Find area and perimeter of shaded area and the perimeter is not 96

Which are equivalent ratios to 4:9?

Firdavs [7]

The second, third, and fifth are equal to 4:9.

7 0

3 years ago

Nead help asap please

marissa [1.9K]

Answer:

with what?

Step-by-step explanation:

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

Unit: Integration

5 0

2 years ago

Mason has 18 raisins Josh has 20 more raisins than Mason Zach has 22 more raisins than Josh How many raisins do Josh and Zach ea

Vedmedyk [2.9K]

Answer:

Josh and Zach each have 38 and 60 raisins.

Step-by-step explanation:

Total no of raisins Mason have = 18

Josh has 20 more raisins than Mason.

Josh = 20 + 18 = 38 raisins

Zach has 22 more raisins than Josh

Zach = 22 + 38 = 60 raisins

Hence, Josh and Zach each have 38 and 60 raisins.

6 0

3 years ago

A stadium has 55,000 seats. Seats sell for $42 in Section A, $24 in Section B, and $18 in Section C. The number of seats in Sect

UkoKoshka [18]

Answer:

Section A = 27,500 seats

Section B = 14,800 seats

Section C = 12,700 seats

Step-by-step explanation:

Section A = $42

Section B = $24

Section C = $18

Revenue = $1,738,800

Total number of seats = 55,000

The number of seats in Section A equals the total number of seats in Sections B and C

A = B + C

A + B + C = 55,000

42A + 24B + 18C = $1,738,800

Substitute A = B + C into the equations

B + C + B + C = 55,000

42(B + C) + 24B + 18C = $1,738,800

2B + 2C = 55,000

42B + 42C + 24B + 18C = 1,738,800

2B + 2C = 55,000

66B + 60C = 1,738,800

Multiply (1) by 30

60B + 60C = 1,650,000. (1)

66B + 60C = 1,738,800. (2)

Subtract (1) from (2)

66B - 60B = 1,738,800 - 1,650,000

6B = 88,800

B = 88,800/6

= 14,800

B = 14,800

Substitute the value of B into

2B + 2C = 55,000

2(14,800) + 2C = 55,000

29,600 + 2C = 55,000

2C = 55,000 - 29,600

2C = 25,400

C = 25,400/2

= 12,700

C = 12,700

Substitute the values of B and 6 into

A + B + C = 55,000

A + 14,800 + 12,700 = 55,000

A + 27,500 = 55,000

A = 55,000 - 27,500

= 27,500

A = 27,500

Section A = 27,500 seats

Section B = 14,800 seats

Section C = 12,700 seats

3 0

3 years ago

Read 2 more answers