The Complete statement is : The location of proton in the atom is inside nucleus , has a charge of +1 elementary charge and the approximate mass of proton is 1.00727647 amu .
The Protons are the positively charged particles, the electrons are negatively charged particles and the neutrons have no charge.
In an atom there are equal number of protons and number of electrons . Thus the atom is electrically neutral in nature. The charge of the proton is equal and opposite of an electron. So , proton has a unit positive charge.
The Protons are found inside the nucleus of atom , the proton carries the elementary charge of 1.00727647 amu (atomic mass units) , the charge on the proton is +1 .
The given question is incomplete , the complete question is
Answer the following questions about the Proton ,
The location of proton in the atom is ______ , has a charge of ______ elementary charge and the approximate mass of proton is _____ amu .
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If a particular sample has 36 participants and the other sample has 40 participants, the total degrees of freedom for the study is __________.
If a particular sample has 36 participants and the other sample has 40 participants, the total degrees of freedom for the study is
What is the degrees of freedom?In Mathematics, the degrees of freedom in a sample are typically used to correct a possible bias that exists between the alternative and null hypotheses.
Mathematically, total degrees of freedom for the study can be calculated by using this mathematical expression:
v = n - k
Where:
v represents the total degree of freedom.n represents the number of individuals in a samplek represents the number of parameters being estimated.Note: k is equal to 2 in this scenario.
Total degrees of freedom, v = n₁ + n₂ - k
Total degrees of freedom, v = 36 + 40 - 2
Total degrees of freedom, v = 74.
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A survey was done 1/4 voted for a restaurant 4/7 voted a library the rest voted for a gym what fraction voted for the gym
The fraction that voted for the gym is calculated as: 5/28.
How to Use Fractions to Solve Word Problems?To find out what fraction voted for the gym, you have to subtract the fractions that voted for the restaurant and the library from 1, which represents the total number of people surveyed.
You can do this by adding the fractions that voted for the restaurant and the library and then subtracting the sum from 1.
(1/4) + (4/7) = (7/28) + (16/28) = (23/28)
so 1 - (23/28) = (5/28)
Therefore, 5/28 of the people surveyed voted for the gym.
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for 14-21 write two equivalent fractions for each
The fractions with different numerators and denominators but the same value are said to be equivalent fractions.
What is an equivalent fraction about?For instance, since 2/4 and 3/6 both equal the 1/2, they are equivalent fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
A rule that says the result of multiplying the numerator and denominator of a fraction by the same nonzero number is a fraction equal to the original fraction.
Equivalent fractions are those that, despite their visual differences, represent the same value. For instance, if you have a cake and cut it into two equal pieces, you will have consumed half of the cake.
In this case, it should be noted 1/2 is the same as 3/6.
Note that an overview was given as your information is incomplete.
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When building a house, the number of days required to build is inversely
proportional to with the number of workers. One house was built in 85 days by 5
workers. How many days would it take to build a similar house with 25 workers?
It would take 17 days to build a similar house with 25 workers.
What is Inverse Proportion?Inverse proportion is a type of proportionality relationship. If two quantities are inversely proportional then as one quantity increases, the other decreases. In inverse proportion, the product of the given two quantities is equal to a constant value
One house was built in 85 days by 5 workers;
The relationship will be;
d ∝ 1/n
where
n = number of workers
d = number of days
d = k/n
when d = 5
k = 85
k = 5 x 85
k = 425
when n = 25
d = 425/25
d = 17
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The distribution of values taken by a statistic in all possible samples of the same size from the same population is None of the above The population parameter The sampling distribution of the statistic The probability that the statistic is obtained The variance of the values
The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.
The population parameter is the true value of the statistic for the entire population. The probability that the statistic is obtained is the probability that it will be obtained in a single sample from the population. The variance of the values is the amount of variation among the values of the statistic in the sample. The formula for calculating the variance is the sum of the squared deviations from the mean, divided by the number of values in the sample. This can be written mathematically as: Variance = Σ (x - X)2/ n, where x is each value in the sample, X is the mean value, and n is the number of values in the sample.
