Answers
The requried solution is as follows,
(A) The height of the stone 5 seconds later is 490 feet.
(B) The stone hits the ground at approximately 7.6 seconds after it is thrown.
(c) The velocity of the stone when it hits the ground is 225.2 feet per second,
A. To solve for the height of the stone 5 seconds later, we can use the equation:
h(t) = -16t² + v₀t + h₀
where h(t) is the height of the stone at time t, v₀ is the initial velocity, and h₀ is the initial height.
Substituting the given values, we have:
h(5) = -16(5)² + 18(5) + 800
h(5) = -400 + 90 + 800
h(5) = 490 feet
Therefore, the height of the stone 5 seconds later is 490 feet.
B. To find the time when the stone hits the ground, we need to find the value of t when h(t) = 0. We can use the same equation:
h(t) = -16t² + v₀t + h₀
Setting h(t) = 0, we have:
0 = -16t² + 18t + 800
We can solve for t using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = -16, b = 18, and c = 800.
Plugging in the values, we get:
t ≈ 7.6 seconds or t ≈ -6.5 seconds
Since time cannot be negative in this context, the stone hits the ground at approximately 7.6 seconds after it is thrown.
C. To find the velocity of the stone when it hits the ground, we can use the formula:
v(t) = v₀ + at
where v(t) is the velocity of the stone at time t, v₀ is the initial velocity, and a is the acceleration due to gravity.
We know that v₀ = 18 feet per second, a = -32 feet per second squared, and t = 11.56 seconds (since this is the time when the stone hits the ground). Substituting these values, we get:
v(11.56) = 18 + (-32)(11.56)
v(11.56) ≈ -351.92 feet per second
Therefore, the velocity of the stone when it hits the ground is -225.2 feet per second, which means it is moving downwards at a speed of -225.2 feet per second.
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Related Questions
find the mean of x,2x,3x,4x,5x
Answers
Answer:
Mean = 3x
Step-by-step explanation:
Mean = \(\frac{SumOfObservations}{No. OfObservations}\)
Mean = \(\frac{x+2x+3x+4x+5x}{5}\)
Mean = \(\frac{15x}{5}\)
Mean = 3x
The mean, also known as the average of x, 2x, 3x, 4x, and 5x is 3x as per the concept of Simplifying.
To find the mean of x, 2x, 3x, 4x, and 5x, we need to add up all the values and divide by the total number of values.
In this case, we have five values.
Mean = (x + 2x + 3x + 4x + 5x) / 5
Simplifying the numerator:
Mean = (15x) / 5
Mean = 3x
Therefore, the mean of x, 2x, 3x, 4x, and 5x is 3x.
The mean, also known as the average, represents the central tendency of a set of values. In this case, the mean is 3x, which indicates that on average, the values x, 2x, 3x, 4x, and 5x are three times the value of x.
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how do u graph the solution y=2x-1 iready
Answers
Answer:
Step-by-step explanation:
y=mx+b
m= slope and b= y intercept
you'll start with a point on the y axis on -1
and the slope will go up so towards the right corner up but 2/1 points
which equivalent is equal to 3(7x-5)
Answers
Answer:
21x -15
Step-by-step explanation:
use distributive property
a(b+c) = ab+ ac
Kevin has a stack of newspapers. Each one weighs 15 pounds. The entire stack weighs 4
1
2
pounds. How many newspapers are in the stack?
Answers
Answer:7
Step-by-step explanation:
What is the minimum value of the cube root parent function on -8≤x≤8?
Answers
Minimum means smallest, so what is the smallest number possible for this set?
-8
---
hope it helps
Answer:
-2
Step-by-step explanation:
I really need help with this I would be really happy happy If you could help me
Answers
as the picture say, we need to do constant/variable
the input variable i
Some questions supply a data set, like the one below, which must be used in order to answer the question.
4
8
9
5
2
7
7
5
8
You can copy the data set into another program, such as a spreadsheet or a statistical software program
Answers
Copying the data set into another program allows you to leverage the capabilities of that program for Statistical analysis.
The provided data set can be copied into another program, such as a spreadsheet or a statistical software program, to perform various data analysis tasks. Let's explore some common operations that can be performed using the data set.
1. Descriptive Statistics: By copying the data set into a spreadsheet or statistical software, you can calculate various descriptive statistics, such as the mean, median, mode, standard deviation, and range of the data. These statistics provide insights into the central tendency, variability, and distribution of the data.
A
1 4
2 8
3 9
4 5
5 2
6 7
7 7
8 5
9 8
2. Data Visualization: Once the data set is copied, you can create visualizations to better understand the data. This can include bar charts, histograms, line plots, or box plots, depending on the nature of the data and the insights you want to gain.
3. Data Manipulation: Copying the data set into a spreadsheet allows you to manipulate and transform the data as needed. You can perform operations like sorting, filtering, grouping, and calculating new variables based on existing ones. This enables you to extract meaningful information from the data set.
4. Statistical Analysis: If you are using statistical software, you can conduct advanced statistical analyses on the data set. This may involve regression analysis, hypothesis testing, analysis of variance (ANOVA), or clustering techniques, depending on the specific research question or objective.
5. Data Integration: If you have additional data sets or variables related to the given data set, copying it into a program allows you to merge or join different data sets, thereby enriching the analysis and providing a more comprehensive understanding of the data.
Overall, copying the data set into another program empowers you to perform a wide range of data analysis tasks, enabling you to explore, understand, and draw meaningful insights from the data.
In summary, copying the data set into another program allows you to leverage the capabilities of that program for statistical analysis, calculations, and visualizations, enabling you to gain deeper insights and draw meaningful conclusions from the data.
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what is the solution set for the inequality?
4x+2< -10
Answers
Answer:
X is greater than negative 4
Step-by-step explanation:
1.-2 from both sides
2. divide 4 from both sides
3. solution set X is greater than negative 4
The top of the cliff is 142 m above sea level. Currently the boat is 100 metres from the buoy and the angle of depression from the top of the cliff to the boat is 64º. Find the distance from the top of the cliff to the buoy. diagram not to scale Top of cliff 142 boat buoy Base of cliff (sea level) 100 m. The distance from the top of the cliff to the buoy is type your answer...
Answers
Answer:
221.0 m
Step-by-step explanation:
First, find x using trigonometric ratio formula:
Reference angle = angle of depression = angle of elevation = 64°
Opposite side length = 142 m
Adjacent side length = x
Thus:
tan(64) = 142/x
x*tan(64) = 142
x = 142/tan(64)
x = 69.3 (nearest tenth)
Next, find distance from top of the hill to the buoy using Pythagorean Theorem.
Let the distance be y.
We would have:
y² = 142² + (69.3 + 100)²
y² = 20,164 + 28,662.49
y² = 48,826.49
y = √48,826.49
y = 221.0 m (nearest tenth)
2/5 - 3/8Write your answer as a fraction in simplest form
Answers
The least common denominator of 2/5 and 3/8 is the least common factor of 5 and 8.
Since 8 and 5 have no factors in common, then the least common denominator of 2/5 and 3/8 is:
\(8\times5=40.\)Therefore:
\(\frac{2}{5}-\frac{3}{8}=\frac{2\times8}{5\times8}-\frac{3\times5}{8\times5}.\)Simplifying the above result we get:
\(\frac{2\times8}{5\times8}-\frac{3\times5}{8\times5}=\frac{16}{40}-\frac{15}{40}=\frac{1}{40}.\)Answer:
\(\frac{1}{40}.\)4.5 m is ...% of 90 cm, an 90cm is ...% of 4.5 m
Answers
Answer:
4.5 m is 5% of 90 cm
90cm is 2000% of 4.5 m
Step-by-step explanation:
(4.5/90) x 100 = 5%
(90/4.5) x 100 = 2000%
For both of these equations, I used the formula
(value/total value)×100 = percentge
A student dropped a textbook from the top floor of his dorm and it fell according to the formula s(t) = −16t 2 + 8√t , where t is the time in seconds and s(t) is the distance in feet from the top of the building.What was the average speed of the fall? Use the fact that the pencil hit the ground in exactly 2.8 seconds. Round your answer to 2 decimal places.
Answers
Answer:
-29.61m/sStep-by-step explanation:
Given the distance of fall of the student in term of the time t expressed by the equation s(t) = −16t² + 8√t, to get the average speed of fall of the pencil after 2.8 secs, we will need to differentiate the given function first since Velocity is the change in distance of a body with respect to time i.e
V = d(s(t))/dt
s(t) = −16t² + 8t^1/2
V = -32t+1/2(8)t^(1/2 - 1)
V = -32t+4t^-1/2
The average speed of the fall Using the fact that the pencil hit the ground in exactly 2.8 seconds, will be gotten by substituting t = 2.8 into the resulting equation.
V = -32t+4(2.8)^-1/2
V = -32t+4/√2.8
V = -32+4/1.6733
V = -32+2.391
v = -29.61m/s
Hence the average speed of the fall is -29.61m/s
The average speed of the fall is -29.61m/s
Calculation of the average speed:\(V = d(s(t))\div dt\\\\s(t) = −16t^2 + 8t^{1/2}\\\\V = -32t+1/2(8)t^{(1/2 - 1)}\\\\V = -32t+4t^{-1/2}\)
Now here t = 2.8 seconds
So,
\(V = d(s(t))\div dt\\\\s(t) = −16t^2 + 8t^{1/2}\\\\V = -32t+1/2(8)t^{(1/2 - 1)}\\\\V = -32t+4t^-1/2\)
V = -32+2.391
v = -29.61m/s
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The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain after 1000 years?
Answers
Answerc
Step-by-step explanation:
simple
Another brand of sheets is on sale 30% off with a regular price of $18.00 per sheet. Which is a better deal, the previous example or this one? Explain. (2 points)
30% OFF EACH SHEET!
Answers
The cost for the sheet is $22.60 and a discount of 30% is given.
How to calculate the value of the sheets?It is important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
From the information, the brand of sheets is on sale 30% off with a regular price of $18.00 per sheet.
