Find the sum of
−
3
7
and its opposite

Answer:

21

Explanation:

To solve this problem, you substitute in the 5 for the x creating this equation: f(5)=6+3(5).

f(5)=15+6

f(5)=21

Answer:

62

Step-by-step explanation:

(x+8)=(2x-15)
8=x-15
+15   +15
23=x

so


23 +8 = 31
23x2-15 = 46-15 =31
Both are the same always since one side is equal to the other
Therefore
62 is the answer!

Answer:

Undefined.

Formula's used:

[tex]\longrightarrow \bold{sec(x) = \dfrac{1}{cos(x)} }[/tex]

[tex]\longrightarrow \bold{cosec(x) = \dfrac{1}{sin(x)} }[/tex]

[tex]\longrightarrow \bold{cot(x) = \dfrac{1}{tan(x)} }[/tex]

[tex]\longrightarrow \bold{tan(x) = \dfrac{sinx}{cos(x)} }[/tex]

[tex]\longrightarrow \bold{sin^2x + cos^2 x = 1 }[/tex]

[tex]\longrightarrow \sf \bold{Sum \ Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx}[/tex]

[tex]\longrightarrow \bold{ \int \:{sec^2(ax+b) = \dfrac{1}{a}tan(ax+b)+c }}[/tex]

[tex]\longrightarrow \bold{\int \:\dfrac{1}{ax+b} =\dfrac{1}{a} ln|ax+b|+c}[/tex]

Explanation:

[tex]\sf \Longrightarrow \int _{\pi }^{2\pi }\:\dfrac{sin^6(x)+cos^6(x)}{sin^3(x) \ * \ cos^3\left(x)}[/tex]

[tex]\sf \Longrightarrow \sf \int _{\pi }^{2\pi }\:\dfrac{sin^6\left(x\right)}{sin^3\left(x\right)\cdot \:cos^3\left(x\right)} +\dfrac{cos^6\left(x\right)}{sin^3\left(x\right)\cdot \:cos^3\left(x\right)}[/tex]

[tex]\Longrightarrow \sf \int _{\pi }^{2\pi }\:\dfrac{sin^3\left(x\right)}{\:cos^3\left(x\right)} +\dfrac{cos^3\left(x\right)}{sin^3\left(x\right)}[/tex]

[tex]\Longrightarrow \sf \int _{\pi }^{2\pi }\ tan^3(x)+ cot^3(x)[/tex]

[tex]\sf \Longrightarrow \sf \int _{\pi }^{2\pi } \tan ^3(x)dx+\int _{\pi }^{2\pi } \cot ^3 (x)dx[/tex]

[tex]\Longrightarrow \sf \bold{ [ }-\ln |\sec \left(x\right) |+\dfrac{\sec ^2(x)}{2}-\dfrac{\cot ^2 (x)}{2}-\ln |\sin(x)| \bold{ ] }^{2\pi }_\pi[/tex]

apply limits

[tex]\sf \Longrightarrow \sf -\ln \left|\sec \left(2\pi \right)\right|+\dfrac{\sec ^2\left(2\pi\right)}{2}-\dfrac{\cot ^2\left(2\pi\right)}{2}-\ln \left|\sin \left(2\pi\right)\right|-(-\ln \left|\sec \left(\pi \right)\right|+\dfrac{\sec ^2\left(\pi\right)}{2}-\dfrac{\cot ^2\left(\pi\right)}{2}-\ln \left|\sin \left(\pi\right)\right|)[/tex]

simplify using trigonometric basic functions

[tex]\Longrightarrow \sf -\ln \left|\dfrac{1}{\cos \left(2\pi \right)}\right|+\dfrac{\left(\dfrac{1}{\cos \left(2\pi \right)}\right)^2}{2}-\dfrac{\cot ^2\left(2\pi \right)}{2}-\ln \left|\sin \left(2\pi \right)\right|- ( -\ln \left|\dfrac{1}{\cos \left(\pi \right)}\right|+\dfrac{\left(\frac{1}{\cos \left(\pi \right)}\right)^2}{2}-\dfrac{\cot ^2\left(\pi \right)}{2}-\ln \left|\sin \left(\pi \right)\right|)[/tex]

⇒  Undefined

Answer:

[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \boxed{\text{un} \text{de} \text{f}}[/tex]

General Formulas and Concepts:
Calculus

Differentiation

Integration

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

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

Integration Methods: U-Substitution + U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

Step 4: Integrate Pt. 3

Identify variables for u-solve.

1st Integral

2nd Integral

Step 5: Integrate Pt. 4

∴ we have found the value of the given integral.

---

Learn more about integration: https://brainly.com/question/14413972

Learn more about calculus: https://brainly.com/question/20197752

---

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

Unit: Integration

Answer:

The smaller number is 24

The larger number is 45

Step-by-step explanation:

smaller number  = x

Larger: 2x - 3

Smaller + larger = 69

x + 2x - 3 = 69                        Combine left

3x - 3 = 69                              add 3 to both sides

3x - 3+3 = 69+ 3                     Combine

3x = 72                                    Divide by 3

3x/3 = 72/3                        

x = 24

Larger number = 2*24 - 3

Larger number = 45

Answer:

0.216 cubic feet

Step-by-step explanation:

v = lwh (volume = length times width times height)

v = 0.6 x 0.6 x 0.6  OR 0.6^3

v = 0.216

Find the circumference:

8km x 2 x 3.14 = 50.24 km

Arc length = 50.24 x 225/360 = 31.4 km

answer: C. 10 pi or 31.4 km

Answer:

2/7

Step-by-step explanation:

Total no. of chocolates in the box =14

No. of dark Chocolates=4

No. of white chocolates=5

No. of milk chocolates=5

Probability of getting a white chocolate

= No. of possible outcomes /Total No. of outcomes

=5/14

Probability of getting a dark chocolate =4/14=2/7

Answer:

Step-by-step explanation:

(1 , -2)   x₁ =1 & y₁ = -2

(-3,10)  x₂= -3 & y₂ = 10

First we need to find the slope.

