The duration for the rocket to hit the ground, its height at 2 seconds, and its maximum height can be calculated using the given quadratic equation for height over time. The maximum height is determined by finding the vertex of the parabola.
Explanation:To determine how long it takes the toy rocket to hit the ground, we need to set the equation for height h to zero and solve for time t. The model for the path of a toy rocket is given by [tex]h = -16t2 - 4.9t2[/tex]. To solve for t, we factor the right side:
[tex]h = -4.9t(16 + t)[/tex]
Since h = 0 when the rocket hits the ground, we set [tex]-4.9t(16 + t) = 0[/tex] and solve for t. There are two solutions: t = 0 (when the rocket is launched) and the positive solution which is when the rocket hits the ground. We disregard the solution t = 0 and solve for the positive solution to find out how long it takes to hit the ground.
To find out how high the rocket was at 2 seconds, we simply plug t = 2 into the original equation:
[tex]h = -16(2)2 - 4.9(2)2[/tex]
And solve for h to get the height at 2 seconds.
To determine the maximum height of the rocket, we need to find the vertex of the parabola represented by the given equation, which is a quadratic function of t. Since the coefficient in front of t2 is negative, the vertex will give us the maximum height. The time it takes to reach the maximum height is given by t = -b/2a, where a and b are coefficients from the equation [tex]h(t) = at2 + bt + c.[/tex] In this case, a = -4.9 and b = -68.
The calculations must be done to find the precise values for the time to hit the ground, the height at 2 seconds, and the maximum height of the rocket, along with the time it takes to reach it.
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Female elk can weigh up to six hundred pounds. In standard form, how many non-zero digits does this weight contain
How does identifying the part and the whole help you to write the percent proportions
Grade 9 mathematics please help asap. Thank you so much!!!
ASAP During a 4-month-long drought, the water level in a lake changed by
−3
1
2
feet. The water level changed at the same rate each month.
What is amount the water level changed in 1 month?
Enter your answer in the box.
3 1/2 = 7/2
7/2 / 4 = 7/8
it changed by -7/8 feet = 10 1/2 inches each month
The amount of changes of water level in a lake for 1 month will be
⇒ - 7/8 feet
What is mean by Fraction?
The fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
In 4 month long drought,
The changes of water level in a lake = - 3 1/2 feet.
Now,
Find the changes in water level for 1 month as;
Since,
The changes of water level in a lake for 4 month = - 3 1/2
After change the mixed fraction in a improper fraction as;
- 3 1/2 = - 7/2
Thus, The changes of water level in a lake for 4 month = - 7 / 2
So, The changes of water level in a lake for 1 month = - 7 / 2 ÷ 4
After divide we get;
The changes of water level in a lake for 1 month = - 7 / (2 x 4)
= - 7 / 8
Therefore,
The amount of changes of water level in a lake for 1 month will be
⇒ - 7/8 feet
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a triangle has sides of lengths 6 and 9. What value could the length of the third side?
Julie's yard is rectangular one side of the yard is 100 feet wide. The total area of the yard is 3000 square feet. What is the length of the other side of the yard ?
Jazmin is completing an art project. She has two pieces of construction paper. The first piece is 4 4 4444 inches wide and the second piece is 3 3 3333 inches wide. Jazmin wants to cut the paper into strips that are equal in width and are as wide as possible. How wide should Jazmin cut each strip?
Answer:
Each strip should 11 inches wide.
Step-by-step explanation:
We are told that Jazmin has two pieces of construction paper. The first piece is 44 inches wide and the second piece is 33 inches wide. Jazmin wants to cut the paper into strips that are equal in width and are as wide as possible.
To find the greatest possible width of each strip we will find GCF of 44 and 33.
Factors of 44 are: 1, 2, 4, 11, 22, 44.
Factors of 33 are: 1, 3,11, 33.
We can see that 11 is the greatest common factor of 44 and 33 as 11*4=44 and 11*3=33, therefore, Jasmine should cut each strip 11 inches wide.
Answer:
11
Step-by-step explanation:
We are told that Jazmin has two pieces of construction paper. The first piece is 44 inches wide and the second piece is 33 inches wide. Jazmin wants to cut the paper into strips that are equal in width and are as wide as possible.
