Solve the equation in the image (yr 8 math, 40pt)

The value of the constant of variation is 3.

The correct option is C.

Direct variations occur when variables in a variation vary proportionately, that is, when they both increase or decrease at the same time. As a result, you can write X Y symbolically if X and Y are in direct variation. The variables alter disproportionally in inverse or indirect variations.

According to the given information:

Let the constant of variation be k

A quantity h varies directly with w and inversely with p

That is,

h∝ w/p

Introducing the constant of variation, k, we get

h = k(w/p)

Also, from the give information,

w = 4

p = 6

h = 2

Putting the parameters into the relation, we get

2  = K x 4/6

6 x 2= 4K

K = (6 x 2)/4

K = 3

Hence, the value of the constant of variation is 3.

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I understand that the question you are looking for is:

A quantity h varies directly with w and inversely with p. If h = 2, w = 4, and p = 6. What is the constant of variation?

A. 1/2

B. 4/3

C. 3

D. 12

Answer:

C

Step-by-step explanation:

The verified user said so

simplifying 1,615×10 to the 2 power would give 161500

Index notation is known as a way of representing numbers (constants) and variables (e.g. x and y) that have been multiplied by themselves a number of times.

Index notations, or indices are use to simplify expressions or solve equations involving powers.

For instance;

8 × 8 × 8 × 8

8 is multiplied by itself 4 times

In index form , it is written as 8 ^4, that is, 8 to the 4 power

From the information given, we have to simply 1,615×10 to the 2 power

It can be written as;

= 1, 615 × 10 × 10

= 1, 615 × 100

= 161500

Thus, simplifying 1,615×10 to the 2 power would give 161500

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Answer: [tex]\Large\boxed{C.~21}[/tex]

Step-by-step explanation:

The goal of the question

Find the value of 2abcosC

Given information

a = 4

b = 3

c = 2

Given formula (Law of Cosine)

[tex]c^2=a^2+b^2-2abcosC[/tex]

Substitute values into the formula (Leave 2abcosC as it is)

[tex](2)^2=(4)^2+(3)^2-2abcosC[/tex]

Simplify the exponents

[tex]4=16+9-2abcosC[/tex]

Simplify by addition

[tex]4=25-2abcosC[/tex]

Add 2abcosC on both sides

[tex]4+2abcosC=25-2abcosC+2abcosC[/tex]

[tex]4+2abcosC=25[/tex]

Subtract 4 on both sides

[tex]4 + 2abcosC-4=25-4[/tex]

[tex]\Large\boxed{2abcosC=21}[/tex]

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Answer:

C

Step-by-step explanation:

a² + b² - 2abcosC = c² ( subtract a² + b² from both sides )

- 2abcosC = c² - a² - b² ( multiply through by - 1 )

2abcosC = a² + b² - c²

a, b, c are the sides opposite vertices A, B, C

here a = 4 , b = 3 , c = 2 , then

a² + b² - c²

= 4² + 3² - 2²

= 16 + 9 - 4

= 25 - 4

= 21

The solution to the system of equations is (-2, 3)

Answer:

below

Step-by-step explanation:

2) 10², the second power of ten

3) 10⁴, the fourth power of ten

4) 1000

5) 400

6) 90,000

7) 10

8) 100,000

9) 50

10) 7000

11) 8

12) 24 x 10⁴

13) 93,000,000

Answer + Step-by-step explanation:

Answer:

You can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°

Step-by-step explanation:

The above is a cyclic quadrilateral.

A Cyclic quadrilateral is having all the vertices of a quadrilateral ( four sided figure) inside a circle, that is a quadrilateral inscribed in a circle.

To find either x or y, we should note:

The sum of opposite angles of a cyclic quadrilateral is 180° or Angles in opposite segment are supplementary.

Therefore,

2x + 2x + 4= 180

4x = 180 - 4

4x = 176

x = 44°

To find y

3y + 8 + y = 180°

4y = 180 - 8

4y = 172

y = 43°

Therefore, you can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°

The total cost of polishing it's outer surface 20 paisa per square cm exists Rs. 738.58.

