If m=5 and n = 2, find the value of 3mn

Answer:

233.48s  

3.84 min

Step-by-step explanation:

In order to solve this problem, we can start by drawing what the situation looks like. See attached picture.

We can model this situation by making use of a trigonometric function. Trigonometric functions have the following shape:

\(y=A cos(\omega t+\phi)+C\)

where:

A= amplitude =-20m because the model starts at the lowest point of the trajectory.

f= the function to use, in this case we'll use cos, since it starts at the lowest point of the trajectory.

t= time

\(\omega=\) angular speed.

in this case:

\(\omega=\frac{2\pi}{T}\)

where T is the period, in this case 6 min or

\(6min(\frac{60s}{1min})=360s\)

so:

\(\omega=\frac{2\pi}{360}\)

\(\omega = \frac{\pi}{160}\)

and

\(\phi\)= phase angle

C= vertical shift

in this case our vertical shift will be:

2m+20m=22m

in this case the phase angle is 0 because we are starting at the lowest point of the trajectory. So the equation for the ferris wheel will be:

\(y=-20 cos(\frac{\pi}{180}t)+22\)

Once we got this equation, we can figure out on what times the passenger will be higher than 13 m, so we build the following inequality:

\(-20 cos(\frac{\pi}{180}t)+22>13\)

so we can solve this inequality, we can start by turning it into an equation we can solve for t:

\(-20 cos(\frac{\pi}{180}t)+22=13\)

and solve it:

\(-20 cos(\frac{\pi}{180}t)=13-22\)

\(-20 cos(\frac{\pi}{180}t)=-9\)

\(cos(\frac{\pi}{180}t)=\frac{9}{20}\)

and we can take the inverse of cos to get:

\(\frac{\pi}{180}t=cos^{-1}(\frac{9}{20})\)

which yields two possible answers: (see attached picture)

so

\(\frac{\pi}{180}t=1.104\) or \(\frac{\pi}{180}t=5.179\)

so we can solve the two equations. Let's start with the first one:

\(\frac{\pi}{180}t=1.104\)

\(t =1.104(\frac{180}{\pi})\)

t=63.25s

and the second one:

\(\frac{\pi}{180}t=5.179\)

\(t=5.179(\frac{180}{\pi})\)

t=296.73s

so now we can build our possible intervals we can use to test the inequality:

[0, 63.25]  for a test value of 1

[63.25,296.73] for a test value of 70

[296.73, 360] for a test value of 300

let's test the first interval:

[0, 63.25]  for a test value of 1

\(-20 cos(\frac{\pi}{180}(1))+22>13\)

2>13 this is false

let's now test the second interval:

[63.25,296.73] for a test value of 70

\(-20 cos(\frac{\pi}{180}(70))+22>13\)

15.16>13 this is true

and finally the third interval:

[296.73, 360] for a test value of 300

\(-20 cos(\frac{\pi}{180}(300))+22>13\)

12>13 this is false.

We only got one true outcome which belonged to the second interval:

[63.25,296.73]

so the total time spent above a height of 13m will be:

196.73-63.25=233.48s

which is the same as:

\(233.48(\frac{1min}{60s})=3.84 min\)

see attached picture for the graph of the situation. The shaded region represents the region where the passenger will be higher than 13 m.

The statement is true. This means that r'(t) is orthogonal (perpendicular) to r(t) for all t.

If |r(t)| = 1 for all t, then r(t) is a unit vector for all t. Differentiating both sides of this equation with respect to t, we get:

|r(t)|' = 0

Using the chain rule and the fact that the magnitude of a vector is the square root of the dot product of the vector with itself, we have:

|r(t)|' = (r(t) · √r(t))

= (2r(t) · r'(t)) / (2|r(t)|)

= r(t) · r'(t) / |r(t)|

= r(t) · r'(t)

Since |r(t)|' = 0, we have:

r(t) · r'(t) = 0

To know more about orthogonal vector,

https://brainly.com/question/28503609

#SPJ11

The probability of drawing a king then getting an 1 is P = 0.006

First we need to find the probability of randomly drawing a king from the deck, that is equal to the quotient between the number of kings on a deck and the total number of cards on the deck.

There are 4 kings and 52 cards, thus the probability is:

p = 4/52

Then we want to get a 1, the probability is computed in the same way, notice that now there are 51 cards on the deck because we already drawn one.

q = 4/51

The joint probability (first drawing a king and then a 1) is equal to the product between the individual ones.

