(a) A body of mass 2kg is placed on a rough plane inclined at an angle of 30° to the
horizontal. The coefficient of friction between the body and the plane is 0.25. Find the
least force needed to prevent the body from slipping down the plane if this force acts
upwards at an angle of 30° to the line of greatest slope.

Answers

Answer 1

Answer:

8.6 N

Step-by-step explanation:

Let T be the unknown force

Let θ be the slope of the inclined plane to horizontal

Let φ be the angle of the force to the plane

Let μ be the coefficient of static friction

Let m be the mass

Let N be the Normal force of plane on mass

Let Ff be the friction force which will have a maximum at μN

Let g be gravity

Forces acting parallel to the plane. Upslope is positive

For minimum force T, friction will be max and acting upslope.

                               F = ma

Tcosφ - mgsinθ + Ff = m(0)

Tcosφ - mgsinθ + μN = 0

Tcosφ - mgsinθ + μ(mgcosθ - Tsin(θ + φ)) = 0

T(cosφ - μsin(θ + φ)) + μmgcosθ - mgsinθ = 0

T  = mg(sinθ - μcosθ) / (cosφ - μsin(θ + φ))

T  = 2(9.8)(sin30 - 0.25cos30) / (cos30 - 0.25sin(30 + 30))

T = 8.5547537...


Related Questions

PLS HELP
Let f(x) = -6x + 3 and g(x) = 5x + 4. Find f · g and state its domain.


A) -30x2 - 9x + 12; all real numbers



B) -30x2 - 9x + 12; all real numbers except x = 4



C) -18x2 - 39x + 20; all real numbers



D) -18x2 - 39x + 20; all real numbers except x = 1

Answers

Answer:

-30x^2-9x+12  all real numbers

Step-by-step explanation:

f(x) = -6x + 3 and g(x) = 5x + 4

f(x) * g(x) = (-6x + 3) * ( 5x + 4)

FOIL

            = -30x^2 -24x+15x +12

Combine like terms

           =-30x^2-9x+12

The domain is what numbers x can take

There are no restrictions so all real numbers

Kylie fell asleep 34% of the way through the trip. If kylie fell asleep after they had traveled 306 miles what wasthe total length of the trip.

Answers

Answer:

900

Step-by-step explanation:

34/100 = 306/x

Cross multiplying, you get:

34x=30600

x=900

Total trip is 900 miles long.

Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22. a. Compute the mean and median number of apples in a bag. (Round your answers to 2 decimal places.)

Answers

Answer:

The mean and median number of apples in a bag are 21.71 and 22 respectively.

Step-by-step explanation:

The mean is the arithmetic mean of a set of numbers. In other words, the mean is the average value of all my data.

The mean is calculated by adding all the values ​​and dividing the sum by the total number of values. In this case:

[tex]Mean=\frac{23+19+26+17+21+24+22}{7}[/tex]

[tex]Mean=\frac{152}{7}[/tex]

Mean= 21.71

The median of a set of numbers is the average number in the set, that is, it is the value that occupies the central place of all the values.

The median can be calculated by putting the numbers in ascending order and then:

if the quantity is numbers it is odd: the median is the number in the center of that distribution. if the number of numbers is even: the median is the mean of the two middle numbers.

In this case:

Putting the numbers in ascending order: 17, 19, 21, 22, 23, 24, 26

Since the quantity is odd numbers, the median is the number in the center of that distribution. So Median= 22

The mean and median number of apples in a bag are 21.71 and 22 respectively.

Round 86,261,785 to the nearest hundred?

Answers

Answer:

86,261,800 is your answer

Answer:

86,261,800

Step-by-step explanation:

Locating the hundreds place...

86,261,785

Look at the digit to the right of it.

86,261,785

Since the digit '8' is greater than or equal to 5, we would round up.

86,261,785 ≈ 86,261,800

Hope this helps.

Q4 Compute the shearing stress at the very top of the vertical web just below the flange. for a beam with the T shaped cross section shown in Figure. The shearing force V on the section of interest is 6000 N. Le​

Answers

ʕ•ﻌ•ʔ[tex]\huge\bold\pink{hello!!!}[/tex]ʕ•ﻌ•ʔ

HERE IS UR ANSWER

_____________________

formula used to calculate shear stresses due to bending, τ = VQ/It. We have just read the internal shear force, V, off of the shear diagram. We also already calculated the moment of inertia for this particular section.

τ=6000N

Type the correct answer in each box.
Consider the expressions shown below.

A B C

Complete each of the following statements with the letter that represents the expression.


is equivalent to expression
.

is equivalent to expression
.

is equivalent to expression
.

