A stone is launched into the air from a height of 240 feet. The height, h, of the stone, in feet, t seconds after launch is given by
the formula h = 16t^2 + 32t+ + 240. After how long will the stone hit the ground?
Answers
A projectile is an object launched into space, and moving under the influence of gravity and momentum. The stone here is an example. Thus, the time taken for the stone to reach the ground is 10 seconds.
On launching of the stone into space, it behaves as a projectile. Thus moving under the influence of gravity and its momentum. Its momentum is the product of its mass and velocity.
The height h, is given as:
h = 16[tex]t^{2}[/tex] + 32t + 240
Differentiating the expression with respect to t, we have;
32t + 32 = 0
t = -1 seconds
Substitute the value of time, t, in the equation for the height;
h = 16 - 32 + 240
= 224
h = 224 m
Total height, S = 240 + 224
= 464
S = 464 m
The total height covered by the stone is 464 m.
From the second equation of free fall,
S = Ut + [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]
S = [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]
464 = [tex]\frac{1}{2}[/tex]*9.8*[tex]t^{2}[/tex]
[tex]t^{2}[/tex] = [tex]\frac{928}{9.8}[/tex]
= 94.694
t = [tex]\sqrt{94.694}[/tex]
= 9.7311
t ≅ 10 seconds
The time taken for the stone to hit the ground is 10 seconds.
Thus option A is the required answer.
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Related Questions
The ratio of boys to girls is 7:5. The ratio of boys with glasses to boys without glasses is 1:6. The ratio of girls with glasses to girls without glasses is 1:3. What fraction of students wear glasses?
Answers
Answer:
3/16
Step-by-step explanation:
Boys with glasses are 1/(1+6) = 1/7 of boys. Boys are 7/(7+5) = 7/12 of the group.
Girls with glasses are 1/(1+3) = 1/4 of girls. Girls are 5/(7+5) = 5/12 of the group.
The fraction of the group that wears glasses is ...
(1/7)(7/12) +(1/4)(5/12) = 1/12 +5/48 = 9/48 = 3/16
3/16 of the students wear glasses.
_____
Additional comment
It appears we can choose a multiple of 48 students to work out the detailed numbers. For 48 students, the ratio of boys to girls is 28 : 20. The ratio of boys with glasses to those without is 4 : 24, and the similar ratio for girls is 5 : 15. In our group of 48 students, 4 boys and 5 girls = 9 students wear glasses. The fraction is 9/48 = 3/16 as shown above.
Graph the original function by indicating how the more basic function has ben shifted, reflected, stretched, or compressed
Answers
What is the equation of this line?
Answers
Answer:
y = 1/2x - 3
Step-by-step explanation:
Howards baseball team won 7/10 of its game. Jeremys team won 2/5 of its game. They both played the same number of games. Whose team won more games, or did they win the same amount?
Answers
Answer:
Jeremy's team won more games
Step-by-step explanation:
Let's transform these fractions into ratios:
[tex]\frac{7}{10} =7:10\\\\\frac{2}{5} =7:10[/tex]
Then, simplify:
[tex]7:10[/tex] ≈ [tex]1:1.4[/tex]
[tex]2:5=1:2.5[/tex]
Finally, compare:
[tex]1:1.4\neq 1:2.5[/tex]
Result:
Jeremy's team won more games since [tex]1:2.5>1:1.4[/tex]
Note:
The way I simplify the ratios may be confusing so here is a quick explanation;
Make the smaller of the two numbers in the ratio into one then divide the larger number by the smaller number for the other part of the ratio
Example:
5:10
5 turns into 1
10 divided by 5 equals 2
Simplified Ratio: 1:2
Jeremy won more games than Howard.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Howard Team won = 7/10
Jeremy team won = 2/5
Now, taking LCM (5, 10)= 10
So, Jeremy team won = 2/5
= 4/10
So, Jeremy won more games than Howard.
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please help..........
THANKS!
Answers
An experiment is conducted examining the effects of a new type of toothpaste on reducing cavities. Individuals in the treatment condition are given the new toothpaste; individuals in the control condition are given the standard toothpaste, but are told that they're receiving the new toothpaste. At the end of the experiment, the control group participants demonstrate a slightly higher decline in cavities. This is an example of a(n):____.
a. Wording bias.
b. Voluntary response bias.
c. Over-sampling effect.
d. Placebo effect.
d. Hawthorne effect.
Answers
The experimental effect highlighted by the scenario described would most likely be an example of placebo effect.
An observed change in the control group which are being given the placebo would have been triggered due to psychological expectation based on the information given. Hence, this is called the placebo effect. The standard toothpaste was not suppose to cause decline in cavities, however, since the group have been told that they we given the new toothpaste which is said to reduce cavities, this could trigger a psychological change hence causing them to have higher cavity decline.Learn more : https://brainly.com/question/25704508
The price of a gallon of milk increased from $5.50 to $7.50. Describe the price increase as a percent.
Answers
Step-by-step explanation:
7.50= (1 + x/100 ) × 5.50
7.50/ 5.50 = 1+x/100
x/100 = 0.36
x= 36.36%
Lin father is paying for a 20 meal he has a 15 off coupon for the meal what is the total after the discount
Answers
Answer:
3
Step-by-step explanation:
20÷100=0.2
0.2×15=3
:)
Answer:
Lin's father would pay $17 for his meal.
Step-by-step explanation:
15*20 = 300
300/100 = 3
20 - 3 = 17
If 18 plums weigh 54 ounces, then 6 plums weigh how many
ounces?
Answers
Answer:
18
Hope this helps :) Please mark this brainiest?
Step-by-step explanation:
18/6=3
54/3=18
Answer:
18 ounces
Step-by-step explanation:
I think this is right because if you take 18 and divide it by 3 it equals 6 so i divided 54 by 3 and got 18 ounces hope this helps
<3
A farm lets you pick 3 pints of raspberries for $12.00. How many pints do you get per dollar?
Answers
Answer:
it would take 4 dollars to get one pint. if that's what your asking.
Step-by-step explanation:
divide 12 by 3 or multiply 3 by 4 which gives you 12. your answer is 4 if i understand correctly.
no link no bot right answer
Answers
HELP FAST PLS I’ll mark u brainliest
Answers
Answer:
about 20 cents
Step-by-step explanation:
#Shop A
Pack of 10pens=£2.30Pack of 70pens:-
[tex]\\ \sf\longmapsto 7(2.30)=16.10[/tex]
#2
Pack of 5=1.60£Pack of 70
[tex]\\ \sf\longmapsto 14(1.60)=20.80[/tex]
But you get half price
20.80/2=10.40Difference:-
[tex]\\ \sf\longmapsto 16.10-10.40=5.70\£[/tex]
A ticket for a show costs $114.50. A parking pass costs $13.00. Let x represent the number of tickets and y represent the cost. How much does it cost for 2 tickets and a parking pass?
Answers
Answer:
X multiplied by Y is $229 plus a parking pass being $242
Step-by-step explanation:
X = 2 (2tickets)
Y = $114.50 (cost of one)
multiplying the tickets by the cost of one will give you $229 and the cost for the parking pass being $13.00 well 29 + 13 = 42 adding 42 to the 200 we left gives you $242 for 2 tickets and a parking pass
Express 405 1/3 in simplest radical form.
Answers
Answer:
3 cube root of 15
Step-by-step explanation:
theres your simple radical form
8(152/3) is 405 1/3 in simplest radical form.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
405 1/3 is equivalent to (405*3 + 1)/3 = 1216/3.
To express 1216/3 in simplest radical form, we can first simplify it by dividing both the numerator and denominator by their greatest common factor, which is 8.
1216/3 = (8*152)/3 = 8(152/3)
Now, we can see that 152/3 cannot be simplified any further, so the simplest radical form of 405 1/3 is: 8(152/3)
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Which of the following statements is incorrect?
a. (-3x)3 = -27x3
b. xo xx-4 = x2
c. x + x-3 = x4
d. 3-2 = -9
Answers
Answer:
The last one is incorrect
A contractor uses a scale drawing of an office floor to determine the amount of carpet he needs to buy 1/4 inch = 4.5 feet the width in the scale drawing of the office floor is 6.4 inches what is the actual width of the office floor
Answers
A scale drawing is a method of drawing that requires either increasing or decreasing the dimensions of a given object. So then, the actual width of the office floor is: 115.2 feet.
A representative factor is a factor the can be used to either increase or decrease the dimensions of an object. It is sometimes referred to as a scale factor.
In the given question, the scale factor is given as:
[tex]\frac{ 1 }{4}[/tex] inch = 4.5 feet
Given that the width in the scale drawing of the office floor is 6.4 inches, let the actual width be represented by x.
So then;
[tex]\frac{ 1 }{4}[/tex] inch = 4.5 feet
6.4 inches = x
x = [tex]\frac{6.4 *4.5}{\frac{1}{4} }[/tex]
= [tex]\frac{28.8}{0.25}[/tex]
x = 115.2
Therefore, the actual width of the office floor is 115.2 feet.
