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LuckyWell [14K]
3 years ago
13

Calculus. Only need answer yo question number 30,14,10 pleassse

Mathematics
1 answer:
Stella [2.4K]3 years ago
4 0

Answer:

See below in bold.

Step-by-step explanation:

14. f(x) = x^6 e^x

Applying the Product Rule:

f'(x) = x^6 e^x + 6x^5 e^x

= e^x(x^6 + 6x^5).

10. f(x) = x^3 - 4

y = x^3 - 4

x^3 = y + 4

x = ∛(y + 4)  so:

f-1(x) = ∛(x + 4).  (you are correct.)

30. 3 sinh 2

=  3(e^4 - 1) / 2 e^2

= 10.88058

= 10.881.

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Please help me! I will give brainliest to the person who answers correctly.
Sveta_85 [38]

Answer:

  • sin(X) = 6/7.5
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Step-by-step explanation:

It is convenient to use the Pythagorean theorem to find XY to start with. That theorem tells you ...

  XZ² = YZ² + XY²

Solving for XY, you find ...

  XY² = XZ² - YZ²

  XY = √(XZ² - YZ²) = √(7.5² -6²) = √(56.25 -36) = √20.25

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The mnemonic SOH CAH TOA is very helpful here. It reminds you that ...

  Sin = Opposite/Hypotenuse

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  Tan = Opposite/Adjacent

  tan(X) = 6/4.5

_____

<em>Comment on the triangle and ratios</em>

The side lengths of this triangle are in the ratios ...

  XY : YZ : XZ = 3 : 4 : 5

If you recognize that the given sides are in the ratio 4 : 5, this tells you that you have a "3-4-5" right triangle with a scale factor of 1.5. At least, you can find XY = 1.5·3 = 4.5 with no further trouble.

The trig ratios could be reduced to sin(X) = 4/5; cos(X) = 3/5; tan(X) = 4/3, but the wording "don't simplify" suggests you want the numbers shown on the diagram, not their reduced ratios.

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