Answers

Answer:

BAC

Step-by-step explanation:

The expression (3x² - 6x + 11) - (10x² - 4x + 6) is equivalent to the expression A, expression (-3x² - 5x - 3) - (-10x² - 7x + 2) is equivalent to the expression C, and expression (12x² + 6x - 5) - (5x² + 8x - 12)  is equivalent to the expression B.

What is polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial shown in the picture.

A = -7x² - 2x + 5

B =  7x² - 2x + 7

C = 7x² + 2x - 5

The expression is:

= (3x² - 6x + 11) - (10x² - 4x + 6)

= -7x² - 2x + 5

= A

= (-3x² - 5x - 3) - (-10x² - 7x + 2)

= 7x² + 2x - 5

= C

= (12x² + 6x - 5) - (5x² + 8x - 12)

= 7x² - 2x + 7

= B

Thus, the expression (3x² - 6x + 11) - (10x² - 4x + 6) is equivalent to the expression A, expression (-3x² - 5x - 3) - (-10x² - 7x + 2) is equivalent to the expression C, and expression (12x² + 6x - 5) - (5x² + 8x - 12)  is equivalent to the expression B.

Learn more about Polynomial here:

brainly.com/question/17822016

#SPJ5

I need to know what goes in the amount box is someone will be kind enough to help me that would be very appreciated

Answers

Answer:

123

Step-by-step explanation:

Yw

A motorist travels 90 miles at a rate of 20 miles per hour. If he returns the same distance at a rate of 40 miles per hour, what is the average speed for the entire trip, in miles per hour? (Explain)

Answers

Answer:

  26 2/3

Step-by-step explanation:

Average speed is total distance divided by total time.

The time for the first trip was ...

  (90 mi)/(20 mi/h) = 4.5 h

The time for the return trip was ...

  (90 mi)/(40 mi/h) = 2.25 h

Then the average for the trip and return is ...

  total miles/total time = (90 +90)/(4.5 +2.25) = 26 2/3 . . . . mi/h

The average speed for the round trip was 26 2/3 miles per hour.

g Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. In poker, a flush (5 in same suit) in any suit

Answers

Answer:

The answer is "[tex]1.54 \times 10^{-6}[/tex]".

Step-by-step explanation:

Calculating the probability of the cards that hand from a 52-card deck.

The aces are high or low in poker.

There are 13 cards in the bridge hand.

A royal flush (5 suit top cards) in poker.

There are 5 various poker hands with [tex]\binom{52}{5}[/tex].

There are four royal flushes, one in each suit.

[tex]P (royal\ flush) =\frac{4}{\binom{52}{5}}\\\\[/tex]

                         [tex]=\frac{4}{2598960}\approx 1.54 \times 10^{-6}[/tex]

When Poll Pasked students to identify their favorite kind
of TV show, 12 students, 30% of the group, said their
favorite was Sports. Poll Q asked 3 times as many
students as Poll P.
G
How many students took Poll Q?

Answers

Answer:A) The number of students who took Poll P

Step-by-step explanation:

i did it on the assignment

How to do questions 19 and 20

Answers

Answer & Step-by-step explanation:

Using the information given in the question we can form the following 3 equations (in the order of the first 3 sentences)

w = 2h (twice the price)

t = h - 4 ($4 less)

3w + 2h + 5t = 136 (total purchasing and cost)

We can solve all 3 equations for h first, by substituting the first two equations, into the third equations w and t

3(2h) + 2h + 5(h-4) = 136

Simplify

6h + 2h + 5h - 20 = 136

13h = 136 + 20

13h = 156

h = 156/13

h = $12

Using this information, we can solve for w and t

w = 2h

w = 2(12)

w = $24

And finally

t = h - 4

t = 12 - 4

t = $8

Solve the following equation algebraically

3x 4 – 1 = 1874

Answers

The answer is x= 5 or x= -5

Someone help so lost I didn’t understand the course and now I’m stuck please help a girl out

Answers

Answer:

the answer is b. you are basically multiplying them

What is the slope of the line that passes through the points (9, 4) and (9,-5)?
Write your answer in simplest form.

Answers

Answer:

slope=undefined

Step-by-step explanation:

(-5-4)/(9-9)

-9/0

[tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

[tex]\frac{(-5-4)}{(9-9)}[/tex]

[tex]\frac{-9}{0}[/tex]

Because the denominator is 0, the slope is undefined.

Rise over run. The run is 0.

