What happens when the function f(x)=cos(x) is transformed by the rule g(x)=f(1/2x)?

A: f(x) is stretched away from the y-axis by a factor of 2.
B: f(x) is compressed toward the y-axis by a factor of 1/2.
C: f(x) is compressed toward the x-axis by a factor of 1/2.

Answer:

[tex]x=a \cos t \implies \dfrac{dx}{dt}=-a \sin t[/tex]

[tex]y= a \sin t \implies \dfrac{dy}{dt}=a \cos t[/tex]

Using the chain rule:

[tex]\begin{aligned}\implies \dfrac{dy}{dx} & =\dfrac{dy}{dt} \times \dfrac{dt}{dx}\\\\& = a \cos t \times \dfrac{1}{-a \sin t}\\\\& = \dfrac{a \cos t}{-a \sin t}\\\\& = - \dfrac{\cos t}{\sin t}\\\\& = - \cot t\end{aligned}[/tex]

Answer:

wouldn't be 4.5 or something close too that maybe 5 or 5.5

Step-by-step explanation:

I got you I think

The expression is assumed here as it's unclear looking

If it's P=(P_o)ln0.015t then the below solution of Part B is correct else they may vary.

#a

#b

As per our assumed equation

It's.

Simplify

Initial amount of account is not given so you have to solve the above equation after putting known P_o

#3

Hence it's less than 3 and greater than 2

The amount that the beneficiaries of his life insurance would receive would be $30000.

The total amount of insurance is 40000

percentage  needed by beneficiaries on this amount = 75%

Hence 75% * 40000

= $30000

Therefore it can be concluded that the amount that the beneficiaries would require on 75% is $30000.

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Answer:

-8

Step-by-step explanation:

Solving for r means that we need to isolate r from the expression.

[tex] \frac{ - 8}{r + 6} = 4[/tex]

Multiply both sides by (r +6) to 'get rid' of the fraction:

-8= 4(r +6)

Expand:

-8= 4r +4(6)

-8= 4r +24

Minus 24 on both sides:

4r= -8 -24

4r= -32

Divide both sides by 4:

r= -32 ÷4

r= -8

Additional:

For a similar question on solving for a variable:

Answer:

r = -8

Step-by-step explanation:

-8/(r + 6) = 4
          -8 = 4(r + 6)
          -8 = 4r + 24
        -32 = 4r
          -8 = r

Answer:

ac = 18

Keys:

[tex]\sf Given\\a = 2\\c = 9\\ac = a \cdot c[/tex]

Step-by-step explanation:

[tex]\sf a(2) \cdot c(9) = 18[/tex]

Answer:

The answer would be 18.

Step-by-step explanation:

ac is equal to a multiplied y c. Since we know that a is equal to 2 and c is equal to 9, we know we have to set up the equation 2(9). (Note: The parentheses around the 9 means you multiply by that number). 2 times 9 is equal to 18, getting you your answer. I hope this helps! :)

Answer:

£ 2121.8

Step-by-step explanation:

The formula to find the compound interest is :

[tex]A=P(1+\frac{R}{100} )^n[/tex]

Here,

A = Amount ⇒ ?

P ⇒ Principal ⇒ £2000

R ⇒ Interest rate ⇒ 3%

n ⇒ Time  ⇒ 2 years

Let us find now.

[tex]A=P(1+\frac{R}{100} )^n[/tex]

[tex]A=2000(1+\frac{3}{100} )^2[/tex]

[tex]A=2000(1+0.03 )^2[/tex]

[tex]A=2000(1.03 )^2[/tex]

[tex]A=2000*1.0609[/tex]

[tex]A=2121.8[/tex]

Therefore, there will be £ 2121.8 in the bank account after 2 years.

Answer:

C. 225°.

Step-by-step explanation:

1) according to the condition minor arc is 135°;

2) the measure of the major arc can be calculated as

360°-135°=225°.

