MATHEMATICS COLLEGE

Write the equation in standard form and then find the center (h, k) and
x^2+8x+ y2 + 4y - 5= 0

Answers

Answer 1
Answer:

Answer:

Center is at (-4, -2) and the radius = 5.

Step-by-step explanation:

Convert to Standard form:

x^2 + 8x + y2 + 4y - 5= 0  

Completing the square:

(x + 4)^2 - 16 + (y + 2)^2 - 4 = 5

(x + 4)^2 + (y + 2)^2  = 5 + 16 + 4

(x + 4)^2 + (y + 2)^2  = 25

(x - h)^2 + (y - k)^2 = r^2     Comparing:-

The center is at (-4, -2) and the radius = 5.

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the states of nature are defined so that they are which of the following, meaning that at least one state of nature must occur at a given time for a chance event? mutually exclusive optimistic outcomes collectively exhaustive certain events

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The states of nature must be mutually exclusive and collectively exhaustive.

The states of nature in decision theory are defined as mutually exclusive and collectively exhaustive, meaning that they are the only possible outcomes of a chance event, and only one of them can occur at a given time.

In other words, the states of nature represent all the possible outcomes of a chance event, and they are mutually exclusive because they cannot occur simultaneously. For example, if the states of nature are "rain" and "no rain," then either it will rain or it will not rain at a given time, but not both.

The term "collectively exhaustive" means that the set of states of nature includes all possible outcomes, so that there are no other possibilities beyond the ones listed. This ensures that the decision maker has considered all possible outcomes when making a decision.

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The 3rd degree Taylor polynomial for cos(x) centered at a = π 2 is given by, cos(x) = − x − π 2 + 1 6 x − π 2 3 + R3(x). Using this, estimate cos(88°) correct to five decimal places.

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Final answer:

Cos(88°) can be estimated using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2. The degrees need to be converted to radians, and by substituting into the polynomial, the cosine value to five decimal places is approximately 0.03490.

Explanation:

To estimate cos(88°) using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2, we first need to convert 88 degrees to radians as cos(x) expects x in radians. 88 degrees is roughly 1.53589 radians. Now, substituting x = 1.53589 into the Taylor polynomial yields the estimate.

The given Taylor polynomial is represented as cos(x) = - (x - π/2) + 1/6 * (x - π/2)³. Substituting x with 1.53589, we get:

cos(1.53589) = - (1.53589 - π/2) + 1/6 * (1.53589 - π/2)³

To get the estimate correct to five decimal places, you calculate the above expression to get roughly 0.03490. Therefore, cos(88°) is approximately 0.03490.

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Final answer:

First, we convert the given angle 88° into radians, since standard trigonometrical functions take angles in radians. We then substitute this into the Taylor series given, keeping in mind the importance of the remainder term.

Explanation:

This problem deals with the concept of Taylor series approximation, which is a widely used method in mathematics to estimate the value of functions. The given Taylor polynomial approximates the cosine function. To estimate cos(88°), we first need to convert the angle from degrees to radians, because the standard trigonometric functions in mathematics take input in radians. Remember that 180° equals π radians. So 88° can be represented as (88/180)π radians.

Substitute this into the provided series − x − π/2 + 1/6 * (x − π/2)³ + R3(x). Be wary of the remainder term R3(x). This term ensures the correctness of the approximation on the interval of convergence. The closer x is to the center, the more accurate the approximation. In practical computations, you might need to take more terms into account to ensure sufficient accuracy to five decimal places in this case.

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In Miami the number of highway accidents increased by 20% over a four year period. How many accidents were there in 2013 if there were 5,120 in 2009?

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x/5120=20/100
x/5120=1/5
5120/5=1024
1024+5120=6144
6144 is the answer.

I need this FAST please help!!!

Answers

Answer:

the answer is   9.879

Which is equivalent to the following expression (3m^2+2mn-n^2)+(m^2+4mn-n^2)

Answers

Based on the available information, the expression (3m² + 2mn - n²) + (m² + 4mn - n²) is equivalent to 4m² + 6mn - 2n².

How the equivalent expression is determined?

To simplify the expression (3m² + 2mn - n²) + (m² + 4mn - n²), we can combine like terms.

Like terms have the same variables and the same exponents.

Let's group the like terms together:

(3m² + m²) + (2mn + 4mn) + (-n²- n²)

Combining like terms within each group, we get:

4m² + 6mn - 2n²

Therefore, in this case, it is concluded that the expression (3m² + 2mn - n²) + (m² + 4mn - n²) is equivalent to 4m² + 6mn - 2n².

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Answer:

4m² + 6mn - 2n²

Step-by-step explanation:

(3m^2+2mn-n^2)+(m^2+4mn-n^2)\n\n=3m^2+2mn-n^2+m^2+4mn-n^2\qquad\text{combine like terms}\n\n=(3m^2+m^2)+(2mn+4mn)+(-n^2-n^2)\n\n=\boxed{4m^2+6mn-2n^2}

Quinton had a gross income of $2741.67 during each pay period in 2009. If he got paid monthly, how much of his pay was deducted for FICA in 2009?

Answers

Answer:

$2,516.85

Step-by-step explanation:

Quinton had a monthly gross income of $2741.67.

He was paid yearly = $2741.67 × 12 = $32,900.04

FICA tax  is social security tax (6.2%) and medicare tax (1.45%)

FICA tax rate = 6.2% + 1.45% = 7.65%

FICA tax deduction = 7.65% × 32,900.04

                                 = 0.0765 × 32,900.04

                                 = $2,516.85

His pay was deducted for FICA $2,516.85

Answer:

$2516.85

Step-by-step explanation:

a p e x
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