Answer: p value = 0.057
The candidate's opponent's claim of ( p < 0.054 ) is false
as p (0.057) is greater than 0.054.
(P > 0.054)
Step-by-step explanation:
p₀ = 5.4% = 0.054
Claim: p < 0.054
n = 500
x = 19
To perform z test for the proportion, we use TI-83, TI-83 plus, or TI-84 calculator
first;
Press STAT and go to TESTS menu.
Go to 1-Prop Z TEST
p₀ : 0.054
x : 19
n : 500
Prop < p₀
Calculate.
Output:
z = -1.582933013
p = 0.0567183695
therefore
p value = 0.057 ( three decimal place)
there the candidate's opponent's claim of ( p < 0.054 ) is false
as p > 0.054
Adelphi Company purchased a machine on January 1, 2017, for $60,000. The machine was estimated to have a service life of ten years with an estimated residual value of $5,000. Adelphi sold the machine on January 1, 2021 for $21,000. Adelphi uses the double declining method for depreciation. Using this information, how much is the gain or (loss) for the equipment sale entry made on January 1, 2021. Enter a loss as a negative number.
Answer:
-$3576
Step-by-step explanation:
Depreciation using double declining method=100%/useful life*2
Depreciation using double declining method=100%/10*2=20%
2017 depreciation=$60,000*20%=$12000
2018 depreciation=($60,000-$12000)*20%=$9600
2019 depreciation=($60,000-$12000-$9600 )*20%=$7680
2020 depreciation=($60,000-$12000-$9600-$7680 )*20%=$6144
carrying value in 2021=$60000-$12000-$9600 -$7680-$6144 =$24576
Loss on disposal of machine=$21,000-$24576 =-$3576
How many three-digit numbers can you make if you are not allowed to use any other digits except 4 and 9?
Answer:
8
Step-by-step explanation:
That total is ...
(number of possibilities in each location)^(number of locations) = 2^3 = 8
The possible numbers are ...
444, 449, 494, 499
944, 949, 994, 999
There are 8 of them.
Find the surface area of this composite solid. I Need answer ASAP Will give brainliest
Answer:
B. 120 m²
Step-by-step explanation:
To find the surface area of the composite solid, we would need to calculate the area of each solid (square pyramid and square prism), then subtract the areas of the sides that are not included as surface area. The sides not included as surface area is the side the pyramid and the prism is joint together.
Step 1: find the surface area of the pyramid:
Surface area of pyramid with equal base sides = Base Area (B) + ½ × Perimeter (P) × Slant height (l)
Base area = 4² = 16 m
Perimeter = 4(4) = 16 m
Slant height = 3 m
Total surface area of pyramid = 16 + ½ × 16 × 3
= 16 + 8 × 3 = 16 + 24
= 40 m²
Step 2: find the area of the prism
Area = 2(wl + hl + hw)
Area = 2[(4*4) + (5*4) + (5*4)]
Area = 2[16 + 20 + 20]
Area of prism = 2[56] = 112 m²
Step 3: Find the area of the sides not included
Area of the sides not included = 2 × area of the square base where both solids are joint
Area = 2 × (4²)
Area excluded = 2(16) = 32 m²
Step 4: find the surface area of the composite shape
Surface area of the composite shape = (area of pyramid + area of prism) - excluded areas
= (40m²+112m²) - 32m²
= 152 - 32
Surface area of composite solid = 120 m²
The mean student loan debt for college graduates in Illinois is $30000 with a standard deviation of $9000. Suppose a random sample of 100 college grads in Illinois is collected. What is the probability that the mean student loan debt for these people is between $31000 and $33000?
Answer:
the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331
Step-by-step explanation:
Given that:
Mean = 30000
Standard deviation = 9000
sample size = 100
The probability that the mean student loan debt for these people is between $31000 and $33000 can be computed as:
[tex]P(31000 < X < 33000) = P( X \leq 33000) - P (X \leq 31000)[/tex]
[tex]P(31000 < X < 33000) = P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P(Z \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{3000}{\dfrac{9000}{10}}}) -P(Z \leq \dfrac{1000}{\dfrac{9000}{10}}})[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq 3.33)-P(Z \leq 1.11})[/tex]
From Z tables:
[tex]P(31000 < X <33000) = 0.9996 -0.8665[/tex]
[tex]P(31000 < X <33000) = 0.1331[/tex]
Therefore; the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331
Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 86 and 125 miles in a day. Round your answer to four decimal places.
Answer:
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = 0.5890 miles
Step-by-step explanation:
Step(i):-
Given mean of the Population = 100 miles per day
Given standard deviation of the Population = 23 miles per day
Let 'X' be the normal distribution
Let x₁ = 86
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{86-100}{23} =-0.61[/tex]
Let x₂= 86
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{125-100}{23} = 1.086[/tex]
Step(ii):-
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = P(-0.61 ≤ Z≤ 1.08)
= P(Z≤ 1.08) - P(Z≤ -0.61)
= 0.5 +A(1.08) - ( 0.5 - A(-0.61))
= A(1.08) + A(0.61) ( A(-Z)= A(Z)
= 0.3599 + 0.2291
= 0.5890
Conclusion:-
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = 0.5890 miles per day
The graph shows a gasoline tank being filled at a rate of 2,500 gallons of gas per
hour. How will the graph change if the rate slows?
The correct answer is The line will be less steep because the rate will be slower
Explanation:
The rate of the graph is defined by the number of gallons filled vs the time; this relation is shown through the horizontal axis (time) and the vertical axis (gallons). Additionally, there is a constant rate because each hour 2,500 gallons are filled, which creates a steep constant line.
However, if the rate decreases, fewer gallons would be filled every hour, and the line will be less steep, this is because the number of gallons will not increase as fast as with the original rate. For example, if the rate is 1,250 gallons per hour (half the original rate), after 8 hours the total of gallons would be 1000 gallons (half the amount of gallons); and this would make the line to be less steep or more horizontal.
Which steps would be used to solve the equation? Check all that apply. 2 and two-thirds + r = 8 Subtract 2 and two-thirds from both sides of the equation. Add 2 and two-thirds to both sides of the equation. 8 minus 2 and two-thirds = 5 and one-third 8 + 2 and two-thirds = 10 and two-thirds Substitute the value for r to check the solution.
Answer:
Subtract 2 and two-thirds from both sides of the equation
8 minus 2 and two-thirds = 5 and one-third
Substitute the value for r to check the solution.
Step-by-step explanation:
2 2/3 + r = 8
Subtract 2 2/3 from each side
2 2/3 + r - 2 2/3 = 8 - 2 2/3
r = 5 1/3
Check the solution
2 2/3 +5 1/3 =8
8 =8
Answer:
1, 3, 5
Step-by-step explanation:
edge
What is m<3 ? M<6 is and m<8 is (x+5
Answer:
m∠3 = 115 degrees
Step-by-step explanation:
angle 6 and angle 8 are on a straight line
we know that sum of angles on straight line is 180
therefore
m∠8 = x+5
m∠6 + m∠8 = 180
2x - 5 + x+5 = 180
=> 3x = 180
=> x = 180/3 = 60
Thus,
m∠6 = 2x-5 = 2*60 - 5 = 115
we know that for two parallel lines cut by a transversal
alternate opposite angles are equal
m∠6 and m∠3 are alternate opposite angles
thus
m∠6 = m∠3 = 115 (answer)
what is the simplest form of this expression 2(w-1) +(-2)(2w+1)
Answer:
-2w - 4
Step-by-step explanation:
What is the simplest form of this expression
2(w - 1) + (-2)(2w + 1) =
= 2w - 2 - 4w - 2
= -2w - 4
Answer: -2w-4
Step-by-step explanation:
subtract 4w of 2w
2w-2-4w-2
subtract 2 of -2
-2w-2-2
final answer
-2w-4
PLEASEEE HELP ME ITS DUE ASAP PLS
Answer:
V ≈ 1436.03 cm³
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3}[/tex]πr³. r represents the radius, which is 7 cm since the diameter is 14 cm, so plug 7 into the equation as r. Also remember that the question states to use 3.14 for pi/π.