To find the greatest possible width of each strip we will find GCF of 44 and 33.
Factors of 44 are: 1, 2, 4, 11, 22, 44.
Factors of 33 are: 1, 3,11, 33.
We can see that 11 is the greatest common factor of 44 and 33 as 11*4=44 and 11*3=33, therefore, Jasmine should cut each strip 11 inches wide.
estimate 392÷9 show how you estimated
there are 17 men and 26 women in a choir the choir is going to sing at a concert one of the men and women are going to be chosen to make a pair to sing the first song. work out the number of different pairs that can be chosen
The total number of different pairs that can be formed for the song, with one man and one woman in each pair, is 442 pairs.
Explanation:This is a classic mathematical problem known as combinations. In this case, we want to know how many different pairs can be formed from a group of 17 men and 26 women where one man and one woman form a pair.
To calculate the number of different combinations, we multiply the number of choices for the first element (a man) by the number of choices for the second element (a woman). Thus, we have 17 different choices for the man and 26 different choices for the woman. So the total number of different pairs that can be formed is: 17 men * 26 women = 442 pairs.
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Three bags of wheat, two bags of corn, and one bag of oats weigh the same as one bag of wheat, one bag of corn and five bags of oats. If two bags of corn and one bag of oats weighs 26 pounds, and one bag of corn weighs 10 pounds, how much does one bag of wheat weigh?
Find the difference between 7/10 and 14/15
Answer:
The answer is - 7/30
Step-by-step explanation:
LCM between 10 and 15 is 30 so that would be your denominator.
The subtract: 7-14 = -7 so that would be your numerator.
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The difference between the numbers of fraction 7 / 10 and 14 / 15 would be 7 / 30.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
The number of the fraction are;
⇒ 7 / 10 and 14 / 15
Now,
Find the difference between the fraction 7 / 10 and 14 / 15 as;
The mathematical expression is,
⇒ 14 / 15 - 7 / 10
Make denominator same to solve the fraction as;
LCM { 10 , 15 } = 30
Therefore, We get the expression ;
⇒ 14 / 15 - 7 / 10
⇒14 × 2 / 15 × 2 - 7 × 3/ 10 × 3
⇒ 28 / 30 - 21 / 30
⇒ (28 - 21) / 30
⇒ 7 / 30
Thus, 14 / 15 - 7 / 10 = 7 / 30
Therefore, The difference between the fraction of numbers 7 / 10 and 14 / 15 would be 7 / 30.
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The total land area on earth is about 6×10 to the seventh power square miles. The layered of Australia is about 3×10 to the six power square miles. About how many times larger is the land on earth than land of Australia
the cost of 3 candles is 19.50 what is the unit price with work shown
Answer:
$6.50/candle
Step-by-step explanation:
The unit price here is the total price divided by the number of candles, or
$19.50
---------------- = $6.50/candle
3 candles
Taylor buys 6 bus tickets. He pays for the tickets with a $20 bill. Let c represent the cost of each ticket. Which expression shows how much change Taylor will receive?
Answer:
(20 - 6c)
Step-by-step explanation:
Taylor buys bus tickets = 6
Let the cost of the one ticket = c
Cost of 6 tickets = $6c
If Taylor has paid $20 for these 6 tickets then the change he will receive = $20 - $6c
Therefore, the expression to calculate the change Taylor will receive will be
(20 - 6c)
An airplane flies 105 miles in 1/2 hour. How far can it fly in 1 and 1/4 hours at the same rate of speed?
Maggie bought 3/4 of a pound of bananas and 4 boxes of cereal for $10.11. If each box of cereal cost $2.40, what was the price of a pound of bananas?
Answer:
$0.51
Step-by-step explanation:
217+37(3x−5)=−4 Drag and drop the statement that shows the solution to the equation into the box.
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Answer on picture
3/8__1/4
greater than
less than
equal too
EXPLAIN
3/8 = 0.375
1/4 = 0.25
0.375 is greater than 0.25
so 3/8 is greater than 1/4
how would i solve |-9x|=64
snow fell 20% of the days in November. How many days in November did it snow. (Hint There are 30 days in November. )
A(n)
is a letter used as a placeholder for an unknown value.