The formula for calculating the area of a rectangle is expressed as A = lw. The area of the box is 48x^4 - 32x^3 cubic units

The formula for calculating the area of a rectangle is expressed as:

A = lw

Given the following parameters

Determine the area

Area = (8x²)6x² - 4x

Area of the box = 48x^4 - 32x^3

Hence the area of the box is 48x^4 - 32x^3 cubic units

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The year, where the number of cars sold exceed 46,000 is 13496

The equation of the function is given as:

y = 4x + 2

When the sales exceed 46000;

It means that y > 46000

So, we have:

4x + 2 > 46000

Subtract 2 from both sides

4x > 45998

Divide both sides by 4

x > 11499.5

The year is then calculated as:

Year = 1996 + x

So, we have:

Year > 1996 + 11499.5

Evaluate

Year > 13495.5

Approximate

y > 13496

Hence; the year, where the number of cars sold exceed 46,000 is 13496

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Answer:

x = 28

Step-by-step explanation:

By Triangle Proportionality Theorem,
14/x = 21/42
14 * 42/21 = x
x = 28

Answer:

10,800 kilograms

Step-by-step explanation:

(24 x 30) x 15 = 10,800

or (24 x 15) x 30

Answer:

Step-by-step explanation:

a)

the area of the field :

= 250 × 150

= 37 500 ft²

……………………

b)

→ the number of bags needed :

37 500 ÷ 1 000

= 37.5

Then he needs 38 bag

→ The cost :

= 38 × 54.00

= 2 052

sin P = 24/26

cos P = 10/26

tan P = 24/10

sin Q = 10/26

cos Q = 24/26

tan Q = 10/24

you have the first part right. using Soh Cah Toa is the best way to find the trig function when given a labeled triangle.

remember the hypotenuse is the longest side and always across from the 90 degree angle.

Answer:

5/1

Step-by-step explanation:

The correct description of the graph:

"One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 2, 1, and 4."

Here we have the function:

[tex]f(x) = \frac{2x - 1}{x - 1}[/tex]

The graph of this function can be seen below:

Then we can see that a curve opens up on quadrant 1, and down on quadrants 2 and 3 (it pass throw quadrant 1 for a little bit).

Then the correct option is:

"One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 2, 1, and 4."

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Answer:

Graph D

Step-by-step explanation:

Hey there !

Answer:

Step-by-step explanation:

In this question we are given with an expression that is -2mn + n - 3m , value of m as -3 , value of n as -2 . And we are asked to evaluate the expression .

Solution : -

For solving such types of expression in which we are provided with values of variables we need to substitute value of variable ( in given equation m and n ) and solve them .

Expression :

[tex] \longmapsto \: \qquad \: \rm{- 2mn + n - 3mn}[/tex]

Substituting value of m and n :

[tex] \longmapsto \: \qquad \: - 2( - 3)( - 2) + ( - 2) - 3( - 3)[/tex]

Simplifying it :

[tex]\longmapsto \: \qquad \: - 2(6) - 2 + 9[/tex]

Multiplying -2 and 6 :

[tex]\longmapsto \: \qquad \: - 12 - 2 + 9[/tex]

Adding -12 and -2 :

[tex]\longmapsto \: \qquad \: - 14 + 9[/tex]

Solving -14 and 9 :

[tex]\longmapsto \: \qquad \: \underline{ \blue{\boxed{\frak{- 5}}}} \quad \bigstar[/tex]

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to evaluate the expression

[tex]\star~\mathrm{-2mn+n-3m}~\star[/tex]

for

[tex]\star~\mathrm{m=-3}~\star[/tex]

[tex]\star~\mathrm{n=-2}~\star[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So, let's compute...

//\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\

                               Evaluating the expression

Since the value of m is -3, we should substitute -3 for m:

[tex]\star~\mathrm{-2(-3)n+n-3(-3)}[/tex]

Since the value of n is -2, we should substitute -2 for n:

[tex]\star~\mathrm{-2(-3)(-2)+(-2)-3(-3)}[/tex]

Simplify!

[tex]\star\mathrm{6(-2)-2+9}[/tex]

Simplify more!

[tex]\star\mathrm{-12-2+9}[/tex]

[tex]\star~\mathrm{-14+9}[/tex]

[tex]\boxed{\mathrm{-5}}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

Step-by-step explanation:

a)  Sum of nine and two ⇒ 9 + 2

Four multiplied by (9+2) :  

       4* (9+2)

[tex]b) \dfrac{(18-6)}{4}[/tex]

[tex]c) \dfrac{45}{3*(3+2)}[/tex]

2) a) Multiply the sum of five and eight by 6

   b) There 5 story books in 6 red bags and 8 art books in 6 blue bags. How many books are there?

3) a) 7*(8-3)

      Multiply the difference of eight and three by 7.

