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3 years ago

Simplify -3c+5d+3c-d

Mathematics

2 answers:

Rina8888 [55]3 years ago

8 0

Answer:

$4d$

-3x+3c+5d-d

=0+4d

=4d

EastWind [94]3 years ago

4 0

Answer:

Step-by-step explanation:

-3c+5d+3c-d

=-3c+3c+5d-d

=4d

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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

If -1 < x < 0 which of the following has the smallest value?

Katyanochek1 [597]

Answer: (B) x^3

Explanation:

If you compare the graphs of

y = x^2
y = x^3
y = x^4

all on the interval -1 < x < 0, you'll find that y = x^3 is the smallest when x = -1

Squaring a negative number leads to a positive result, and similarly that happens with x^4 as well. This is because x^4 = (x^2)^2.

Plugging x = -1 into x^3 leads to y = -1 as a result.

6 0

3 years ago

Please help me on this question

labwork [276]

Answer:

y = 4

Step-by-step explanation:

Make equal ratios. y 10 4

x 22.5 9

If you divide 10 and 22.5, you get 0.44 repeating. If you divide 4 and 9, you will also get 0.44 repeating.

7 0

3 years ago

Read 2 more answers

To find the area of a trapezoid with those numbers

Yuliya22 [10]

Area=14.6

To find a trapezoid

Top +Bottom /2 multiplied by height

So 2.5+ 4.8= 7.3

7.3/2= 3.65

3.65x4=14.6

3 0

4 years ago

What is the area of a square rug that measures 6 feet on a side? 3 square feet 24 square feet 12 square feet 36 square feet

QveST [7]

Well we know the area of a square is l*w, or s^2. So we can use s^2 where s=6 in your case. Now 6^2 is 6*6, which is 36.

So the area of a square rug that measures 6 feet is 36 feet

Answer= 36 feet

4 0

3 years ago

Read 2 more answers