PLEASE HELP its math

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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The unit rate of Mikayla and brie is 0.16 miles per minutes and 0.25 miles per minutes respectively.

Brie runs faster.

Mikayla

2 miles in 12 1/2 minutes

Unit rate = miles / minutes

= 2 ÷ 12 1/2

= 2 ÷ 25/2

= 2 × 2/25

= 4/25

= 0.16 miles per minutes

Brie

5 miles in 22 1/4 minutes

Unit rate = miles / minutes

= 5 ÷ 22 1/4

= 5 ÷ 89/4

= 5 × 4/89

= 20/89

= 0.25 miles per minutes

Lucy

4 4/5 pounds for $18.50

Unit rate = pounds / price

= 4 4/5 ÷ 18.50

= 24/5 ÷ 18.50

= 24/5 × 1/18.50

= 24/92.50

= $0.26 per pound

Sophie

3 1/2 pounds for $14.75

Unit rate = pounds / price

= 3 1/2 ÷ 14.75

= 7/2 ÷ 14.75

= 7/2 × 1/14.75

= 7/29.5

= $0.24 per pound

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The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].

According to the statement

we have given that the statement and we have to find the derivative of that term.

So, We know that the

The given equation is

[tex]g(t) = \int\limits^x_4 {e^{5t^{2} - 4t} } \, dt[/tex]

Now find the derivative of that term

We find the derivative of the given term is with the help of the FTC.

And then

[tex]\frac{dg(x) }{dt} = {e^{5x^{2} - 4x} } \, \frac{dx}{dx}[/tex]

Then the equation become is

[tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex]

So, this is the derivative of the given equation.

So, The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].

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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

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]

Hope this helps!! :)

Please let me know if you have any questions

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

[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]

Answer: D

Step-by-step explanation: a^2+b^2=c^2

so use y value for b2 and 6 square root 3 as a and check with it.

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: 46.7 in/3

Step-by-step explanation:

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:

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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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 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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The mpg and hp is print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))

MPG is an abbreviation for 'miles-consistent with gallon and it is used to give you an indication of the fuel financial system of a vehicle or industrial vehicle. It helps you to work out how reasonably-priced or high-priced an automobile might be to run.

As for a new vehicle, an awesome MPG is around 50 to 60. Having this stepped forward gasoline economy facilitates minimizing going for walks fees and cheaper avenue tax due to decreased CO2 emissions. consistent with What car's featured blog, here are a number of the most gasoline-green automobiles in the marketplace nowadays.

The gas economic system of a car relates to the space traveled via an automobile and the quantity of fuel fed on. intake can be expressed in terms of the volume of gasoline to travel a distance, or the gap traveled according to the unit quantity of gasoline consumed.

The car has the “best” combination of mpg and hp, where mpg and hp must be given equal weight.

#sum the scaled values of mpg and hp and add a new column called combination

myCars$combination<-scale(myCars$hp)+scale(myCars$mpg)

#Which car has the best combination of mpg and hp?

print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))

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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

The rule of the translation that maps the rocket from position I to position 2 is 4 units right and 4 units up

The translation is added as an attachment

From the attached figure, we have the following corresponding coordinates:

Figure 1 = (0, 0)

Figure 2 = (4, 4)

The rule of translation is calculated as:

(x, y) = T<Figure 2 - Figure 1>

This gives

(x, y) = T<4 - 0, 4 - 0>

Evaluate

(x, y) = T<4, 4>

Hence, the rule of the translation that maps the rocket from position I to position 2 is 4 units right and 4 units up

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Complete question

In an animated film, a simple scene can be created by translating a figure against a still background. Write a rule for the translation that maps the rocket from position I to position 2.

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.

The spherical coordinate that is converted from the given rectangular coordinate is (12.62, 46.67°, 35.3°).

Here, the given rectangular coordinate is (5, 5.3, 10.3).

Therefore, the value of 'x' is 5, the value of 'y' is 5.3 and the value of 'z' is 10.3.

We can convert the rectangular coordinate (x, y, z) into spherical coordinate (ρ, θ, Φ) by the below mentioned method.

We know, ρ² = (x²+y²+z²)

Therefore, ρ

= √(x²+y²+z²)

= √[(5)²+(5.3)²+(10.3)²]

= √(25+28.09+106.09)

= √(159.18)

= 12.62

Again, tan θ = (y/x)

Therefore, θ = tan⁻¹(y/x) = tan⁻¹(5.3/5) = tan⁻¹(1.06) = 46.67°

Similarly, cos Φ = (z/ρ)

Therefore, Φ = cos⁻¹(z/ρ) = cos⁻¹(10.3/12.62) = cos⁻¹(0.816) = 35.3°

Here, the spherical coordinate is (ρ, θ, Φ).

Therefore, the required spherical coordinate for the given rectangular coordinate is (12.62, 46.67°, 35.3°).

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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:

  x = 22

  BD = 20 units

Step-by-step explanation:

The formula for the area of a rhombus can be used with the given values to write an equation that can be solved for x and for BD.

The formula is ..

  A = 1/2(d1)(d2) . . . . where d1 and d2 are the lengths of the diagonals.

Using the given values, we have ...

  120 = 1/2(12)(x-2)

Dividing by 6, we find ...

  20 = x -2 = BD

  22 = x . . . . . . . . add 2

The value of x is 22.

The length of BD is 20.

Answer:

x=12

BD=10

Step-by-step explanation:

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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Answer:

b) It is false

Answer:

Yup Yup

Step-by-step explanation:

yessah

Inequalities help us to compare two unequal expressions. The given inequality x<8 can be written in the interval notation as x=(-∞,8).

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways. They do not, however, intend to indicate any particular location. Instead, they serve as a concise approach to expressing an inequality or a set of inequalities.

The given inequality x<8 can be written in the interval notation as,

x = (-∞,8)

Hence, The given inequality x<8 can be written in the interval notation as x=(-∞,8).

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Answer:

15:7

Step-by-step explanation:

you put the numbers in order first the number of on time trains to off time trains

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

The ticket price which will maximize the student's council is: C. $3.10.

Price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.

Based on the information provided about Valley High School student council, we can logically deduce the following data:

Mathematically, the equation which model the profit is given by:

Profit = price × number of tickets sold

P(x) = (2 + 0.2x)(420 - 20x)

P(x) = 840 + 84x - 40x - 4x²

P(x) = -4x² + 44x + 840.

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -44/2(-4)

Xmax = -44/-8.

Xmax = 5.5

Ticket price for maximum profit is given by:

Ticket price = 2 + 0.2x

Ticket price = 2 + 0.2(5.5)

Ticket price = $3.10.

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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.

Ileana  have to invest for 8 years :

Simple interest is a simple and straightforward formula for figuring out how much interest will be charged on a loan. Simple interest is calculated by dividing the daily interest rate by the principle and the number of days between payments.

The principal amount must be multiplied by the time, interest rate, and time period in order to calculate simple interest. Simple Interest = Principal x Interest Rate x Time is the written formula.

Principal amount = $15,500

interest = $5,084

Time = ?

Rate = 4.1% simple interest

to find the simple interest :

                                         I = [tex]\frac{(p*t*r)}{100}[/tex]

       Then:

         Time = [tex]\frac{I*100}{P*R}[/tex]

                  = [tex]\frac{(5084*100)}{(15500*4.1)}[/tex]

                  = [tex]\frac{508400}{63,550}[/tex]

                  = 8 years

Ileana  have to invest for 8 years

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