Two point charges of equal magnitude are7.5 cm apart. At the midpoint of the line
connecting them, their combined electric field
has magnitude of 45 N/C. Find the magnitude
of the charges.

Answers

Answer 1

Answer: q 1 = q 2 = Q
E = k * Q / r²
The combined electric field:
E = 2 * k * Q / r²
k = 9 · 10^9 Nm²/C²
r = 0.075 : 2 = 0.0375 m
45 N/C = 2 · 9 · 10^9 · Q / 0.0375²
45 = 18 · 10 ^9 Q / 0.0014062
Q = 45 · 0.0014062 / 18 · 10^9
Q = 0.003515 · 10^(-9) C
Q = 3.5155 · 10 ^ (-12) C = 3.5155 pC

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Find the first five terms of the sequence defined by each of these recurrencerelations and initial conditions.
a) an = 6an-1, a0 = 2
b) an = −2an-1, a0 = −1
c) an = an-1 – an-2, a0 = 2, a1 = −1

Answers

a) The first five terms of the sequence are 2, 12, 72, 432, 2592.
b) The first five terms of the sequence are -1, 2, -4, 8, -16.

c) The first five terms of the sequence are 2, -1, -3, -2, 1.

To find the first five terms of the sequence defined by each of these recurrence relations and initial conditions, we will use the given recurrence relation and initial conditions to find the next terms in the sequence.

a) an = 6an-1, a0 = 2

The first term is given as a0 = 2. We will use the recurrence relation to find the next terms.
a1 = 6a0 = 6(2) = 12
a2 = 6a1 = 6(12) = 72
a3 = 6a2 = 6(72) = 432
a4 = 6a3 = 6(432) = 2592

So, the first five terms of the sequence are 2, 12, 72, 432, 2592.

b) an = −2an-1, a0 = −1

The first term is given as a0 = -1. We will use the recurrence relation to find the next terms.
a1 = -2a0 = -2(-1) = 2
a2 = -2a1 = -2(2) = -4
a3 = -2a2 = -2(-4) = 8
a4 = -2a3 = -2(8) = -16

So, the first five terms of the sequence are -1, 2, -4, 8, -16.

c) an = an-1 – an-2, a0 = 2, a1 = −1

The first two terms are given as a0 = 2 and a1 = -1. We will use the recurrence relation to find the next terms.
a2 = a1 - a0 = -1 - 2 = -3
a3 = a2 - a1 = -3 - (-1) = -2
a4 = a3 - a2 = -2 - (-3) = 1

So, the first five terms of the sequence are 2, -1, -3, -2, 1.

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A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sandwiches cost $7.75 each and the soups cost $4.50 each. If the total cost of all 18 lunches was $113.50, how many sandwiches were ordered? A. 7
B. 8
C. 9
D. 10

Answers

Let a be the number of soups ordered and b be the number of sandwiches ordered. We know that, a + b = 18, so a = 18 - b. Now we form an equation for the total cost, which is: 4.5a + 7.75b = 113.5. Now, we substitute the value of a into the cost equation to form a single equation in terms of b, number of sandwiches, only. 4.5(18 - b) + 7.75b = 113.5. Solving for b, we get b = 10. Therefore, the answer is D.

What is the surface area of the figure?Solid Figures, Part 1

A.300 cm2

B.220 cm2

C.390 cm2

D.195 cm2

Answers

What is the surface area of the figure?Solid Figures, Part 1

A.300 cm2

B.220 cm2

C.390 cm2

D.195 cm2

The surface area of the figure is 220 cm2. The answer is letter B.

"2.3 U is the set of cities in a country.A is the set of cities that have a zoo.
B is the set of cities that have a symphony.
Describe A ∩ B′ in words."

Answers

A ∩ B is the subset of cities that have both a zoo and a symphony

Final answer:

'A ∩ B′' in a set theory context represents the set of cities that have a zoo and do not have a symphony.

Explanation:

In the field of mathematics, particularly in set theory, the notation A ∩ B′ refers to the intersection of two sets. The 'A' represents the set of cities with a zoo, and 'B' is the set of cities with a symphony. The symbol '∩' stands for intersection and 'B′' stands for the complement of B, or in other words, cities that do not have a symphony.

Therefore, A ∩ B′ represents the set of cities that have a zoo and do not have a symphony. This would be the common elements of these two particular sets - cities with a zoo (set A) and cities without a symphony (complement of set B).