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The initial bacterium count in a culture is 500. A biologist later makes a sample count ofbacteria in the culture and finds that the relative rate of growth is 40% per hour.(a)Find a function that models the number of bacteria after t hours.(b)What is the estimated count after 10 hours?(c)When will the bacteria count reach 80,000?(d)Sketch the graph of the function . n(t)
a) The function is P = 500e^0.4t
b) The count after 10 hours is 27299
c) it would reach 80000 in 13 hours
What is the function?We know that at this time we are dealing with the population of the bacteria and we have to invoke the exponential growth ideology and we would have;
P = Poe^rt
P = population at time t
Po = Initial population
r = Population growth rate
t = Time taken
Then we have;
P = 500e^0.4t
After ten hours;
P= 500e^0.4 * 10
P = 27299
The count would reach 80000 when;
80000 = 500e^0.4 t
80000/500 = e^0.4 t
160 = e^0.4 t
ln160 = e^0.4 t
ln160 = 0.4t
t = ln160/0.4
t = 13 hours
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show me prymind with base length: 8 feet side length: 6.56 feet (calculated using the pythagorean theorem) height: 12 feet rmid
A diagram of a pyramid with the given measurements is not possible to generate.
But we can calculate he base length, side length and height of a pyramid using the Pythagorean theorem.
In a pyramid, the slant height (rmid) can be found using the Pythagorean theorem. If the base length (b) and the height (h) of the pyramid are known, the slant height (rmid) can be calculated using the formula:
rmid = sqrt(b^2 + h^2)
In this case,
rmid = sqrt(8^2 + 12^2) = sqrt(64 + 144) = sqrt(208) = 14.4
You can also use this information to find the side length of the pyramid, which is the length of one of the triangular faces. Using the Pythagorean theorem again:
side length = sqrt(rmid^2 - (b/2)^2)
In this case,
side length = sqrt(14.4^2 - (8/2)^2) = sqrt(207.36 - 16) = sqrt(191.36) = 6.56
So, based on the information provided, the base length of the pyramid is 8 feet, the side length is 6.56 feet and the height is 12 feet and the slant height is 14.4 feet.
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Expand a^2= (b-x)^2 +h^2
The expanded value of the given equation is a²+2bx = b² + x ²+ h² .
Expansion - what is it?Multiplication distributes over addition, so an expansion of a product of sums represents it as a sum of products.
Expansion is a scale-increasing affine transformation, sometimes known as enlargement or dilatation. It is also frequently referred to as an enlargement and is the polar opposite of a geometric contraction. An expansion and a translation are equivalent to a central dilation.
We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression.
Given : a^2= (b-x)^2 +h^2
a² = (b-x)² + h²
we know that (c-d)² = c²+d² + 2cd
So, a² = b² + x² -2bx + h²
a²+2bx = b² + x ²+ h²
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In exercises 5–8 tell whether a correlation is likely in the situation. If so tell her there’s a casual relationship. Explain your reasoning. 6. favorite color and color of shoes 
ANSWER FAST PLEASE
WILL GIVE BRAINLIEST
There may be a correlation, but there is no direct link. This is because it is more likely that you will get shoes in the color you want.
It's likely that the preferred color and the color of the shoes are related. A person's favorite color may or may not match the color of their shoes, so there is no direct correlation. Particularly, the color of the shoes may have influenced the preferred color.
There may be a correlation, but there is no direct link.
How does correlation work?Correlation is a method for figuring out how two variables relate to each other. You learned that putting two variables on a "scatter plot" can help you figure out if they are usually connected. Despite the fact that there are other measures of association for variables measured at the ordinal or higher level of measurement, correlation is the strategy that is utilized the most frequently.
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A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 79.
The linear regression equation for this data is given as follows:
y = x - 6.
The projected grade for a student with homework grade of x = 79 is given as follows:
73.
