A test charge of 5.88e-7 c experiences a northward force of 4.10e-4 n when placed a distance of 25.0 cm from a source charge. what is the strength of the electric field at this location? round to the appropriate number of sig figs and do not put your answer in scientific notation.

Answer:

y + 13 = 5(x + 2)

Step-by-step explanation:

the point is (-2 , -13)

Point slope form is: y - y1 = m(x - x1)

y1= -13

x1= -2

y - -13 = 5 (x - -2)

y +13 = 5(x+2)

We know that LM and NP are the same lengths (since they are opposite sides of the rectangle), so let's label them both as y:

d1^2 = (3x + 1)^2 + y^2

d2^2 = y^2 + (8x - 4)^2

To find the length of each diagonal of the rectangle LMNP, we can use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the longest side (the hypotenuse). Since a rectangle is a special case of a parallelogram, we know that its opposite sides are congruent, so LN = MP.

Let's label the diagonals as d1 and d2. Then, using the Pythagorean theorem, we have:

d1^2 = LN^2 + NP^2

d2^2 = LM^2 + MP^2

Since LN = MP, we can substitute 3x + 1 for LN and 8x - 4 for MP:

d1^2 = (3x + 1)^2 + NP^2

d2^2 = LM^2 + (8x - 4)^2

We know that LM and NP are the same lengths (since they are opposite sides of the rectangle), so let's label them both as y:

d1^2 = (3x + 1)^2 + y^2

d2^2 = y^2 + (8x - 4)^2

To find the values of x and y, we need more information. Without any additional information about the rectangle, we cannot solve for d1 and d2.

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Answer:

12

Step-by-step explanation:

6+2x=3x

6=x

ST=2x

ST=12

\(\textbf{Answer: }\)

\(\text{c=5}\)

\(\underline{\textbf{Skills needed: Modular arithmetic}}\)

\(\textbf{Step-by-step explanation below: }\)

1) \(\text{c is the remainder of: } -23 \div 7 \text{, but c has to be positive}\)

2) \(\text{We immediately know that 7 * -3 = -21, and that c can equal -2} \\ \text{but c has to be positive}\)

3) \(\text{Our best bet, is to add another negative 7 to 7*-3} \\ \text{This means that we are multiplying 7 by -4}\)

4) \(\text{7*-4 is -28, which means that c is 5 in this new case} \\ \text{Therefore, c is 5 }\)

5) \(\text{Hope you understand, and have a nice day!}\)

Given the average, sum, and one of a list, the greatest integer that can be on the list is 235.

The average of a data set can be obtained by adding up all the data values, then dividing by the number of data.

Information from the problem:

Sum = 350

Average = 50

xₙ = 100

          Average = sum of all data / number of data

                    50 = 350 / number of data

number of data = 350 / 50

                          = 7

To find out the greatest member on the list, we want the other numbers to be as small as possible.

As the list members should be positive integers, first we can assume the first 5 numbers are 1, 2, 3, 4, and 5; and the 6th number is 100

Sum of all data = x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇

350 = 1 + 2 + 3 + 4 + 5 + 100 + x₇

350 = 115 + x₇

x₇ = 350 - 115

   = 235

Now the list consists of 1, 2, 3, 4, 5, 100, 235. Its sum is 350 and the average is 50, which is consistent with the given problem.

Thus, the biggest number that can be on the list is 235.

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Answer:

14130 yd^3

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3

The diameter is 30 so the radius is d/2 = 30/2 = 15

V = 4/3 pi (15)^3

V = 4500 pi

Letting pi = 3.14

V = 14130 yd^3

Answer:

Last one

Step-by-step explanation:

The volume of the sphere is given by the relation:

V= \(\frac{4}{3}\) *π* 15³

V= 14137.166 yd³

wich is approximatively 14130yd³

The inequality represented by the graph is y ≥ -x + 2

A graph is a pictorial representation of data and the graph presented represents inequality data

The graph shows a linear function written in the form

y = mx +c

where slope, m calculated as

c = intercept

x = input variables

y = output variables

calculation of slope

The points used for the slope is gotten from the graph as (0. 2)  (1, 1)

m = (y₂ -y₁) / (x₂ - x₁)

substituting the values

= ( 2 - 1 ) / ( 0 - 1 )

= 1 / -1

= -1

y intercept, c this is a point where the graph cuts the y axis

c = 2

The two points result greater than or equal to written with the symbol ≥

hence the equation is

y ≥ -x + 2

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Answer:

E

Step-by-step explanation:

NO

Answer:

two solutions

Step-by-step explanation:

Any quadratic equation will always have two solutions.

Hope this helps!

Answer:

leg = 1

hypotenuse = √2 or 1.41

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find:-

Answer:-

The given equation to us is,

\(\longrightarrow -4(2p+5) + 8p = -11 \\\)

Simplify by opening the brackets,

\(\longrightarrow -8p - 20+8p = -11 \\\)

Rearrange the terms,

\(\longrightarrow (-8p + 8p ) - 20 = -11\\\)

Both the terms inside the brackets would cancel each other and the resultant will be 0 ,

\(\longrightarrow -20 = -11 \\\)

Here we arrived a contradiction, -20 is not equal to -11 .

Henceforth, the system has no solutions .

Therefore, the correct choice is option C .

Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

Answer:

SSS

Step-by-step explanation:

The equation models the median monthly cost for the rent of a one bedroom apartment in San Fransisco.

If the year 2013 can be counted as t=0

Then the next year 2014 will be t=1

And the next year, 2015, will be t=2

To determine how much less would James pay if he moved in 2014 instead of 2015, you have to calculate the median cost for both yeanrs and calculate their difference.

Median cost for 2015 (t=2)

Median cost for 2014 (t=1)

Subtract the median cost of 2014 to the median cost of 2015:

He woul have paid $250 less if he rented the place in 2014.

We can make use of a slope field to sketch the two approximate solutions of the differential equation. The slope field for the differential equation is dy/dx.

a) We will now mark the point (0,4) on the slope field as shown in the image below.

Solution 1: We will begin at the point (0, 4) and move along the slope lines to obtain the first solution. This first solution is shown in blue in the image below,

Solution 2: For the second solution, we will begin at the point (0,4) and move along the slope lines in the opposite direction to obtain the second solution. This second solution is shown in red in the image below.

Substituting x = 0 and y = 4, we get: 4 = sin(0) + C4 = 0 + CC = 4

Therefore, the particular solution is: y = sin(x) + 4

Below is the graph of the solution: Graph of y = sin(x) + 4

We can compare this graph of the particular solution with the sketches in part (a).

The graph of the solution matches the first solution in blue.

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Based on the word problem, the number is 9

This refers to the type of number that is expressed as the ratio of two integers that has a non-zero denominator.

Let the numerator be x

Let the denominator be x+2

If 5 is subtracted from the numerator

x - 5

If 5 is added to the denominator

x +2 + 5

x-5/x+7= 1/4

Cross multiply the values

It becomes

4x- 20 = x+ 7

3x= 27

x= 9

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1. The solution to the first differential equation is given by e^2yx - ysin(xy) + y^2 + C = 0, where C is an arbitrary constant.

2. The general solution to the second differential equation is x(3x - y^2) = C, where C is a positive constant.

To solve the first-order differential equations, let's solve them one by one:

1. (e^2y - ycos(xy))dx + (2xe^2y - xcos(xy) + 2y)dy = 0

We notice that the given equation is not in standard form, so let's rearrange it:

(e^2y - ycos(xy))dx + (2xe^2y - xcos(xy))dy + 2ydy = 0

Comparing this with the standard form: P(x, y)dx + Q(x, y)dy = 0, we have:

P(x, y) = e^2y - ycos(xy)

Q(x, y) = 2xe^2y - xcos(xy) + 2y

To check if this equation is exact, we can compute the partial derivatives:

∂P/∂y = 2e^2y - xcos(xy) - sin(xy)

∂Q/∂x = 2e^2y - xcos(xy) - sin(xy)

Since ∂P/∂y = ∂Q/∂x, the equation is exact.

Now, we need to find a function f(x, y) such that ∂f/∂x = P(x, y) and ∂f/∂y = Q(x, y).

Integrating P(x, y) with respect to x, treating y as a constant:

f(x, y) = ∫(e^2y - ycos(xy))dx = e^2yx - y∫cos(xy)dx = e^2yx - ysin(xy) + g(y)

Here, g(y) is an arbitrary function of y since we treated it as a constant while integrating with respect to x.

Now, differentiate f(x, y) with respect to y to find Q(x, y):

∂f/∂y = e^2x - xcos(xy) + g'(y) = Q(x, y)

Comparing the coefficients of Q(x, y), we have:

g'(y) = 2y

Integrating g'(y) with respect to y, we get:

g(y) = y^2 + C

Therefore, f(x, y) = e^2yx - ysin(xy) + y^2 + C.

The general solution to the given differential equation is:

e^2yx - ysin(xy) + y^2 + C = 0, where C is an arbitrary constant.

2. x(yy' - 3) + y^2 = 0

Let's rearrange the equation:

xyy' + y^2 - 3x = 0

To solve this equation, we'll use the substitution u = y^2, which gives du/dx = 2yy'.

Substituting these values in the equation, we have:

x(du/dx) + u - 3x = 0

Now, let's rearrange the equation:

x du/dx = 3x - u

Dividing both sides by x(3x - u), we get:

du/(3x - u) = dx/x

To integrate both sides, we use the substitution v = 3x - u, which gives dv/dx = -du/dx.

Substituting these values, we have:

-dv/v = dx/x

Integrating both sides:

-ln|v| = ln|x| + c₁

Simplifying:

ln|v| = -ln|x| + c₁

ln|x| + ln|v| = c₁

ln

|xv| = c₁

Now, substitute back v = 3x - u:

ln|x(3x - u)| = c₁

Since v = 3x - u and u = y^2, we have:

ln|x(3x - y^2)| = c₁

Taking the exponential of both sides:

x(3x - y^2) = e^(c₁)

x(3x - y^2) = C, where C = e^(c₁) is a positive constant.

This is the general solution to the given differential equation.

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In the triangle LMN angle N is 76 degree.

Given,

In the question:

There is two isosceles triangle in the figure:

Triangle JKL and Triangle LMN

Angle J = 64 degree

To find the angle Angle N

Now, According to the question:

The triangle is isosceles.

<J = 64 degrees

All triangles have 180

<JLK = 180 - 64 - 64

Angle JLK = 52degree.

Angle JLK = MLN  = 52 degree (Vertical opposite angle )

M is the left over from the 2 equal angles.

N = 180 - <M - < MLN                      

N = 180 - 52 - 52

N = 76 degree

Hence, In the triangle LMN angle N is 76 degree.

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The bearing of how far east of point G is point H is 51.68 m

Bearing is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass. It is used to describe a particular direction in which an object is traveling.

How to determine this

When point G and point H are 58 m apart

Point H is at a bearing of 63 degrees

i.e At point H = 63°

To calculate how far east of point G is to point H

When North to East is 90°

So, 90° - 63°

= 27°

x meter away from point H to the East

= cos 27° * 58 m

= 0.9114 * 58 m

= 52.86 m

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Answer:

y²(y + 3)(5y - 3)

Step-by-step explanation:

Given

5\(y^{4}\) + 12y³ - 9y² ← factor out y² from each term

= y²(5y² + 12y - 9) ← factor the quadratic

Consider the factors of the product of the y² term and the constant term which sum to give the coefficient of the y- term

product = 5 × - 9 = - 45 and sum = + 12

The factors are + 15 and - 3

Use these factors to split the y- term

5y² + 15y - 3y - 9 ( factor the first/second and third/fourth terms )

= 5y(y + 3) - 3(y + 3) ← factor out (y + 3) from each term

= (y + 3)(5y - 3), so

5y² + 12y - 9 = (y + 3)(5y - 3)

Then

5\(y^{4}\) + 12y³ - 9y² = y²(y + 3)(5y - 3) ← in factored form

In  linear equation, 60m  is the height of flagpole c .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Height/ Shadow

Shadow of the pole = 12 m

Height of the pole = x m

Tim's shadow = Height of the pole - Tim's distance

12 m - 10 m =  2 m

Tim's height = 2 m

Hence:

x/12 = 2/10

Cross Multiply

2x = 12 × 10

x = 120/2

x = 60 m

Approximately = 60m

Hence, the height of the flagpole = 60m

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Answer:

Just as one die has six outcomes and two dice have 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 216 outcomes. This idea generalizes further for more dice. If we roll n dice then there are 6n outcomes.

We can also consider the possible sums from rolling several dice. The smallest possible sum occurs when all of the dice are the smallest, or one each. This gives a sum of three when we are rolling three dice. The greatest number on a die is six, which means that the greatest possible sum occurs when all three dice are sixes. The sum of this situation is 18.

When n dice are rolled, the least possible sum is n and the greatest possible sum is 6n.

There is one possible way three dice can total 3

3 ways for 4

6 for 5

10 for 6

15 for 7

21 for 8

25 for 9

27 for 10

27 for 11

25 for 12

21 for 13

15 for 14

10 for 15

6 for 16

3 for 17

1 for 18

The recursive formula in this case is;

Arithmetic, t0=15

and tn=2.8+tn−1

where n≥1

Option A

A recursive formula is a formula that defines a sequence of values in terms of its previous values. It provides a way of defining a sequence in a compact form, with each term of the sequence depending on one or more preceding terms.

In mathematics, recursive formulas are often used to define sequences. We can see that in this sequence, the first term is 15 and the common difference is obtained by simple subtraction .

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Answer:

x=-4

y=2

Step-by-step explanation:

2x+3y=-2

3x-y=-14

y=3x+14

substitute y

2x+3(3x+14)=-2

2x+9x+42=-2

11x=-44

x=-4

y=3(-4)+14

y=-12+14

y=2

Answer:

9

Step-by-step explanation:

10

The probability of drawing two orange balls, given that at least one ball is orange, is 1/5.

There are a total of 6 possible outcomes when selecting 2 balls from the urn without replacement: (O,O), (O,B), (B,O), (B,B), (O,B), (B,O).

The event that at least one of the balls selected is orange corresponds to the outcomes (O,O), (O,B), and (B,O). The probability of this event is the sum of the probabilities of the individual outcomes:

P(at least one orange) = P(O,O) + P(O,B) + P(B,O)

To calculate the individual probabilities, we can use the formula for the number of combinations of n items taken k at a time:

C(n,k) = n! / (k! (n-k)!).

The probability of each outcome is the number of ways it can occur divided by the total number of possible outcomes:

P(O,O) = C(2,2) / C(4,2)

= 2! / (2! (2!)) / (4! / (2! (2!)))

= 1/6

P(O,B) = C(2,1) * C(2,1) / C(4,2)

= 2 * 2! / (1! (2!)) / (4! / (2! (2!)))

= 2/6

P(B,O) = P(O,B) = 2/6

So,

P(at least one orange) = 1/6 + 2/6 + 2/6

=> 5/6

And the probability that both balls are orange is:

P(both orange) = P(O,O) = 1/6.

So, the probability of drawing two orange balls, given that at least one ball is orange, is 1/5.

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Answer:

I can't see the rest of the answers, but I believe it is the first answer. Both triangles are congruent.