External radius of the hollow cylinder = 10.5 cm

Internal radius of the hollow cylinder = 10.1 cm

Height of the hollow cylinder = 56 cm

Cost to Polish Outer Surface: 20 paisa/sq. cm.

Surface Area of Hollow Cylinder = Circumference [tex]*[/tex] height

Surface area of hollow cylinder = 2 π r h

= 2 π (10.5 cm) 56 cm

= π (21)(56)

= 3692.64 [tex]cm^2[/tex] (Using π ≈ 3.14 rounding to 2 digits)

Total Cost of metallic cylinder [tex]$= 3692.64 cm^2 * 20 paisa/cm^2[/tex]

= 73,852.8 paisa

= Rs. 738.58

Therefore, the total cost of polishing it's outer surface 20 paisa per square cm exists Rs. 738.58.

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Answer:

11.7647%

Hope this helps!

Answer:

$0.34 per ounce

Step-by-step explanation:

A 5 pound box can be changed to ounces. There are 16 ounces in a pound. So we have 5 groups of 16.

5 × 16 is 80 ounces.

There are 80 ounces in 5lbs.

To get a price per ounces, divide.

dollars/ounces

= 27.20/80

= 0.34 dollars/oz.

This is 34cents per ounce.

the sum between negative 4 and 13, this can be tought as:

The expression is just the sum:

-4 + 13

So we have the sum between negative 4 and 13, this can be tought as:

Now, none of the written options (a, b, and c) depict any of this, so I assume that the correct option is the one that you did not write, which is option D.

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The lateral area of a cone is 147ft².

The total surface area of the cylinder is 867ft².

The total surface area is 1014ft²

The lateral area of a cone is defined as the area covered by the curved surface of the cone.

Lateral area of a cone = πr x √(r² + h²)

Where:

3.14 x 6 x √(36 + 25) = 147ft²

Total surface area of the cylinder : πr(r + 2h),

(3.14 x 6) x (6 + 40) = 867ft²

Total surface area = 867 + 147=  1014ft²

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The formula for moose population is P = 4760 + (number of years x 200).

The moose population in 2003 would be 6760.

When a population increases linearly, it means that it increases by the same amount each year.  

Rate of linear increase: (population in 1999 - population in 1993) / difference in years

(5960 - 4760) / (1999 - 1993)

1200 / 6 = 200

Linear function : initial population + (rate of increase x number of years)

Population in 2003: 4760 + (200 x 10)

4760 + 2000 = 6760

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The matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].

In this question,

The angle is -π/3 = -60°

Clockwise rotations are denoted by negative numbers.

Matrix for counter-clockwise direction for an angle α is

[tex]\left[\begin{array}{cc}cos\alpha &-sin\alpha \\-sin\alpha &cos\alpha \end{array}\right][/tex]

Then, matrix for clockwise direction for an angle α

Put α = -α in the above matrix,

⇒ [tex]\left[\begin{array}{cc}cos(-\alpha) &-sin(-\alpha) \\-sin(-\alpha) &cos(-\alpha) \end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{cc}cos\alpha &sin\alpha \\sin\alpha &cos\alpha \end{array}\right][/tex]

Now substitute α = 60°

Then matrix becomes,

⇒ [tex]\left[\begin{array}{cc}cos60 &sin60 \\sin60 &cos60 \end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex]

Hence we can conclude that the matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].

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In the given equation the value of x is 4.

According to the statement

we have given that the a equation and we have to solve that equation for x and find the value of the x.

So, For the value of x in given statement:

The given equation is

x⁴ = 256

we know that the 2 changes into the square root after rearrangement in the equation so, the equation become

(x²)² = 256

Now,

(x²) = √256

Then equation becomes

(x²) = 16

This is because the square root of the 256 is 16.

Now another square changes into square root then

x = √16

And

x = 4

So, In the given equation the value of x is 4.

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The second-order equation as its equivalent system of first-order equations is

[tex]\left[\begin{array}{ccc}u(1)\\\\v(1)\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}7.5\\\\9\end{array}\right][/tex]

An equivalent system that has the identical answer is known as an equivalent structure. Given a gadget of two equations, we can produce an equal system by way of replacing one equation by means of the sum of the 2 equations, or by way of changing an equation by means of a couple of of itself.

