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3 years ago

Na função y = x² - 2x +1, temos que a = 1, b = -2 e c = 1, calcule as coordenadas do vértice da parábola

Mathematics

1 answer:

MrRissso [65]3 years ago

4 0

Answer:

(1, 0)

Step-by-step explanation:

x = -b / 2a

x = 2 / 2(1)

x = 2 / 2

x = 1

y = x^2 - 2x + 1

y = (1)^2 - 2(1) + 1

y = 1 - 2 + 1

y = -1 + 1

y = 0

vértice: (1, 0)

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A multi level parking lot has 6 levels and there are total of 1,327 parking spots.

MrRissso [65]

Answer: (1) There are 233 parking spots on the top level

(2) There are 72 parking spots reserved for drivers with disabilities

(3) There are 970 spots for hourly parking

(4) He would spend $7200 for parking in a year

Step-by-step explanation: In the first instance, there is a total of 1327 parking spots altogether allocated into various categories.

(1) There are 6 levels in all, and the first level has 162 parking spots. herefore the remaining 5 levels would have 1165 parking spots left as shown below;

Remainder = 1327 - 162

Remainder = 1165

If however the remaining 1165 parking spots are distributed equally among the other 5 levels, then each level would have 233 parking spots each as shown below;

Five levels = 1165

Each level = 1165/5

Each level = 233

Therefore the top level has 233 parking spots

(2) On each level (out of all 6 levels), there are 12 spots reserved for drivers with disability. Therefore at all parking levels you would have 72 spots as shown;

Reserved spot per level = 12

Reserved spot for 6 levels = 12 * 6

Reserved spot for 6 levels = 72

Therefore there are 72 spots reserved for driver with disability

(3) Other than the spots reserved for drivers with disability (72), there are 285 parking spots for monthly rental. The rest are for hourly parking, and this is calculated as shown;

Hourly parking + monthly rental + reserved parking = 1327

Hourly parking + 285 + 72 = 1327

Hourly parking + 357 = 1327

Hourly parking = 1327 - 357

Hourly parking = 970

Therefore there are 970 spots available for hourly parking.

(4) If the daily parking rate is $30, and Jack parks his car for 5 days in a week, then he would spend

30 * 5 = 150

If he parks for 4 weeks in a month, then he would spend

150 * 4 = 600

Therefore to pay for parking in a year (12 months) he would spend

600 * 12 = 7200

Therefore he would spend $7,200 for parking in a year

4 0

3 years ago

Using the pattern, give the coefficients of (x + y)^5 and (x + y)^6

musickatia [10]

Answer:

$(x+y)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$

$(x+y)^6=x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6$

Step-by-step explanation:

In order to find the values of $(x+y)^5$ and $(x+y)^6$ , you need to apply the binomial theorem (high-level math you most likely don't need to worry about, it's easier than multiplying all the binomials together).

$(x+y)^5$ = $\sum _{i=0}^5\binom{5}{i}x^{\left(5-i\right)}y^i$ = $\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5$ = $x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$ .

$(x+y)^6$ = $\sum _{i=0}^6\binom{6}{i}x^{\left(6-i\right)}y^i$ = $\frac{6!}{0!\left(6-0\right)!}x^6y^0+\frac{6!}{1!\left(6-1\right)!}x^5y^1+\frac{6!}{2!\left(6-2\right)!}x^4y^2+\frac{6!}{3!\left(6-3\right)!}x^3y^3+\frac{6!}{4!\left(6-4\right)!}x^2y^4+\frac{6!}{5!\left(6-5\right)!}x^1y^5+\frac{6!}{6!\left(6-6\right)!}x^0y^6$ = $x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6$ .

5 0

3 years ago

The distance s that an object falls is directly proportional to the square of the time t of the fall. If an object falls 16 feet

Lemur [1.5K]

Answer: if S is the distance, the fact that the distance is proportional to the square of the time means that S(t) = a* $t^{2}$ where a is a constant of proportionality, with units of $\frac{feet}{s^{2} }$ .