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3 years ago

Six is less than or equal to the sum of a number n and 15

Mathematics

1 answer:

Debora [2.8K]3 years ago

6 0

Answer:

6(less than or equal sign) n+15

Step-by-step explanation:

the less than or equal sign is a less than sign with one line under it

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What is the common denominator for 2/7 and 1/2

jeyben [28]

Answer:

2/7 and 1/2

The common denominator = 7× 2

= 14

Step-by-step explanation:

4 0

3 years ago

Simplify y+1.2y+1.2z

Arlecino [84]

Answer:

2.2y+1.2z

Step-by-step explanation:

Add y + 1.2y

Now you can't simplify anymore so this is your answer

2.2y+1.2z

8 0

2 years ago

Ill give brainiest if it was 11:30 am and its now 11:47 am, how many hours was that

Kaylis [27]

Answer:

0 hours and 17 minutes

Step-by-step explanation:

47 - 30 = 17

6 0

3 years ago

The perimeter of a rectangle is equal to 163 yard. The width is 8 more than twice the length. Find the length and width.

Sedaia [141]

Answer:

l = 29.4 yards

w = 66.8 yards

General Formulas and Concepts:

Order of Operations: BPEMDAS
Perimeter of a Rectangle: P = 2w + 2l

Step-by-step explanation:

Step 1: Define

P = 163 yards

w = 2l + 8

l = l

Step 2: Set up equation

P = 2w + 2l

163 = 2(2l + 8) + l

Step 3: Solve for l

Distribute 2: 163 = 4l + 16 + l
Combine like terms: 163 = 5l + 16
Subtract 16 on both sides: 147 = 5l
Divide both sides by 5: 147/5 = l
Rewrite: l = 147/5
Evaluate: l = 29.4 yards

Step 4: Find w

Define: w = 2l + 8
Substitute: w = 2(29.4) + 8
Multiply: w = 58.8 + 8
Add: w = 66.8 yards

4 0

3 years ago

Help evaluating the indefinite integral

Dafna11 [192]

Answer:

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

General Formulas and Concepts:
Calculus

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]:

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

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] 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 find the indefinite integral.

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

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

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

Unit: Integration

5 0

2 years ago