MATHEMATICS HIGH SCHOOL

(461065) João Augusto lança uma bola para cima e ela descreve uma trajetória vertical. Os instantes de tempo em que a bola sai e retorna à mão de João Augusto são representados pelas raízes da equação – 5t² + 40t = 0. Durante quantos segundos a bola permaneceu no ar?

Answers

Answer 1

Answer:

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Answer 2

Answer:

Final answer:

João Augusto's ball remained in the air for 8 seconds. This was determined by the roots of the equation -5t² + 40t = 0, which represents the ball's vertical trajectory.

Explanation:

The equation given in the question represents the motion of the ball thrown into the air. Specifically, it is a parabolic equation which describes the motion of an object under the influence of gravity. We can determine the duration of the ball's flight by finding the roots of this equation.

The equation -5t² + 40t = 0 can be factored into -5t(t - 8) = 0. Therefore, the roots of this equation are 0 and 8, which represent the instants of time. In this case, t = 0 is the time when João Augusto launched the ball, and t = 8 is the time when he caught it again.

So, the ball remained in the air for 8 seconds.

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Zakary ate 34 hot dogs. jerald ate 30 times as much as zakary did. how many hot dogs did jerald eat?

Answers

1020 hotdogs. Just multiply the two

In a pot worth $2.35, there are 6 quarters, 5 dimes, 5 pennies, and the rest of the coins are nickels. What is the ratio of nickels to dimes?

Answers

Answer:

6:5

Step-by-step explanation:

It is given that a pot worth $2.35 and there are 6 quarters, 5 dimes, 5 pennies, the rest of the coins are nickels.

We know that

$1 = 100 cents

1 penny = 1 cent = $0.01

1 nickel = 5 cents. = $0.05

1 dime = 10 cents. = $0.10

1 quarter = 25 cents = $0.25

The value of 6 quarters is

$6* 0.25=1.50$

The value of 5 dimes is

$5* 0.10=0.50$

The value of 5 pennies is

$5* 0.01=0.05$

Let x be the number of nickels. So, the value of x nickels is

$x* 0.05=0.05x$

Total value of 6 quarters, 5 dimes, 5 pennies, and x nickels is

$Total =1.50+0.50+0.05+0.05x$

$Total =2.05+0.05x$

It is given that the pot worth is $2.35.

$2.05+0.05x=2.35$

Subtract 2.05 from both sides.

$0.05x=0.30$

Divide both sides by 0.05.

$x=6$

The number of nickels is 5.

$(Nickel)/(Dimes)=(6)/(5)=6:5$

Therefore, the ratio of nickels to dimes is 6:5.

In a pot worth $2.35 containing 6 quarters, 5 dimes, 5 pennies, and some nickels, the ratio of nickels to dimes is 6:5.

To find the ratio of nickels to dimes, we need to determine the number of nickels and dimes in the pot. We know that there are 6 quarters, 5 dimes, and 5 pennies in the pot, which is a total of 16 coins. Therefore, the number of nickels should be the difference between the total number of coins and the sum of quarters, dimes, and pennies.

The total value of the coins in the pot is $2.35. Since 6 quarters are worth $1.50, 5 dimes are worth $0.50, and 5 pennies are worth $0.05, the remaining value should come from the nickels.

Thus, the value of the nickels is $2.35 - $1.50 - $0.50 - $0.05 = $0.30. Since each nickel is worth $0.05, the number of nickels is $0.30 ÷ $0.05 = 6.

The ratio of nickels to dimes is therefore 6:5, which means that for every 6 nickels, there are 5 dimes.

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The altitude of an equilateral triangle is 18 inches. Find the length of a side

Answers

Let the length of equilateral triangle be x.

Each of the angle in an equilateral triangle is = 60°

The opposite to the 60° is the 18 inches. Hypotenuse is the side.

Sin 60° = 18 / Hypotenuse

Hypotenuse = 18 / Sin60°. Sin60° = √3 / 2

x = 18 / (√3 / 2)

= 18 / √3 * 2/1 = 36 / √3

x = 36 / √3

Rationalize the surd = 36 / √3 * (√3 / √3 ) = 36√3 / 3

x = 12√3 ≈ 12 * 1.732 ≈ 20.784

Length of side, x = 12√3 ≈ 20.784 inches.

E=mc
$e = mc {}^(2)$

solve for c