P = (4/52)*(4/51) = 0.006

Learn more about probability at:

https://brainly.com/question/25870256

#SPJ1

The term that describes an event that increases the likelihood of a response being repeated is known as reinforcement.

Reinforcement can be defined as any consequence that strengthens or increases the probability of a behavior occurring again in the future. This can include positive reinforcement, which involves adding a desirable consequence after a behavior, or negative reinforcement, which involves removing an aversive consequence after a behavior. Both types of reinforcement have been shown to be effective in increasing the likelihood of a behavior being repeated.

Overall, understanding the concept of reinforcement is essential in the field of psychology, particularly in the areas of behaviorism and behavior modification. By providing positive consequences after desired behaviors, individuals can be motivated to continue engaging in those behaviors, which can lead to long-term positive changes. Reinforcement can also be used to shape new behaviors or replace unwanted behaviors with more desirable ones.

To know more about positive changes visit:-

https://brainly.com/question/15411632

#SPJ11

We know that the line passes through the origin, which means that the coordinates of the point on the line are (0,0). We also know that the line has a slope of 2. Therefore, we can use the point-slope form of the equation of a line to find its equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. Plugging in the values we know, we get:

y - 0 = 2(x - 0)

which simplifies to:

y = 2x

Thus, the equation of the line containing the origin and with a slope of 2 is y = 2x.

Answer:

Step-by-step explanation:

If something is an apple then it is a fruit

Which gives If p then q

Where: A = apple and F = fruit so then we should write

"If something is not a fruit, then it is not an apple so, We have this, ~F → ~A that is an contrapositive conditional statement  and the shorthand that represent the contrapositive statement is then, ~F → ~A.

Answer:

Step-by-step explanation:

Remember PEMDAS

2 - 8 : (2^4 : 2) =

2 - 8 : (16 : 2) =

2 - 8 : 8 =

2 - 1 =

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

The age of the decaying sample according to the decay formula is 42,009 years.

The rate of radioactive carbon-14 decay depends on the function

\(A(t) = A_{0} e^{-0.0001216t}\)

where \(A_{0}\) is the quantity found in living plants and animals, t is in years, and is the age.

60% of the carbon-14 of a current-day sample was present in a sample taken from a refuse deposit close to the Strait of Magellan. We need to evaluate the age of the sample,

A = 60 % of \(A_{0}\) = (3/5)\(A_{0}\)

Putting this in the decay equation, we have,

\(\frac{3}{5} A_{0} = A_{0} e^{-0.0001216t}\\\\ 0.6= e^{-0.0001216t}\\ \\ln0.6 = -0.00001216t\\\\-0.51082 = -0.00001216t\\\\t = 42,008.68\)

Thus, the age of the sample is 42,009 years.

To read more about the decay formula, visit https://brainly.com/question/13720265

#SPJ4

Answer:

- 439

Step-by-step explanation:

evaluate f(- 7) and substitute the value obtained into s(x)

f(- 7) = 3(- 7) = - 21 , then

s(- 21) = 2 - (- 21)² = 2 - 441 = - 439

Answer:

A. (s*t)(-7)=-439

Step-by-step explanation:

(s*t)(-7) is the same as s(t(-7)). First find t(-7)

t(-7)=3(-7)=-21

t(-7)=-21

Plug -21 into s(t(-7)) for t(-7).

Find s(-21).

s(-21)=2-(-21)^2=-441+2=-439

Hope this helps!

If not, I am sorry.

∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

Know more about derivative here:

https://brainly.com/question/25324584

#SPJ11

Answer:

x

=

12

Explanation:

Move the variable to one side, and the constant to the other, to get

2

x

=

24

Then, divide both sides by 2 to get

x

=

12

Step-by-step explanation:

Answer:

x  =  3 &  −

12

Step-by-step explanation:

Find all solutions for  x  by breaking the absolute value into the positive and negative components.

Let's solve your equation step-by-step.

|2x+9|=15  Solve Absolute Value.

|2x+9|=15

We know either 2x + 9 = 15 or 2x + 9 = −15

2x + 9 = 15(Possibility 1)

2x + 9 − 9 = 15 − 9(Subtract 9 from both sides)

2x=6  (Divide both sides by 2)

x=3  

2x + 9 = −15(Possibility 2)

2x + 9 − 9 = −15 − 9(Subtract 9 from both sides)

2x=−24  (Divide both sides by 2)

x=−12

Answer:

x=3 or x=−12

1. 31 employees absent between 3 up to 6 days.

2. 91 employees absent fewer than six days.

3. 22 employees absent more than five days.

4.  20 employees absent from 6 up to 12 days.

1. How many employees were absent between 3 up to 6 days?
To find the number of employees absent between 3 up to 6 days, look at the cumulative number of employees for that range: 31 employees.

2. How many employees were absent fewer than six days?
To find the number of employees absent fewer than six days, add the cumulative number of employees for the ranges 0 up to 3 and 3 up to 6: 60 + 31 = 91 employees.

3. How many employees were absent more than five days?
To find the number of employees absent more than five days, add the cumulative number of employees for the ranges 6 up to 9, 9 up to 12, and 12 up to 15: 14 + 6 + 2 = 22 employees.

4. How many employees were absent from 6 up to 12 days?
To find the number of employees absent from 6 up to 12 days, add the cumulative number of employees for the ranges 6 up to 9 and 9 up to 12: 14 + 6 = 20 employees.

for such more question on employees

https://brainly.com/question/27404382

#SPJ11

Answer:

If 5 is zero then (x - 5) is a factor.

Only 4. has this factor.

Step-by-step explanation:

The coordinate of point G after a rotation of 180° is (4,2).

The complete question is added as an attachment

Rotation is a given a rigid motion or transformation which refers to movement of a figure around a center of rotation.

In this question it is asked to find the coordinates of the new vertices after the 180 degrees rotation, which is define or represented by the rule:

(x, y) = (-x, -y)

From the figure, we have

G = (4,2)

So, we have

G' = (-4,-2)

Hence, the image is (-4,-2)

Read more about rotation at

brainly.com/question/1571997

#SPJ1

Answer:

D. G'(4,2)

Step-by-step explanation:

Answer:

x = 3.3 and -0.3

Step-by-step explanation:

Given the expression

1/x-4 + x/x-2=2/x^2-6x+8

Find the LCM

x-2+x(x-4)/(x-4)(x-2) = 2/x^2-6x+8

Since the denominator, are the same they cancels out

x +1 + x(x-4) = 2

x+1 + x²-4x = 2

x²-3x + 1 - 2 = 0

x² - 3x - 1 = 0

Factorize

x =3±√9+4/2

x =3±√13/2

x = 3±3.6/2

x= 6.6/2 and -0.6/2

x = 3.3 and -0.3

Answer:

its -1 trust me I used another website to answer this question

Step-by-step explanation:

I took the diagnostic also

Answer:

\(\mathrm{Factoring}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}\)

Step-by-step explanation:

This is a particularly tough question. It involves polynomial division(a real laborious process) and solving using quadratic formula.

I presume your school has provided you the resources for both.

Anyways, here goes a brief explanation

To find the roots(zeros) of a polynomial, \(f(x)\) , set \(f(x) = 0\)  and solve for values of \(x\)

In general, if \(a\) is a zero of \(f(x)\), then \(f(x) \div(x-a)\)  will leave no remainder. In other words, it is a factor of the polynomial. It also means \(x - a = 0\)

The given polynomial is  \(4 x^{3} - 15 x^{2} - 31 x + 30\)

We are given that \(- 2\)  is a zero of \(f(x)\). This simply means that \(f(-2) = 0\)

Plugging \(-2\) into the function gives

\(f(-2) = 4(-2)^3 -15(-2)^2 - 31x + 30\\\\ = 0 =4\left(-8\right)-15\cdot \:4-31\left(-2\right)+30\)

Which indeed is 0

Here \(a = -2\) , so \(x - (-2)\) which is \(x + 2\) is a factor of\(f(x)\). It also means that
\(x-(-2) = 0 \;or\; x + 2 = 0\)

Steps to factor the polynomial \(4 x^{3} - 15 x^{2} - 31 x + 30\) :

Multiplying both sides of the above by \(4\) gives \(4x -3 = 0.\) So \(4x-3\) is the third factor, replacing \(x - \dfrac{3}{4}\)

The factors of \(4 x^{3} - 15 x^{2} - 31 x + 30\)
are:

\(x+2, x-5 \;and \;4x-3\)

Answer:
\(\mathrm{Factor}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}\)

Use a polynomial division calculator which you can find on the web and a quadratic formula calculator (on the we or on your own calculator)

Answer:

Step-by-step explanation:

Let's do an example.

60:90:100

100 plus 90 plus 60 is 250

ben gets 90 of that 250

or 9/25.