Therefore, the cost for the sheet will be:
= $18 - (30% × $18)
= $18 - $5.40
= $12.60
The cost for the brand of sheet is $22.60.
Note that the information was incomplete and the calculation was based on the information given.
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y = 3x2 - 6x y - x + 1 = 0
Answers
Answer:
y=0
x=no real solution
Please Give Brilianst!!!
Step-by-step explanation:
first we know y=0, so -6xy=0
\(3x^{2}\)-0-x+1=0
\(3x^{2}\)-x+1=0
(3x+2)(x-1)+3=0
x, no real solution
Eliza earns $400 per week plus $15 for each new customer she signs up.Let c represent the number of new customers Eliza signs up.
Is she signs up 10 people then how much will she make in total?
Answers
Answer:
550
Step-by-step explanation:
Srry if im wrong but if im right will you consider giving me brainly
Hope it helps
:D
Answer:
thx for free poins
Step-by-step explanation:
What is the Answer pls help
Answers
Thank you for the help!
Answers
Answer:
c 57
Step-by-step explanation:
First accurate answer gets brainliest
Answers
Answer: \(20x^2 + 47x+24\)
Step-by-step explanation:
We just multiply the values on the edges like we are finding the area of a square, L * L = area.
4x * 5x = 20x^2
4x * 8 = 32x
3 * 8 = 24
3 * 5x = 15x
Next add the answers together
20x^2 + 47x + 24
Answer:
option 3
Step-by-step explanation:
you need to times (4x+3) by (5x+8)
so you basically need to expand the brackets and collect like terms
17. Evaluate: 30 - 21 + 3 x 2
6
16
26.5
14
Answers
In art class students are mixing blue and red paint to make purple paint. Isaiah mixes 3 cups of blue paint and 7 cups of red paint. Casho mixes 4 cups of blue paint and 13 cups of red paint. Use Isaiah and Casho's percent of red paint to determine whose purple paint will be redder.
Answers
Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.
To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.
Isaiah's Ratio:
Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.
To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:
Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%
Casho's Ratio:
Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.
To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:
Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)
Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).
Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.
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Find the smallest whole number by which 16087 should be multiplied or divided to get a perfect square
Answers
There is no whole number by which you can multiply or divide 16087 to make it a perfect square.
To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.
In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.
To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.
A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.
Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.
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Add the polynomials 2x3+x2–3 and 2x² + 4x – 1.
Answers
The polynomial 2x³ + x² - 3 can be expressed as: 2x³ + x² + 0x - 3
The polynomial 2x² + 4x - 1 can be expressed as: 0x³ + 2x² + 4x - 1
The addition of the polynomials is computed as follows:
2x³ + x² + 0x - 3
+
0x³ + 2x² + 4x - 1
-------------------------------
2x³ + 3x² + 4x - 4
The distance between City A and City B is 2700 miles. On a certain wall map, this distance is represented by 9 inches. The actual distance between City C and City D is 4100 miles. How far apart are they on the same map?
Answers
The city C and city D are 13.67 inches apart on the same map.
In the question ,
it is given that ,
Distance between city A and city B is 2700 miles represented by 9 inches on the map .
Distance between city C and city D is 4100 miles ,
let it be represented by x inches on the map.
By using the concept of Ratio , we get
2700 miles : 9 inches = 4100 miles : x inches
2700/9 = 4100/x
Simplifying we get ,
2700*x = 4100*9
x = (4100*9)/2700
x = 36900/2700
x = 13.6666
x ≅ 13.67 inches
Therefore , On the map the city C and city D will be 13.67 inches apart .
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What the meaning of statement this?
Answers
This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.
The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:
∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))
The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.
The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.
The statement can be interpreted as follows:
"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."
In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.
It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.
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What is the rate of change, or slope, for this set of ordered pairs: (-3,9 and (0,15) *please show work*
Answers
(y2-y1)/(x2-x1)
Hope this helps!!!
Answer:
Step-by-step explanation:
slope, m=(y2-y1)/(x2-x1) in this case
m=(15-9)/(0- -3)
m=6/3
(m=2)
Olivia earns $12 an hour at the grocery store. She kept track of her hours per week and how much she earned in the following table. Graph the values in the table on the coordinates plane shown. what will you label the x-axis?
Answers
Answer:
12 times y = x
Step-by-step explanation:
I see on you paper you want to do intervals of 2 so just take 12 and multiply it by the desired number. Equation: 12 x # = the y axis point. This is where #=x-axis and plugging it in the equation gives you the y point.
Is the following relation a function? (1 point)
Answers
9514 1404 393
Answer:
no
Step-by-step explanation:
One of the elements in the set x has multiple arrows from it. That is an indication the relation is NOT A FUNCTION.
Each x-value can map to only one y-value if the relation is a function.
Solve the equation for y.
3x+2y=6
Group of answer choices
y=9x/2
y=−3/2x+3
y=−3x+6
y=(3x)(6)/2
PLEASE HURRY
Answers
Answer:
\(3x + 2y = 6 \\ 6 - 3x = 2y \\ y = \frac{6 - 3x}{2} \\ \\ thank \: you\)
pls answer the first question
