Answer:
a. 24.12 ft³/hr b. 0.0768 ft/hr
Step-by-step explanation:
a. Find the rate at which the volume of water in the pool is increasing at time t=6 hours.
The net rate of change of volume of the cylinder dV/dt = volume flow rate in - volume flow rate out
Since volume flow rate in = P(t) and volume flow rate out = R(t),
dV/dt = P(t) - R(t)
[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]
We need to find the rate of change of volume when t = 6.
From the table when t = 6, P(6) = 47 ft³/hr
Also, substituting t = 6 into R(t), we have R(6)
[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]
[tex]\frac{dV}{dt} = 47 - 18e^{0.04X6}\\\frac{dV}{dt} = 47 - 18e^{0.24}\\\frac{dV}{dt} = 47 - 18 X 1.27125\\\frac{dV}{dt} = 47 - 22.882\\\frac{dV}{dt} = 24.118 ft^{3}/hr[/tex]
dV/dt ≅ 24.12 ft³/hr
So, the rate at which the water level in the pool is increasing at t = 6 hours is 24.12 ft³/hr
b. How fast is the water level in the pool rising at t=6 hours?
Since the a rate at which the water level is rising is dV/dt and the volume of the cylinder is V = πr²h where r = radius of cylinder = 10 ft and h = height of cylinder = 5 feet
dV/dt = d(πr²h)/dt = πr²dh/dt since the radius is constant and dh/dt is the rate at which the water level is rising.
So, dV/dt = πr²dh/dt
dh/dt = dV/dt ÷ πr²
Since dV/dt = 24.12 ft³/hr and r = 10 ft,
Substituting the values of the variables into the equation, we have that
dh/dt = dV/dt ÷ πr²
dh/dt = 24.12 ft³/hr ÷ π(10 ft)²
dh/dt = 24.12 ft³/hr ÷ 100π ft²
dh/dt = 0.2412 ft³/hr ÷ π ft²
dh/dt = 0.2412 ft³/hr
dh/dt = 0.0768 ft/hr
So, the arate at which the water level is rising at t = 6 hours is 0.0768 ft/hr
use de moivre's theorem to write
[2(cos 12 degrees + i sin 12 degrees)]^5
in standard form
DeMoivre's theorem says
(2 (cos(12°) + i sin(12°)))⁵ = 2⁵ (cos(5×12°) + i sin(5×12°))
… = 32 (cos(60°) + i sin(60°))
… = 32 (1/2 + √3/2 i )
… = 16 + 16√3 i
give an example of a piecewise function
Answer:
f(x) = 6 when -5 < x ≤ -1
Step-by-step explanation:
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
Answer:
x=5
Step-by-step explanation:
im so bad at explaining things but i hope this helped
Hoang spends $10 on movie tickets, $50 on rent, and $3 on snacks. How much money did Hoang spend on variable expenses?
Answer:
63
Step-by-step explanation:
50+10=60 60+3=63 dollars
he spends 63$ on variable expenses
What is the solution of the equation x2 -14x + 67 = 0?
A. X= 7+3in12
B.X = 7+31V-2
C.X= 7+ 2/8
D.X = 7+ 217
[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]
What is the solution of the equation x^2 - 14x + 67 = 0?
[tex]\tt{First \: option. \: x = 7 \underline{+}3i\sqrt{2}}[/tex][tex]\color{pink}{==========================}[/tex]
#CarryOnLearning
[tex]\sf\color{pink}{༄⁂✰Bae \: Yoonah}[/tex]
In an experiment, the initial temperature of a solution is -5 °C. The solution is heated up at 3 °C per minute for 19 minutes and then it is cooled at 4 °C per minute for 6 minutes. Calculate the final temperature, in °C, of the solution.
Answer:
28°C
Step-by-step explanation:
First you do 3*19=57°C
-5+57= 52°C
then you do 4*6=24 °C
as its being cooled you takeaway
52-24=28°C
d(1)=2
d(n)=d(n−1)⋅(−2)^n
What is the third term in the sequence?
Answer:
- 16
Step-by-step explanation:
The way this is given, you have to find the second term before you can fine the third.
a2 = d(n - 1) * (-2)^2
a2 = 2 * (-2)^2
a2 = 2 * 4
a2 = 8
a3 = d(3 - 1) * (-2)^3
a3 = 2 * (-2)^3
a3 = 2 * - 8
a3 = - 16
A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
A. −3x + 5y = 13
B. −3x + y = −7
C. −3x + y = 17
D. −3x + 5y = −13
Which answer is an equation in point-slope form for the given point and slope?
Point: (1, 9); Slope: 5
A. y − 1 = 5 (x + 9)
B. y − 9 = 5 (x − 1)
C. y + 9 = 5 (x−1)
D. y − 9 = 5 (x+1)
Answer:
−3x + y = −7 y - 9 = 5 (x - 1)
Step-by-step explanation:
y2 - y1 / x2 - x1
5 - (-1) / 4 - 2
6/2
= 3
slope intercept: −3x + y = −7
y - 9 = 5 (x - 1)
For an avid bird watcher, the probability of spotting a California Condor while birdwatching in the Grand Canyon area is 0.3. The probability of being able to take a clear picture of the bird suppose one is able to spot it is 0.8. What is the probability that the bird watcher is able to take a clear picture of a California Condor
Answer:
the probability of taking a clear picture of a California candor is .24
Please help!! Can’t figure this out for the life of me.
Select the correct answer from each drop-down menu.
If _______, then AABC and ADEF are congruent by the ASA criterion.
If _______, then AABC and ADEF are congruent by the SAS criterion.
AABC and ADEF are congruent if ______
Answer:
Angle b is congruent to angle E
CA=FD
Step-by-step explanation:
If _______, then triangle ABC and triangle DEF are congruent by the ASA criterion. ASA is angle side angle . We know angle C= angle F and side CB = side FE We need to know angle B = angle E
If _______, then triangle ABC and triangle DEF are congruent by the SAS criterion. SAS is side angle side, we know side CB = side FE and then angle C= angle F then we need side CA = side FD
If ∠ABC = ∠DEF, then ΔABC and ΔDEF are congruent by the ASA criterion.
If AC = DF, then ΔABC and ΔDEF are congruent by the SAS criterion.
What are congruent figures?Two figures are said to be congruent of they have the same shape and all the corresponding sides and angles are congruent.
The HL (hypotenuse leg) congruence theorem states that if the hypotenuse and one leg of a triangle is congruent to another triangle, then both triangles are congruent.
In triangle ABC and DEF;
BC = EF and ∠ACB ≅ ∠DFE
Hence:
If ∠ABC = ∠DEF, then ΔABC and ΔDEF are congruent by the ASA criterion.
If AC = DF, then ΔABC and ΔDEF are congruent by the SAS criterion.
Find out more on congruent figures at: https://brainly.com/question/1675117
help with 4b thank you.
First let's compute dx/dt
[tex]x = t - \frac{1}{t}\\\\x = t - t^{-1}\\\\\frac{dx}{dt} = \frac{d}{dt}\left(t - t^{-1}\right)\\\\\frac{dx}{dt} = 1-(-1)t^{-2}\\\\\frac{dx}{dt} = 1+\frac{1}{t^{2}}\\\\\frac{dx}{dt} = \frac{t^2}{t^{2}}+\frac{1}{t^{2}}\\\\\frac{dx}{dt} = \frac{t^2+1}{t^{2}}\\\\[/tex]
Now compute dy/dt
[tex]y = 2t + \frac{1}{t}\\\\y = 2t + t^{-1}\\\\\frac{dy}{dt} = \frac{d}{dt}\left(2t + t^{-1}\right)\\\\\frac{dy}{dt} = 2 - t^{-2}\\\\\frac{dy}{dt} = 2 - \frac{1}{t^2}\\\\\frac{dy}{dt} = \frac{2t^2}{t^2}-\frac{1}{t^2}\\\\\frac{dy}{dt} = \frac{2t^2-1}{t^2}\\\\[/tex]
From here, apply the chain rule to say
[tex]\frac{dy}{dx} = \frac{dy*dt}{dx*dt}\\\\\frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx}\\\\\frac{dy}{dx} = \frac{dy}{dt} \div \frac{dx}{dt}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2} \div \frac{t^2+1}{t^{2}}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2} \times \frac{t^{2}}{t^2+1}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2+1}\\\\[/tex]
We could use polynomial long division, or we could add 2 and subtract 2 from the numerator and do a bit of algebra like so
[tex]\frac{dy}{dx} = \frac{2t^2-1}{t^2+1}\\\\\frac{dy}{dx} = \frac{2t^2-1+2-2}{t^2+1}\\\\\frac{dy}{dx} = \frac{(2t^2+2)-1-2}{t^2+1}\\\\\frac{dy}{dx} = \frac{2(t^2+1)-3}{t^2+1}\\\\\frac{dy}{dx} = \frac{2(t^2+1)}{t^2+1}-\frac{3}{t^2+1}\\\\\frac{dy}{dx} = 2-\frac{3}{t^2+1}\\\\[/tex]
This concludes the first part of 4b
=======================================================
Now onto the second part.
Since t is nonzero, this means either t > 0 or t < 0.
If t > 0, then,
[tex]t > 0\\\\t^2 > 0\\\\t^2+1 > 1\\\\\frac{1}{t^2+1} < 1 \ \text{ ... inequality sign flip}\\\\\frac{3}{t^2+1} < 3\\\\-\frac{3}{t^2+1} > -3 \ \text{ ... inequality sign flip}\\\\-\frac{3}{t^2+1}+2 > -3 + 2\\\\2-\frac{3}{t^2+1} > -1\\\\-1 < 2-\frac{3}{t^2+1}\\\\-1 < \frac{dy}{dx}\\\\[/tex]
note the inequality signs flipping when we apply the reciprocal to both sides, and when we multiply both sides by a negative value.
You should find that the same conclusion happens when we consider t < 0. Why? Because t < 0 becomes t^2 > 0 after we square both sides. The steps are the same as shown above.
So both t > 0 and t < 0 lead to [tex]-1 < \frac{dy}{dx}[/tex]
We can say that -1 is the lower bound of dy/dx. It never reaches -1 itself because t = 0 is not allowed.
We could say that
[tex]\displaystyle \lim_{t\to0}\left(2-\frac{3}{t^2+1}\right)=-1\\\\[/tex]
---------------------------------------
To establish the upper bound, we consider what happens when t approaches either infinity.
If t approaches positive infinity, then,
[tex]\displaystyle L = \lim_{t\to\infty}\left(2-\frac{3}{t^2+1}\right)\\\\\\\displaystyle L = \lim_{t\to\infty}\left(\frac{2t^2-1}{t^2+1}\right)\\\\\\\displaystyle L = \lim_{t\to\infty}\left(\frac{2-\frac{1}{t^2}}{1+\frac{1}{t^2}}\right)\\\\\\\displaystyle L = \frac{2-0}{1+0}\\\\\\\displaystyle L = 2\\\\[/tex]
As t approaches infinity, the dy/dx value approaches L = 2 from below.
The same applies when t approaches negative infinity.
So we see that [tex]\frac{dy}{dx} < 2[/tex]
---------------------------------------
Since [tex]-1 < \frac{dy}{dx} \text{ and } \frac{dy}{dx} < 2[/tex], those two inequalities combine into the compound inequality [tex]-1 < \frac{dy}{dx} < 2[/tex]
So dy/dx is bounded between -1 and 2, exclusive of either endpoint.
Give the domain and range of G={(6.0),(-9,-3),(1,-3)}
Answer:
Step-by-step explanation:
D={ 6 , -9 , 1 }
R={ 0 ,-3 }
What is the value of x?
X + y = 10;
Z + z = 6;
Z + y = 5;
A) 9
B) 8
C) 7
D) 6
E) 1
Answer:
B
Step-by-step explanation:
z+z=6, z=3. z+y=5, y=2, x+y=10, x=8
Describe domain and range of the graph.
Let θ be an angle in quadrant IV such that sinθ = -2/5 .
Find the exact values of secθ and tanθ.
If θ lies in the fourth quadrant, then sin(θ) < 0 and cos(θ) > 0. So we have from the Pythagorean identity,
sin²(θ) + cos²(θ) = 1 ==> cos(θ) = +√(1 - sin²(θ)) = √21/5
Then
sec(θ) = 1/cos(θ) = 5/√21
and
tan(θ) = sin(θ)/cos(θ) = (-2/5)/(√21/5) = -2/√21
Find the equation of a line that is perpendicular to x+y=8 and passes through the point (8, 10).
Answer:
Y = -x + 2
Step-by-step explanation:
y = -x + 8
y = 1x + b
10 = 8 + b
b = 2
Answer:
y-y1=m(x-x1)
y-10=8(x-8)
y-10=8x-64
y-10+64-8x
y+54-8x
y-8x+54
The number formed by adding 1 to the greatest 8 – digit number is?
Answer:
the answer would be 100,000,000
Greatest 8 Digit Number: 99,999,999
Adding 1 = 99999999+1
= 100,000,000
Must click thanks and mark brainliest
Please help with Question 2b
Answer:
MUST BE IN HLA, NOT FROM C TO ASSEMBLY.
PROGRAM 6: Same
Write an HLA Assembly language program that implements a function which correctly identifies when all four parameters are the same and returns a boolean value in AL (1 when all four values are equal; 0 otherwise). This function should have the following signature:
procedure theSam
If a cube has an edge of length e, then the lateral surface area is:
Answer:
The total lateral surface of this cube is 4*e^2
Step-by-step explanation:
A cube is a figure with all the sides of the same length, so each face of a cube is a square.
Remember that the area of a square of sidelength L is:
A = L^2
Now, when we want to find the lateral surface of a figure, we ignore the bases of the figure.
So, if a cube has 6 faces, if we ignore the two bases, we are left with 4 square faces.
And if the edge length is e, then each one of these four faces has an area:
A = e^2
So the total lateral surface is 4 times that:
S = 4*e^2
The total lateral surface of this cube is 4*e^2
Answer:
4e2
Step-by-step explanation:
I got it correct on founders edtell
Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year.
177; 204; 211; 211; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174;
185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270;
280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230;
250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265
Organize the data from smallest to largest value.
Part (a)
Find the median.
Part (b)
Find the first quartile. (Round your answer to one decimal place.)
Part (c)
Find the third quartile. (Round your answer to one decimal place.)
Part (d)
Construct a box plot of the data.
Answer:
im not sure but i do have a tip when you go to goo gle i want you to simplify your question (not what you asked on here) then copy your question as it is simple then search it on here because its slightly for others to understand
Step-by-step explanation:
.
An exterior angle of a regular polygon cannot have the measure of
Select one:
a. 120
b. 40
c. 50
d. 90
e. 30
I need help completing this problem ASAP
Answer:
It is E. radicand
Step-by-step explanation:
Answer:
Radicand
Step-by-step explanation:
Radicand is the number found inside the radicals
Example:
[tex]\sqrt[4]{5} ; 2\sqrt[4]{5}[/tex] are like terms
5 -> radicand and 4 is the index
A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 40%. The test statistic is a.1.44. b.1.25. c..95. d..80.
Answer:
a. 1.44
Step-by-step explanation:
We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 40%.
At the null hypothesis, it is tested if the proportion is of at most 40%, that is:
[tex]H_0: p \leq 0.4[/tex]
At the alternative hypothesis, it is tested if the proportion is of more than 40%, that is:
[tex]H_1: p > 0.4[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.4 is tested at the null hypothesis:
This means that [tex]p = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]
A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A.
This means that:
[tex]n = 200, X = \frac{90}{200} = 0.45[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.45 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}[/tex]
[tex]z = 1.44[/tex]
Thus the correct answer is given by option a.
A hospital director is told that 54% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 120 patients found that 60 were insured. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
Z -0.879173965
Step-by-step explanation:
Z -0.879173965
ρ 0.5
π 0.54
n 120
The value of the test statistic is the z-score z = -0.88
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the test statistic value be represented as z
Now , the probability of emergency room visitors are insured is q = 0.54
The total number of patients n = 120
The number of patients that were insured = 60
So , the percentage of people that were insured p = 60/120 = 0.5
Now , test statistic value z = ( p - q ) / [ √ ( q ( 1 - q )/n² ]
The value of z score is
z = [ 0.5 - 0.54 ] / √ 0.54 ( 1 - 0.54 ) / 120²
On simplifying the equation , we get
The value of z score is z = -0.88
Hence , the test statistic is z = -0.88
To learn more about z score click :
https://brainly.com/question/25638875
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the mean salary if of 5 employees is $35900. the median is $37000. the mode is $382000. If the median payed employee gets a $3100 raise, then…
New median:
New mode:
Answer:
Step-by-step explanation:
New median:40100
New mode:385100
Cual es el capital que prestado al 10% bimestral durante 6 meses y 10 días produce un interés de 1140
Respuesta:
3650
Explicación paso a paso:
Dado que :
Principal, P = capital prestado
Tasa anual, r = 10% * 6 = 60%
Interés = 1140
Periodo = 6 meses y 10 días = (6 * 30) +10 = 190 días
Conversión a años:
Periodo = 190/365
Usando la relación:
Interés = principal * tasa * tiempo
1140 = P * 60% * (190/365)
1140 = 0.3123287P
P = 1140 / 0,3123287
P = 3650
A person earns $23,600 one year and gets a 5% raise in salary. What is the new salary?
Answer:
24780
Step-by-step explanation:
might not be right but 24780 because 23600*5% is 1180 and add that to the original 23600 to get 24780
5% more is 105% in total, including the the 100% we start with, so:
23,600 * 1.05 = 24780
A 500-kg concrete block 95 cm longcm wide and cm high. It can exert three different pressures on a horizontal surface depending on which faceit rests on the highest pressure is
Pressure is force per unit area. If the block is sitting at rest on the surface, it applies a pressure of mg/A, where mg is the block's weight and A is the area of the face that makes contact with the surface.
The smaller the value of A, the larger the pressure. So the highest pressure the block can exert is achieved when it's resting on the face with the smallest dimensions.
If the block is a cube with side length 95 cm, then the pressure exerted by each face is the same.
Let S be a set of linearly dependent vectors in Rn. Select the best statement. A. The set S could, but does not have to, span Rn. B. The set S spans Rn, as long as no vector in S is a scalar multiple of another vector in the set. C. The set S cannot span Rn. D. The set S must span Rn. E. The set S does not span Rn if some vector in S is a scalar multiple of another vector in the set. F. The set S spans Rn, as long as it does not include the zero vector. G. none of the above
Answer:
The set S could, but does not have to, span Rn ( A )
Step-by-step explanation:
Assume S is a set of linearly dependent vectors in Rn
The best statement from the options is ; The set S could, but does not have to, span Rn
This is because S could span Rn ( as stated in option c ) but will not necessary span Rn ( as seen in option D )
8 thousand+7tens=6thiusand+. tens
Answer:
207 tens
Step-by-step explanation:
If you mean
8,000 + 70 = 6000 + X tens
then it should be 207 tens
