A composite solid consists of a cube with edges of length 6cm and a square pyramid with base edges of length 6cm and height of 6
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Answer:
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Derivative Property [Addition/Subtraction]:
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
- Integrals
Integration Rule [Reverse Power Rule]:
Integration Property [Multiplied Constant]:
Integration Methods: U-Substitution and U-Solve
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify given.</em>
<em />
<u>Step 2: Integrate Pt. 1</u>
<em>Identify variables for u-substitution/u-solve</em>.
- Set <em>u</em>:
- [<em>u</em>] Differentiate [Derivative Rules and Properties]:
- [<em>du</em>] Rewrite [U-Solve]:
<u>Step 3: Integrate Pt. 2</u>
- [Integral] Apply U-Solve:
- [Integrand] Simplify:
- [Integral] Rewrite [Integration Property - Multiplied Constant]:
- [Integral] Apply Integration Rule [Reverse Power Rule]:
- [<em>u</em>] Back-substitute:
∴ we have used u-solve (u-substitution) to <em>find</em> the indefinite integral.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer:
see explanation
Step-by-step explanation:
let pq = x
given oq - pq = 1 then oq = 1 + x
Using Pythagoras' identity, then
(oq)² = 7² + x²
(1 + x)² = 49 + x² ( expand left side )
1 + 2x + x² = 49 + x² ( subtract 1 from both sides )
2x + x² = 48 + x² ( subtract x² from both sides )
2x = 48 ( divide both sides by 2 )
x = 24 ⇒ pq = 24
and oq = 1 + x = 1 + 24 = 25 ← hypotenuse
sinq = =
cosq = =