Can you explain how you got your answer?

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:

Answer:

0.9%

Step-by-step explanation:

I took the test

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

Answer:

104ft/s

Step-by-step explanation:

[tex]\frac{f(b)-f(a)}{b-a}=\frac{f(3)-f(1)}{3-1}=\frac{266-58}{2}=\frac{208}{2}=104[/tex]

Thus, the average rate of change of the function between x=1 and x=3 is 104ft/s

Answer:

9

Step-by-step explanation:

10

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.

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

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

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

Unit: Integration

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:

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:

54861/1000 convert to a decimal = 54.861

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:

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.

Answer:

can you clear more I don't understand

Part A

Part B

Answer:

See below ↓↓

Step-by-step explanation:

Part A

Part B

Answer:

24

Step-by-step explanation:

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

x=24

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]

Using the distributive property, it is found that the equivalent expression is:

18c - 30d + 36

It is a property that the outside term multiplies each of the inside terms.

In this problem, the expression is:

6(3c - 5d + 6).

Hence, we apply the property, with the outside term 6 multiplying each of the inside terms, hence the equivalent expression is given by:

6(3c - 5d + 6) = 18c - 30d + 36.

More can be learned about the distributive property at https://brainly.com/question/2807928

[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]

========================================================

Explanation:

6/150 = 0.04 = 4% of the population are albino.

That leaves 100% - 4% = 96% that aren't albino.

96% of 1200 = 0.96*1200 = 1152

------------

Another way to look at it:

4% of the population are albino, so there are 0.04*1200 = 48 albino tigers.

This means there are 1200-48 = 1152 non-albino tigers.

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:

160

Step-by-step explanation:

If there were only 2 options, all the people who didn't pick one chose the other one.

So if 25% of the people voted for the aquarium the remaing 75% voted for the zoo.

Since three times as many people voted for the zoo, we can see that 120/3=40, so 40 people chose the aquarium.

To find the total number of students, we add 120 and 40 to get 160

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:

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:

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:

(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: 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

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

24

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

I hope this helps you

:)