A plastic rod has been bent into a circle of radius R=8.20 cm. It has a charge Q1
​
=+4.20 pC uniformly distributed along one-quarter of its circumference and a charge Q2
​
=−6Q 1
​
uniformly distributed along the rest of the circumference (in the above figure). With V=0 at infinity, what is the electric potential at
(a) the center C of the circle and (b) point P, on the central axis of the circle at distance D=6.71 cm from the center?

The conversion of 77 f to c is equal to 25°C.

To convert temperatures in degrees Fahrenheit to Celsius, deduct 32 and multiply by .5556 ( or 5/9).

Temperatures, across the world, are measured either in Fahrenheit( the US temperature scale) or Celsius( the metric scale), two of the most popular and extensively used scales.

Temperature Conversion- Degrees Fahrenheit into Degrees Celsius.

To convert a temperature from Fahrenheit (°F) to Celsius (°C),  we can use the formula:

°C = (°F - 32) x 5/9

By applying this formula, we can convert 77 °F to Celsius as follows

°C = (77 - 32) x 5/9

°C = 45 x 5/9

°C = 25

Therefore, 77°F is equal to 25°C.

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The measures of the unknown angles are

x = 46

and

y = 88

From the question, we are to determine the measures of the unknown angles in the triangle.

From the diagram, we can observe that the triangle is an isosceles triangle as the legs of the triangle are congruent to each other.

Since the triangle is an isosceles triangle, the base angles of the triangle must be equal

The base angles are 46° and x°

Thus,

x = 46

Also,

We can write that

y° + 46° + x° = 180° (Sum of angles in a triangle)

y° + 46° + 46° = 180°

y° + 92° = 180°

y° = 180° - 92°

y° = 88°

Thus,

y = 88

Hence, x = 46 and y = 88

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A cheetah could run 630 miles in 6 hours

Answer:

It can run 630 miles in 6 hours.

Step-by-step explanation:

If the cheetah can run 105 miles per hour

then,

in 6 hours, it can run 105*6 miles.

105*6= 630

Hope this helps.

The rate of growth of the minimum wage in New York State from 1966 to 2015 is approximately 6.41%.

To determine the rate of growth of the minimum wage in New York State from 1966 to 2015, we can use the following formula:

rate of growth = ((final value / initial value)^(1/number of years) - 1) * 100%

where the initial value is the minimum wage in 1966, the final value is the minimum wage in 2015, and the number of years is the difference between the two years.

Plugging in the values, we get:

rate of growth = [tex](($8.75 / $1.25)^{1/(2015-1966)) - 1} * 100%[/tex]

= [tex]((7)^{1/49) - 1} * 100%[/tex]

=[tex](1.0641 - 1) * 100%[/tex]

= 6.41%

Therefore, the rate of growth of the minimum wage in New York State from 1966 to 2015 is approximately 6.41%.

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In the given question, the rocket will hit the ground in 7 seconds. The width of the rectangle is 3 cm. Kirk makes the wall in 5.5 hours. The student needs 97 marks.

The relation between the height and the time of the toy rocket has been given in the question as,

h = -4.9t²+33.6t + 4.9

where,

h= height of the rocket after getting launched

t= time after which the rocket has been launched

So, if we have to calculate how much time the rocket takes to reach the ground,

we have to take h=0 (at ground).

So, the equation becomes

0 = -4.9t²+33.6t + 4.9

Now, the roots of this equation will give the time at which the rocket will hit the ground.

So, after calculating we get

t = -0.1428 sec

or

t = 7 sec

since negative time is not possible,

the time at which the rocket will hit the ground is 7 seconds.

The length of the rectangle is = 5b-7 cm

Hence, the area is = b(5b-7) = 24

Hence, the width comes out to be = 3 cm

Kirk would be able to make the wall in 5.5 hours. This is because Jeff can make it one hour earlier than him i.e., K-1 hours. So, we get -

= (K-1) + K = 10

= 2K = 11

= K = 5.5 hours

The student already has 87 + 85 + 91 = 263 marks. He needs at least -

= (263 + x) / 4 = 90

= 97 marks

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Answer:

F  = (9/5)C  + 32 is a function because every Celsius temperature is associated with only one Fahrenheit temperature.

hope this helps!!

