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Veronika [31]
3 years ago
5

What is the simplified form of 45? A. 5 B. 9.5 C. 3/5 D. 5/3

Mathematics
2 answers:
DENIUS [597]3 years ago
7 0

Answer:

Since radical 45 is equal to radical 9 times radical 5, and because radical 9 is equal to 3 (since 9 is a perfect square), we can simplify radical 45 to 3 times radical 5 

leva [86]3 years ago
7 0

Answer:

the answer is 5

Step-by-step explanation:

when u simplifying its the lowest number u can go but make sure u can multiply to get the answer

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. William fills 1/3 of a water bottle in 1/6 of a minute. How much time will it
Alex Ar [27]

Answer:

It will take him

\frac{1}{2}

of a minute to fill the bottle.

Step-by-step explanation:

I'm really not sure this is right but..

we can solve using proportions. Cross-multiply and divide.

\frac{ \frac{1}{3} of \: a \: water \: bottle}{\frac{1}{6} minute} \:  =  \frac{ \frac{3}{3} of \: a \: water \: bottle}{x}  \\  \\  \frac{ \frac{1}{6} }{ \frac{1}{3} }  =  \frac{ \frac{1}{3} x}{ \frac{1}{3} }  \\  \\  \frac{1}{2}  = x

5 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:
<u>Calculus</u>

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]:

  1. f(x) = cxⁿ
  2. 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:

<u>Step 1: Define</u>

<em>Identify given.</em>

<em />\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution/u-solve</em>.

  1. Set <em>u</em>:
    \displaystyle u = 4 - x^2
  2. [<em>u</em>] Differentiate [Derivative Rules and Properties]:
    \displaystyle du = -2x \ dx
  3. [<em>du</em>] Rewrite [U-Solve]:
    \displaystyle dx = \frac{-1}{2x} \ du

<u>Step 3: Integrate Pt. 2</u>

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

---

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

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

---

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

Unit: Integration

5 0
2 years ago
Please help me my mums gonna kill me if I fail this assignment.
Vika [28.1K]

Answer:

17 in,3 in, and 19in

so the third answer

Step-by-step explanation:

6 0
3 years ago
Given f(x) = 6x^4 – 10x^3 + 40x – 50, find f(2)
ASHA 777 [7]
F(x)=6x^4-10x^3+40x-50, plug 2 in for x
f(2)=6(2)^4-10(3)^3+40(2)-50
f(2)=12^4-30^3+80-50
f(2)=20735-27,000+80-50
f(2)=-6,235
4 0
3 years ago
kwasi thought of a number, multiplied it by7/2 and added 16 to the results.if the final answer was 30.what number did he think o
ziro4ka [17]

Answer:

4

Step-by-step explanation:

  1. represent the number he thought of with x

\frac{7}{2} x + 16 = 30

  1. multiply through with the LCM which is 2
  2. 2 \times  \frac{7}{2}x + 16 \times 2 = 30 \times 2
  3. 7x + 32 = 60
  4. 7x = 60 - 32
  5. 7x = 28
  6. \frac{7x}{7}  =  \frac{28}{7}
  7. x = 4
7 0
3 years ago
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