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2 years ago

Solve the equation for the bold variable

Mathematics

1 answer:

evablogger [386]2 years ago

4 0

The answer to problem 14 is the equation c = 3i/e

To get this answer, you multiply both sides by 3 to undo the division of 3. Also, you divide both sides by 'e' to undo the multiplication of 'e'.

So it would look something like this

i = ec/3

3*i = 3*ec/3 ... multiply both sides by 3

3*i = ec

ec = 3i

ec/e = 3i/e ... divide both sides by e

c = 3i/e

==============================================

Problem 15)

P = 2L + 2W

2L + 2W = P

2L + 2W-2L = P-2L ... subtract 2L from both sides

2W = P-2L

2W/2 = (P-2L)/2 ... divide both sides by 2

W = (P-2L)/2

So the final answer is W = (P-2L)/2

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If S is countable and nonempty, prove their exist a surjection g: N --> S

aleksley [76]

Answer with Step-by-step explanation:

We are given S be any set which is countable and nonempty.

We have to prove that their exist a surjection g:N $\rightarrow S$

Surjection: It is also called onto function .When cardinality of domain set is greater than or equal to cardinality of range set then the function is onto

Cardinality of natural numbers set = $\chi_0$ ( Aleph naught)

There are two cases

1.S is finite nonempty set

2.S is countably infinite set

1.When S is finite set and nonempty set

Then cardinality of set S is any constant number which is less than the cardinality of set of natura number

Therefore, their exist a surjection from N to S.

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2 years ago

Given the triangle below, what is m < b, rounded to the nearest tenth?

ahrayia [7]

Option A:

m∠B = 42.1°

Solution:

Given data:

b = 18, c = 15 and m∠C = 34°

Using sine formula:

$$\frac{b}{\sin B}=\frac{c}{\sin C}$

Substitute the given values.

$$\frac{18}{\sin B}=\frac{15}{\sin 34^\circ}$

Do cross multiplication.

$${18} \times {\sin 34^\circ}={15} \times{\sin B}$

Divide by 15 on both sides.

$$\frac{{18} \times {\sin 34^\circ}}{15} =\frac{{15} \times{\sin B}}{15}$

$$\frac{{6} \times0.559}{5} =\sin B$

$$0.6708=\sin B$

$$\sin ^{-1}0.6708= B$

$42.1^\circ =B$

Switch the sides.

m∠B = 42.1°

Option A is the correct answer.

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2 years ago