Does this graph show a function? Explain how you know.
5
O A. Yes; the graph passes the vertical line test.
O
B. No; there are y-values that have more than one x-value.
C. Yes; there are no y-values that have more than one x-value.
O
D. No; the graph fails the vertical line test.

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]

Double Integrals

Polar Coordinates Conversions:

Integral Conversion [Polar Coordinates]:
[tex]\displaystyle \iint_T {f(x, y)} \, dA = \iint_R {f(r, \theta)r} \, dr \, d\theta[/tex]

The formatting of the question was thrown off, so I have defined it down below.

We are given an integral and asked to convert to polar coordinates as well as evaluate it:
[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx[/tex]

It would be quite difficult to evaluate the given integral using conventional methods, so we apply polar conversion to evaluate the integral. Let's start out by converting the function and the bounds.

[Bounds] Cartesian to Polar:

[tex]\displaystyle \left \{ {{-8 \leq x \leq 8} \atop {0 \leq y \leq \sqrt{64 - x^2}}} \right \longrightarrow \left \{ {{0 \leq r \leq 8} \atop {0 \leq \theta \leq \pi}} \right[/tex]

[Function] Cartesian to Polar:

[tex]\displaystyle f(x ,\ y) = \sin(x^2 + y^2) \longrightarrow f(r ,\ \theta) = \sin r^2[/tex]

Now that we've converted to polar coordinates, we can convert the integral using our integral conversion listed under "Multivariable Calculus":

[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx \longrightarrow \int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta[/tex]

We can now evaluate the polar integral using basic integration techniques listed under "Calculus":

[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \int \limits^{\pi}_{0} \underbrace{\int \limits^{8}_{0} r \sin r^2 \, dr \, }_{u = r^2 ,\ du = 2r \, dr} d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \int \limits^{8}_{0} 2r \sin r^2 \, dr \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \int \limits^{r = 8}_{r = 0} \sin u \, du \, d\theta \\\end{aligned}[/tex]

[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos u \bigg) \bigg| \limits^{r = 8}_{r = 0} \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos r^2 \bigg) \bigg| \limits^{r = 8}_{r = 0} \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos 64 + 1 \bigg) \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( 1 - \cos 64 \bigg) \, d\theta \\\end{aligned}[/tex]

[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \frac{1}{2} \bigg(1 - \cos 64 \bigg) \bigg( \theta \bigg) \bigg| \limits^{\pi}_{0} \\& = \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }\end{aligned}[/tex]

∴ the integral equals:
[tex]\displaystyle \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }[/tex]

[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx = \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }[/tex]

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Topic: Multivariable Calculus

Unit: Double Integrals

Answer:

People like oranges

Step-by-step explanation:

Given:

Mo likes oranges. Jai likes oranges. Ben likes oranges.

We have a few different options;

Option A: People don't like other fruit, such as apples. This can't be possible because we have only been given people who like oranges.

Option B: People on like oranges. This can't be possible because only is the case where people do not like any fruit except oranges, and we are not sure of this.

Option C: People like oranges. This can be possible because Mo, Jai, and Ben likes oranges

Option D: People like fruit. This can't be possible because we are not sure if people like all fruits or not

People like oranges.

the action or process of inducting someone to a position or organization.

We have a few different options;

Option A: People don't like other fruit, such as apples. This can't be possible because we have only been given to people who like oranges.

Option B: People like oranges. This can't be possible because only is the case where people do not like any fruit except oranges, and we are not sure of this.

Option C: People like oranges. This can be possible because Mo, Jai, and Ben like oranges

Option D: People like fruit. This can't be possible because we are not sure if people like all fruits or not

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Answer:

3L

Step-by-step explanation:

Perimeter is the sum of side lengths

Since the triangle is equilateral, it has all sides equal and each has length of L

So perimeter is:

Answer:

(4,7)

Step-by-step explanation:

f(x)=5x-13

Let this equal to 7

7=5x-13  

Add 13 to each side

7+13 = 5x-13+13

20 = 5x

Divide by 5

20/5 = 5x/5

4 =x

The ordered pair is

(4,7)

Answer:

x = 5

Step-by-step explanation:

0.5x + 3.5 = 6

0.5x = 6 - 3.5

0.5x = 2.5

x = 2.5 / 0.5

x = 5

Answer:

11

Step-by-step explanation:

Just multiply 4 times 2 3/4 and youll get 11

If one cup of soy milk contains 4g total fat then [tex]2\frac{3}{4}[/tex] cups of soy milk contains 11g of  total fat.