Viola has covered a horizontal distance of 199.7 meters when driving 200 meters up a hill that makes an angle of 3 degrees with the horizontal.

Viola drives 200 meters up a hill that makes an angle of 3 degrees with the horizontal. To find the horizontal distance she covered, we can use the cosine formula:

Cos(θ) = adjacent/hypotenuse

In this case, the adjacent side is the horizontal distance we are trying to find, the hypotenuse is the distance she drove (200 meters), and the angle is 3 degrees. Plugging in these values, we get:

Cos(3º) = adjacent/200

Rearranging the equation to solve for the adjacent side, we get:

adjacent = 200*cos(3)

Using a calculator, we find that cos(3) is approximately 0.9986. Multiplying this by 200 gives us:

adjacent = 199.72

Therefore, the horizontal distance that Viola covered is approximately 199.72 meters.

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The final inequality  that represents how many blankets Elle can make in her workshop would be:

3x ≤ 52 and x ≥ 16

In mathematics, an inequality is a statement that compares two values or expressions using an inequality symbol such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

An inequality indicates that one value or expression is smaller, greater, or not equal to the other value or expression.

 The inequality "y <= 10" states that the value of "y" is less than or equal to 10.

Let "x" be the number of blankets Elle can make in her workshop.

Since each blanket requires 3 ft. of material, the total amount of fleece required for "x" blankets would be 3x ft.

We know that Elle has 52 ft. of fleece in her workshop, so we can set up the inequality:

3x ≤ 52

This inequality states that the amount of fleece required for "x" blankets must be less than or equal to the amount of fleece Elle has available.

To satisfy the condition of making at least 16 blankets, we can add the requirement that "x" must be greater than or equal to 16.

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Therefore , the solution of the given problem of parallelograms comes out to be ∠y = 62 degree.

A simple square with two sets of equal intervals is referred to as a parallelogram in Euclidean geometry. The opposite ends of a parallelogram, a special type of quadrilateral, were both straight and equal. There are four distinct parallelogram types, and two of them are exclusive of one another. The four different shapes are rhombuses, equilateral triangles, triangles, and rectangles. A quadrilateral is a parallelogram if it has two pairs of parallel sides.

Here,

Given :

A  parallelogram ABCD and a triangle AED

So,

To find angle y:

∠D + 118 = 180

=> ∠D = 180 -118

=>∠D= 62 Degree

So,

According to alternate interior angle :

∠D= ∠y

=> 62 = ∠y

Thus ,∠y = 62 degree.

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the equation of the line will be 5y = 7x -7. Option c is correct.

A linear equation is an algebraic equation of the form y = mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, a linear equation that passes through the points (5,0) and (0, -7)

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept

since, slope = (y - y')/(x -x')

In our case,

slope = (-7 -0)/(0-5)

slope = 7/5

b = -7

thus,

the equation of the line will be:

y = 7/5x -7

multiply by 5 on both sides

5y = 7x -7

Therefore, the equation of the line will be 5y = 7x -7.

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The measure of each interior angle of a decagon is 144 degrees.

1. A decagon is a 10 sided polygon.

2. The sum of the interior angles of any polygon with n sides is (n - 2) * 180 degrees.

3. For a decagon, n = 10, therefore the sum of the interior angles is (10 - 2) * 180 degrees = 8 * 180 degrees = 1440 degrees.

4. Therefore, the measure of each interior angle of a decagon is 1440 degrees / 10 = 144 degrees.

The measure of each interior angle of a decagon is 144 degrees.

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The sum of all the odd integers numbering from 1 to 99 is given by th e term 2500.

S = n(a + l)/2, where S is the sum of the successive numbers, n is the number of integers, an is the first term, and l is the last term, is the formula for computing the sum of integers.

Finding the sum of odd numbers from 1 to 99

so the series become

1 + 3 + 5 + 7 + ......+ 99

So this is arithmetic series with common difference of d = 2 and first term be a = 1 and last term be 99

l = a + (n-1)d

99 = 1 + (n-1) 2

n-1 = 98/2

n-1 = 49

n = 50

We know that sum of nth term of AP

s = n/2(a + l)

s = 50/2 (1 + 99)

s = 25(100)

s = 2500

Therefore, the sum of all odd number from 1 to 99 is 2500.

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The number of mini hotdogs in the combination meal is 10.

The number of chicken wings in the combination meal is 4.

How many chicken wings and mini hotdogs were sold?

70h + 60c = 1220 equation 1

h - c = 10 equation 2

Where:

h = number of hotdogs

c = number of chicken wings

The elimination method would be used to solve the equations:

Multiply equation 1 by 70

70h - 70c = 700 equation 3

Subtract equation 3 from equation 2:

130c = 520

Divide both sides of the equation by 130

c = 520 / 130

c = 4

Substitute for c in equation 2:

h - 4 = 10

h = 10 + 4

h = 14

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Answer:

5. 2

15. 6

30. 12

Step-by-step explanation:

For every 5 miles walked, he walks for 2 hours each.

For example:

Miles. Hours

5. 2

10. 4

15. 6

20. 8

25. 10

30. 12

270 people enter the line for the escalator during" the time interval 0 < / < 300 and  80 people are at Mn Line at time 300. 414.285714 sec. is the first time that there are no people in line for the escalator and 33. 0133 time is the number of people in line minimum.

X(t) = 44 ( t/100)³ * (1-t/300)⁷

for 0≤t≤300

for t≥ 300

a) Total number of people = ∫³⁰⁰₀ r(t)*dt

∫³⁰⁰₀ 44(t/100)³ * (1-t/300)⁷ * dt

∫³⁰⁰₀ (11 (1-t/300)⁷ / 250000 * t³) * dt

∫³⁰⁰₀ -11 / 250000 * (t-300)⁷ * t³ * (1/300)⁷ dt

= -11 (1/300)⁷ / 250000 ∫³⁰⁰₀ (t-300)⁷ * t³ * dt

Now Integrate with respect to 't'

using substitution

Let  u = t-300

du = dt

∫ u⁷ * (u + 300)³ * du

∫ (u¹⁰ + 900 u⁹ +270000 u⁸ + 27000000 u⁷) * du

= u¹¹/11 + 90 u¹⁰ + 30000 u⁹ + 3375000 u⁸

Undo the substitution

u= (t-300)

= [ (t-300)¹¹ / 11 + 90 (t-300)¹⁰ + 30000(t-300)⁹ + 337500(t-300)⁸]³⁰⁰₀

Substitutes the limits

= [0- ((-300)¹¹/ 11 + 90 * (-300)¹⁰ + 30000 * (-300)⁹ + 3375000 * (-300)⁸]

= 270 people

b) Constant rate of 0.7 people per second

This is the rate of exit

at t = 0.20 people in line

People in a line at t = 300 is = 20+ ∫³⁰⁰₀ ((r(t) - 0.7 ) * dt

= 20 + ∫³⁰⁰₀ 44(t/100)³ * (1-t/300)⁷- 0.7 dt

= 20 + 270 - 0.7 * 300

= 80 people

c) t = 300 sec

people = 80

when t>300 , r(t) = 0

rate of exit remains the same

= 80 + ∫ ( 0-0.7) * dx

= 80 + [-0.7x] = 0

= 80 - [0.7x] = 0

= 80 - 0.7 t + 0.7 * 300 = 0

= 80 - 0.7t + 210 = 0

= - 0.7 t = -290

t = 414.285714 sec.

d) f(t) = 20 + ∫⁶₀ (r(x) - 0.7) * dx

f(t) = r(t) - 0.7

f(t) = 0       (for critical point)

r(x) = 44 (t/100)³ * (1-t/300)⁷

r(t) = 0

we get t= 33.0133 sec.

t = 166.575 sec.

Now check for the value

when t=0

f(t) 20

when t= 33.0133

f(t) = 3.803 ≈ 4

when t = 166.575

f(t) = 158.07 ≈ 158

when t= 300

f(t) = 80

so the minimum number of people is 4 at the time t= 33. 0133

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For the defined function  f(t)=e^rt and g(t)=e^st where r is not equal to s it was proved that the f and g are linearly independent function in F(r,r).

For the defined function f and g we have,

f(t)=e^rt

g(t)=e^st

Where r is not equal to s.

To prove f and g are linearly independent function we need,

f( t) ± g(t) = 0

Substitute the value of f(t) and g(t) we get,

⇒ e^rt ± e^st  = 0

⇒ e^rt ( 1 ± e^( s - r )t = 0

This implies ,

e^rt = 0 or ( 1 ± e^( s - r )t = 0

But e^rt is always greater than zero for all the values of r and t.

e^rt = 0 is not possible.

If ( 1 ± e^( s - r )t = 0

This is possible if and only if r = s .

Which is against the given condition.

Therefore, f(t) and g(t) are linearly independent function in f( r , r).

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The above question is incomplete, the complete question is:

Let f, g, element F(r,r) be the function defined by f(t)=e^rt and g(t)=e^st, where r cannot equal s. prove that f and g are linearly independent in F(r,r).

The blanks when completed is: If 3 = x, then x = 3

From the question, we have the following parameters that can be used in our computation:

3 = x x = 3

The above equation is an illustration of the symmetric property of equation

The symmetric property of an equation states that if one side of an equation is equal to the other side, then the other side is equal to the first side.

In other words, if we have an equation that says a = b, then we can use the symmetric property to say that b = a

Using the above as a guide, we have the following:

If 3 = x, then x = 3

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Answer:

no solution

Step-by-step explanation:

7 | y + 6 | + 3 < - 18 ( subtract 3 from both sides )

7 | y + 6 |  < - 21 ( divide both sides by 7 )

| y + 6 | > - 3

the absolute value function cannot be negative

thus the equation has no solution

The third term in the expansion of [tex](cy - 3)^{4}[/tex] is c² times greater than the third term in the expansion of [tex](y - 3)^{4}[/tex].

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.

Now in the given question ,

When c = 1, we have:

[tex](y - 3)^{4}[/tex] =[tex]y^4 - 12y^3 + 54y^2 - 108y + 81[/tex]

When c > 1, we have:

[tex](cy - 3)^4 = c^4y^4 - 12c^3y^3 + 54c^2y^2 - 108cy + 81[/tex]

Expanding [tex](y - 3)^4[/tex] and [tex](cy - 3)^4[/tex], we can see that the third term in each expansion is:

[tex]54y^2[/tex] for [tex](y - 3)^4[/tex]

[tex]54c^2y^2[/tex] for [tex](cy - 3)^4[/tex]

To compare the third terms, we divide the third term in [tex](cy - 3)^4[/tex] by the third term in [tex](y - 3)^4[/tex]:

[tex](54c^2y^2) / (54y^2) = c^2[/tex]

So the third term in the expansion of [tex](cy - 3)^4[/tex] is c² times greater than the third term in the expansion of[tex](y - 3)^4[/tex].

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Answer:

It will take him 13 Months to save up $12 a month to buy the shoes.

Hope this helps

Step-by-step explanation:

The conversion of 22 kg to lbs is 48.50164 lbs.

Kilogram (kg) and pound (lbs) are both units of mass or weight.

Kilogram is the base unit of mass in the International System of Units (SI). It is defined as the mass of the International Prototype of the Kilogram (IPK), a platinum-iridium cylinder kept at the International Bureau of Weights and Measures.

To convert 22 kilograms (kg) to pounds (lbs), we can use the conversion factor of 1 kg = 2.20462 lbs.

So, we can multiply 22 kg by 2.20462 lbs/kg to get the equivalent weight in pounds:

22 kg × 2.20462 lbs/kg = 48.50164 lbs (rounded to five decimal places)

Therefore, 22 kg is approximately equal to 48.50164 lbs.

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If y*=y1/2(y2+1) then -3(16* - 9*) = -10.5y1(y2 + 1), called polynomial.

A polynomial is an expression that consists of variables, numbers, and operations (like addition, subtraction, multiplication, and division). It is similar to a mathematical equation, but instead of an equals sign, it uses coefficients and variables in a power form. The power of a polynomial is determined by the highest power of the variables in the expression.

For example, if the polynomial is x2 + 5x + 2, then the power is 2. Polynomials are used in many areas of mathematics, such as calculus, algebra, and number theory.

If y*= y1/2(y2+1) then -3(16* - 9*)

= -3(16(y1/2(y2 + 1)) - 9(y1/2(y2 + 1)))

= -3(8y1(y2 + 1) - 4.5y1(y2 + 1))

= -3(3.5y1(y2 + 1))

= -10.5y1(y2 + 1)

In this problem, 16* is equal to 16(y1/2(y2 + 1)) and 9* is equal to 9(y1/2(y2 + 1)). When -3 is multiplied to 16* - 9*, the result is -3 times the difference of 16* and 9*. The expression then simplifies to -10.5y1(y2 + 1).

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The equation for the temperature  with respect to x minutes is

y(x)=  580 - 56x

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

The temperature at any  instant of time in minutes( x)  is given by

y(x)=  initial temperature  - (decrement rate * number of minutes)

=>  y(x)=  580 - 56x

The equation for the temperature  with respect to x minutes is

y(x)=  580 - 56x

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187 centimeter is approximately equal to 6.1351 feet

To convert 185cm to feet, we can use the following formula:

1 cm = 0.0328 feet

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The distance in feet = conversion factor × The distance in centimeter

Substitute the values in the equation

187 cm = 187 x 0.0328

Multiply the numbers

= 6.1351 feet ( rounded to four decimal places )

Therefore, 187 cm is 6.13517 feet.

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The table of values for the function f(x)=1/2 are shown as follow:

What is function?

A function is an expression or relationship that involves one or more variables. It has several inputs and outputs. Each input has a single output. The function describes how the inputs relate to the output.

The function f(x) = 1/2 is a horizontal line that crosses the y-axis at the point (0, 1/2). Since the value of f(x) is constant for all values of x, the table of values for this function will have the same output value of 1/2 for every input value of x.

The table of values for the function f(x)=1/2 are shown as follow:

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Answer:

see explanation

Step-by-step explanation:

One method of solution is given below

x² + 5 = 86 ( subtract 5 from both sides )

x² = 81 ( take the square root of both sides )

x = ± [tex]\sqrt{81}[/tex] = ± 9

To solve the equation x^2 + 5 = 86, we need to isolate the variable x on one side of the equation. We can do this by performing the opposite operations on each side of the equation.

   Subtract 5 from both sides of the equation:

   x^2 = 81

   Take the square root of both sides of the equation:

   x = ±9

Therefore, the solutions to the equation x^2 + 5 = 86 are x = 9 and x = -9.

A joint ("and") distribution summarizes the information from one variable only, without considering any information from another variable.

Joint distribution mostly is based on joint probability, which also means it can be simply defined as the probability of two events also known as variables which happen to be happening together. These two events are usually coined event A and event B, and hence can formally be written as: p (A and B).

It also can be defined as the two-way frequency table, that is, a table which displays the frequencies or “counts” for two categorical variables.

Similarly a joint probability distribution is simply the description of the probability that a given individual takes on two specific values for the variables.

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