The number of customers served in the ice cream shop in June, July and August are 125, 25 and 250 customers respectively

let

Total = June + July + August

400 = x + (x- 100) + 2x

400 = x + x - 100 + 2x

400 = 4x - 100

400 + 100 = 4x

500 = 4x

x = 500/4

x = 125

So,

June = x

= 125 customers

July = x - 100

125 - 100

= 25 customers

August = 2x

= 2(125)

= 250 customers

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Thank you :)

[tex]\pink{ \rule{1pt}{90000000pt}}\color{blue}{ \rule{1pt}{90000000pt}}\color{yellow}{ \rule{1pt}{90000000pt}}\purple{ \rule{1pt}{90000000pt}} \green{\rule{1pt}{90000000pt}}

[/tex]

The residuals of the linear regression equation are -1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18 and -0.7

The regression equation is given as:

y = 0.141x + 0.842

Next, we calculate the predicted values (y) at the corresponding x values.

So, we have:

y = 0.141 * 13.8 + 0.842 = 2.78

y = 0.141 * 18 + 0.842 = 3.38

y = 0.141 * 16.7 + 0.842 = 3.20

y = 0.141 * 18 + 0.842 = 3.38

y = 0.141 * 0.7 + 0.842 = 0.94

y = 0.141 * 21.9 + 0.842 = 3.93

y = 0.141 * 15.5 + 0.842 = 3.03

y = 0.141 * 9.2 + 0.842 = 2.14

y = 0.141 * 19.5 + 0.842 = 3.59

y = 0.141 * 16.7 + 0.842 = 3.20

The residuals are then calculated using:

Residual = Actual value - Predicted value

So, we have:

Residual = 1.42 - 2.78 = -1.36

Residual = 3.7 - 3.38 = 0.32

Residual = 3.21 - 3.20 = 0.01

Residual = 4 - 3.38 = 0.62

Residual = 1.11 - 0.94 = 0.17

Residual = 3.69 - 3.93 = -0.24

Residual = 3.92 - 3.03 = 0.89

Residual = 2.23 - 2.14 = 0.09

Residual = 3.77 - 3.59 = 0.18

Residual = 2.5 - 3.20 = -0.7

Hence, the residuals of the linear regression equation are -1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18 and -0.7

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Answer:

y = 6l + 43

Step-by-step explanation:

y=mx + b

y = y coordinate

m = slope

x = x coordinate

b = y intercept

The y intercept is when x = 0, so the initial cost before buying the laces, which was the cost of the sneakers

b = 43

The slope is you purchase one pair of laces, it increases by 6 each time

m = 6

The y coordinate will represent the total cost spent

y

The x coordinate will represent the total number of laces purchase and we are told that the variable is l

x = l

combine:

y = 6l + 43

The approximation of the circumference of the ride is 138 feet to the nearest foot

The given parameters are:

The radius is calculated using:

[tex]r = \sqrt{(x - a)^2 + (y -b)^2}[/tex]

So, we have:

[tex]r = \sqrt{(16 - 0)^2 + (15.1 -0)^2}[/tex]

Evaluate

r = √484.01

Evaluate the square root

r = 22.0

The circumference is calculated using

C = 2πr

So, we have:

C = 2π * 22.0

Evaluate

C = 138

Hence, the approximation of the circumference of the ride to the nearest foot is 138 feet

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Answer: D and F

Step-by-step explanation:

For the first inequality, we know that y>x, so this eliminates options A, B, C, and E. This means we only need to check D and F.

Both D and F have a y coordinate greater than 2 and an x coordinate greater than 4, so they are both correct.

Answer:

-3(x+1)² + 2

Step-by-step explanation:

-3(x+1)² + 2 because the +2 indicates the y value of the turning point and the turning point is a maximum meaning the coefficient must be negative leaving this answer

Answer:

Let Musa's mark be = m

Emmanuel's mark be = e

Faith's mark be = f

m = e + 7

e = 25

m = 25 + 7 = 32

f = 1/4 m + e

f = (1/4 × 32) + 25

f = 8 + 25

f = 33

You have to maintain a minimum level of financial responsibility when transporting any type of hazardous material in intrastate commerce Option A is correct.

Interstate commerce refers to any transaction or movement of goods, services, or money over state lines.

You operate a motor carrier for hire. When shipping any quantity of hazardous material in intrastate trade, A mandates that you maintain a minimum degree of financial accountability.

Hence option A is correct.

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Answer: A is correct

Step-by-step explanation:

Answer:

3 ways

Step-by-step explanation:

2×3=6. That is how you do it