How to obtain the equation for the regression line?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
The points from this data-set are given as follows:
(70, 55), (89, 92), (79, 81), (84, 74), (84, 77), (70, 65) and (64, 68).
Inserting these points into a calculator, the regression equation is given as follows:
y = x - 6.
The projected grade for a student with homework grade of x = 79 is obtained as follows:
y = 79 - 6
y = 73.
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What is the sum of the geometric sequence −2, −6, −18, … if there are seven terms?
Group of answer choices
−728
−128
−1,458
−2,186
The sum of the first seven terms is given by -2186
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar², ar³, ...
The geometric sequence is given here by -2,-6,-18...
We can observe that the common ratio is r=3
thus the sequence of upto 7 terms is given by
-2,-6,-18,-54,-162,-486.-1458
Thus the sum of all seven terms is given by
S=-2-6-18-54-162-486-1458
=-2186
Hence, The sum of the first seven terms is given by -2186
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in trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the [ select ] , the value of the hypotenuse is [ select ] , and is the angle adjacent to the [ select ] .
In trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the y-axis , the value of the hypotenuse is positive , and is the angle adjacent to the y-axis and hypotenuse.
A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. They represent, successively, Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent.
So, when we graph a right angle triangle, we draw a side of triangle perpendicular to y-axis and another side will be on y-axis. The remaining side left would be hypotenuse that will always be positive and is adjacent to the side perpendicular to y-axis and the side on the y-axis.
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Answer the questions in image!
(The answers are already there, just figure out which go where.)
50 points!
Solve the equation on the
interval [0, 2π).
3 sin x = sin x + 1
The solution to the equation on the interval is x = π/6 + 2πn, where n is any non-negative integer less than 2.
How to determine the solutionFrom the question, we have the following parameters that can be used in our computation:
3 sin x = sin x + 1
Interval = [0, 2π).
To solve the equation 3sin(x) = sin(x) + 1, we first subtract sin(x) from both sides to get 2sin(x) = 1.
So, we have
2sin(x) = 1
Then, we divide both sides by 2
sin(x) = 1/2.
Therefore, x = arcsin(1/2) + 2πn, where n is any integer.
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As a town gets smaller the population of its high school decreases by 4% each year the senior class has 160 students now. In how many years will it have about 100 students? write an equation. then solve the equation without graphing.
The number of years that it will it have about 100 students is 11 years.
How to calculate the number of tears?Final population = Initial population * (1-0.04)^years
Where 0.04 is the percentage decrease (4%) converted to decimal form, and "years" is the number of years in the future.
We can use this formula to find the number of years it will take for the senior class to have about 100 students:
Final population = 100
Initial population = 160
100 = 160 * (1-0.04)^years
We can solve for "years" by taking the natural logarithm of both sides:
ln(100) = ln(160 * (1-0.04)^years)
ln(100) = ln(160) + ln((1-0.04)^years)
and then we can solve for the power of (1-0.04)
ln(100) - ln(160) = ln((1-0.04)^years)
now we can get the value of years
years = (ln(100) - ln(160)) / ln(1-0.04)
which is around 10.72 , so it would take about 11 years for the senior class to have about 100 students.
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division problem can be described using this model
The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.
What is division?
Division is a mathematical operation that involves dividing one number (the dividend) by another (the divisor). The result of this operation is called the quotient. Division is the inverse of multiplication, meaning that the product of a number divided by itself is equal to one. Division can also be used to find the number of times one number is contained in another. Division can be expressed in a variety of ways, such as by using fractions, decimals, or by using a long division algorithm.
When you look at the diagram, The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.
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The size of a pentagon are given as x, x+1,x+3,x-2 and 6.If the perimeter is less than 78cm and x is an interger.Find the largest value of x
The largest value of x is 13.
What is perimeter?A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.
Given:
The size of a pentagon are given as x, x+1,x+3,x-2 and 6.
The perimeter is less than 78 cm and x is an integer.