V = [tex]\frac{4}{3}[/tex] (3.14)(7)³
V ≈ 1436.03 cm³
Express the confidence interval 0.333 less than p less than 0.999 in the form Modifying Above p with caret + or - E. Modifying Above p with caret + or - E = + or -.
We are being asked to express the confidence interval " [tex]0.333 < p < 0.999[/tex] " in the form [tex]P + / - E[/tex]. Well, just take a look at procedure below for the first half of the problem,
[tex]P = ( 0.999 + 0.333 ) / 2,\\E = ( 0.999 - 0.333 ) / 2[/tex]
As you can see, for this first bit we took the average of the numbers, for the second we subtracted one from the other, and now let us approximate each value -
[tex]P = ( About ) 0.666,\\E = ( About ) 0.333[/tex]
And so, [tex]P + / - E[/tex] should be [tex]0.666 + / - 0.333[/tex]. That is our solution!
Use this information to evaluate the following. Hint: do not try to solve for the value of a.
loga 2 = 0.32
loga 3 = 0.50
loga 5 = 0.73
a. loga 15 =
b. loga (5/3) =
c. loga(8a7)
Answer:
a. 1.23
b. 0.23
c. 7.96
Step-by-step explanation:
Use laws of logarithms:
log(a*b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(a^b) = b*log(a)
log_k(k) = 1
a. log_a(15) = log_a(3*5) = log_a(3) + log_a(5) = 0.50 + 0.73 = 1.23
b. log_a(5/3) = log_a(5) - log_a(3) = 0.73 - 0.50 = 0.23
c. log_a(8*a^7) = log_a(8) + log_a(a^7) = log_a(2^3) + log_a(a^7)
= 3log_a(2) + 7log_a(a) = 3(0.32) + 7(1) = 7.96
Need help with number 20
Answer:
A
Step-by-step explanation:
Since we are given BC is congruent to DC and angle b and d are 90. We can prove that <C is congruent to itself by reflexive property of congruence. We can also you use linear pair theorem to prove <CDA is congruent to <CBE. Since they are right angles, we can prove that they are congruent by rt <s thm. Thus, we cna prove they are congruent by ASA. Hope it helps
Based upon market research, the Hawthorne Company has determined that consumers are willing to purchase 135 units of their portable media player each week when the price is set at $26.10 per unit. At a unit price of $9.10, consumers are willing to buy 305 units per week.
Required:
a. Determine the weekly demand equation for this product, assuming price, p, and quantity, x, are linearly related.
b. Determine the weekly revenue function.
c. Determine the number of units consumers will demand weekly when the price is $93.00 per portable media player.
d. Determine the number of units consumers will demand weekly when the revenue is maximized.
e. Determine the price of each unit when the revenue is maximized
Answer:
a. P= -0.1x + 39.6
b. R(x) = -0.1x^2 + 39.6x
c. x = -534 units
d. Number of units demand weekly when the revenue is maximized is 198 units
e. Price p = 15.8 units
Step-by-step explanation:
So for the demand equation let price =p
x= number of units sold
m = per unit price
b = initial fix amount
a. p = mx + b
When p = 26.10 $, x = 135 units so equation
26.10 = m(135) + b .......................(1)
When p = 9.10, x = 305 units so equation
9.10 = m(305) + b .......................(2)
subtracting equation (2) from equation (1)
26.10 - 9.10 =135x +b - 305x - b
17.00 = -170m
m= 17/-170
m= -0.1
Lets plug the value of m in the first equation
26.10 = m(135) + b
26.10 = (-0.1)(135) + b
26.10 = -13.5 + b
b= 26.10 + 13.5
b= 39.6
So the equation would be P= -0.1x + 39.6
b. Revenue = price * quantity
R(x) = p * x
R(x) = x (-0.1x + 39.6)
R(x) = -0.1x^2 + 39.6x
c. Here we have p = $ 93.00
P= -0.1x + 39.6
93 = -0.1x + 39.6
93 - 39.6 = -0.1x
-0.1x = 53.4
x = 53.4 / -0.1
x = -534 units
d. R(x) = -0.1x^2 + 39.6x
On differentiating it with respect to x.
R'(x) = -0.1(2)x^2-1 + 39.6x^1-1
R'(x) = -0.2x + 39.6
So for the maximum revenue differentiation of revenue function must be 0.
0 = -0.2x + 39.6
0.2x = 39.6
x = 39.6 / 0.2
x = 198 units
Number of units demand weekly when the revenue is maximized is 198 units
e. Price p = -0.1x + 39.6
on plugging the value x =238
Price p = -0.1(238) + 39.6
Price p = -23.8 + 39.6
Price p = 15.8 units
if my medical expenses are $40,000 per year for 35 years with an increase of 6% a year what is the total amount?
Answer:
$4,457,391.19
Step-by-step explanation:
The sum of n terms of a geometric sequence with common ratio r and initial value "a" is ...
S = a(r^n -1)/(r -1)
Here, your growth factor is r = 1 +6% = 1.06. So, the sum of expenses over 35 years will be ...
S = $40,000(1.06^35 -1)/(1.06 -1) = $4,457,391.19
Applying the Segment Addition Postulate
Point D is on segment BC. Segment BC measures 8x
units in length.
С
D
B
What is the length of segment BC?
units
3x + 8
4x + 10
Answer:
144
Step-by-step explanation:
Find: Length of segment BC
CD+DB=BC
3x+8+4x+10=BC
7x+18=BC
BC also equals 8x (given on the screen shot)
7x+18= 8x
x=18
18 times 8 = 144
Check:
3( 18) + 8 + 4(18) + 10
54+8 + 72+10
64+ 80= 144 TRUE
Explain the areas in which you will find integration to be significant in your day to day work as an EHT.
Answer:
Step-by-step explanation:
An EHT is an Environmental Health Technician. Integration (Integral Calculus, if that's what you mean) will be applied to an Environmental Health Technician's job in the following way:
1. In the analysis or examination of samples from an environment, such as soil sample, water sample, domestic waste sample, septic waste sample, etc.
Essentially, Integral Calculus (and other forms of Maths) must be studied, before a person is able to be an Environmental Health Technician.
Degrees in any of the following fields are a necessary criterion;
- Applied Science
- Public Health
- Environmental Science
- Biochemistry
- Health Data Analysis
a geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .
Answer: [tex]\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}[/tex]
Step-by-step explanation:
a₁, 375, a₃, a₄, 81
First, let's find the ratio (r). There are three multiple from 375 to 81.
[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]
Next, let's find a₁
[tex]a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625[/tex]
Lastly, Use the Infinite Geometric Sum Formula to find the sum:
[tex]S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}[/tex]
A pet store has 10 puppies, including 2 poodles, 3 terriers, and 5 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement find the probability that both select a poodle.
The probability is
Answer:
2/10 for Rebecka and either 2/9 or 1/9 for Aaron depending on if Rebecka selects a poodle or not.
Step-by-step explanation:
do some math
Suppose the finishing times for cyclists in a race are normally distributed and have a known population standard deviation of 9 minutes and an unknown population mean. A random sample of 18 cyclists is talken and gives a sample mean of 146 minutes. Find the confidence interval for the population mean with a 99% confidence level.