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Answer:
115.2 /\
Step-by-step explanation: / \
What the person above me said. / \
Evaluate the expression( 3x2)2
Answers
Answer:
12
Step-by-step explanation:
Help I offer all of my points
Answers
Answer:
100 bags
Step-by-step explanation:
You're going to want to multiply each amount of pounds the bags are by two. So 30 × 2 is 60. 15 × 2 = 30. 5 × 2 = 10.
60 + 30 = 90
90 + 10 = 100 (BRAINLIEST PLEASE OvO)
Write 640 : 30 in the lowest form.
Answers
Answer:
should be 64:3
Step-by-step explanation:
divide by 10
-5(X+2)=35 APPLY THE DISTRIBUTIVE PROPERTY
Answers
Hello!
-5(x+2)=35
-5x-10=35
-5x=35+10
-5x=45
x=-9
Hope it helps!
~Just a determined gal
#CarryOnGainingKnowledge
[tex]MysteriousNature[/tex]
Answer:
x = -9
Step-by-step explanation:
-5(x + 2) = 35
~Distribute
(-5 * x) + (-5 * 2) = 35
~Simplify
-5x - 10 = 35
~Add 10 to both sides
-5x = 45
~Divide -5 to both sides
x = -9
Best of Luck!
At a birthday party, 20% of the guests wear glasses.
If there are 30 guests, how many wear glasses?
Answers
20x30=600
600/100=6
6 guests were wearing glasses
Answer:
if 100% =30 guests what about 20%=6%
135 rational or irrational
Answers
Answer:
Rational
Step-by-step explanation:
I hope this helps!
In February Lana got a puppy that weighed 13 kilograms. By October the puppy weighed 16.9 kilogram. What was the puppy’s weight increase?.
Answers
Answer:
3.9
Step-by-step explanation:
16.9 take away 13 and you get 3.9 kilograms
Given that angle a = 54° and angle b = 48°, work out 3.
a
b
х
The diagram is not drawn accurately.
х
Answers
9514 1404 393
Answer:
x = 78°
Step-by-step explanation:
The sum of the interior angles of a triangle is 180°.
x + a + b = 180°
x = 180° -a -b . . . . . . . . add -a-b to both sides
x = 180° -54° -48°
x = 78°
16.
Identify the axis of symmetry of the parabola.
A. x = -2
B. x = 1
C. x = -3
D. x = -1
Answers
Answer:
i don't know
Step-by-step explanation:
Parents of children with developmental disorders can apply for federal funding for psychosocial rehabilitation. A government sociologist wants to know what percentage of applicants for this funding are in poverty. She obtains access to all their applications, groups the applications by state, and takes a simple random sample from each state's applications. Identify the population of interest to the sociologist.
a. Applicants for the federal funding who were in poverty
b. Applicants for the federal funding
c. Applicants who received the federal funding
d. Applicants whose applications were examined
Answers
Answer:
Applicants for the federal funding
Step-by-step explanation:
HELP PLEASE
What is (are) the x intercept(s) of the function graphed above?
-4
-14 and 4.5
-5,1, and 4
-4, -1 and 5
Answers
Answer:
-4, -1, and 5
Step-by-step explanation:
1. The x-intercepts of a function is where the function intersects with the x-axis.
2. Given the information above, we can see that the function intersects the x-axis at (-4,0), (-1,0), and (5,0).
This means that the x-intercepts are -4, -1, and 5.Consider the graph of the of the quadratic function g(x). See below
Answers
Answer:
I believe the correct answers would be...
32.) B
33.) C
Step-by-step explanation:
32.)
Since the function is shifted downward 1 unit from the x-axis, "q" would be -1
33.)
If the function is shifted upward 4 units, the "+4" would be on the outside of the parentheses.
At gym A is 76.50 for 8.5 hours. At gym B cost is 10.50 for 3/4 hours which plan of offers the best deal
Answers
Tell me if you want step by step explanation!
Hope this helped. :)
Each student in Mr. Ricardo's class has one camera that holds
320 pictures. He asks each student to delete 1/4 of the pictures and turn in the rest. Which of the following functions best represents the number of pictures, p that Mr. Ricardo will collect depending on the number of cameras, that his students have?
A) p=80c
B) p=160c
C) p=240c
D) p=320c
Answers
Answer:
C) p = 240cStep-by-step explanation:
Each camera has 320 pictures.
If 1/4 of pictures deleted, remaining number is:
320 - 1/4*320 = 320 - 80 = 240Total number of pictures is:
p = 240cCorrect choice is C