 192
x = 13.85

rounded to nearest tenth, x = 13.9




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I don't need you to work it out, just theorem(s) i need to reach the answer :)
VikaD [51]
Not sure why such an old question is showing up on my feed...

Anyway, let x=\tan^{-1}\dfrac43 and y=\sin^{-1}\dfrac35. Then we want to find the exact value of \cos(x-y).

Use the angle difference identity:

\cos(x-y)=\cos x\cos y+\sin x\sin y

and right away we find \sin y=\dfrac35. By the Pythagorean theorem, we also find \cos y=\dfrac45. (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)

Meanwhile, if \tan x=\dfrac43, then (by Pythagorean theorem) \sec x=\dfrac53, so \cos x=\dfrac35. And from this, \sin x=\dfrac45.

So,

\cos\left(\tan^{-1}\dfrac43-\sin^{-1}\dfrac35\right)=\dfrac35\cdot\dfrac45+\dfrac45\cdot\dfrac35=\dfrac{24}{25}
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3 years ago
If 3v/7=6, then v=<br><br> What is the Answer to the problem?
Dmitrij [34]

<u>Let's solve this problem step-by-step</u>:

 \frac{3v}{7} =6\\\frac{3v}{7} *1=6\\\frac{3v}{7} *\frac{7}{7}=6\\ 3v = 6 * 7\\3v=42\\v=14

<u>Thus v = 14</u>

<u />

<u>Answer: v= 14</u>

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Many electronics follow a failure rate described by an exponential probability density function (PDF). Solar panels are advertis
katovenus [111]

Answer:

The right answer is "0.3193".

Step-by-step explanation:

According to the question,

Mean,

\frac{1}{\lambda}  = 13

\lambda = \frac{1}{13}

As we know,

The cumulative distributive function will be:

⇒ 1-e^{-\lambda x}

hence,

In the first 5 years, the probability of failure will be:

⇒ P(X

                    =1-e^{-(\frac{1}{13} )\times 5}

                    =1-e^(-\frac{5}{13})

                    =1-0.6807

                    =0.3193

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