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MAXImum [283]
3 years ago
7

If Angle A = 5x-10, find the value(s) for x that would ensure that Angle A was an obtuse angle.

Mathematics
1 answer:
morpeh [17]3 years ago
3 0

Answer:

20 < x < 38.

Step-by-step explanation:

An obtuse angle has a value between 90 and 180.

90 < 5x - 10 < 180

5x - 10 > 90

5x > 100.

x > 20.

5x - 10< 180

5x < 190

x < 38

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(Explanation)

Step-by-step explanation:

Part A:

The graph of y = x^{2} + 2 will be translated 2 units up from the graph of y = x^{2}.

If you plug in 0 for x, you get a y-value of 2. The 2 is also not included with the x^{2}, which is why it doesn't translate left.

This is what graph A should look like:

[Attached File]

Part B:

The graph of y = x^{2} - 2 will be translated 2 units down from the graph of y = x^{2}.

If you plug in 0 for x, you get a y-value of -2. The 2 is also not included with the x^{2}, which is why it doesn't translate right.

This is what graph B should look like:

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Part C:

The graph of y = 2x^{2} is a stretched version of the graph y = x^{2}. Numbers that are greater than 1 stretch and open up and numbers less than -1 stretch and open down.

This is what graph C should look like:

[Attached File]

Part D:

The graph of y = \frac{1}{2}x^{2} is a compressed version of the graph y = x^{2}. Numbers that are in-between 0 and 1, and -1 and 0 are compressed.

This is what graph D should look like:

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What is the volume of this cube?
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Step-by-step explanation:

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Answer:

\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }

General Formulas and Concepts:
<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:
\displaystyle (cu)' = cu'

Derivative Property [Addition/Subtraction]:
\displaystyle (u + v)' = u' + v'
Derivative Rule [Basic Power Rule]:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Integration

  • Integrals

Integration Rule [Reverse Power Rule]:
\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Property [Multiplied Constant]:
\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given.</em>

<em />\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution/u-solve</em>.

  1. Set <em>u</em>:
    \displaystyle u = 4 - x^2
  2. [<em>u</em>] Differentiate [Derivative Rules and Properties]:
    \displaystyle du = -2x \ dx
  3. [<em>du</em>] Rewrite [U-Solve]:
    \displaystyle dx = \frac{-1}{2x} \ du

<u>Step 3: Integrate Pt. 2</u>

  1. [Integral] Apply U-Solve:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du
  2. [Integrand] Simplify:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du
  3. [Integral] Rewrite [Integration Property - Multiplied Constant]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du
  4. [Integral] Apply Integration Rule [Reverse Power Rule]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C
  5. [<em>u</em>] Back-substitute:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }

∴ we have used u-solve (u-substitution) to <em>find</em> the indefinite integral.

---

Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

---

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

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