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lions [1.4K]
3 years ago
5

The coordinates of point T are (0,4). The midpoint of ST is (1,-5). Find the coordinates of point S.

Mathematics
1 answer:
katrin2010 [14]3 years ago
8 0
The answer is (2,-15)
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Las "leyes asociativas" dicen que no importa cómo agrupemos los números (es decir, cuál calculamos primero). Entonces esto sería asociativo.
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Terry has a credit card that uses the average daily balance method. For the first 18 days of one of his billing cycles, his bala
Temka [501]

Complete question:

Terry has a credit card that uses the average daily balance method. For the first 18 days of one of his billing cycles, his balance was $350, and for the last 12 days of the billing cycle, his balance was $520. If his credit card's APR is 14%, which of these expressions could be used to calculate the amount Terry was charged in interest for the billing cycle?

(0.14/365 31)(18 $350 + 12 $520 / 31)

(0.14/365 30)(18 $350 + 12 $520 / 30)

(0.14/365 30)(12 $350 + 18 $520 / 30)

(0.14/365 31)(12 $350 + 18 $520 / 31)

Answer:

(0.14/365 30)(18 $350 + 12 $520 / 30)

Step-by-step explanation:

Number of days in a year = 365

Number of days in billing cycle = (18 + 12) = 30

Interest rate per year = 14% = 0.14

Amount charged monthly :

(Monthly rate × average daily balance)

MONTHLY RATE:

(Annual interest / number of days in year) * days in billing cycle

(0.14 / 365) × 30

Average daily balance :

First 18 days ; balance = $350

Last 12 days ; balance = $520

Sum of balance / days in billing cycle

[(18 × $350) + (12 × 520)] / 30

THEREFORE, MONTHLY INTEREST CHARGE :

((0.14 / 365) × 30) ((18 × $350) + (12 × 520) / 30)

4 0
3 years ago
Integral of 17/(x^3-125)
daser333 [38]

Answer:

17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

Step-by-step explanation:

∫ 17 / (x³ − 125) dx

= 17 ∫ 1 / (x³ − 125) dx

= 17 ∫ 1 / ((x − 5) (x² + 5x + 25)) dx

Use partial fraction decomposition:

= 17 ∫ [ A / (x − 5) + (Bx + C) / (x² + 5x + 25) ] dx

Use common denominator to find the missing coefficients.

A (x² + 5x + 25) + (Bx + C) (x − 5) = 1

Ax² + 5Ax + 25A + Bx² − 5Bx + Cx − 5C = 1

(A + B) x² + (5A − 5B + C) x + 25A − 5C = 1

Match the coefficients and solve the system of equations.

A + B = 0

5A − 5B + C = 0

25A − 5C = 1

A = 1/75

B = -1/75

C = -2/15

So the integral is:

= 17 ∫ [ 1/75 / (x − 5) + (-1/75 x − 2/15) / (x² + 5x + 25) ] dx

Simplify:

= 17/75 ∫ [ 1 / (x − 5) − (x + 10) / (x² + 5x + 25) ] dx

Factor ½ from the numerator of the second fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 20) / (x² + 5x + 25) ] dx

Split the fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − ½ (15) / (x² + 5x + 25) ] dx

Multiply the last fraction by 4/4:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 30 / (4x² + 20x + 100) ] dx

Complete the square:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 15 / ((2x + 5)² + 75) ] dx

Split the integral:

= 17/75 ∫ 1 / (x − 5) dx − 17/150 ∫ (2x + 5) / (x² + 5x + 25) dx − 17/5 ∫ 1 / ((2x + 5)² + 75) dx

The first integral is:

∫ 1 / (x − 5) dx = ln│x − 5│

The second integral is:

∫ (2x + 5) / (x² + 5x + 25) dx = ln(x² + 5x + 25)

The third integral is:

∫ 1 / ((2x + 5)² + 75) dx = 1/√75 tan⁻¹((2x + 5) / √75)

Plug in:

= 17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

4 0
3 years ago
Avi a gymnast weights 40 kg
adell [148]

What is the question?

7 0
3 years ago
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