Write an integer for the following situation a gain of 20 pounds

Answer:

Step-by-step explanation:

Answer:

[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]

Step-by-step explanation:

We begin with the integral [tex]\int{sin^2(x)cos(3x)} \, dx[/tex]

First, we can apply the power reducing formula to [tex]sin^2(x)[/tex]

This formula states: [tex]sin^2(x)=\frac{1}{2} -\frac{1}{2} cos(2x)[/tex]

This gives us

[tex]\int{(\frac{1}{2} -\frac{1}{2} cos(2x))(cos(3x)} \, dx \\\\\int{(\frac{1}{2}cos(3x) -(\frac{1}{2} cos(2x)cos(3x)} \, dx \\\\\frac{1}{2} \int{cos(3x)} \, dx -\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]

Now, we can use integrate the first integral

[tex]\frac{1}{2} \int{cos(3x)} \, dx\\u=3x\\du=3dx\\\\\frac{1}{6} \int{3cos(u)} \, du\\\\\frac{1}{6} sin(u)+C\\\\\frac{1}{6} sin(3x)+C[/tex]

And now we can begin to integrate the second

[tex]-\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]

To integrate this, we need to use the Product-to-sum formula, which states

[tex]cos(\alpha )cos(\beta )=\frac{1}{2} [cos(\alpha +\beta )+cos(\alpha -\beta )[/tex] . For this formula, we will use [tex]\alpha =3x\\\beta =2x[/tex]

This gives us

[tex]-\frac{1}{2} \int{\frac{1}{2}[cos(5x)+cos(x)] } \, dx \\\\-\frac{1}{4} \int{[cos(5x)+cos(x)] } \, dx\\\\-\frac{1}{4}\int{cos(5x)} \, dx -\frac{1}{4}\int{cos(x)} \, dx[/tex]

We can then use the same process of u-substitution as the previous to get the answer of [tex]-\frac{1}{20} sin(5x)-\frac{1}{4} sin(x)+C[/tex]

Lastly, we can add the values of the two integrals together to give us the final solution of

[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]

Answer: Two lines of equal length

A point equidistant from two end points

Step-by-step explanation:

The mid - point of a line segment  is the point on the segment that is equidistant from the endpoints.

It is not equidistant to all point on the segment , it is only equidistant from the endpoints.

With this , the first option is out.

The midpoint of a line divides the line into two equal part , so the second option holds and the third option holds too.

Answer:

y=-1/3x+5/2

Step-by-step explanation:

Slope intercept form makes this a breeze. Essentially, just plug these values into the following formula:

y = [SLOPE]x + [Y-INTERCEPT]

Answer:

y=-1/3x+5/2

Hope this helps

Answer:

see the explanation

Step-by-step explanation:

we know that

The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

Remember that if two triangles are congruent, then its corresponding angles and its corresponding sides are congruent

In this problem

PO≅SO ----> given problem

NO≅TO ----> because O is the midpoint NT

∠PON≅∠SOT -----> by vertical angles

so

two sides and the included angle of triangle PON are congruent to two sides and the included angle of triangle SOT

therefore

Triangles PON and SOT are congruent by SAS

hence

∠N≅∠T ----> by definition of congruence (corresponding angles are congruent)

Answer:

[tex]y=-4x-8[/tex]

Step-by-step explanation:

we know that

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

so

1) Find the slope of the given line [tex]y=10-4x[/tex]

The slope is [tex]m=-4[/tex]

2) Find the y-intercept of the given line  [tex]y=-9x-8[/tex]

The y-intercept is [tex]b=-8[/tex]

therefore

The equation of the line with

[tex]m=-4[/tex]

[tex]b=-8[/tex]

is equal to

[tex]y=-4x-8[/tex]

Answer:

The are certain things that need to be carefully observed when you add or combine the polynomials. Here is the list of certain rules for adding/combining polynomials.

Step-by-step explanation:

The are certain things that need to be carefully observed when you add or combine the polynomials - especially the polynomials with more than one variable.

Here are some of the rules for adding polynomials:

Lets add and simplify the following polynomials.

(4x + 7y) + (5x – 3y)

4x + 7y + 5x – 3y

4x + 5x + 7y - 3y

9x + 4y

So, 9x + 4y is the answer.

Note: I can not further combine or add 9x + 4y as they are un-like. The reason is simple; un-like polynomials have different variables.

The polynomials can be add vertically too.

Here is the vertical method of adding (4x + 7y) and (5x – 3y) .

4x    +7y

5x     -3y

________

9x + 4y

________

Keywords: add, combine, polynomials

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Answer:

The speed of slower car is 55 miles per hour.

Step-by-step explanation:

Given as :

The speed of slower car = [tex]s_2[/tex] = s  mph

The speed of faster car = [tex]s_1[/tex] = ( s + 20 ) mph

The distance cover by slower car = [tex]d_2[/tex] = 165 miles

The distance cover by faster car = [tex]d_1[/tex] = 225 miles

The time taken by both cars for travelling = t hours

The speed of the cars remains constant

Now, According to question

∵ Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]

So, For slower car

t = [tex]\dfrac{d_2}{s_2}[/tex]

Or, t = [tex]\dfrac{165}{s}[/tex]           ............1

So, For faster car

t = [tex]\dfrac{d_1}{s_1}[/tex]

Or, t = [tex]\dfrac{225}{s+20}[/tex]           ............2

Now, equating both the equations

I.e  [tex]\dfrac{225}{s+20}[/tex] = [tex]\dfrac{165}{s}[/tex]  

By cross multiplying

Or, 225 × s = 165 × (s + 20)

Or, 225 s = 165 s + 3300

Or, 225 s - 165 s = 3300

Or, 60 s = 3300

∴  s = [tex]\dfrac{3300}{60}[/tex]

I.e s = 55 miles per hour

So , The speed of slower car = [tex]s_2[/tex] = s = 55 miles per hour

Hence , The speed of slower car is 55 miles per hour.  Answer

Answer: 34

Step-by-step explanation:

The average rate of change of f(x)= x³-9x in interval [1,6] is 34.

If f(x) is a function the [a,b] is interval then the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Given the function is f(x)= x³-9x and the interval is [1,6].

then first we have to find the value of f(1) and f(6).

So  

f(1) = (1)³-9(1)

    = 1-9

    = -8

and

f(6) = (6)³-9(6)

    = 216- 54

    = 162

therefore average rate of change of f is

[tex]\frac{f(6)-f(1)}{6-1}= \frac{162+8}{6-1}[/tex]

              = 170/5

              = 34

Hence the average rate of change of f is 34.

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Answer:

The amount invested at 9% was $3,200 and the amount invested at 13.5% was $1,800

Step-by-step explanation:

Let

x ----> the amount invested at 9% (first fund)

5,000-x ----> the amount invested at 13.5% (second fund)

Remember that

[tex]9\%=9/100=0.09[/tex]

[tex]13.5\%=13.5/100=0.135[/tex]

The total interest earned is equal to

[tex]\$5,531-\$5,000=\$531[/tex]

we know that

The amount earned by the first fund at 9% plus the amount earned by the second fund at 13.5% must be equal to $531

so

the linear equation that represent this situation is equal to

[tex]0.09x+0.135(5,000-x)=531[/tex]

solve for x

[tex]0.09x+675-0.135x=531[/tex]

[tex]0.135x-0.09x=675-531[/tex]

[tex]0.045x=144[/tex]

[tex]x=\$3,200[/tex]

so

[tex]\$5,000-x=\$5,000-\$3,200=\$1,800[/tex]

therefore

The amount invested at 9% was $3,200 and the amount invested at 13.5% was $1,800

Answer:

length = x + 5

Step-by-step explanation:

Given

area = x² + 8x + 15 and area = length × width

We require to factorise x² + 8x + 15

Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)

The factors are + 5 and + 3, since

5 × 3 = 15 and 5 + 3 = 8, thus

x² + 8x + 15 = (x + 5)(x + 3)

x + 3 is the width, thus x + 5 is the length

To find the solution to the given equation y = -3x - 4 from the provided pairs, substitute the values and solve, giving the solution as (0,-2).

The given equation is y = -3x - 4.

To find which ordered pair is a solution, substitute the given pairs into the equation and check:

(1,0): y = -3(1) - 4 = -3 - 4 = -7

(0,-2): y = -3(0) - 4 = -4

(13,-3): y = -3(13) - 4 = -39 - 4 = -43

Therefore, the ordered pair that is a solution of the equation is (0,-2).

Answer:

3/2

Step-by-step explanation:

(3/4)/(1/2)=(3/4)(2/1)=6/4=3/2

Answer: in decimal form it is 0.375

Step-by-step explanation:

Answer:

l-5l < l-6l

Step-by-step explanation:

the absolute will remove the negative of both numbers

Answer: |−5| < |−6|

Step-by-step explanation:

The function of the absolute symbol is to cancel out negative , considering the values one after the other.

/ - 6/ < 5  is the same as 6 < 5 ....... this is not true

(ii) /-6/ < /5/ is the same as 6 < 5 ..... this is not true

(iii) /-5/ < / -6/ is the same as 5 < 6 ...... this is true

(iv) /-5/ < -6 is the same as 5 < -6 ..... this is not true

bisect = to cut into two equal halves.

so from that theorem Juan used we can derive that once both diagonals bisect each other, the halves of AO = OC and DO = OB.

Answer:

The zeros are 4, -6, and 1.

Step-by-step explanation:

Given f(x) = x³ + x² - 26x + 24

(x - 4) is a factor of f(x). That means it is a zero of f(x).

To find the remaining factors algebraically, we take out the factor (x - 4) from f(x).

That is, [tex]$ f(x) = x^3 + x^2 - 26x + 24 $[/tex]

[tex]$ \implies x^3 - 4x^2 + 5x^2 - 20x - 6x + 24 $[/tex]

Taking [tex]$ x^2 $[/tex] out, we have:

[tex]$ = x^2(x^2 - 4) + 5x(x - 4) - 6(x - 4) $[/tex]

Taking (x - 4) common out, we have:

[tex]$ = (x - 4) \{x^2 + 5x - 6\} $[/tex]

[tex]$ = (x - 4)(x^2 + 6x - x - 6) $[/tex]

[tex]$ = (x - 4)\{x(x + 6) -1(x + 6)\} $[/tex]

[tex]$ = (x - 4)(x + 6)(x - 1) $[/tex]

This means the zeros are 4, -6, & 1.

Answer:

perimeter of the shaded region = 88 +44+28 =160 cm

Step-by-step explanation:

perimeter of shaded region = length AO + arc OB + arc AB

length AO = radius of bigger circle

radius of bigger circle = OX + OB = 2×radius of smaller circle = 2×14 cm = 28 cm

therefore AO = 28 cm

length of arc oB= half of circumference of smaller circle = [tex]\pi[/tex]×14 = 44 cm

length of arc ab = half of circumference of bigger circle  = [tex]\pi[/tex]×28 =[tex]\frac{22}{7}[/tex]×28= 88

therefore perimeter of the shaded region = 88 +44+28 =160 cm

area of the shaded region = half of area of bigger circle - half of area of smaller circle

                                           =[tex]\frac{1}{2} \pi 28^{2} -\frac{1}{2} \pi 14^{2}[/tex]

                                           =[tex]\frac{\pi }{2} (28^{2} -14^{2} )[/tex]

  solving we gen area of shaded region = 924

Answer:

x=-3

Step-by-step explanation:

2x+7=4+x

2x-x+7=4

x+7=4

x=4-7

x=-3

Answer:

Speed of Plane = 600 miles per hour

Speed of Wind = 150 miles per hour

Step-by-step explanation:

The distance equation is D = RT

Where

D is the distance

R is the rate

T is the time

Let rate of airplane be "x" and rate of wind be "c"

Also, note:  rate with wind is airplane's and wind's, so that would be "x + c"

and rate against the wind is airplane's minus the wind's, so that would be "x - c"

Now,

2250 miles with wind takes 3 hours, so we can write:

D = RT

2250 = (x + c)(3)

and

2250 miles against the wind takes 5 hours, we can write:

D = RT

2250 = (x - c)(5)

Simplifying 1st equation:

[tex]2250 = (x + c)(3)\\3x+3c=2250[/tex]

Simplifying 2nd equation:

[tex]2250 = (x - c)(5)\\5x -5c=2250[/tex]

Multiplying the 1st equation by 5, gives us:

[tex]5*[3x+3c]=2250\\15x+15c=11250[/tex]

Multiplying the 2nd equation by 3 gives us:

[tex]3*[5x -5c=2250]\\15x-15c=6750[/tex]

Adding up these 2 equations, we solve for x. Shown below:

[tex]15x+15c=11250\\15x-15c=6750\\---------\\30x=18000\\x=600[/tex]

Now putting this value of x into original 1st equation, we solve for c:

[tex]3x+3c=2250\\3(600)+3c=2250\\1800+3c=2250\\3c=450\\c=150[/tex]

Speed of Plane = 600 miles per hour

Speed of Wind = 150 miles per hour

This looks confusing. Can you try reposting this to make it look clear?

Answer:

 x = 4/3

Step-by-step explanation:

x = amount of flour

 x =  amount of milk / 2.5

 x =(3 1/3) / 2.5

 change both to improper fractions

 x = 10/3 / (5/2)

  invert and mutiply

 x = 10/3 * 2/5

Answer:45%

Step-by-step explanation:

I believe it’s 45%

Divide 86.4 by 192 and multiply the result by 100 to get the percentage, hence it is 45%.

A figure or ratio that may be stated as a fraction of 100 is a percentage.

If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.

Here we have to find:

86.4 is what percent of 192

Divide 86.4 by 192:

86.4 / 192 = 0.45

Multiply the result by 100 to convert it into a percentage,

Therefore,

0.45 x 100 = 45%

Hence,

86.4 is 45 percent of 192.

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Answer:

The scale is [tex]\frac{1}{60}[/tex]

Step-by-step explanation:

The correct question is

An artist is making a mural by reproducing a painting at a different scale. the original painting is 10 1/2 inches long and 4 inches wide. the mural will cover an entire wall that is 52.5 feet long and 20 feet wide. what will be the scale that relates to the original painting to the mural?

we know that

To find out the scale divide the measure of the original painting by the measure of the mural

so

Long

[tex]\frac{10.5}{52.5}\ \frac{in}{ft}[/tex]

Remember that

[tex]1\ ft=12\ in[/tex]

Convert feet to inches

[tex]\frac{10.5}{52.5*12}=\frac{10.5}{630}\ \frac{in}{in}=\frac{10.5}{630}[/tex]

simplify

[tex]\frac{1}{60}[/tex]

That means ----> 1 unit in the original painting represent 60 units in the mural

Verify the scale with the wide (both scale must be equals)

wide

[tex]\frac{4}{20}\ \frac{in}{ft}[/tex]

Remember that

[tex]1\ ft=12\ in[/tex]

Convert feet to inches

[tex]\frac{4}{20*12}=\frac{4}{240}\ \frac{in}{in}=\frac{4}{240}[/tex]

simplify

[tex]\frac{1}{60}[/tex]

That means ----> 1 unit in the original painting represent 60 units in the mural

Answer:

Rose is 34.

Anne is 14.

Step-by-step explanation:

Let rose be x years age now and anne be y years old now. Then:

x + 6 = 2 (y + 6)

x - 4 = 3(y - 4)

Subtracting:

6 - -4 =  2y + 12 - (3y - 12)

10 = - y + 24

-y = -14

y = 14

Substituting for y:

x + 6 = 2(14+6)

x = 40 - 6 = 34.

Answer:

42÷227=42/227

Step-by-step explanation:

Answer:

0.185

Step-by-step explanation:

Do the long division.

Answer:

13/20 of her money was spent.

Step-by-step explanation:

To find the answer you have to add these two fractions together, and to do that you must find a common denominator.

For this problem I chose to use 20 for the denominator since it is the smallest number that both 4 and 5 have in common.

Keep in mind that, whatever you do to the denominator, you must also do to the numerator, so if you multiply 5 by 4, you must also multiply 2 by 4.

5/20 + 8/20 = 13/20

Answer:

The lateral Area of a cube [tex]= 17.64in^{2}[/tex]

Step-by-step explanation:

In Mathematics Geometry, the lateral surface of a solid object like cube would be the face of the sold on its side, excluding base. Meaning, any surface, apart from base, would be included to determine the lateral surface of the solid.

A cube has six sides - also called faces.

A cube has a base i.e. the bottom side of the cube, and an ant-bottom base i.e. the top side of the cube.

So, lateral area of a cube would exclude both bottom side base and anti-bottom side base. In other words, it is the area of all the sides of the object, excluding the area of its base and top.

Hence, lateral area of a cube is the square of all the remaining four sides of the object, excluding the area of its base and top.

Hence, the lateral area of a cube can be calculated by the formula:

Lateral Area of a cube [tex]= 4s^{2}[/tex], where s is the length of one edge.

So,

As the given length of edge = s = 2.1

So,

lateral Area of a cube [tex]= 4s^{2}[/tex]

                                     [tex]= 4(2.1)^{2}[/tex]

                                     [tex]= 17.64in^{2}[/tex]

Keywords: cube, lateral area

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Answer:

b 21%

Step-by-step explanation:

good luck and hurry :)

The given 22 teachers from the total of 104 teachers in the survey gives

the teachers who teach math and not English as approximately; 21%

The relative frequency table is presented as follows;

[tex]\begin{tabular}{|c|c|c|c|}&English&Not english & Total\\Math&34&22&56\\Not math&40&8&48\\Total&74&30&104\end{array}\right][/tex]

Required:

The joint relative frequency for teachers teaching math and not English

Solution:

The joint relative frequency is the ratio of the frequency of a given category to the total number of data points within the category.

The number of teachers that teach math but not English = 22

Total number of teachers in the survey = 104

Therefore;

[tex]The \ joint \ relative \ frequency = \dfrac{22}{104} \times 100\approx \mathbf{21\%}[/tex]

Therefore;

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Answer:

[tex]\frac{8}{17}[/tex]

Step-by-step explanation:

The total length of CF is 17 units and the length of DE is 8 units, so the probability of p being on DE is [tex]\frac{8}{17}[/tex]

Answer:

8/17 is correct.

Step-by-step explanation:

Answer:

115.1

Step-by-step explanation: