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3 years ago

Simplify 6^-6/6^-5 . rewrite the expression in the form 6^n

Mathematics

1 answer:

HACTEHA [7]3 years ago

6 0

Answer: $=\frac{1}{6}\quad \left(\mathrm{Decimal:\quad }\:0.16666\dots \right)$

Step-by-step explanation:

$\frac{6^{-6}}{6^{-5}}$

$=6^{-6-\left(-5\right)}$

$=6^{-6+5}$

$=6^{-1}$

$=\frac{1}{6}$

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Area of the bounded curves y=x^2, y=√(7+x)

N76 [4]

Answer:

$\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 5.74773$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
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 Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

U-Substitution

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

Step 1: Define

$\displaystyle \left \{ {{y = x^2} \atop {y = \sqrt{7 + x}}} \right.$

Step 2: Identify

Graph the systems of equations - see attachment.

Top Function: $\displaystyle y = \sqrt{7 + x}$

Bottom Function: $\displaystyle y = x^2$

Bounds of Integration: [-1.529, 1.718]

Step 3: Integrate Pt. 1

Substitute in variables [Area of a Region Formula]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx$
[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - \int\limits^{1.718}_{-1.529} {x^2} \, dx$
[Right Integral] Integration Rule [Reverse Power Rule]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - \frac{x^3}{3} \bigg| \limits^{1.718}_{-1.529}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - 2.88176$

Step 4: Integrate Pt. 2

Identify variables for u-substitution.

Set u: $\displaystyle u = 7 + x$
[u] Basic Power Rule [Derivative Rule - Addition/Subtraction]: $\displaystyle du = dx$
[Limits] Switch: $\displaystyle \left \{ {{x = 1.718 ,\ u = 7 + 1.718 = 8.718} \atop {x = -1.529 ,\ u = 7 - 1.529 = 5.471}} \right.$

Step 5: Integrate Pt. 3

[Integral] U-Substitution: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{8.718}_{5.471} {\sqrt{u}} \, du - 2.88176$
[Integral] Integration Rule [Reverse Power Rule]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = \frac{2x^\Big{\frac{3}{2}}}{3} \bigg| \limits^{8.718}_{5.471} - 2.88176$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 8.62949 - 2.88176$
Simplify: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 5.74773$

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

Unit: Integration

5 0

3 years ago

What is the sum of a rational number and an irrational number

shepuryov [24]

Answer:

Irrational Number

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers

What is the vertex of each function

cricket20 [7]

Answer:

Step-by-step explanation:

note :

f(x) =a(x-h)²+k

the vertex is : (h,k)

continu .........

7 0

3 years ago

6. Peggy Carter is selling tickets to see Captain America. On the first night she sold 12 adult tickets and 11 student tickets f

Nataliya [291]

Answer:

student ticket = $11

(adult ticket = $15)

Step-by-step explanation:

Let a = price of adult ticket

Let s = price of student ticket

Given:

On the first night she sold 12 adult tickets and 11 student tickets for $301 dollars

⇒ 12a + 11s = 301

Given:

On the second night she made $134 selling 6 adult tickets and 4 student tickets

⇒ 6a + 4s = 134

Multiply 6a + 4s + 134 by 2 then subtract from 12a + 11s = 301 to eliminate a:

⇒ (6a + 4s = 134) × 2: 12a + 8s = 268

12a + 11s = 301

- (12a + 8s = 268)

--------------------------

3s = 33

⇒ s = 33 ÷ 3 = 11

Substitute found value of s into one of the equations and solve for a:

⇒ 12a + 11(11) = 301

⇒ 12a + 121 = 301

⇒ 12a = 180

⇒ a = 15

Therefore, the price of an adult ticket is $15 and the price of a student ticket is $11

6 0

2 years ago

The regular tax to be paid with any purchase is 8%. How much tax did Anthony pay if he bought school supplies worth ₱5 000?

Dvinal [7]

Answer:

400

Step-by-step explanation:

8% of 5000 is 400. Math:

5000 x 0.08 = 400

4 0

3 years ago