             [tex]2\frac{3}{4}[/tex] cups contains x grams of total fat.

         ⇒ x  =  4([tex]\frac{11}{4}[/tex])

         ⇒ x  = 11 grams

     Hence 11 grams of total fat is there in [tex]2\frac{3}{4}[/tex] cups of soy milk.

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Answer:

4 OR 4.5 SECONDS

Step-by-step explanation:

Answer:

Irrational, non-terminating

Step-by-step explanation:

This number is irrational because it is a non-terminating decimal. Notice how it continues with the '...'. <3

Answer:

10 miles

Step-by-step explanation:

3a/5 + 4 = a

a = race long

4 = a - 3a/5

4 = 5a/5 - 3a/5

4 = 2a/5

4*5/2 = a

a = 10

The length of the entire race is 10 miles.

Let length of race = r

Miles left after running 3/5 of race :

We can solve the expression thus :

r - 3r/5 = 4

r - 3r = 4 * -5

r - 3r = -20

-2r = -20

divide both sides by -2 to isolate r

r = 10

Hence, the length of the entire race is 10 miles.

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Answer:

the rectangle's width is approximately 3.39 inches

and the length is approximately 13.56 inches.

Step-by-step explanation:

Recall that the area of a rectangle is Length times Width

If we name the length "L" and the width "W", we have:

L * W = 46

Also: "the length is 4 times the width" can be written in math form as:

L = 4 * W

and now we can replace the length L by 4 * W in the formula for the area:

[tex]L\,*\,W = 46\\(4\,W) \,W = 46\\4\,W^2=46\\W^2=\frac{46}{4} =11.5\\W=\sqrt{11.5} \\W\approx 3.39[/tex]

and now we find the value of L:

[tex]L=4\.(3.39) = 13.56[/tex]

Therefore, the rectangle's width is approximately 3.39 inches

and the length is approximately 13.56 inches.

Answer:

4/9

Step-by-step explanation:

0.4444... can be written as a geometric series with first term 0.4 and common ratio 0.1.  Each new digit is 0.1 times the previous digit.

                               0.4

Then 0.4444... = ------------ = 0.4/0.9 = 4/9

                             1 - 0.1

You may check this result by dividing 4 by 9 on a calculator.

Answer:

$3,636.70

Step-by-step explanation:

Given the following:

Initial price of Gold (A) = $2500

Rate of appreciation (r) = 5.5% = 0.055

Worth of gold in 7 years will be?

Period (p) = 7

Using the compound interest formula :

Let F = final amount

F = A( 1 + r/n)^nt

n = number of times Appreciation occurs per period.

Since rate compounds yearly, then, n = 1

F = $2500( 1 + 0.055/1)^(7*1)

F = $2500(1 + 0.055)^7

F = $2500(1.055)^7

F = $2500(1.454679161133794609375)

F = $3636.6979

Amount in 7 years = $3,636.70

Answer:

-1.5

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

-1.5

-1 1/2

-6/4

Answer:

84

Step-by-step explanation:

The least common denominator of the 7, 6, 12, which are the denominators of the fractions in the given linear equation, is the least expression or number that is divisible by 7, 6, 12.

To find the LCD, express each number as factors of itself as follows:

[tex] 7 = 1*7 [/tex]

[tex] 6 = 2*3 [/tex]

[tex] 12 = 2^2*3 [/tex]

Find the product of the highest terms

The product = LCD = [tex] 1*2^2*3*7 = 84 [/tex]

LCD of 7, 6, 12 = 84

Answer:

84

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) = x² - 2x - 24

g(x) = x + 4

To find (f-g)(x) subtract g(x) from f(x)

That's

(f-g)(x) = x² - 2x - 24 - ( x + 4)

(f-g)(x) = x² - 2x - 24 - x - 4

Group like terms

We have

(f-g)(x) = x² - 2x - x - 24 - 4

Simplify

We have the final answer as

Hope this helps you

Answer:

[tex]34.12 * 11 = 375.32[/tex]

Step-by-step explanation:

Given

11 * 34.12

Required

Multiply

To start with, we have to ignore the decimal points;

So, we have

    3412

  *      11

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

   3 4 1 2

3 4 1 2

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

3 7 5 3 2

The next step is as follows;

34.12 is in 2 decimal places

11 is has no decimal (0 decimal place)

Add the decimal places together

[tex]Decimal\ Place = 2 + 0 = 2[/tex]

This implies that the result will be in 2 decimal placed;

Hence:

[tex]34.12 * 11 = 375.32[/tex]

Answer:

m<3 + m<4:= 180°

m<2 + m<4 + m<6 = 180°

m<2 + m<4 = m<5

Step-by-step explanation:

<3 and <4 are linear pairs. They are angles on a straight line. Angles in a straight line sum up to give 180°. Therefore, the statement "m<3 + m<4:= 180°" is TRUE.

<2, <4, <6 are interior angles of a triangle. The sum of the angles in a ∆ = 180°. Therefore, the statement, "m<2 + m<4 + m<6 = 180°" is TRUE.

<2 and <4 are opposite interior angles of the ∆, while <5 is an exterior angle to the ∆. Based on the external angle theorem of a ∆, the statement, "m<2 + m<4 = m<5" is TRUE.

<1 and <2 are a linear pair, and are angles on a straight line. Their sum cannot give us 90°.

m<4 + m<6 ≠ m<2. Rather, 180 - (m<4 + m<6) = m<2 (sum of angles in a ∆)

m<2 + m<6 ≠ m<5. Rather, m<2 + m<4 = m<5

The correct equations are:

m∠5 + m∠6 = 180°

m∠2 + m∠3 =  m∠6

m∠2 + m∠3 + m∠5 = 180°

m∠2 + m∠5 =  m∠4

Triangle is a polygon with three angles and three sides. The sum of angles in a triangle is 180 degree.

From the diagram:

m∠5 + m∠6 = 180° (angle in a straight line)

But:

m∠2 + m∠3 + m∠5 = 180

m∠2 + m∠3 + m∠5 = m∠5 + m∠6

m∠2 + m∠3 =  m∠6

Also:

m∠2 + m∠3 + m∠5 = 180° (sum of angles in a triangle)

But:

m∠3 + m∠4 = 180° (angle in a straight line)  

m∠2 + m∠3 + m∠5 = m∠3 + m∠4

m∠2 + m∠5 =  m∠4

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La mentalidad de crecimiento, ya que a diferencia de la mentalidad fija, nos permite ver en otras personas la mentalidad de mejorar y perseverar.

Answer:

1:6

Step-by-step explanation:

1 yard = 3 feet. 4 yards = 12 feet.

Ratio of 2 feet:12 feet = 1:6 Ans D

The ratio of 2 feet to 4 yards is 1 : 6

The ratio is given as:

Ratio = 2 feet : 4 yards

Convert yard to feet

Ratio = 2 feet : 4 * 3 feet

Evaluate

Ratio = 2 feet : 12 feet

Divide the ratio

Ratio = 1 : 6

Hence, the ratio of 2 feet to 4 yards is 1 : 6

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Answer:

Translation

Step-by-step explanation:

The object is only moved, which is what happens when a translation occurs

Answer:

The true statements are;

(i) m - n = n - m

(ii) +m (-n) = m - n

(iii) 0 = m - n

Step-by-step explanation:

We are given that m and n are both integers and we have to select all the statements that are true if m and n are also equal to each other.

(i) The given situation is: m - n = n - m

LHS = m - n

       = m - m   {because m and n are equal}

       = 0

RHS = n - m

       = n - n   {because m and n are equal}

       = 0

Hence, the given statement is true because LHS = RHS = 0.

(ii) The given situation is: +m (- n) = m - n

LHS = +m (- n)

       = m - n

       = m - m  {because m and n are equal}

       = 0

RHS = m - n

       = n - n   {because m and n are equal}

       = 0

Hence, the given statement is true because LHS = RHS = 0.

(iii) The given situation is: 0 = m - n

LHS = 0

RHS = m - n

       = m - m   {because m and n are equal}

       = 0

Hence, the given statement is true because LHS = RHS = 0.

(iv) The given situation is: m + n = 0

RHS = 0

LHS = m + n

       = m + m   {because m and n are equal}

       = 2m

Hence, the given statement is not true because LHS [tex]\neq[/tex] RHS.

#1) m - n = n - m

#2) +m (-n) = m - n

#3) 0 = m - n

hope this HELPS!!!!!!!

Answer:

Negative change

Step-by-step explanation:

Given

[tex]Monday\ Temperature = 5\ deg[/tex]

[tex]Thursday\ Temperature = -8\ deg[/tex]

First, we need to calculate the overall change in temperature

This is calculated by subtracting the initial temperature from the final temperature

[tex]Overall\ Change = Thursday\ Temperature - Monday\ Temperature[/tex]

[tex]Overall\ Change = -8\ deg - 5\ deg[/tex]

[tex]Overall\ Change = -13\ deg[/tex]

The overall change shows a negative change in the temperature.

This is as a result of a drop in temperature from Monday to Thursday

Answer:

subtract 5

Step-by-step explanation:

subtract 5 from each side of the equal sign..

Answer:

the answer is subtract 5

Step-by-step explanation:

Answer: y= -2.5

Step-by-step explanation:

Distribute the -2 and 3 into the parentheses. -6 + 6 cancels out so you are left with 3y on the right side. Add 2y to the right side leaving you with -2=5y. Divide both sides by -2

Answer:

Step-by-step explanation:

[tex] \sf{ - 2(y + 1) = 3(y - 2) + 6}[/tex]

Distribute -2 through the parentheses

Similarly, Distribute 3 through the parentheses

⇒[tex] \sf{ - 2y - 2 = 3y - 6 + 6}[/tex]

Since two opposites add up to zero , remove them

⇒[tex] \sf{ - 2y - 2 = 3y}[/tex]

Move 3y to Left hand side and change it's sign

Similarly, move -1 to right hand side and change it's sign

⇒[tex] \sf{ - 2y - 3y = 2}[/tex]

Collect like term

⇒[tex] \sf{ - 5y = 2}[/tex]

Divide both sides of the equation by -5

⇒[tex] \sf{ \frac{ - 5y}{ -5 } = \frac{2}{ - 5} }[/tex]

Calculate

⇒[tex] \sf{ - 0.4}[/tex]

Hope I helped!

Best regards!

Answer:

the vetrex

Step-by-step explanation:

Answer:

The answer is

Step-by-step explanation:

Since the triangle is a right angled triangle we can use trigonometric ratios to find y

To find y we use cosine

cos∅ = adjacent / hypotenuse

From the question

y is the adjacent

The hypotenuse is 15

So we have

[tex] \cos(35) = \frac{y}{15} \\ y = 15 \cos( 35 ) \\ y = 12.28728[/tex]

We have the final answer as

Hope this helps you

Step-by-step explanation:

(i) Sum the forces at point M in the x direction.

∑F = ma

-T sin 30° − T sin 30° + 5 N = 0

2T sin 30° = 5 N

T = 5 N

(ii) Sum the forces on the ring in the x direction.

∑F = ma

T sin 30° − N = 0

N = 2.5 N

Sum the forces on the ring in the y direction.

∑F = ma

T cos 30° − mg − Nμ = 0

Nμ = T cos 30° − mg

2.5 μ = 5 cos 30° − 2

μ = 0.932

(iii) Sum the forces on the ring in the y direction.

∑F = ma

T cos 30° − m₁g − m₂g + Nμ = 0

m₂g = T cos 30° − m₁g + Nμ

m (10) = 5 cos 30° − 2 + (2.5)(0.932)

m = 0.466 kg