Rotate 180 degrees about the origin

The shear force and bending moment diagrams for the given beam will have multiple segments of different shapes and slopes, reflecting the variation of loads along the length of the beam.

To construct the shear and bending diagrams for the given beam, we need to analyze the beam for the different sections where the load is applied. We can break down the beam into five sections:

Leftmost section (0 ≤ x ≤ L/4)

Second section (L/4 < x ≤ L/2)

Third section (L/2 < x ≤ 5L/12)

Fourth section (5L/12 < x ≤ 7L/12)

Rightmost section (7L/12 < x ≤ L)

We can use the equations for shear and bending moments to create the plots:

For section 1: 0 ≤ x ≤ L/4

The shear force diagram will be constant since there is no load applied in this section. The bending moment diagram will be a sloping line, which will be zero at x = 0 and will increase linearly with x as we move toward the right end of the section.

For section 2: L/4 < x ≤ L/2

The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a maximum value at the midpoint of the section.

For section 3: L/2 < x ≤ 5L/12

The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. At x = 5L/12, a load of P/3 is added, causing the shear force to increase suddenly. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local minimum at x = 5L/12.

For section 4: 5L/12 < x ≤ 7L/12

The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local maximum at x = 7L/12.

For section 5: 7L/12 < x ≤ L

The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. At x = L/3, a load of P/3 is added, causing the shear force to decrease suddenly. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a minimum value at the midpoint of the section.

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Both calculations from part (1) and part (2) yield the same result of $0.86 for the new cost of the candy bar after 11 years.

Part 1 of 2:

The new cost of the candy bar after 11 years can be calculated by applying a 3% price increase each year to the original cost of $0.60.

To calculate the new cost after 11 years, we can use the formula:

New Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

New Cost = $0.60 * (1 + 3%)^11

        ≈ $0.60 * (1 + 0.03)^11

        ≈ $0.60 * (1.03)^11

        ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the new cost of the candy bar after 11 years is $0.86.

Part 2 of 2:

If the cost of the candy bar increased by 3% of the original cost each year for 11 years, we can calculate the final cost by multiplying the original cost by (1 + 3%) for each year.

Using the formula:

Final Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

Final Cost = $0.60 * (1 + 3%)^11

          ≈ $0.60 * (1 + 0.03)^11

          ≈ $0.60 * (1.03)^11

          ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the final cost would also be $0.86.

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Note: The complete question is - What will be the cost of the candy bar after a specific number of years if it originally sold for $.60 and undergoes a 3% price increase each year?

Approximately 17.65% of Ana's salary is withheld for taxes.

To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.

Number of hours worked per week (H) = 25 hours

Hourly wage (W) = $10

Net salary (S) = $212.50

Calculate the total earnings before taxes:

Total earnings = Hours worked * Hourly wage

Total earnings = 25 hours * $10/hour

Total earnings = $250

Determine the amount of tax withheld:

Tax withheld = Total earnings - Net salary

Tax withheld = $250 - $212.50

Tax withheld = $37.50

Calculate the percentage of salary withheld for taxes:

Percentage withheld = (Tax withheld / Net salary) * 100

Percentage withheld = ($37.50 / $212.50) * 100

Percentage withheld ≈ 17.65%

Therefore, approximately 17.65% of Ana's salary is withheld for taxes.

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Answer:

300 units

Step-by-step explanation:

Answer:

5x+x=42

6x=42

x=7

Step-by-step explanation:

Answer:

y = 5x

x + y = 42

Step-by-step explanation:

If y is 5 times greater than x, this can be represented by y = 5x

The sum of x and y is 42, so this can be represented by x + y = 42

So, the system of equations will be:

y = 5x

x + y = 42

Check the picture below.

I think you were asking how many roots does the polynomial 7+5r⁴-32² have in all

For no. of total roots of a polynomial, we notice the highest power of the variable. Here, the variable is 4, whose highest power (degree) is 4. So, the polynomial above will have 4 roots in all.

And if you're asked to calculate no. of real roots or no. of complex roots, then Rather than using The concept of derivates, you can use Descarte's Sign Rule

Let, we call the polynomial, f(r) = 7+5r⁴ - 32²

We need to write the polynomial in simplest form, if we do, we will be having;

→ f(r) = 5r⁴ - 1017

Note the sign change of each term, how many times the sign changed , like from +ve to +ve doesn't counts, +ve to -ve counts 1 and then -ve to +ve again counts 1, so no. of sign change of f(r) will give the total no. of +ve real roots

Now, replace r by -r, and do the same, notice no. of sign changes, so no. of sign change of f(-r) will give the total no. of -ve real roots

So, we will be having total no. of real roots, as the sum of those obtained in above two cases.