Whats is the job of dentisy​

Answers

Answer:

A dentist, also known as a dental surgeon, is a medical professional who specializes in dentistry, the diagnosis, prevention, and treatment of diseases and conditions of the oral cavity. The dentist's supporting team aids in providing oral health services. Wikipedia

I need help with this​

Answers

Answer:

A. More students prefer Model A1 calculators than the Model C3 calculators.

A rectangle with a length of 5 cm and a width of 2 cm is enlarged by a scale factor of 5. What would be the area of the new rectangle?
Area of old rectangle is multiplied by 25
Area of old rectangle is multiplied by 5
Area of old rectangle is multiplied by 20
Area of old rectangle is multiplied by 10

Answers

Area is in square units.

Square the factor: 5^2 = 25

The new area would be the area of the old rectangle multiplied by 25

Answer: Area of old rectangle is multiplied by 25

Step-by-step explanation:

Original rectangle

Length = 5 cmWidth = 2 cm

Area = 2 · 5 = 10 cm²

New rectangle

Length = 5 · 5 = 25 cmWidth = 2 · 5 = 10 cm

Area = 25 · 10 = 250 cm²

The area of the new rectangle = area of old rectangle × 25

Can anyone explain please?

Answers

Answer:

x = 55

Step-by-step explanation:

In a rhombus, each diagonal bisects a pair of opposite angles.

For this parallelogram t be a rhombus, the angles with measures 2x - 40 and x + 15 must be congruent.

2x - 40 = x + 15

Subtract x from both sides.

x - 40 = 15

Add 40 to both sides.

x = 55

Answer:

Hello,

x=55

Step-by-step explanation:

The rhombus is formed of 2 isocele triangles

(since sides are equals)

The drawn diagonal  bissects the angle

x+15=2x-40

2x-x=15+40

x=55

A normal population has mean and standard deviation . (a) What proportion of the population is greater than ? (b) What is the probability that a randomly chosen value will be less than .

Answers

Answer:

0.0171

0.89158

Step-by-step explanation:

Given :

μ = 60

Standard deviation , σ = 17

The probability that a randomly chosen score is greater than 96;

P(Z > Zscore)

Zscore = (score, x - μ) / σ

Zscore = (96 - 60) / 17 = 2.118

P(Z > 2.118) = 1 - P(Z < 2.118) = 1 - 0.9829 = 0.0171

The probability that a randomly chosen score is less than 81;

P(Z < Zscore)

Zscore = (score, x - μ) / σ

Zscore = (81 - 60) / 17 = 1.235

P(Z < 1.235) = 0.89158

Last question pls help me

Answers

Answer:

Step-by-step explanation:

684 dollars

identify the function as a power function, a polynomial function, or neither.

f(x)=4(x^3)^3

Answers

Answer:7

Step-by-step explanation:7

A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 5 tables is $53. The total cost to rent 8 chairs and 3 tables is $42. What is the cost to rent each chair and each table?

Answers

Answer:

c=cost of one chair rental

t=cost of one table rental

8c+3t=42

2c+5t=53

multiply the second equation, each term on both sides, by -4

8c+3t=42

-8c-20t=-212

add the two equations

-17t=-170

divide both sides by -17

t=$10 to rent one table

substitute t=10 into either original equation

2c+5(10)=53

2c+50=53

2c=3

c=$1.50 to rent one chair

what is the slope intercept equation of the line below?

Answers

Answer:

[tex]{ \tt{slope, \: m = \frac{1 - ( - 1)}{1 - 0} }} \\m = 2 \\ y - intercept : y = mx + c \\ { \tt{1 = (2 \times 1) + c}} \\ c = - 1 \\ { \boxed{ \bf{y = 2x - 1}}}[/tex]

A group of dental researchers are testing the effects of acidic drinks on dental crowns. They have five containers of crowns labeled V, W, X, Y, and Z. They will randomly select one of the containers to be the control for the experiment by drawing one of five well-mixed slips of paper with the same labels from a hat. Which of the following is the probability model for the control container?

Answers

Answer:

[tex]\begin{array}{cccccc}{x} & {V} & {W} & {X} & {Y} & {Z} & P(x) & {0.20} & {0.20} & {0.20} & {0.20} & {0.20} \ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]S = \{V,W,X,Y,Z\}[/tex]

[tex]n(S) = 5[/tex]

Required

The probability model

To do this, we simply calculate the probability of each container.

