Rendell cycles 42 km at an average speed of 18 km/hr. Find the time taken, giving your

The Naturally Made Bath and Body store pays $550 a month for rent and utilities. The average cost for its products to be manufac

Oksi-84 [34.3K]

The break-even point occurs when the cost function equals the revenue function: 550 + 3.00x = 5.50x
Naturally Made needs to sell 220 products to break even
The cost or revenue when it sells the break-even number of products will be $1,210

4 0

2 years ago

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Write the coordinates of the vertices after a rotation of 180 degrees counterclockwise around the origin.

Umnica [9.8K]

90 degrees you are looking to your side

180 degrees you are looking behind you

around origin of 0,0

the image is flipped into the negative world if it is in posiitve or vice versa

8 0

2 years ago

The box plot summarizes the number of people enrolling in fitness classes each month during one year at the city gym. The mean o

FrozenT [24]

Answer:

first blank: mean

second blank: greater than

third blank: increased

fourth blank: greater than

Step-by-step explanation:

I can't see the options in each blank, even though I completed them with reasonable options.

The MAD of a set of data is the average distance between each data value and the mean. 400 is further than the mean than the MAD. This, increases the variability of the originally data set. As a consequence, the inclusion of 400 will result in a greater MAD

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1 year ago

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Evaluate the series shown. Then write an equivalent series using summation notation such that the lower index starts at 0.

Vitek1552 [10]

The summation indicates the sum from n = 1 to n = 3 of the expression 2(n+5).

2 (n+5) = 2n + 10

2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.

For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16

So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42

Sum of an Arithmetic Series can also be written as:

$S_{n} = \frac{n}{2}(2a_{1} +(n-1)d)$

Using the value of a₁ and d, we can simplify the expression as:

$S_{n} = \frac{n}{2} (24+2(n-1)) \\ \\ 
 S_{n} =n (12+(n-1))\\ \\ 
 S_{n} =n (11+n)$

This expression is equivalent to the given expression and will yield the same result.

For n=3, we get the sum as:

S₃ = 3(11+3) = 42

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2 years ago

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Part A What is the electric field at the position (x1,y1)=(5.0 cm , 0 cm) in component form? Express your answer in terms of the

erik [133]

The complete Question is

A −12 nC charge is located at (x, y)=(1.0 cm, 0 cm).

Part A) What is the electric field at the position (x1, y1)=(5.0 cm, 0 cm) in component form?

Part B) What is the electric field at the position (x2, y2)=(−5.0 cm, 0 cm) in component form?

Part C) What is the electric field at the position (x3, y3)=(0 cm, 5.0 cm) in component form?

Express your answer in terms of the unit vectors i^ and j^. Use the 'unit vector' button to denote unit vectors in your answer.

Answer:

A) E = - 67500i + 0j N/C

B) E = 30000i + 0j N/C

C) E = 8143.18i - -40715.66j N/C

Step-by-step explanation:

Part A)

Magnitude of the charge = Q = -12 nC = $-12 \times 10^{-9}$ C

Since, its the negative charge, the direction of Electric Field lines will be directed toward the charge

Location of the charge = (1, 0)

We need to find the electric field at point (5, 0)

The formula for the magnitude of electric field due to a point charge is:

$E=\frac{kQ}{r^{2}}$

Here,

k = Coulomb's Law Constant = $9 \times 10^{9}$

Q = Magnitude of the charge

r = Distance between the charge and the point where we need to find the value of E

We can find r by using the Distance Formula.

So,

$r=\sqrt{(5-1)^{2}+(0-0)^{2}}=4$ cm = 0.04 m

Using these values in the formula, we get:

$E=\frac{9\times 10^{9} \times 12 \times 10^{-9}}{(0.04)^{2}}= 67500$ N/C

Since, two point (5, 0) is to the right of the given charge (as shown in the first image) i.e. in horizontal direction, all of the electric field experienced by it will be in horizontal direction and the vertical component would be zero. Also the direction of Electric field will be towards the charge i.e. in left direction so the x-component of Electric field will be negative.

Thus, we can write the value of E in vector form to be:

E = - 67500i + 0j N/C

Part B)

We need to find the Electric Field at point (-5, 0)

Using the similar procedure as used in the previous step, first we find r:

$r=\sqrt{(-5-1)^{2}+(0-0)^{2}}=6$ cm = 0.06

Using the values in the formula of Electric field, we get:

$E = \frac{9 \times 10^{9} \times 12 \times 10^{-9}}{(0.06)^2}=30000$ N/C

In this case again, the point is located in a horizontal direction to the given charge, so all the Electric Field experienced by it will be in horizontal direction and the vertical component will be zero. The direction of Electric field will be towards the charge i.e towards Right, so the x-component will be positive in this case.

So, value of the electric field in component form would be:

E = 30000i + 0j N/C

Part C)

We need to find the value of electric field at the point (0, 5). First we find the value of r:

$r=\sqrt{(1-0)^2+(0-5)^2}=\sqrt{26}=5.1$ cm = 0.051 m

Using the values in the formula of E, we get:

$E=\frac{kQ}{r^{2}}=\frac{9 \times 10^{9} \times 12 \times 10^{-9}}{(0.051)^{2}}=41522$ N/C

The point (0, 5) is neither exactly to the left or exactly up. So, for this point we need to find both the horizontal and vertical components as shown in the 2nd figure below.

From the triangle, we have the opposite and adjacent side to the angle, so using the tangent we can find the value of angle theta.

$tan(\theta)=\frac{5}{1}\\\theta=tan^{-1}(5)=78.69$

The two angles shown in the figure will be equal as there are alternate interior angles. Now the angle which E will make with positive x-axis will lie in the 4th quadrant as it lies below the horizontal line. So, the angle with positive x-axis would be:

360 - 78.69 = 281.31 degrees

Ex = E cos(θ) = 41522 cos(281.31) = 8143.18 N/C

Ey = E sin(θ) = 41522 sin(281.31) = -40715.66 N/C

So, in component form the Electric field will be:

E = 8143.18<em>i</em> - -40715.66<em>j</em>

3 0

2 years ago