[tex]\boxed{Slope = $\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$}[/tex][tex]\boxed{Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]

          [tex]=\dfrac{10-[-2]}{-3-1}\\\\\\=\dfrac{10+2}{-4}\\\\\\=\dfrac{12}{-4}\\\\\\= - 3[/tex]

m = -3

Equation of the line: y = mx + b

y = -3x + b

To find the value of b, take one of the point and substitue in the above equaiton.

(1 , -2)

-2 = -3*1 + b

-2 = -3 + b

-2 + 3 = b

b = 1

Equation of the line:

y = -3x + 1

Answer:

(x-2)^2+(y-1)^2 = 10^2

(x-2)^2+(y-1)^2 = 100

Step-by-step explanation:

distance between points is diameter

x^2=  (8--4)^2+(-7-9)^2

x^2=12^2+16^2

x^2=144+256

x^2=400

diameter x=20 so radius =10

center point =midpoint (-4+8)/2 and (-7+9)/2

center point =(2,1)

(x-2)^2+(y-1)^2 = 10^2

(x-2)^2+(y-1)^2 = 100

Answer:

22 is the perimeter.

Step-by-step explanation:

You find the perimeter by adding up all of the sides of a shape. 9 + 9 = 18. 18 + 4 = 22.

24

[tex]Convert\ the\ unit\ for\ \frac{12in}{1ft}:\\ \downarrow\\ 24[/tex]

I hope this helps you

:)

20 separate tickets in total costs £314.

Now we should find out what percentage 262 is of 314.

262÷314×100=83.4%

if 262 is 83.4% of 314, then Sandro saves (100%-83.4%) 16.6%.

ANSWER 16.6%

qartveli xar mgoni dd

Answer:

9

Step-by-step explanation:

10

Answer:

65

Step-by-step explanation:

[tex]\frac{3(2^5)-13(-2)+2^3}{-2^2+3^2-3} =\frac{3(32)+26+(8)}{(-4)+(9)-3} =\frac{96+34}{2} =\frac{130}{2}=65[/tex]

Part A

Part B

Answer:

See below ↓↓

Step-by-step explanation:

Part A

Part B

Answer: 56 yd

Step-by-step explanation: if you continue the 8 yd line across, it would show that the missing side is 4yd less than the 13 yd side, meaning the missing side is 9 yd long. So after adding 7 + 13+ 15+ 4 + 8 + 9= 56 yd

Answer:

54861/1000 convert to a decimal = 54.861

Answer:

can you clear more I don't understand

Answer:

24

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=24

Using it's concept, it is found that the probability that the coin shows tails and he rolls a 5 is of [tex]\frac{1}{12}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the coin has two outcomes, one of which is tails, while the number cube has six outcomes, one of which is five. Since the coin and the number cube are independent, we just multiply the probabilities, hence:

[tex]p = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]

The probability that the coin shows tails and he rolls a 5 is of [tex]\frac{1}{12}[/tex].

More can be learned about probabilities at https://brainly.com/question/14398287

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's expand the given expression ~

[tex]\qquad \sf  \dashrightarrow \: - 3y( {y}^{4} + 2 {y}^{3} - 5 {y}^{2} - y + 4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: ( - 3y \cdot {y}^{4} ) + ( - 3y \cdot2 {y}^{3} ) + ( - 3y \cdot - 5 {y}^{2} ) + ( - 3y \cdot - y) + ( - 3y \cdot4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 3{y}^{5} - 6{y}^{4} + 1 5 {y}^{3} + 3{y}^{2} - 12y[/tex]

Correlation measures the relationship between variables

The true statements are:

For a correlation coefficient to be valid, the following, must be true:

Using the above highlights, the true statements are: (b) (c) and (e)

Read more about correlation coefficients at:

https://brainly.com/question/18054482

Answer:

a) 1,2; 3.4

b) <1=<6, <6+<6+72=180, 2<6=108, <6=54.

<1=54

You can tell this by "these are parallel lines"

Answer:

The answer is B. 1/4^8

Step-by-step explanation:

Every time the power it to the negative it inverse it.

An example, 2^-2 = 1 / 2^2

So, 4^-8 = 1 / 4^8

Answer:

The graph shows a steady declining plot as the aveage traffic volume increases. Since y axis is speed the correct answer is that as traffic volume increases the average vehicle speed decreases.

Step-by-step explanation:

If Carly's bedroom is 15.3ft long and 8.7 ft long then it is necessary to multiply them because you need to find the area of the room so 15.3*8.7= 133.11. We have to do the same for Carter's room so we multiply 14.4 and 9.6 to find the area of the room which is 138.24.

Now that we have both the areas we can compare which room is bigger. Carly's room is 133.11 ft in total and Carter's room is 138.24 ft in total. So it is clear that Carter's room is going to be more expensive to cover with carpet since Carter's room is bigger than Carly's.

Carly:-

Area:-

#Carter

Area:-

Carter's room is expensive

Answer:

through lengthy mafs, your answer should be 307 mi (wrong somehow)

Step-by-step explanation:

if you want an explanation, please, dont be afraid to comment ;)

(to other people who look this up the answer is actually 318 i dont know, but i got it wrong