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3 years ago

What is the justification for step 2 in the solution process?

Mathematics

1 answer:

igomit [66]3 years ago

3 0

Answer:

y = 11

Step-by-step explanation:

Solve for y

12y - 40 - 4y = 6y - 18

8y -40 = 6y - 18

8y - 6y - 40 = -18

2y - 40 = -18 ( the justification for step 2 is to isolate y on one side of the equation in order to solve for y )

2y - 40 + 40 = 40 - 18

2y = 22

2y/2 = 22/2

y = 11

Check :

12(11) - 40 - 4(11) = 6 (11) - 18

132 - 40 - 44 = 66 - 18

48= 48

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express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 2 π , 4 π ]

Lemur [1.5K]

The limit as a definite integral on the interval $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π , 4π] is $\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$ .

<h3>What is meant by definite integral?</h3>

A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.

Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.

If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.

Let the equation be

$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$

substitute the values in the above equation, we get

= $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π, 4π],

simplifying the above equation

$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$

To learn more about definite integral refer to:

brainly.com/question/24353968

#SPJ4

8 0

1 year ago

I got zero, but that’s wrong.

meriva

Answer:

Expected value is 4,000

Step-by-step explanation:

To find expected value ⇒ multiply the value by it's probability

40% × ( -25,000 ) = - 10,000

Breaking means neither add nor subtract a given amount

20% × 0 = 0

35% × 40,000 = 14,000

∴ Expected value = -10,000 + 14,000 = 4,000

LOSS: -10,000

BREAK EVEN: 0

WIN: 14,000

Expected value is 4,000

<em>hope this helps....</em>

3 0

3 years ago

A dinner check is to be split among 3 people. Greg’s portion of the check is twice Kelly’s. Joe’s portion is $1.50 less than 4 t

defon

Answer:

Kelly owes $16.5

Greg owes $33

Joe owes $64.5

Step-by-step explanation:

Let

Kelly's portion = x

Greg's portion = 2x

Joe's portion = 4x - 1.50

Total bill = $114.00

Total bill = Kelly's portion + Greg's portion + Joe's portion

114 = x + 2x + (4x - 1.50)

114 = 3x + 4x - 1.50

114 = 7x - 1.50

Add 1.50 to both sides

114 + 1.50 = 7x - 1.50 + 1.50

115.5 = 7x

Divide both sides by 7

x = 115.5 / 7

= 16.5

x = $16.5

Kelly's portion = x

x = $16.5

Greg's portion = 2x

= 2 × 16.5

= $33

Joe's portion = 4x - 1.50

= 4(16.5) - 1.50

= 66 - 1.50

= $64.5

Therefore,

Kelly owes $16.5

Greg owes $33

Joe owes $64.5

7 0

3 years ago

Find all the integers,b, that make up the trinomial x2 + bx + 10 factorable.

KonstantinChe [14]

By the fundamental theorem of algebra, we can write

$x^2+bx+10=(x-r_1)(x-r_2)$

Expanding the right hand side, we get

$x^2+bx+10=x^2-(r_1+r_2)x+r_1r_2\implies\begin{cases}r_1+r_2=-b\\r_1r_2=10\end{cases}$

We want $b$ to be an integer, which means $r_1,r_2$ must also be integers. This means $r_1,r_2$ must be factors of 10. There are several possibilities: