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Gnom [1K]
3 years ago
11

Insert a parenthesis 5+2*9-3=42

Mathematics
2 answers:
anastassius [24]3 years ago
6 0

5 + 2 * 9 - 3 = 42

Right now there is an imaginary parentheses around (2 * 9) because you always solve multiplication first.

If we put a parentheses around (5 + 2), the answer would be:

7 * 9 - 3 = 60

If we put a parentheses around (9 - 3), the answer would be:

5 + 2 * 6 = 17

If we put parentheses around (5 + 2) and (9 - 3), the answer would be:

7 * 6 = 42

Your answer is: (5 + 2) * (9 - 3) = 42

Setler79 [48]3 years ago
4 0

Since, we are given

5+2*9-3=42

We know that

7*6=42

we can also write it as

(5+2)*6=42

(5+2)*(9-3)=42

so, we can insert parenthesis this way

and we get

(5+2)*(9-3)=42.............Answer

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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:

<u>Calculus</u>

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:

  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 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:

<u>Step 1: Define</u>

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

<u>Step 2: Identify</u>

<em>Graph the systems of equations - see attachment.</em>

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

Bottom Function:  \displaystyle y = x^2

Bounds of Integration: [-1.529, 1.718]

<u>Step 3: Integrate Pt. 1</u>

  1. Substitute in variables [Area of a Region Formula]:                                   \displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx
  2. [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
  3. [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}
  4. 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

<u>Step 4: Integrate Pt. 2</u>

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

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

<u>Step 5: Integrate Pt. 3</u>

  1. [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
  2. [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
  3. 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
  4. 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
A teepee is designed to have a diameter of 10 ft and a volume of 366ft³ what is the height? A.15ft , b.14 ft, c 5ft, or 1 ft
Katarina [22]

Answer:

B.  14 ft approx

Step-by-step explanation:

Given data

A teepee  has a conical shape

Diameter= 10ft

radius= 5 ft

Volume = 366ft³

Height = ????

The expression for the volume is

V= 1/3πr^2 h

substitute

366= 1/3*3.142*5^2*h

366= 1/3*78.55*h

366= 26.18h

h= 366/26.18

h=13.98 ft

h= 14 ft approx

Hence the Height is 14 ft approx

5 0
3 years ago
Read 2 more answers
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