Systems of linear equations are equivalent if and handiest in the event that they have an equal set of solutions. In other phrases, two systems are equal if and only if each answer of one in all of them is likewise a solution of the opposite.

In the structures sciences, a machine equivalent system is the conduct of a parameter or thing of a machine in a way just like a parameter or component of a distinctive system. Similarity means that mathematically the parameters and additives will be indistinguishable from each different.

Taking v = u, we have:

u" + 4u' + 6u = 4sin(3t)

--> v' + 4v + 6u = 4sin(3t)

So the system of equations is:

u' = 0u + 1v

v' = -6u - 4v + 4sin(3t)

So we can write it as:

u(1) = 7.5

v(1) = u'(1) = 9

So the initial condition matrix is:

[tex]\left[\begin{array}{ccc}u(1)\\\\v(1)\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}7.5\\\\9\end{array}\right][/tex]

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Answer:

Step-by-step explanation:

Miles per hour: [tex]\frac{10miles}{4hrs} = 2.5\frac{miles}{hour}[/tex]

Feet per hour:

      [tex]2.5\frac{miles}{hours} (\frac{5280ft}{1mile} )[/tex]

     [tex]=13,200\frac{ft\\}{hr}[/tex]

Answer:

$0.99 or 99 cents

Step-by-step explanation:

Since 6 ounces is worth $5.94, divide 5.94 by 6 to get the unit price. This is  $0.99 or 99 cents.

The order of the stages of recession will be 4, 2, 3, 1, 3.

What happens in a recession?

Who benefits in a recession?

Rental agents, landlords, and property management companies can thrive during a recession when renting is likely to become a more appealing option, if not the only one available.

So, these stages are occur -

4. peak production

2. falling production

3. falling demand (occurs twice)

1. job loss

3. falling demand (occurs twice)

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The complete question is-

There are five stages in a recession.

1. job loss

2. falling production

3. falling demand (occurs twice)

4. peak production

In which order do these stages occur?

4, 3, 2, 1, 3

3, 2, 1, 3, 4

4, 3, 2, 3, 1

4, 2, 3, 1, 3

4, 2, 3, 1, 3.Answer:4, 2, 3, 1, 3.

4, 2, 3, 1, 3.Step-by-step explanation:4, 2, 3, 1, 3.

Answer:[tex]\Large\boxed{First~choice.~y\leq \frac{1}{2}x+2 }[/tex]

Step-by-step explanation:

Given function form

Point-Slope form : y = mx + b

Given the information from the graph

Since the graph crosses (0, 2), b = 2

Find the slope

Choose any two points from the graph

(x₁, y₁) = (0, 2)

(x₂, y₂) = (2, 3)

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (3 - 2) / (2 - 0)

Slope = 1 / 2

m = 1 / 2

Therefore, the equation form of the inequality is y = (1/2)x + 2

Since it is a solid line, the values on the line are also included. Thus, it must be either greater than or equal to, or less than or equal to.

The shaded region is below the solid line, therefore, it is ≤

Therefore, the inequality is [tex]\Large\boxed{y\leq \frac{1}{2}x+2 }[/tex]

To double-check the sign, we can substitute (0, 0) into the inequality to see whether it is true.

y ≤ (1/2) x + 2

0 ≤ (1/2) 0 + 2

0 ≤ 2              TRUE

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Answer:

length is (-7,-1) and radius is 6

Step-by-step explanation:

We are given the expression of the equation of a circle that is

x2 + y2 + 14x + 2y + 14 = 0.

Using completing the squares:

x2 + y2 + 14x + 2y + 14 = 0(x+7)^2 + (y+1) ^2 = -14 + 49 + 1(x+7)^2 + (y+1) ^2 = 36 center thus is at (-7,-1) and the radius is equal to square root of 36 equal to 6.

Answer:

Step-by-step explanation:

The domain is an x thing. We are being asked to determine what x values to function takes on. We see that the blue dot on the left is at the x-value of 2. It doesn't go any farther to the left of 2. Since the dot is closed, the inequality symbol will have the "equal to" line underneath.

