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faltersainse [42]
3 years ago
9

spencer spent 4 hours doing chores over the weekend. If he spent 2/3 for an hour on each chore, how many chores did he do.

Mathematics
1 answer:
Elina [12.6K]3 years ago
4 0
2/3 + 2/3 + 2/3 + 2/3
8/3
2 2/3
You might be interested in
For right triangle , triangle rst shown below, what is tan r
-Dominant- [34]

You know, it would really be helpful if we could have a peek at
the picture that's "shown below".  Just a peek would be enough. 
Right now, the only thing I see below is my dog.

Now ... follow me here ... if you're looking for tan(r), then 'r' is
one of the angles in the triangle, and I'm guessing that all three
of those letters are angles.

tan(r)  is going to be the ratio of two of the sides ... I mean

                             (one side) divided by (another side).

There's no way to go any farther, because you haven't given us
any names for the sides, or any way to describe them.

Betcha the names of the sides are on that picture that's supposed
to be shown below.

8 0
3 years ago
here is an equation that is true for all values of x:5(x+2)=5x+10. Elena saw this equation and says she can tell 20(x+2)=4(5x+10
Trava [24]

Elena is wrong, because the two sides of equation are not equal for all values of x

Step-by-step explanation:

An equation of x is true for all values of x when the left hand side

is equal to the right hand side

To prove that an equation is true for all values of x do that

  • Simplify the left hand side and the right hand side
  • Solve the equation to find x, you will find the x in the left hand side is equal to x in the right hand side, so they canceled each other, and the numerical terms in the two sides equal each other, that means the equation is true for any values of x

Lets check that with given equation 5(x + 2) = 5x + 10

∵ 5(x + 2) = 5x + 10

- Simplify the left hand side

∵ 5(x) + 5(2) = 5x + 10

∴ 5x + 10 = 5x + 10

- Subtract 5x from both sides

∴ 10 = 10

∵ L.H.S = R.H.S

∴ The equation is true for all values of x

Lets do that with Elena's equation

∵ 20(x + 2) = 4(5x + 10) + 31

- Simplify the two sides of the equation

∵ 20(x) + 20(2) = 4(5x) + 4(10) + 31

∴ 20x + 40 = 20x + 40 + 31

- Add like terms in the right hand side

∴ 20x + 40 = 20x + 71

- Subtract 20x from both sides

∴ 40 = 71 ⇒ and that not true

∵ L.H.S ≠ R.H.S

∴ The equation is not true for all values of x

Elena is wrong, because the two sides of equation are not equal for all values of x

Learn more:

You can learn more about the equations in brainly.com/question/11306893

#LearnwithBrainly

5 0
3 years ago
How do I evaluate this using trigonometric substitution?<br><br>∫dx/(81x^2+4)^2
Daniel [21]

Answer:

\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C

General Formulas and Concepts:

<u>Alg I</u>

  • Terms/Coefficients
  • Factor
  • Exponential Rule [Dividing]: \displaystyle \frac{b^m}{b^n} = b^{m - n}

<u>Pre-Calc</u>

[Right Triangle Only] Pythagorean Theorem: a² + b² = c²

  • a is a leg
  • b is a leg
  • c is hypotenuse

Trigonometric Ratio: \displaystyle sec(\theta) = \frac{1}{cos(\theta)}

Trigonometric Identity: \displaystyle tan^2\theta + 1 = sec^2\theta

TI: \displaystyle sin(2x) = 2sin(x)cos(x)

TI: \displaystyle cos^2(\theta) = \frac{cos(2x) + 1}{2}

<u>Calc</u>

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

IP [Addition/Subtraction]:                                                             \displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx

U-Substitution

U-Trig Substitution: x² + a² → x = atanθ

Step-by-step explanation:

<u>Step 1: Define</u>

\displaystyle \int {\frac{dx}{(81x^2 + 4)^2}}

<u>Step 2: Identify Sub Variables Pt.1</u>

Rewrite integral [factor expression]:

\displaystyle \int {\frac{dx}{[(9x)^2 + 4]^2}}

Identify u-trig sub:

\displaystyle x = atan\theta\\9x = 2tan\theta \rightarrow x = \frac{2}{9}tan\theta\\dx = \frac{2}{9}sec^2\theta d\theta

Later, back-sub θ (integrate w/ respect to <em>x</em>):

\displaystyle tan\theta = \frac{9x}{2}  \rightarrow \theta = arctan(\frac{9x}{2})

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

  1. [Int] Sub u-trig variables:                                                                                 \displaystyle \int {\frac{\frac{2}{9}sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta
  2. [Int] Rewrite [Int Prop - MC]:                                                                           \displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta
  3. [Int] Evaluate exponents:                                                                                \displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4tan^2\theta + 4]^2}} \ d\theta
  4. [Int] Factor:                                                                                                      \displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4(tan^2\theta + 1)]^2}} \ d\theta
  5. [Int] Rewrite [TI]:                                                                                              \displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4sec^2\theta]^2}} \ d\theta
  6. [Int] Evaluate exponents:                                                                                \displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{16sec^4\theta} \ d\theta
  7. [Int] Rewrite [Int Prop - MC]:                                                                          \displaystyle \frac{1}{72} \int {\frac{sec^2\theta}{sec^4\theta} \ d\theta
  8. [Int] Divide [ER - D]:                                                                                         \displaystyle \frac{1}{72} \int {\frac{1}{sec^2\theta} \ d\theta
  9. [Int] Rewrite [TR]:                                                                                            \displaystyle \frac{1}{72} \int {cos^2\theta} \ d\theta
  10. [Int] Rewrite [TI]:                                                                                              \displaystyle \frac{1}{72} \int {\frac{cos(2\theta) + 1}{2}} \ d\theta
  11. [Int] Rewrite [Int Prop - MC]:                                                                          \displaystyle \frac{1}{144} \int {cos(2\theta) + 1} \ d\theta
  12. [Int] Rewrite [Int Prop - A/S]:                                                                          \displaystyle \frac{1}{144} [\int {cos(2\theta) \ d\theta + \int {1} \ d\theta]  

<u>Step 4: Identify Sub Variables Pt.2</u>

Determine u-sub for trig int:

u = 2θ

du = 2dθ

<u>Step 5: Integrate Pt.2</u>

  1. [Ints] Rewrite [Int Prop - MC]:                                                                       \displaystyle \frac{1}{144} [\frac{1}{2} \int {2cos(2\theta) \ d\theta + \int {1 \theta ^0} \ d\theta]
  2. [Int] U-Sub:                                                                                                     \displaystyle \frac{1}{144} [\frac{1}{2} \int {cos(u) \ du + \int {1 \theta ^0} \ d\theta]
  3. [Ints] Integrate [Trig/Int Rule - RPR]:                                                             \displaystyle \frac{1}{144} [\frac{1}{2} sin(u) + \theta + C]
  4. [Expression] Back Sub:                                                                                 \displaystyle \frac{1}{144} [\frac{1}{2} sin(2 \theta) + arctan(\frac{9x}{2}) + C]
  5. [Exp] Rewrite [TI]:                                                                                           \displaystyle \frac{1}{144} [\frac{1}{2}(2sin(\theta)cos(\theta)) + arctan(\frac{9x}{2}) + C]
  6. [Exp] Multiply:                                                                                                 \displaystyle \frac{1}{144} [sin(\theta)cos(\theta) + arctan(\frac{9x}{2}) + C]
  7. [Exp] Back Sub:                                                                                             \displaystyle \frac{1}{144} [sin(arctan(\frac{9x}{2}))cos(arctan(\frac{9x}{2})) + arctan(\frac{9x}{2}) + C]

<u>Step 6: Triangle</u>

Find trig values:

\displaystyle tan\theta = \frac{9x}{2}

\displaystyle \theta = arctan(\frac{9x}{2})

tanθ = opposite / adjacent; solve hypotenuse of right triangle, determine trig ratios:

sinθ = opposite / hypotenuse

cosθ = adjacent / hypotenuse

Leg <em>a</em> = 2

Leg <em>b</em> = 9x

Leg <em>c</em> = ?

  1. Sub variables [PT]:                                                                                         \displaystyle 2^2 + (9x)^2 = c^2
  2. Evaluate exponents:                                                                                      \displaystyle 4 + 81x^2 = c^2
  3. [Equality Property] Square root both sides:                                                  \displaystyle \sqrt{4 + 81x^2} = c
  4. Rewrite:                                                                                                           c = \sqrt{81x^2 + 4}

Substitute into trig ratios:

\displaystyle sin\theta = \frac{9x}{\sqrt{81x^2 + 4}}

\displaystyle cos\theta = \frac{2}{\sqrt{81x^2 + 4}}

<u>Step 7: Integrate Pt.3</u>

  1. [Exp] Sub variables [TR]:                                                                               \displaystyle \frac{1}{144} [\frac{9x}{\sqrt{81x^2 + 4}} \cdot \frac{2}{\sqrt{81x^2 + 4}} + arctan(\frac{9x}{2}) + C]
  2. [Exp] Multiply:                                                                                                 \displaystyle \frac{1}{144} [\frac{18x}{81x^2 + 4} + arctan(\frac{9x}{2}) + C]
  3. [Exp] Distribute:                                                                                             \displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C
3 0
2 years ago
What is the solution for x in the equation? 16x − 4 + 5x = -67 A.x=-3 B.x=3 C.x=1/3 D. x=-1/3
lozanna [386]

Answer:

A. X=-3

Step-by-step explanation:

16x-4+5x=-67

21x=-67+4

21x=-63

Divide through by 21

X=-3

8 0
3 years ago
Find the equation for the
natima [27]

Answer: i think its B

Step-by-step explanation:

4 0
3 years ago
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