Answer:

x = 27°

Step-by-step explanation:

Because of the two parallel lines, we can conclude that

corner DAB = corner FDE = 2x

In ∆DAB

Corner DAB = 2x

Corner BDA = 2x (given)

Corner ABD = 72 (given)

The sum of three corners in any trianle, adds up to 180°.

So if one corner is 72° and the other two corners are the same, then the two corners together, must be 180-72 = 108°.

For each corner that is 108/2= 54

so corner BDA = 54° and also corner DAB = 54°.

Given was BDA = 2x and BDA = 54°

so 2x = 54°

then x = 27°

The cost recovery deduction for the current year is $985

So, the correct option C.$985

Cost recovery deduction is the tax deduction that a taxpayer can take for recovering the cost of a business asset. In other words, the cost recovery deduction allows a taxpayer to recover the cost of a business asset gradually over the asset’s useful life through tax deductions. Cost recovery deductions can be calculated using one of the following methods:

Here, we are using the straight-line method because it was mentioned in the problem that Michelle opts to use the straight-line option under MACRS. Therefore, to calculate the cost recovery deduction, we will use the formula:

Cost recovery deduction = Cost of property x Depreciation percentage

In this problem:

Cost of the property (Truck) = $9,200 + $650 (sales tax) = $9,850

Depreciation percentage = 1/5 (because it's a five-year property) = 0.2

Therefore, substituting the values in the formula, we get:

Cost recovery deduction = $9,850 x 0.2 = $1,970

But since the asset was placed in service in the current year, we have to use the half-year convention, which means that only half of the full-year depreciation amount is allowed in the first year of service.

Thus, the cost recovery deduction for the current year is:

$1,970 / 2 = $985

Therefore, the correct answer is option C: $985.

Learn more about  annual sales at

https://brainly.com/question/30005665

#SPJ11

Consider that the dresser costs $40 to Violet. So the cost price C is $40.

She wants to sell the dresser for at least %65,

Then the selling price S must be greater than or equal to $65,

Since there is no discount or any overhead expense, the selling price is the same as the marked price M,

Then the minimum marked price will be $65.

Therefore, option (C) is the correct choice (but the % symbol should not be there).

The measure of the segment JK is 0 unit

A line is the shortest distance between two points

Given the following parameters

GJ = 70.2

JH = 26.5

GK = 70.2

Determine the measure of JK

JK = JG + GK

Since JG = -GJ then;

JK = -GJ + GK

JK = -70.2 + 70.2

JK = 0

Hence the measure of the segment JK is 0 unit

Learn more on line segment here: https://brainly.com/question/2437195

#SPJ1

Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex". If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point (h, k).

Answer:

11x11 is 121

11 x 11 can also be rewritten as 11^2.

Answer:

121

Step-by-step explanation:

There are two ways to doing this.

1.  multiplying double digits using the traditional algorithm

Single Sampling Plan: AQL = 0, LTPD = 3.41, AOQ = 1.79 Double Sampling Plan: AQL = 0, LTPD = 2.72, AOQ = 1.48

The values for the ASN (Average Sample Number) curves for the given single sampling plan and double sampling plan are:

Single Sampling Plan (n=80, c=3):

ASN curve values: AQL = 0, LTPD = 3.41, AOQ = 1.79

Double Sampling Plan (n1=50, c1=1, r1=4, n2=50, c2=4, r2):

ASN curve values: AQL = 0, LTPD = 2.72, AOQ = 1.48

The ASN curves provide information about the performance of a sampling plan by plotting the average sample number (ASN) against various acceptance quality levels (AQL). The AQL represents the maximum acceptable defect rate, while the LTPD (Lot Tolerance Percent Defective) represents the maximum defect rate that the consumer is willing to tolerate.

For the single sampling plan, the values n=80 (sample size) and c=3 (acceptance number) are used to calculate the ASN curve. The AQL is 0, meaning no defects are allowed, while the LTPD is 3.41. The Average Outgoing Quality (AOQ) is 1.79, representing the average quality level of outgoing lots.

For the equally effective double sampling plan, the values n1=50, c1=1, r1=4, n2=50, c2=4, and r2 are used. The AQL and LTPD values are the same as in the single sampling plan. The AOQ is 1.48, indicating the average quality level of outgoing lots in this double sampling plan.

These ASN curve values provide insights into the expected performance of the sampling plans in terms of lot acceptance and outgoing quality.

To learn more about average  click here

brainly.com/question/30873037

#SPJ11

Answer:

joe momma, you should know that baka. ha how u like them apples