A variable is the letter used as a placeholder for an unknown value, playing a pivotal role in mathematical reasoning and problem-solving processes.
A placeholder for an unknown value in mathematics, algebra, and other fields is typically represented by a variable. Variables are symbols, often letters like x, y, or z, used to denote unspecified or changing quantities.
They serve as placeholders for values that can vary or are yet to be determined within a given context. In algebraic equations, variables enable the representation of relationships between quantities, facilitating problem-solving and mathematical modeling.
By assigning specific values to variables, equations can be solved, functions can be evaluated, and patterns can be analyzed. Variables are fundamental in various mathematical concepts, including equations, inequalities, functions, and formulas, allowing for flexible and dynamic representations of mathematical relationships.
I HAVE 2 QUESTIONS PLEASE HELP ME AND REAL ANSWERS PLEASE OR I WILL REPORT.
The cost to rent a hall for Alysa's Sweet Sixteen birthday party is $300. Her Mom said she must keep the party cost to no more than $5.00 a person. She watched her mom write an expression on her notes that is listed below. What does the variable represent in this expression?
300+200
------------------
X
A. The number of people attending
B. The amount to rent the hall
C. The amount of food
D. The total cost of the party
What is the sum of the coefficients in the expression
2m^2n + 2mn^2 - m + 3n + 9
PLEASE HELP ME
Answer:
Step-by-step explanation:
1. For her birthday, the mother stated that 5.0 per person, so then the number of people is going to change the party's budget. Now the numerator shows what the girl is going to spend, in comparisson to what she is sopposed to X. So then X is the cost of the party.
2. This one is tricky because we have to take into account that we can onky sum coefficients if they are alike. We can play with this expression by factorizing in different modes
A grocery store gives away a $10 gift card to every 25th customer and a $20 gift card to every 60th customer. Which customer will be the first to receive both gift cards?
2p=kx-t how do you solve for x
To solve for 'x' in the equation 2p=kx-t, you would first need to isolate 'x' on one side of the equation. Add 't' to both sides to get 2p + t = kx, then divide through by 'k' to solve for 'x'. Hence, x = (2p + t) / k.
Explanation:To solve the equation 2p=kx-t for x, you would first need to isolate x on one side of the equation. This can be done by adding 't' to both sides of the equation, which results in 2p + t = kx.
Then, to isolate 'x', you would divide both sides of the equation by 'k'. So, the solution for x would be x = (2p + t) / k.
This rearrangement allows you to solve for x in terms of p, t, and k. This is an exercise in algebra, with the goal of isolating the variable you are attempting to solve for, in this case, x.
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the perimeter of the rectangle is 400 inches.what is the value of j
4 1/5
-
2 7/10
________
There were 58 adults who completed the 16-mile charity bike ride. There were 65 (1 pt) children who completed the 10-mile charity bike ride. What is the total number of miles ridden by all the adults and children in the bike
Identify the multiplier for 2/9 = 6/27
The multiplier for the number 2 / 9 will be 3 / 3.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.
The given number is 2 / 9. The multiplier for the number will be calculated as below:-
2/9 = 6/27
( 2 / 9) x ( 3 / 3 ) = ( 6 / 27)
( 6 / 27 )= ( 6 / 27 )
Therefore, the multiplier for the number 2 / 9 will be 3 / 3.
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how to show the tens fact you used. write the difference.
14-6=____
10-___=____
The tens facts approach simplifies subtraction by reducing numbers to multiples of ten. In the given problem the difference of 14-6 is 8 and this can be represented with tens facts as 10-2=8.
Explanation:The question pertains to the calculation of the difference between numbers using tens facts. Tens facts are a strategy applied in subtraction operations to simplify problems by making them multiples of ten. Here, the problem involves 14-6. In order to represent this using tens facts, the target is to reduce the first number (14) to a multiple of ten, which is 10 in this case. You can achieve this by subtracting the 4 from 14 to get 10. It's the same total of 4 that we also subtract from the 6 to arrive at our answer of 2. So, it can be shown as;
14 - 6 = 810 - 2 = 8Learn more about Tens Facts here:https://brainly.com/question/29636684
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you used p minutes one month on your cell phone the next month you used 75 fewer minutes