0.10 0.05 0.025 0.005 0.01
1.282 1.645 1.960 2.326 2.576
Answer:
The 99% confidence interval for the population mean is between 140.54 minutes and 151.46 minutes
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.576[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.576*\frac{9}{\sqrt{18}} = 5.46[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 146 - 5.46 = 140.54 minutes
The upper end of the interval is the sample mean added to M. So it is 146 + 5.46 = 151.46 minutes
The 99% confidence interval for the population mean is between 140.54 minutes and 151.46 minutes
Brainliest for correct awnser! Hannah thinks of a number. She multiplies the number by 2, adds 4, and then divides the result by 3. The number she ends up with is 6. What number did Anna start with? If you work backward to solve this problem, what do you do first?A.Multiply 6 by 2B.Multiply 6 by 3C.Divide 6 by 2D.Subtract 4 from 6
Answer:
B. Multiply 6 by 3
Step-by-step explanation:
Do the opposite order of what Hannah did. The last step that she did was divide by 3, so you would multiply the result (6) with 3:
B. Multiply 6 by 3
Your step by step for getting the number Hannah started with:
First, multiply 6 with 3:
6 x 3 = 18
Next, subtract 4:
18 - 4 = 14
Next, divide by 2:
14/2 = 7
Hannah started with the number 7.
~
Answer: Hannah started with 7.
B. Multiply 6 by 3
Explanation:
Let the number be y
2 × y = 2y
(2y + 4)/3 = 6
2y + 4 = 6×3 = 18
2y + 4 = 18
2y = 18 - 4 = 14
y = 14/2 = 7
To solve the problem backward, the first step is to multiply 6 by 3.
Translate into an algebraic expression and simplify if possible. I have a total of 10 gigabytes of data on my computer, x gigabytes are movies and the rest is music. How many gigabytes of music is stored on my computer?
Answer:
simple really
Step-by-step explanation:
10 gigabytes of data on my computer, x gigabytes are movies and the rest is music.
so it will have to be 10-X= remaining gigabites of music
Answer:
Movies: x gig
pictures: x/2 gig
music: 10 - x - x/2 = 10 - (3/2)x
Give examples of three sets A,B,C for which A-(B-C)=(A-B)-C.
ASK YOUR TEACHER Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = x3 + x − 9, [0, 2]
Answer:
Yes
Step-by-step explanation:
The Mean Value Theorem states that if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that
[tex]f'(c)=\dfrac{f(b)-f(a)}{b-a}[/tex]
Given [tex]f(x)=x^3+x-9$ in [0,2][/tex]
f(x) is defined, continuous and differentiable.
[tex]f(2)=2^3+2-9=1\\f(0)=0^3+0-9=-9[/tex]
[tex]f'(c)=\dfrac{f(2)-f(0)}{2-0}=\dfrac{1-(-9)}{2}=5[/tex]
[tex]f'(x)=3x^2+1[/tex]
Therefore:
[tex]f'(c)=3c^2+1=5\\3c^2=5-1\\3c^2=4\\c^2=\frac{4}{3} \\c=\sqrt{\frac{4}{3}} =1.15 \in [0,2][/tex]
Since c is in the given interval, the function satisfy the hypotheses of the Mean Value Theorem on the given interval.
Evaluate. Write your answer as a fraction or whole number without exponents. 1/10^-3 =
Answer:
1000
Step-by-step explanation:
=> [tex]\frac{1}{10^{-3}}[/tex]
According to the law of exponents, [tex]\frac{1}{a^{-m}} = a^{m}[/tex]
So, it becomes
=> [tex]10^{3}[/tex]
=> 1000
Do you think that it is possible to obtain a good indication of the precise degree of protection accorded by a country to its import-substitute industries? Why or why not? (Remember that, in addition to tariffs, protection is also provided by various non-tariff barriers.)
Answer:
The answer is below
Step-by-step explanation:
First we have that free trade refers to the movement of goods, services, capital and knowledge from one place to another. But in reality, free trade does not exist since there are many tariffs and non-tariff barriers.
However,
- Tariff barriers are taxes imposed on imports into a country according to quantity or quantity. Tariff barriers increase the price of imports in the country, which affects the demand for goods and services. Countries agree to lower these tariff barriers, which make trade reasonable for countries that sign agreements.
- Non-tariff barriers are barriers that do not directly affect import prices. It does not impose a tax directly on imports. It tries to reduce imports by using barriers other than taxes.
Therefore countries try to protect their domestic industries using various tariff and non-tariff barriers. The amount of the barriers cannot be precisely decided, since the barriers are not only to protect national industries, but some barriers are imposed to avoid the economic and political monopoly of a foreign country in the national country.
Government actions:
The government applies various health and safety regulations to domestic and foreign products, since consumers in the country must be protected against any impurities. Still, these restrictions are also more than required, leading to protectionism.
The government uses various tariff and non-tariff barriers not only to protect national industries but also for various social, economic, and political reasons.
Therefore, it is difficult to establish tariff and non-tariff barriers in a country accurately.
the number 117 is divisible by nine and only if the sum of the digits in 117 are evenly divisible by 9, truth or false
Answer:
true
Step-by-step explanation:
The test for divisibility by 9 is to add all the digits of the number. If that sum is divisible by 9, then the number is divisible by 9.
A jug of milk contains 3 quarts of milk. Micheal pour 1 pint of milk from the jug. How many pint of milk is left in the jug
Answer:
5 pints of milk.
Step-by-step explanation:
Note the unit conversion:
1 quart = 2 pint.
There are 3 quarts of milk. Multiply 3 with 2 to get the amount of pints in the jug:
3 x 2 = 6
The jug of milk has 6 pints of milk. Michael then pours 1 pint of milk. Subtract 1 from 6:
6 - 1 = 5
There are 5 pints of milk left in the jug.
~
Answer:
[tex]2.5[/tex]
Step-by-step explanation:
1 quart = 2 pints
1 pint = 0.5 quarts
[tex]3 - 0.5 = 2.5[/tex]
[tex]=2.5q[/tex]
Hope this helps.
Please help me this
And show your working out
Thanks I will appreciate it
Answer:
3x / 2 + 9 = 5
3x / 2 = -4
3x = -8
x = -8/3
(2 + v) / 3 = 9
2 + v = 27
v = 25
32 / (d - 2) = 10
32 = 10 * (d - 2)
3.2 = d - 2
d = 5.2
2p - 4 = 3p / 2
2 * (2p - 4) = 3p
4p - 8 = 3p
p - 8 = 0
p = 8
3b / 2 = 12
3b = 24
b = 8
a silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by
Question:
A silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by
s(t) = -16t² + v₀t + s₀
Determine the position and velocity functions for the coin.
Answer:
position function: s(t) = (-16t² + 64) ft
velocity function: v(t) = (-32t) ft/s
Step-by-step explanation:
Given position equation;
s(t) = -16t² + v₀t + s₀ ---------(i)
v₀ and s₀ are the initial values of the velocity and position of the coin respectively.
(a) Since the coin is dropped, the initial velocity, v₀, of the coin is 0 at t = 0. i.e
v₀ = 0.
Also since the drop is from the top of a building that is 64 feet tall, this implies that the initial position, s₀, of the coin is 64 ft at t=0. i.e
s₀ = 64ft
Substitute the values of v₀ = 0 and s₀ = 64 into equation (i) as follows;
s(t) = -16t² + (0)t + 64
s(t) = -16t² + 64
Therefore, the position function of the coin is;
s(t) = (-16t² + 64) ft
(b) To get the velocity function, v(t), the position function, s(t), calculated above is differentiated with respect to t as follows;
v(t) = [tex]\frac{ds(t)}{dt}[/tex]
v(t) = [tex]\frac{d(-16t^2 + 64)}{dt}[/tex]
v(t) = -32t + 0
v(t) = -32t
Therefore, the velocity function of the coin is;
v(t) = (-32t) ft/s