A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is given by the function .How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary. h=-16t^2+112t+30
A. 7 s; 30 ft
B. 3.5 s; 366 ft
C. 3.5 s; 618 ft
D. 3.5 s; 226 ft

Answers

Answer 1

Answer: To determine the time it takes for boulder to reach its maximum height, derive the equation and equate to zero.
h = -16t² + 112t + 30
dh / dt = 0 = -32t + 112
The value of t from the equation above is 3.5 s. Substitute this value of t to the original question,
h = -16(3.5 s)² + 112(3.5 s) + 30 = 226 ft
Thus, the answer is letter D.

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Urgent!!!!If you were 6' 6 1/2" tall, about how many meters tall would you be? Hint: "There are 3.28 feet in a meter."

6.4 meters
2 meters
1.8 meters
7 meters
3.5 meters

Answers

The height of the person (6 feet and 6.5 inches) is equivalent to 1.994 meters (approx. 2 meters).

How to determine the equivalent height by conversion factor

In this problem we know that height of a person measure in feet and inches, please notice that 1 foot is 12 inches and 1 meter is 3.28 foot. The conversion formula is shown below:

y = k · x

Where:

x - Original height, in feet.
k - Conversion factor, in meters per foot.
y - Resulting height, in feet.

Now we proceed to determine the equivalent height:

y = (1 m / 3.28 ft) · [6 ft + (6.5 in) · (1 ft / 12 in)]

y = (1 m / 3.28 ft) · (6 ft + 0.541 ft)

y = (1 m / 3.28 ft) · (6.541 ft)

y = 1.994 m

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Step-by-step explanation:

2 meters is the answer

please give me brainliest

A game has 3 possible outcomes, with probabilities p1, p2, and p3. The amount of money that you will win or lose for each outcome is v1, v2, and v3, respectively. What is the expression p1v1 + p2v2 + p3v3 equal to?

Answers

We have the following given
p1 - probability for outcome 1
p2 - probability for outcome 2
p3 - probability for outcome 3
v1 - amount of money that you will win or lose for outcome 1
v2 - amount of money that you will win or lose for outcome 2
v3 - amount of money that you will win or lose for outcome 3

Therefore,
p1v1 + p2v2 + p3v3 is the average money you win or lose in playing the game.

Answer:

Option b) The average amount you will win (or lose) per game in the long run

Step-by-step explanation:

The number( √5 +2)(√5 - 2) is a. an irrational number b. a rational number c. not a natural number d. none of these

Answers

Answer:

The number (√5 + 2)(√5 - 2) can be simplified using the difference of squares formula, which states that (a + b)(a - b) = a² - b². In this case:

(√5 + 2)(√5 - 2) = (√5)² - 2² = 5 - 4 = 1

So, the number (√5 + 2)(√5 - 2) is equal to 1, which is a rational number because it can be expressed as a ratio of two integers (1/1). Therefore, the correct answer is:

b. a rational number

Final answer:

The expression ( √5 +2)(√5 - 2) can be simplified using the difference of squares formula. The result is a rationalnumber, making option b. a rational number the correct answer.

Explanation:

The expression ( √5 +2)(√5 - 2) can be simplified using the difference of squares formula. The difference of squares formula states that a^2 - b^2 = (a + b)(a - b). In this case, a = √5 and b = 2. Plugging these values into the formula, we have (√5)^2 - 2^2 = ( √5 +2)(√5 - 2) = 5 - 4 = 1.

Since 1 is a rational number (it can be expressed as a fraction), the correct answer is b. a rational number.

Learn more about Simplifying algebraic expressions here:

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Add −3 1/6+53/4 I need help

Answers

Answer: 8 11/12

Step-by-step explanation:

3 1/6+ 5 3/4

19/6+ 23/4

38/12+69/12

107/12

8 11/12

To solve this problem, you must understand what is the Common Denominator Rule:

The Common Denominator rule is when you use the common factors of the denominators to make them the same number. This will allow you to add and subtract fractions.

First, let’s put these two mixed fractions as improper fractions. Learn more about making that conversion here: brainly.com/question/35061276

$(23)/(4)$

$(-19)/(6)$

Now that you have your fractions, look at the denominators: 6 and 4.

A common factor between 4 and 6 is the number 12. Multiply the denominators and numerators of each fraction by the number that will turn the denominator into 12:

$((23)(3))/((4)(3))$ = $(69)/(12)$