The function then continues along the x axis and stops at 5, closed hole. This means that the function does not go past the x value of 5 but it is included in our domain.

2 ≤ x ≤ 5. That is choice B.

The data set in discuss which contains three points and two of the residuals are 7 and -3 would have its third residual as; -4.

According.tinthe task content, the data set in discuss has three points and consequently should have three residuals.

Additionally, two of the three residuals have been given and on this note, it follows that the third residual must have a value such that the algebraic sum of all residuals is 0.

Hence, we have; -3 + 7 +x = 0;

x = 3-7 = 4.

Ultimately, the third residual is; -4.

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To find the area, we take into account that your data is:

To calculate the area of the circle, we use the following formula:

Area: π * r²

We substitute the data in the formula, and we begin to solve.

taking the square root

Multiply the two numbers

Therefore, the area of the circle is 113.04 cm². The correct alternative is option "A".

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In the question, it is given that a circle has a radius of 6 cm , we have to find the Area.

To Find the area of the circle , we must know this formula:

[tex] \quad\quad\quad \longrightarrow\underline{\boxed{\color{violet}{A=\pi*r^2}}}[/tex]

Now, we will substitute the values in the formula:

[tex]\rightarrow\sf{A=\pi*r^2} \: \: \: \: \: \: \: ( \red{\pi = 3.14})[/tex]

[tex]\rightarrow\sf{A = 3.14 * 6^2}[/tex]

[tex]\rightarrow\sf{A = 3.14 * 36}[/tex]

[tex]\rightarrow\sf{A = 113.0}[/tex]

The area of circle is 113.0 approx .

[tex] \color{blueviolet}{ \mathfrak{llNotYourll}}[/tex]

Missing data:

Viewer's Age Group  Excellent Good Average Poor Marginal Total

16–25                          52                 42       12       7           113

26–35                          33                50         5       9          97

36–45                          58                 12       28      34         132

46–55                          25                17       22       12            76

56 +                               12                 5          3         8             28

Marginal Total             180               126      70      70           446

A rating of good or excellent indicates the audience liked the movie, while a rating of poor indicates the audience disliked the movie.

A movie producer accomplished a survey behind a preview screening of her latest movie to estimate how the film would be accepted by viewers from various age groups. The table displays the numbers of viewers in various age groups who ranked the film excellent, good, average, and poor.

25/446 = 0.05605

0.05605 [tex]*[/tex] 100% = 5.605%

Out of the entire respondents, the percentage of respondents from the 46–55 age group who ranked the film excellent exists at 5.605%.

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Answer: 9 cm² : 25 cm²

Step-by-step explanation:

    The area of a square can be found with x² where x is the length of one side.

    x² : x²

    3² : 5²

    9 : 25

           9 cm² : 25 cm²

You can use the well-known binomial series,

[tex]\displaystyle (1+x)^\alpha = \sum_{k=0}^\infty \binom \alpha k x^k[/tex]

where

[tex]\dbinom \alpha k = \dfrac{\alpha(\alpha-1)(\alpha-2)\cdots(\alpha-(k-1))}{k!} \text{ and } \dbinom \alpha0 = 1[/tex]

Let [tex]\alpha=\frac12[/tex] and replace [tex]x[/tex] with [tex]3x[/tex]; then the series expansion is

[tex]\displaystyle (1+3x)^{1/2} = \sum_{k=0}^\infty \binom{\frac12}k (3x)^k[/tex]

and the first 4 terms in the expansion are

[tex]\sqrt{1+3x} \approx 1 + \dfrac{\frac12}{1!}(3x) + \dfrac{\frac12\cdot\left(-\frac12\right)}{2!}(3x)^2 + \dfrac{\frac12\cdot\left(-\frac12\right)\cdot\left(-\frac32\right)}{3!}(3x)^3[/tex]

which simplify to

[tex]\sqrt{1+3x} \approx \boxed{1 + \dfrac32 x - \dfrac98 x^2 + \dfrac{27}{16} x^3}[/tex]

You can also use the standard Maclaurin coefficient derivation by differentiating [tex]f[/tex] a few times.