And, no. of complex roots will be given by Degree (highest power) - no. of real roots,as the root can only be of two natures either real or complex. If you apply Descarte's Rule in the above polynomial, you will obtain two complex and two real roots (Refer for attachment for better understanding)

The lengths of the other two sides of the right triangle are 24m and 25m, respectively.

Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we have the equation:

\(7^2 + x^2 = (x + 1)^2\)

Expanding and simplifying this equation, we get:

\(49 + x^2 = x^2 + 2x + 1\)

Now, we can cancel out \(x^2\) from both sides of the equation:

49 = 2x + 1

Next, we can isolate 2x:

2x = 49 - 1

2x = 48

Dividing both sides by 2, we find:

x = 24

Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.

Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.

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Answer: It’s angle measures

Step-by-step explanation: iready

Answer:

Purple Circle : 28.27

Yellow Circle : 43.98

Step-by-step explanation:

Radius of Purple Circle : 4.5

2 * π * 4.5 = 28.27

Radius of Yellow Circle : 7

2 * π * 7 = 43.98

Answer:

a. Yes, the lines are parallel. The rectangles create an optical illusion that makes the lines appear to be crooked.

b. Yes, the lines (3rd and 4th in diagram) are parallel. To show this is true, place two rulers or straightedges along the lines. You’ll then see that they’re parallel.

Step-by-step explanation:

PENN

Answer:

1.

a. 12° + 68° = 80 neither

b. 95°+ 85° = 180°  Supplementary angles

c.  43° + 48° = 91° neither

d.  70°+ 20° = 90°  Complimentary angles

2.

angle a = 140

angle b = 105

angle c = 60

3.

a. ∠1 = ∠AEB

b. ∠2 = ∠BEC

c. ∠3 = ∠CED

d. ∠4 = ∠DEA

4.

a. right

b. straight

c. obtuse

d. acute

5.

a. adjacent

b. adjacent

c. vertical

d. vertical

6.

a. perpendicular

b. parallel

c. neither

d. perpendicular

7.

a. Yes

b. Yes

Step-by-step explanation:

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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\( log(4 \times 3) = log(4) + log(3) = \)

\( log( {2}^{2} ) + log(3) = \)

\(2 log(2) + log(3) \)

_____________________________________________

\( log(2 \times {3}^{2} ) = \)

\( log(2) + log( {3}^{2} ) = \)

\( log(2) + 2 log(3) \)

_____________________________________________

\( log( ({x \times y})^{3} ) = \)

\( log( {x}^{3} \times {y}^{3} ) = \)

\( log( {x}^{3} ) + log( {y}^{3} ) = \)

\(3 log(x) + 3 log(y) \)

Have a great time ❤

Answer:

B and D

Step-by-step explanation:

A would be:

57 + 2j

C would be:

13-t

The answers are given below.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given:

1) 2Sin(9θ).Cos(5θ)=1/2(Sin14θ+Sin4θ)

2) Sin(3θ)Sin(5θ)Cos(3θ)Cos(5θ)=1/2(Sin8θ+Sin2θ)

3)Cos6θ+Cos4θ=2Cos5θCosθ

4)Sin(13θ/2)+Sin9θ=2Sin(11θ/2)Sinθ

5)Cosθ=2√5/5

6)Cos2θ=23/2

7)Tan(π/12)=2-√3

8)Sin(165°)=√6-√2 /4

9)Cos(5π/18)Cos(2π/9)-Sin(5π/18)Sin(2π/9)=Cos(π/2)

                                                                      =0

Hence, these are the answers .

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Answer:

Step-by-step explanation:

Oof, this question is long.

Alr,

1.

a) Time = Distance/ speed = 384000/299792.458 = 1.28 seconds

b) Time = Distance/speed = 149600000/299792.458 = 499.0 or 8.317 minutes.

2.

If the distance 4.37 light years, if we travel at the speed of light, we can reach there in 4.37 years.

so, Speed = Distance/time

Speed = 4.37 light years/100 years

Speed = 0.0437 light year/year

So, the speed would be 0.0437 x speed of light. or 13100 or 1.31 x 10⁴.

Answer:

19.135

Step-by-step explanation:

Triangle = 1/2 b h

1/2 x 8.9 x 4.3 = 19.135

Answer:

Slope is 1/5
y intercept is (0,0)

The fraction of the money the youngest boy does get is 5x/22.

Given that, three brothers share some money. The oldest 5/11 of the money.

Let the total money be x.

Share of oldest boy = 5/11 ×x

= 5x/11

Remainder = x-5x/11

Remainder = 6x/11

The next boy gets 7/12 of the remainder.

Share of next boy = 7/12 × 6x/11

= 7x/22

Share of youngest boy = 6x/11 - 7x/22

= (12x-7x)/22

= 5x/22

Therefore, the fraction of the money the youngest boy does get is 5x/22.

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Answer:

f(x) = -3x+60

Step-by-step explanation:

For the slope of the function:

For the intercept of the function:

Therefore:

f(x) = -3x+60

Answer:

c

Step-by-step explanation:

The volume of the two prisms compares that the volume of prism B will double.

We are given that side length of the cube measured 18 inches in length. She built another prism (Prism B) with the same dimensions as the cube, except she doubled its height.

When the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is same as its base, then its volume is:

V = B x h

So, the volume of the two prism A= V = B x h

V = 18 x h = 18h

the volume of the two prism B= V = B x h

V = 18 x 2h = 36h

So, the volume of prism B will double thus the correct option is B.

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The complete question is;

Anna built a prism (Prism A) out of a cube of wood. The side length of the cube measured 18 inches in length. Anna built another prism (Prism B) with the same dimensions as the cube, except she doubled its height.

How does the volume of the two prisms compare?

The volume of prism B will triple.

The volume of prism B will double.

The volume of prism B will decrease.

The volume of prism B will be cut in half.

Answer:

The sample mean birth weight for the 195 boys is 3.04 kilograms and the sample standard deviation is 0.71 kilograms.

Step-by-step explanation:

The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.

From the information, we are told to convert 2 litres into ml. This will be:

= 1000 × 2

= 2000ml

The number of eggs that will be bought to make 500 muffins will be:

= 500 × 2

= 1000 eggs.

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Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).

Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.

90 students are in a club and play a sport.

140 total students play a sport.

Therefore, 140 - 90 = 50 students play a sport but are not in a club.

The total number of students who play a sport is 140 + 50 = 190.

200 total students are in a club.

Therefore, 200 - 90 = 110 students are in a club but do not play a sport.

The total number of students who do not play a sport is 325 - 190 = 135.

The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.

This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.

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Answer:

5

Step-by-step explanation:

in a 45 45 90 triangle the 2 equal smaller sides (a) are the same and the hyp is a√2

Answer:

\(\boxed{\sf \ \ x=-2, \ y=-3 \ \ }\)

Step-by-step explanation:

Hello,

I assume that you want to solve this system of two equations

   (1) 5x - y  = -7

   (2) 4x + 2y = -14

We will multiply (1) by 2 and add to (2) so that we can eliminate the terms in y

2*(1)+(2) gives

   10x - 2y + 4x + 2y = -7*2 -14 = -14 - 14 = -28

   <=>

   14x = - 28 we can divide by 14 both parts

   x = -28/14 = -2

and then we replace x in (1)

   5*(-2)-y=-7

   -10-y=-7 add 7

   -10-y+7=0

   -3-y=0 add y

   -3 = y

which is equivalent to y = -3

do not hesitate if you have any question

Answer:

x = -2, y = -3

Step-by-step explanation:

5x - y = -7

4x + 2y = – 14

Multiply the first equation by 2

2(5x - y) = 2*-7

10x -2y = -14

Add this to the second equation to eliminate y

10x -2y = -14

4x + 2y = – 14

---------------------------

14x = -28

Divide by 14

14x/14 = -28/14

x = -2

Now find y

4x+2y = -14

4*-2 +2y = -14

-8+2y = -14

Add 8 to each side

2y = -6

Divide by 2

2y/2 = -6/2

y = -3

The values of the two integers are -43 and -143.

Let the value of the smaller integer be "x".

Since, the sum of two integers is -186.

Smaller integer + Larger integer = -186

x + ( 3x - 14 ) = -186

Solve for x

x + 3x - 14 = -186

4x - 14 = -186

4x = -186 + 14

4x = -172

x = -172/4

x = -43

Hence;

The smaller integer = x = -43

The largere integer = 3x - 14 = 3(-43) - 14 = -143.

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Answer: $13.45

Step-by-step explanation:

1. 48.85 + 4.95 = 53.8

2. 53.8/4 = 13.45

3. Shrimp basket = $13.45