So, we have:

[tex]P(V) = \frac{n(V)}{n(S)} = \frac{1}{5} = 0.20[/tex]

[tex]P(W) = \frac{n(W)}{n(S)} = \frac{1}{5} = 0.20[/tex]

[tex]P(X) = \frac{n(X)}{n(S)} = \frac{1}{5} = 0.20[/tex]

[tex]P(Y) = \frac{n(Y)}{n(S)} = \frac{1}{5} = 0.20[/tex]

[tex]P(Z) = \frac{n(Z)}{n(S)} = \frac{1}{5} = 0.20[/tex]

So, the probability model is:

[tex]\begin{array}{cccccc}{x} & {V} & {W} & {X} & {Y} & {Z} & P(x) & {0.20} & {0.20} & {0.20} & {0.20} & {0.20} \ \end{array}[/tex]

Answer:

answer is V=.20, W=.20, X=.20, Y=.20, X=.20

Step-by-step explanation:

A data set contains an independent and a dependent variable. Which must be true of the data set if a linear function can be used to represent the data?

The set must have a constant additive rate of change.
The set must have a constant multiplicative rate of change.
The values in the set must be positive.
The values in the set must be increasing.

Answers

9514 1404 393

Answer:

  (a) The set must have a constant additive rate of change

Step-by-step explanation:

If a linear function is suitable for representing the data, the data will demonstrate a constant slope. That is, for evenly spaced values of the independent variable, the differences of the values of the dependent variable will be constant. We can say ...

  The set must have a constant additive rate of change.

Find the equation of a line that passes through the points (2,7) and (4,6). Leave your answer in the form y = m x + c

Answers

Answer:

I think the answer would be

y = 0.5x -8

tough this might be wrong?

Step-by-step explanation:

(2, 7) ( 4,6)

to find the gradient- mx

y2-y1/ x2 - x1

chose which would be 1/ 2

if I chose (2,7) as 1 then (4, 6) as 2

mx = 6- 7/ 4-2

= -0.5x

y = -0.5x + c

substitute

6 = -0.5(4) + c

6= -2+ c

c = -8


At a store, 2 gallons of milk cost $6.
Which is the value of the ratio of dollars to gallons of milk?
0.33
per gallon
$3 per gallon

Answers

Answer:

B

Step-by-step explanation:

$3 per gallon

that is the procedure above

If a square root parent function is vertically compressed by a factor of 1/6,
what is the equation of the new function, G(x)?
O A. G(x)=1/6square root of x
B. G(x) = Square root of 6x
C. G(x) = 6 square root of x
D. G(x) = -6 square root of x

Answers

Answer:

the answer could be B i think cause that makes total sense

I think the answer is b

Which of the following best describes a type of growth that is exponential at
first but slows as the amount reaches a certain maximum value?

A. Exponential decay
B. Exponential growth
C. Linear growth
D. Logistic growth

Answers

9514 1404 393

Answer:

  D. Logistic growth

Step-by-step explanation:

The logistic growth function models a situation where the rate of growth is jointly proportional to the population and to the difference between the population and the carrying capacity.

Attached is an example of such a function.

The Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects and diseases. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5, and three others were sprayed with Action. When the grapes ripened, 390 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 420 vines sprayed with Action were checked. The results are:

Insecticide Number of Vines Checked (sample size) Number of Infested Vines
Pernod 5 390 23
Action 420 46

At the 0.05 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action?

Answers

Answer:

The p-value of the test is 0.0088 < 0.05, which means that at the 0.05 significance level, we can conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Pernod 5:

23 out of 390, so:

[tex]p_P = \frac{23}{390} = 0.059[/tex]

[tex]s_P = \sqrt{\frac{0.059*0.941}{390}} = 0.0119[/tex]

Action:

46 out of 420, so:

[tex]p_A = \frac{46}{420} = 0.1095[/tex]

[tex]s_A = \sqrt{\frac{0.1095*0.8905}{420}} = 0.0152[/tex]

Test if there is a difference in proportions:

At the null hypothesis, we test if there is not a difference, that is, the subtraction of the proportions is 0. So

[tex]H_0: p_A - p_P = 0[/tex]

At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0. So

[tex]H_1: p_A - p_P \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_A - p_P = 0.1095 - 0.059 = 0.0505[/tex]

[tex]s = \sqrt{s_A^2+s_P^2} = \sqrt{0.0119^2+0.0152^2} = 0.0193[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.0505 - 0}{0.0193}[/tex]

[tex]z = 2.62[/tex]

P-value of the test and decision:

The p-value of the test is the probability of a difference in proportions of at least 0.0505 to either side, which is P(|z| > 2.62), that is, 2 multiplied by the p-value of z = -2.62.

Looking at the z-table, z = -2.62 has a p-value of 0.0044.

2*0.0044 = 0.0088

The p-value of the test is 0.0088 < 0.05, which means that at the 0.05 significance level, we can conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action.

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