[tex]f(x) = (1+3x)^{1/2} \implies f(0) = 1[/tex]

[tex]f'(x) = \dfrac32 (1+3x)^{-1/2} \implies f'(0) = \dfrac32[/tex]

[tex]f''(x) = -\dfrac94 (1+3x)^{-3/2} \implies f''(0) = -\dfrac94[/tex]

[tex]f'''(x) = \dfrac{81}8 (1+3x)^{-5/2} \implies f'''(0) = \dfrac{81}8[/tex]

Then the 3rd order Maclaurin polynomial is the same as before,

[tex]\sqrt{1+3x} \approx f(0) + \dfrac{f'(0)}{1!} x + \dfrac{f''(0)}{2!} x^2 + \dfrac{f'''(0)}{3!} x^3 = 1 + \dfrac32 x - \dfrac98 x^2 + \dfrac{27}{16} x^3[/tex]

Now,

[tex]\sqrt{1.3} = \sqrt{1+3x} \bigg|_{x=\frac1{10}} \\\\ ~~~~~~~~ \approx 1 + \dfrac32 \left(\dfrac1{10}\right) - \dfrac98 \left(\dfrac1{10}\right)^2 + \dfrac{27}{16} \left(\dfrac1{10}\right)^3 \\\\ ~~~~~~~~ = \dfrac{18,247}{16,000} \approx \boxed{1.14044}[/tex]

Compare to the actual value which is closer to 1.14018.

[tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex] is the maclaurin polynomial and estimate value of [tex]\sqrt{1.3}[/tex] is 1.14. This can be obtained by using the formula to find the maclaurin polynomial.

Given the polynomial,

[tex]f(x)=\sqrt{1+3x}=(1+3x)^{\frac{1}{2} }[/tex]

The formula to find the maclaurin polynomial,

[tex]f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}[/tex]

Next we have to find f'(x), f''(x) and f'''(x),

By putting x = 0 , we get,

Therefore the maclaurin polynomial by using the formula will be,

[tex]\sqrt{1+3x}=f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}[/tex]

[tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex]

To find the value of [tex]\sqrt{1.3}[/tex]  we can use the maclaurin polynomial,

[tex]\sqrt{1.3}[/tex] is  [tex]\sqrt{1+3x}[/tex] with x = 1/10,

[tex]\sqrt{1+3(1/10)}=1+\frac{3}{2} (1/10)-\frac{9}{8} (1/10)^{2} + \frac{81}{8}(1/10)^{3}[/tex]

[tex]\sqrt{1+3(1/10)}=\frac{18247}{16000} = 1.14[/tex]

Hence [tex]\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}[/tex] is the maclaurin polynomial and estimate value of [tex]\sqrt{1.3}[/tex] is 1.14.

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The system of equations to find the value of x, the first number, and y, the second number are;

y = -x + 84

y = x² + 6

The system of equation are equations that contains more than two equation and unknown.

Let the two unknown numbers x and y

If the sum of two numbers is 84, hence;

x +y = 84

y = -x + 84

If the square of the first number is 6 more than the second number, hence;

x² = y + 6

Substitute equation 2 into 2 to have:

x² = y + 6

x² = (-x+84) + 6

x² = -x+84 + 6

x² +x+84 + 6  = 0

x² +x + 90 = 0

Hence the system of equations to find the value of x, the first number, and y, the second number are;

y = -x + 84

y = x² + 6

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[tex]m = m \\ \frac{97 - 68}{2 - 1} = \frac{134 - 97}{3 - 2} \\ 29 = 37 \\ this \: function \: is \: non \: linear[/tex]

[tex]f(1) = 68 \: \: \: f(2) = 97 \: \: \: \: f(3) = 134 \\ f(x) = ax {}^{2} + bx + c[/tex]

[tex]f(1) = 68 \\ 7.8(1) {}^{2} - 2.9(1) + 67.1 = 68 \\ 7.8 - 2.9 + 67.1 = 68 \\ 72 = 68 \\ this \: is \: false[/tex]