The perimeter of the pentagon = the sum of all the sides.
x + x+1 + x+3 + x-2 + 6 < 78
4x + 10 - 2 < 78
4x < 70
x < 14
The largest value of x is 13.
Therefore, the largest value of x is 13.
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56 parts were lost. 3% of the total parts were lost. How many total parts were there?
Answer:
3% = 56
100% = ?
Rule of three:
56 x 100
—————
3
Answer = 1,866.667 ≈ 1.867
Step-by-step explanation:
dont mind the answer below have a great day ______
\|/
In a right triangle, sin(7x+5)=cos(8x-5). Find the smaller of the triangles two acute angles
In a case whereby a right triangle, sin(7x+5)=cos(8x-5), the smaller of the triangles two acute angles is 43°.
How can the smaller of the triangles two acute angles be calculated?The concept that will be used is right triangle. An acute angle is one that is smaller than 90 degrees in length. The correct angle is larger than this angle (which is equal to 90 degrees).
We can see that sin(7x+5)=cos(8x-5)
An it implies that 7x+5 -8x-5 =90°
15x=90
x= 6
Then 7(6)+5= 47° 8(6)-5 = 43°
Hence the smaller of the triangles two acute angle is 43°
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How to solve -7=5x-2. 2 step equations using inverse operations
Answer:
-1
Step-by-step explanation:
Add 2 to both sides of the equation: -7 + 2 = 5x - 2 + 2. This gives you -5 = 5x.
Divide both sides of the equation by 5: -5/5 = 5x/5. This gives you -1 = x.
So the solution to the equation is x = -1.
Alternatively, you can also use inverse operations to solve the equation by isolating x to one side.
Add 2 to both sides of the equation: -7 + 2 = 5x - 2 + 2. This gives you -5 = 5x
Divide both sides of the equation by 5: -5/5 = 5x/5. This gives you -1 = x
So the solution to the equation is x = -1.
4. A distributor of fasteners is opening a new plant and considering whether to use a mechanized process or a manual process to package the product. The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag. The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag. The company expects to sell each bag of fasteners for $2.75. a) What is the break-even point for the manual process (in units)?
166158 is the break-even point for the manual process
What is Expression?An expression is combination of variables, numbers and operators.
Given that The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag.
Let the number of bags will be x
36234+2.14x..(1)
The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag.
84420+1.85x..(2)
From equation 1 and 2
36234+2.14x=84420+1.85x
2.14x-1.85x=84420-36234
0.29x=48186
Divide both sides by 0.29
x=166158
Hence, 166158 is the break-even point for the manual process
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Realiza el ejercicio utilizando las fórmulas para la curva normal.
Calcular la proporción de estudiantes que siguen una distribución normal, con media 78 y desviación estándar 36 y tienen puntuaciones que exceden por lo menos en cinco puntos de la puntuación que marca la frontera entre el Apto y No-Apto (es declarado No-Apto el 25 % de los estudiantes que obtuvieron las puntuaciones más bajas).
Datos:
Distribución normal
u = 78
O = 36
The proportion of students that had a grade at least 5 points greater than the 25th percentile is given as follows:
0.7054 = 70.54%.
How to obtain the z-scores?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 78, \sigma = 36[/tex]
The 25th percentile is X when Z = -0.675, hence:
-0.675 = (X - 78)/36
X - 78 = -0.675 x 36
X = 53.7
The proportion of students with a grade of at least 58.7 is one subtracted by the p-value of Z when X = 58.7, hence:
Z = (58.7 - 78)/36
Z = -0.54
Z = -0.54 has a p-value of 0.2946.
1 - 0.2946 = 0.7054 = 70.54%.
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The t-test takes into account the _____ and _____ of the data, and the p-value tells us _____.
The p-value is the chance of finding a t-value with an absolute value at least as great as the one we actually observed in the sample data assuming the null hypothesis is actually true. The t-value is a way to measure the difference between the population means.
We reject the null hypothesis of the test if the p-value is less than a predetermined threshold (for example, 0.05). We are primarily concerned with the p-value for each form of t-test, and we merely employ the t-value as a first step in that process.
You'll see that we merely used the t-value as a first step before determining the p-value. The genuine value in which we were most interested was the p-value, but first, we had to determine the t-value.
Therefore the p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data. The t-value is a way to measure the difference between population means.
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Hassan's history class is taking a field trip to the state capitol building. The capitol building is
50 miles from Hassan's school. The class plans to stop after 45 minutes, or 0.75 hours, to
view a local monument. The bus driver plans to drive at an average speed of 40 miles per
hour.
Which equation can you use to find how many hours, x, the second part of the trip will take?
The equation that can be used to find how many hours, x, the second part of the trip will take is:
distance = rate x time
Which equation can you use to find how many hours?Where distance is the remaining distance from the capitol building to the school, rate is the average speed of the bus, and time is the time it takes to travel that distance.So, if we know that the distance is 50 miles and the rate is 40 miles/hour, we can find the time it takes to travel the remaining distance by plugging these values into the equation and solving for x:50 miles = 40 miles/hour x xthen by dividing both sides by 40 miles/hourx = 50/40 = 1.25 hours The equation to use to find how many hours, x, the second part of the trip will take is:distance = rate x timeIn this case, the distance is the remaining distance from the capitol building to the school, which is 50 miles - (40 miles/hour x 0.75 hours) = 35 miles. The rate is the average speed of the bus, which is 40 miles/hour. Therefore, the equation to find the time, x, of the second part of the trip is:35 miles = 40 miles/hour x xTo solve for x, divide both sides of the equation by 40 miles/hour:x = 35 miles / 40 miles/hour = 0.875 hours, or 52.5 minutes.To learn more about capitol building refer to;
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an ordinary annuity pays 1000 quarterly for two years. how many payments are there?
The number of payments for the ordinary annuity that pays $1,000 quarterly for two years is 8.
What is an ordinary annuity?An ordinary annuity's cash flows or payments occur at the end of the period, unlike an annuity due.
For quarterly payments, in a year, payments are made 4 times, that is, every three months.
For two years, the payments will be made 8 times (4 x 2).
Thus, we expect the ordinary annuity to pay $8,000 ($1,000 x 2 x 4).
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Please help, I really need this.
Answer:
Step-by-step explanation:
The slope's simplest form is 1/2.
The figure below is dilated by a factor of centered at the origin. Plot the resulting image.
A graph of the resulting image after a dilation by a factor of 1/4 centered at the origin is shown in the image attached below.
What is dilation?In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin as follows:
Ordered pair T (8, 8) → Ordered pair T' (8 × 1/4, 8 × 1/4) = Ordered pair T' (2, 2).
Ordered pair R (-8, -4) → Ordered pair R' (-8 × 1/4, -4 × 1/4) = Ordered pair R' (-2, -1).
Ordered pair S (4, -8) → Ordered pair S' (4 × 1/4, -8 × 1/4) = Ordered pair S' (1, -2).
Lastly, we would use an online graphing calculator to plot the resulting data points.
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NO LINKS!!
58. You invest $200 in an annuity that earns 7% annual interest. After how many years will the value of the annuity double?
Answer:
The time taken for $200 invested at 7% annual interest compounded yearly:
[tex]\boxed{\mathrm{10.245 \; {years}}}[/tex]
which roughly works out to
[tex]\boxed{\mathrm{10\;years\;and\;3\;months}}[/tex]
Step-by-step explanation:
The formula for the accrued value of an amount P deposited at i% interest for a time period of t years compounded annually is given by the formula
[tex]\boxed{A = P(1 + r)^t\;\cdots[1]}[/tex]
Here A is the accrued value, P the principal and r = i/100
If you are given A, P and r we can compute t by taking the logarithms on both sides
In Equation [1] we get
[tex]\dfrac{A}{P} = (1 + r)^t \;\cdots[2][/tex]
Taking logs on both sides,
[tex]\log A - \log P = \log((1+r)^t)\\\\\log x^a = a \log x\\\\\\[/tex]
Therefore the right side becomes
[tex]t \log (1+r)[/tex]
Replacing right side of equation [2] with this expression yields
[tex]\log A - \log P = t \log (1+r)\\\\\textrm{Or, }\\\\t =\dfrac{ \log A - \log P}{\log (1 + r)}\\\\[/tex]
This is the general equation for determining how long it will take for the principal P to reach the value A if compounded annually at rate r(in decimal)
Since we are interested in seeing our principal P=200 double to A = 400 at r = 7% = 7/100 = 0.07
and
1 + r = 1 + 0.07 = 1.07
[tex]t = \dfrac{\log 400 - \log 200}{\log 1.07}\\\\[/tex]
[tex]t = \boxed{10.245 \; \textrm{years}}[/tex]
or approximately
[tex]\boxed{\mathrm{10\;years\;and\;3\;months}}[/tex]
Answer:
10.24 years (approx. 10 years 3 months)
Step-by-step explanation:
Most fixed annuities pay annual compound interest.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
A = $400 (double the principal)P = $200r = 7% = 0.07To calculate after how many years the value of the annuity will double, substitute the given values into the formula and solve for t:
[tex]\implies 400=200(1+0.07)^t[/tex]
[tex]\implies 2=(1.07)^t[/tex]
[tex]\implies \ln 2=\ln (1.07)^t[/tex]
[tex]\implies \ln 2=t \ln 1.07[/tex]
[tex]\implies t=\dfrac{\ln 2}{\ln 1.07}[/tex]
[tex]\implies t=10.2447683...\rm years[/tex]
Therefore, the value of the annuity will double after 10.24 years (approximately 10 years 3 months).
In a garden 5/6 of the area is filled with native plants. The native plants take up to 107/4 m2 . Let g represent the total area of the garden. chooses 2 answers. pleas help me :(
The total area of the garden is given as follows:
32.1 m².
How to obtain the total area of the garden?The total area of the garden is obtained applying the proportions in the context of this problem.
The area of native plants is given as follows:
107/4 = 26.75 m².
This area of 26.75 m² represents a fraction of 5/6 of the total area g of the garden, hence the total area of the garden is obtained applying the proportion as follows:
5g/6 = 26.75.
g = 26.75 x 6/5
g = 32.1 m².
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A ball is thrown straight down from the top of a 220-foot building with an initial velocity of - 22 feet per second. (Use the position function s(t)=−16t2+v0t+s0 for free-falling objects.)
(a) What is its velocity after 3 seconds?
(b) What is its velocity after falling 108 feet?
The velocity after 3 second is -118 ft/sec and the velocity after falling 108 feet is -87.6 ft/sec.
(a)
For the given position function
[tex]s(t)=-16t^2+v_0.t+s_0[/tex]
The ball is dropped from top of the building of height 220 ft, therefore
[tex]s_0=220ft[/tex]
Also, the initial velocity of the ball is −22 feet per second, thus.
[tex]v_0=22\frac{ft}{s}[/tex]
We will differentiate the position function to find the velocity function and then calculate velocity at (a) t=3sec and (b) after failing 108 ft.
Differentiate Position function to acquire the velocity function v(t).
[tex]s(t)=-16t^2+v_0.t+s_0\\\\s'(t)=-32t+v_0[/tex]
Now substitute t=3s,
v(3) = -32(3) + (-22)
v(3)= -118 ft/sec
b)
To find the velocity of ball after falling 108 ft, first we need to find the time at which ball is dropped 108 ft. and then find velocity at that time using velocity function.
let s(t)=108 ft, then using position function, we can write
[tex]s(t)=-16.t^2+v_0t+s_0\\\\108=-16t^2+(-22)t+220\\\\-16t^2-22t+112=0[/tex]
After solving the quadratic equation, we get
t= -3.42 and 2.05
Since time always positive,
therefore t=2.05 sec.
v (2.05) = -32(2.05)-22
v (2.05) = -87.6 ft/sec
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