Answer:
Approximately [tex]0.0435\; \text{in} \cdot \text{s}^{-1}[/tex]. (Given that [tex]V = \pi\, r\, h^{2} - (1/3)\, h^{3}[/tex].)
Step-by-step explanation:
Let [tex]t[/tex] denote time. Both the volume of water in the bowl, [tex]V[/tex], and the height of water in the bowl, [tex]h[/tex], are dependent on [tex]t\![/tex] (as if the [tex]V\![/tex] and [tex]h[/tex] are functions of [tex]\! t[/tex].)
Implicitly differentiate both sides of the equation [tex]V = \pi\, r\, h^{2} - (1/3)\, h^{3}[/tex] with respect to [tex]\! t[/tex]:
[tex]\displaystyle \frac{d}{d t}[V] = \frac{d}{d t}\left[\pi\, r\, h^{2} - (1/3)\, h^{3}\right][/tex].
[tex]\displaystyle \frac{d V}{d t} = 2\, \pi\, r\, h\, \frac{d h}{d t} + (1/3)\, (3\, h^{2})\, \frac{d h}{d t}[/tex].
Both [tex]h[/tex] (current height of water in the bowl) and [tex](d V) / (d t)[/tex] (rate at which water is poured into the bowl) are given: [tex]h = 2.4\; \text{in}[/tex] and [tex](d V) / (d t) = 5\; \text{in}^{3}\cdot \text{s}^{-1}[/tex]. The question is asking for [tex](d h) / (d t)[/tex], the rate at which the water level in the bowl is rising.
Thus, rearrange the equation to find an expression for [tex](d h) / (d t)[/tex] in terms of [tex]h[/tex], [tex]r[/tex], and [tex](d V) / (d t)[/tex]. Substitute in the values [tex]h = 2.4\; \text{in}[/tex], [tex](d V) / (d t) = 5\; \text{in}^{3}\cdot \text{s}^{-1}[/tex], and [tex]r= 8\; \text{in}[/tex]; solve for [tex](d h) / (d t)\![/tex], the rate at which the water level is rising:
[tex]\displaystyle \frac{d V}{d t} = \left(2\, \pi\, r\, h\, + (1/3)\, (3\, h^{2})\right)\, \frac{d h}{d t}[/tex].
[tex]\begin{aligned} \frac{d h}{d t} &= \frac{\displaystyle \frac{d V}{d t}}{2\, \pi\, r\, h\, + (1/3)\, (3\, h^{2})} \\ &= \frac{\displaystyle \frac{d V}{d t}}{2\, \pi\, r\, h\, + h^{2}} \\ &= \frac{5\; \text{in}^{3} \cdot \text{s}^{-1}}{2\, \pi \, (8\; \text{in})\, (2.4\; \text{in}) + (2.4\; \text{in})^{2}} \\ &\approx 0.0435\; \text{in} \cdot \text{s}^{-1} \end{aligned}[/tex].
According to the number line, what is the distance between points A and B?
A
B
SARE
+++
-16-14-12-10 -8 -6 -4 -2
02
4
6
8 10 12 14 16
O 6 units
O 7 units
O 12 units
0 14 units
Answer:
14 units
Step-by-step explanation:
i think you just need to minus it to get the distance between it
like :
=point B - point A
=12 - (-2)
=12 +2
=14
so it 14 units
According to the number line the distance between points A and B is 14 units.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the distance between points A and B.
The length along a line or line segment between two points on the line or line segment.
A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
The point A is at -2
The point B is at 12 on the number line
AB=OB-OA
=12-(-2)
=12+2
=14 units.
Hence, According to the number line the distance between points A and B is 14 units.
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18 lollipops and 36 candy bars whats the ratio of lollipops to candy bars
Answer:
1:2
Step-by-step explanation:
18:36
Simplify:
36÷2=1, making 2 a good 2nd term
There are 2 candy bars every 1 lollipop.
1:2
1:2 is the ratio of lollipops to candy bars.
What is ratio?The relationship in quantity, amount, or size between two or more things.
Given that there are 18 lollipops and 36 candy bars,
Ratio = 18/36 = 1/2
Hence, 1:2 is the ratio of lollipops to candy bars.
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NO LINKS!!! Please help me with this problem. Part 14
Explanation:
The Law of Cosines can be used to write a quadratic in x. The desired form corresponds to its solution using the quadratic formula.
[tex]L^2=r^2 +x^2 -2rx\cdot\cos{\theta}\\\\x^2-2rx\cdot\cos{\theta}+(r^2-L^2)=0[/tex]
Using the quadratic formula gives the positive value of x as ...
[tex]x=\dfrac{-(-2r\cdot\cos{\theta})+\sqrt{(-2r\cdot\cos{\theta})^2-4(1)(r^2-L^2)}}{2(1)}\\\\\boxed{x=r\cos{\theta}+\sqrt{r^2\cos^2\theta+L^2-r^2}}[/tex]
How many times greater is 10,000 than 100?
Show the solution and a proper answer, please.
Mario has $50, which is $8 more than twice the amount of money that Kevin has. How much money does Kevin have?
Answer:
21
Step-by-step explanation:
First you would subtract 8 from 50 (50 - 8). Once you have that answer, 42, you divide it in half (42/2). Your final answer is 21. The full equation is:
(50 - 8)/2
Solve this Question.
Answer:
x = 1
explanation:
[tex]\sf \rightarrow \dfrac{3}{x} -1 = 2[/tex]
[tex]\sf \rightarrow \dfrac{3}{x} = 2+1[/tex]
[tex]\sf \rightarrow \dfrac{3}{x} = 3[/tex]
[tex]\sf \rightarrow {3} = 3(x)[/tex]
[tex]\sf \rightarrow \dfrac{3}{3} = (x)[/tex]
[tex]\sf \rightarrow x = 1[/tex]
checking if x = 1,
[tex]\sf \rightarrow \dfrac{3}{1} -1 = 2[/tex]
[tex]\sf \rightarrow3 -1 = 2[/tex]
[tex]\sf \rightarrow 2 = 2[/tex]
→ Hence proved x : 1 as L.H.S = R.H.S
Step-by-step explanation:
[tex] \frac{3}{x} - 1 = 2 \\ [/tex]
Adding 1 on both sides, we get[tex] \frac{3}{x} - 1 + 1 = 2 + 1 \\ \frac{3}{x} = 3[/tex]
By performing cross multiplication, we get[tex]3 \times x = 3 \times 1 \\ 3x = 3[/tex]
Dividing both sides by 3, we get
[tex] \frac{3x}{3} = \frac{3}{3} \\ x = 1[/tex]
Hence, the value of x is 1.What are all the ZEROS? Show all the work!
(2x+6)(x-4)
Answer:
4 and -3
Step-by-step explanation:
2x+6=0
2x=-6
-3
x-4=0
x=4
So its 4 and -3
Answer:
-3,4
Step-by-step explanation:
(2x+6)(x-4) = 0
Using the Zero Factor Principle: If ab =0 then a=0 or b=0
2x+6=0 or X-4=0
solve 2x+6=0:
2x+6=0
Subtract 6 from both sides
2x+6-6 0-6
Simplify
2x = -6
Divide both sides by 2
2x/2 = -6/2
Simplify
X=-3
then x-4 =0
add 4 from to both sides
x=4
zeros : -3,4
(-3,0),(4,0)
Hello. Can someone please help me with this probability math homework? Appreciated
hope it's helpful at you all
In the diagram, SOP GNQ. Find the value of x.
Answer:
D. 33
Step-by-step explanation:
Triangle OSP is dilation of 1.5 of triangle NGQ, and side SP corresponds to side GQ.
22*1.5 = 33
Hope this helps :)
The phantoms won 8 more games than the Aztecs last year. Their combined wins were 32. Finds the
number of games won by each team last year,
Step-by-step explanation:
let aztecs = x
since the phantoms won 8 more than the aztecs
then, the phantoms = x + 8
and their combined win was 32
therefore
x + x + 8 = 32
2x + 8 =32
2x = 32 - 8
2x = 24 , x = 12
so , aztecs won 12 games and the phantoms won 20 games.
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Solve the equation algebraically.
2lnx + 7 = ln(4x) + 10
Round your final answers to two decimal places.
Answer:
x = 80.34 (2 dp)
Step-by-step explanation:
[tex]2\ln(x)+7=\ln(4x)+10[/tex]
[tex]\implies \ln(x^2)+7=\ln(4x)+10[/tex]
[tex]\implies \ln(x^2)-\ln(4x)=10-7[/tex]
[tex]\implies \ln\left(\dfrac{x^2}{4x}\right)=3[/tex]
[tex]\implies \ln\left(\dfrac{x}{4}\right)=3[/tex]
[tex]\implies e^{\ln\left(\dfrac{x}{4}\right)}=e^3[/tex]
[tex]\implies \dfrac{x}{4}=e^3[/tex]
[tex]\implies x=4e^3[/tex]
[tex]\implies x=80.34 \textsf{ (2 dp)}[/tex]
The scatterplot shows the relationship of scores for students who took a math test and history test. Based on a line of best fit, what score would be the BEST prediction for a student's history test if they made a 60 on their math test?
A) 50
B) 60
C) 70
D) 75
Answer:
c
Step-by-step explanation:
lucky guess
Melissa made $221 for 17 hours of work. At the same rate, how much would she make for 13 hours of work?
Answer:
$169 Is correct.
Step-by-step explanation:
We know that Melissa made $221 for 17 hours, so using this ratio, we can calculate how much she made for 13 hours as follows
13 hours× [tex]\frac{221}{17~hours} =[/tex] $169
Therefore, the answer is $169
Proportion and give 6:8= n :12
Answer:
n = 9
Step-by-step explanation:
6/8 = n/12
(6/8)(12) = (n/12)(12)
n = 9
Meaning of Constituted Authority
Answer:
ENGLISH:CONSTITUTED AUTHORITIES. Those powers which the constitution of each people has established to govern them, to cause their rights to be respected, and to maintain those of each of its members.SPANISH:AUTORIDADES CONSTITUIDAS. Los poderes que la constitución de cada pueblo ha establecido para regirlos, hacer respetar sus derechos y mantener los de cada uno de sus miembros.An office manager budgeted $400 for
office supplies. The manager ordered
2 toner cartridges for $89 each and a
box of printer paper for $27. Each price
includes tax.
What is the greatest number of
additional boxes of printer paper the
manager can order with the money left
in the budget?
A. 2
B. 7
C. 8
D. 10
Answer:
B. 7
Step-by-step explanation:
To find this out, first, we multiply 89*2, which is 178, the amount already spent on toner.
Then, we add 27 to this to find the total amount spent so far. This comes out to $205 spent so far.
To find out how much we have left to spend, we subtract the amount spent from the original.
400-205 = $195, the amount of money left.
To find out how much paper we can buy, we divide the cost of one paper box, by the amount of money we have left.
195/27 = 7.222222222222222222222222222222
Since we cannot buy 7.222222222222222222222222 boxes, we can only buy 7. This is the answer.
The graph shows the distance $y$ (in miles) that a bus travels in $x$ hours. Find and interpret the slope of the line.
The slope of the line is (Answer here)
. The bus is traveling at a speed of (Answer here)
miles per hour.
Answer:
Slope is 60/1 or simply 60. Miles per hours is also 60
Step-by-step explanation:Rise/Run Up60 Over1 which is why slope =60, mph is same as slope or just calculate how many miles car goes in one hour by reading the graph.
5. Solve the differential equations using Laplace transforms
y'' − 3y' + 2y = 1, y(0) = 1, y'(0) = 0
y'' + y' − 2y = x², y(0) = 0 and y'(0) = 0
y'' + y' − 2y = e⁻³ˣ, y(0) = 0 and y'(0) = 0
Answer:
First problem: [tex]y(x)=\frac{1}{2}+e^x-\frac{1}{2}e^{2x}[/tex]
Step-by-step explanation:
Solve for Y(s) by taking the transform of every term
[tex]y''-3y'+2y=1,\:y(0)=1,\:y'(0)=0\\\\\mathcal{L}\{y''\}-3\mathcal{L}\{y'\}+2\mathcal{L}\{y\}=\mathcal{L}\{1\}\\\\s^2Y(s)-sy(0)-y'(0)-3[sY(s)-y(0)]+2Y(s)=\frac{1}{s}\\\\s^2Y(s)-s-3[sY(s)-1]+2Y(s)=\frac{1}{s}\\\\s^2Y(s)-s-3sY(s)+3+2Y(s)=\frac{1}{s}\\\\(s^2-3s+2)Y(s)-s+3=\frac{1}{s}\\\\(s-1)(s-2)Y(s)=\frac{1}{s}-3+s\\\\Y(s)=\frac{1}{s(s-1)(s-2)}-\frac{3+s}{(s-1)(s-2)}[/tex]
Perform partial fraction decomposition
[tex]Y(s)=\frac{1-3s+s^2}{s(s-1)(s-2)}\\\\Y(s)=\frac{s^2-3s+1}{s(s-1)(s-2)}\\ \\\frac{s^2-3s+1}{s(s-1)(s-2)}=\frac{A}{s}+\frac{B}{s-1}+\frac{C}{s-2}\\\\s^2-3s+1=A(s-1)(s-2)+B(s)(s-2)+C(s)(s-1)[/tex]
Solve for each constant
[tex]s^2-3s+1=A(s-1)(s-2)+B(s)(s-2)+C(s)(s-1)\\\\(2)^2-3(2)+1=A(2-1)(2-2)+B(2)(2-2)+C(2)(2-1)\\\\-1=2C\\\\-\frac{1}{2}=C[/tex]
[tex]s^2-3s+1=A(s-1)(s-2)+B(s)(s-2)+C(s)(s-1)\\\\(1)^2-3(1)+1=A(1-1)(1-2)+B(1)(1-2)+C(1)(1-1)\\\\-1=-B\\\\1=B[/tex]
[tex]s^2-3s+1=A(s-1)(s-2)+B(s)(s-2)+C(s)(s-1)\\\\(0)^2-3(0)+1=A(0-1)(0-2)+B(0)(0-2)+C(0)(0-1)\\\\1=2A\\\\\frac{1}{2}=A[/tex]
Take the inverse transform to solve the IVP
[tex]Y(s)=\frac{\frac{1}{2}}{s}+\frac{1}{s-1}+\frac{-\frac{1}{2}}{s-2}\\ \\y(x)=\frac{1}{2}+e^x-\frac{1}{2}e^{2x}[/tex]
Explain why the initial value of any function of the form
f(x) = a(bº) is equal to a.
bettie bought are reel of thread for sowing that is 14.5 meters long. Bettie uses 425 centimeters for a project. How many meters are left on the reel?
Of the twenty-two students in a classroom, ten are transfer students, seven are nursing students, four are AAS students and one student is undecided:
If one student is chosen randomly, find the probability that the student is not an AAS student.
Answer:
Find the value of x. Please help me with this?
The interior angles of any triangle sum to 180° in measure, and in ∆ABC, the angles at vertices A and C are congruent. If we call their measure a, then
24° + 2a = 180° ⇒ 2a = 156° ⇒ a = 78°
The angle at vertex C and the angle with measure (2x - 18)° are supplementary, meaning they add up to 180° :
a + (2x - 18)° = 180°
Solve for x :
78° + (2x - 18)° = 180°
(2x - 18)° = 102°
2x = 120
x = 60
If the answer is 5 why isn't 5 an option?
Answer:
because they made a mistake
Jia wishes to briskly walk 150 minutes per week. When briskly walking, Jia takes 100 steps per minute. Approximately how many briskly-walked steps should Jia take per day to achieve the 150 minutes weekly goal?
Group of answer choices
250
2,100
15,000
105,000
Answer:
15000
Step-by-step explanation:
150x100
15000
can someone pls answer both of these ?'s i WILL mark BRAILIEST
What is the perimeter of the figure to the nearest tenth of a millimeter?
A. 9.4 millimeters
B. 12.0 millimeters
C. 21.4 millimeters
D. 30.8 millimeters
Answer:
i think the answer is C
Step-by-step explanation:
i normally just do length divided by width to figure this out
Anna made her uncle a garden. The width is 7 2 5 ft and the length is 5 1 2 ft. What is the area of the garden?
Answer:
The answer to that is 371200ft2
Step-by-step explanation:
725 x 512 = 371200ft2
Answer:
the answer is 40 7\10
Step-by-step explanation:
7 2\5 x 5 1\2= 407\10 = 40 7\10
Is 0.88 greater than 1.5?
Answer:
No 1.5 is greater than 0.88
Step-by-step explanation:
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- Nathaniel Cross
find the circumference and the area of a circle with diameter of 6 ft
use 3.14
Answer:
Step-by-step explanation:he equation for circumference is:
c=2%28pi%29r
The equation for area is:
a=%28pi%29r%5E2
First, we'll find the circumference.
The 'r' in the equation stands for radius. The radius of a circle is half of its diameter, so the circle's radius is half of 6--3 inches.
So, we can substitute 3 in for 'r' and 3.14 in for pi
c=2%28pi%29r
c=2%2A3.14%2A3
Then, we can simply multiply.
c=2%2A3.14%2A3
c=18.84
Therefore, the circumference of the circle is 18.84
Next, we'll find the circle's area.
Again, we can substitute 3 in for 'r' and 3.14 in for pi
a=%28pi%29r%5E2
a=3.14%2A3%5E2
The, we'll square three and multiply.
a=3.14%2A3%5E2
a=3.14%2A9
a=28.26
Therefore, the circumference is 18.84 and the area is 28.26.
A sociologist was curious about how much smartphone access has changed for American teenagers. They obtained separate random samples of teenagers from
2017
20172017 and
2013
20132013. Here are their results:
Has access to smartphone?
2017
20172017
2013
20132013
Yes
450
450450
120
120120
No
150
150150
280
280280
Total
600
600600
400
400400
They want to use these results to construct a
95
%
95%95, percent confidence interval to estimate the difference in the proportion of teens each year who had access to a smartphone
(
p
2017
−
p
2013
)
(p
2017
−p
2013
)left parenthesis, p, start subscript, 2017, end subscript, minus, p, start subscript, 2013, end subscript, right parenthesis. Assume that all of the conditions for inference have been met.
Which of the following is a correct
95
%
95%95, percent confidence interval based on their data?
Using the z-distribution, as we are working with a proportion, it is found that the 95% confidence interval for the difference in the proportions of teenagers with access to smartphones in 2017 and in 2013 is of (0.393, 0.507).
What is the mean and the standard error of the distribution of differences?In 2017, 450 out of 600 students had access, hence:
[tex]p_1 = \frac{450}{600} = 0.75, s_1 = \sqrt{\frac{0.75(0.25)}{600}} = 0.0177[/tex]
In 2013, 120 out of 400 students had access, hence:
[tex]p_2 = \frac{120}{400} = 0.3, s_2 = \sqrt{\frac{0.3(0.7)}{400}} = 0.0229[/tex]
For the distribution of differences, we have that the mean and the standard error are, respectively, given by:
[tex]p = p_1 - p_2 = 0.75 - 0.3 = 0.45[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0177^2 + 0.0229^2} = 0.0289[/tex]
What is the confidence interval?It is given by:
[tex]p \pm zs[/tex]
95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
Then:
[tex]p - zs = 0.45 - 1.96(0.0289) = 0.393[/tex]
[tex]p + zs = 0.45 + 1.96(0.0289) = 0.507[/tex]
The 95% confidence interval for the difference in the proportions of teenagers with access to smartphones in 2017 and in 2013 is of (0.393, 0.507).
More can be learned about the z-distribution at https://brainly.com/question/25890103
Answer:
0.45+-0.057
Step-by-step explanation: