Using implicit differentiation, it is found that the height is changing at a rate of -0.875 m/sec.
The volume of a rectangular solid of length l, width w and height h is given by:
[tex]V = lwh[/tex]
Applying implicit differentiation, the rate of change of the volume is given by:
[tex]\frac{dV}{dt} = wh\frac{dl}{dt} + lh\frac{dw}{dt} + lw\frac{dh}{dt}[/tex]
In this problem:
Volume is decreasing at a rate of 2 m3/sec, hence [tex]\frac{dV}{dt} = -2[/tex]The length and width walls move toward each other at a rate of 0.25 m/ sec, hence [tex]\frac{dl}{dt} = \frac{dw}{dt} = 0.25[/tex]Length and width are 2 m and the height is 1.5 m, hence [tex]l = w = 2, h = 1.5[/tex]Then:
[tex]\frac{dV}{dt} = wh\frac{dl}{dt} + lh\frac{dw}{dt} + lw\frac{dh}{dt}[/tex]
[tex]-2 = 2(1.5)(0.25) + 2(1.5)(0.25) + 2(2)\frac{dh}{dt}[/tex]
[tex]4\frac{dh}{dt} = -3.5[/tex]
[tex]\frac{dh}{dt} = -\frac{3.5}{4}[/tex]
[tex]\frac{dh}{dt} = -0.875[/tex]
The height is changing at a rate of -0.875 m/sec.
A similar problem is given at https://brainly.com/question/9543179
Solve the equation.
-9x + 1 = -x + 17
Step-by-step explanation:
-9x + 1 = -x + 17
collect like terms
-9x + x = 17-1
-8x = 16
divide both sides by -8
-8x/-8 = 16/8
x = 2
Help, please! You will be extremely smart if you answer this question, and if you do I will give brainliest. The test ends soon please help.
Answer:
B. y=6-1/3t
Step-by-step explanation:
If you graph this equation, it matches the given graph. Hope this helps :)
Find a formula for the inverse of the following function, if possible.
[tex]P(x) = 3\sqrt[3]{x} - 1[/tex]
[tex]P^{-1}(x) = \\\\[/tex]
or does not have an inverse function
to find the inverse of any expression, we start off by doing a quick variables switcheroo and then solve for "y", so let's do so
[tex]\stackrel{P(x)}{y}~~=~~3\sqrt[3]{x}-1\implies \stackrel{\textit{quick switcheroo}}{x~~ =~~3\sqrt[3]{y}-1}\implies x+1 = 3\sqrt[3]{y}\\\\\\\cfrac{x + 1}{3}=\sqrt[3]{y}\implies \left( \cfrac{x + 1}{3} \right)^3 =y\implies \cfrac{(x+1)^3}{3^3}=y\implies \cfrac{(x+1)^3}{27}=\stackrel{\stackrel{y}{\downarrow }}{P^{-1}(x)}[/tex]
I have more questions then this
Answer:1-1/3
2-16 in.
3-10.49
4-1/10
Step-by-step explanation:
i hope this helps
the domain and range in this graph will be:
a. Domain : all real nums, Range : all real nums
b. Domain : - 4 Range: 2
c. domain: 2 range : 5
Answer:
a.
Step-by-step explanation:
this is a line going from -infinity to +infinity in x and in y direction.
for b or c to be right the function would have to be a single point, as nothing else is valid as value.
what is 1/2 divided by 75.096868
Answer:
Step-by-step explanation:
5. The price for
seedless oranges is $1.55 for the first
pound and $0.75 for each additional pound. Paul Paid $
5.35 to buy sour oranges.
How many pounds of seedless oranges did he buy?
Answer:
5 1/15 lb
Step-by-step explanation:
Equation:
5.35 = 1.55 + 0.75x [tex]\longmapsto\\[/tex] Subtract 1.55 from both sides
3.8 = 0.75x [tex]\longmapsto[/tex] Divide both sides by 0.75
5 1/15 lb
-Chetan K
whats a median because i forgor
Answer:
the one in the middle. if you have a serie of numbers like 2, 5, 9, 7, 12, 23, 46 then 7 is the median because it's in the middle (after putting them in an increasing order of course)
Which equation represents this sentence?
6 times the difference of a number and 5 is equal to 36
5−6x=36
6(x−5)=36
6x−5=36
6(5−x)=36
The equation that represents this sentence "6 times the difference of a number and 5 is equal to 36" will be; 6(x - 5) = 36
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given a statement as "6 times the difference of a number and 5 is equal to 36"
Therefore, the 6 times means the multiplication.
Let the number be x then;
the difference of a number and 5 is equal to 36 means the subtraction that is;
(x - 5) = 36
Therefore, the equation becomes
6(x - 5) = 36
The equation that represents this sentence "6 times the difference of a number and 5 is equal to 36" will be; 6(x - 5) = 36
Learn more about equations here;
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Which description represents the expression 5x – 9?
ANSWERS
A. 9 is subtractive from the product of 5
and
B. 5 times the difference of a number 9
C. 9 is subtracted from the sum of 5 and a number
D. 9 more than the product of 5 and a number
If 10 milligrams are contained in 2 milliters. how many milligrams are contained in 28 milliliters?
Answer:
28,000 milligrams is your answer
What is the probability of rolling a number greater than 7 on a 6-sided die rolled
list all the prime numbers between 90 and 100
Im pretty sure the only prime number in between 90 and 100 is 97
need help with this :)))))))
Answer:
C
Step-by-step explanation:
For Triangles to be similar, there have to be a corresponding length and angle
Evaluate the expression 5(7 − 4)2 ÷ 3 + 11
Answer:
21
Step-by-step explanation:
5(7-4)*2/3+11
5*3*2/3+11
15*2/3+11
30/3+11
10+11
21
Answer:
21
Step-by-step explanation:
Subtract 4 from 7
5 ⋅ 3 ⋅ 2 ÷ 3 + 11
Multiply 5 by 3.
15 ⋅ 2 ÷ 3 + 11
Multiply 15 by 2.
30 ÷ 3 + 11
Divide 30 by 3.
10 + 11
Add 10 and 11.
21
Let g(x)=Intragal from 0 to x f(t) dt, where r is the function whos graph is shown.
Picture attached with question and graphs. As well as points needed
If
[tex]\displaystyle g(x) = \int_0^x f(t) \, dt[/tex]
then g(x) gives the signed area under f(x) over a given interval starting at 0.
In particular,
[tex]\displaystyle g(0) = \int_0^0 f(t) \, dt = 0[/tex]
since the integral of any function over a single point is zero;
[tex]\displaystyle g(4) = \int_0^4 f(t) \, dt = 8[/tex]
since the area under f(x) over the interval [0, 4] is a right triangle with length and height 4, hence area 1/2 • 4 • 4 = 8;
[tex]\displaystyle g(8) = \int_0^8 f(t) \, dt = 0[/tex]
since the area over [4, 8] is the same as the area over [0, 4], but on the opposite side of the t-axis;
[tex]\displaystyle g(12) = \int_0^{12} f(t) \, dt = -8[/tex]
since the area over [8, 12] is the same as over [4, 8], but doesn't get canceled;
[tex]\displaystyle g(16) = \int_0^{16} f(t) \, dt = 0[/tex]
since the area over [12, 16] is the same as over [0, 4], and all together these four triangle areas cancel to zero;
[tex]\displaystyle g(20) = \int_0^{20} f(t) \, dt = 24[/tex]
since the area over [16, 20] is a trapezoid with "bases" 4 and 8, and "height" 4, hence area (4 + 8)/2 • 4 = 24;
[tex]\displaystyle g(24) = \int_0^{24} f(t) \, dt = 64[/tex]
since the area over [20, 24] is yet another trapezoid, but with bases 8 and 12, and height 4, hence area (8 + 12)/2 • 4 = 40, which we add to the previous area.
plz help on a timed test will pay 10 points and make brainlest
What other countries have set up early earthquake warning systems? Which of these countries are in the Ring of Fire? Why is it important for these Ring of Fire countries to have warning systems?
Answer:
Mexico, Japan, South Korea, Taiwan, and the United States, Chile, Japan, the US west coast; Chile, Japan, the US west coast; So all that is left for the people who live around the Ring of Fire is to be aware of the danger, perhaps to live further inland, build safer, earthquake-resistant housing, and for nations everywhere to improve oceanic and land-based early-warning systems to help minimize the risk to life
Step-by-step explanation:
What is 2+100009 it for my homework and I need it done today
Answer:
100011
Step-by-step explanation:
Is 26% greater than 3/8?
Answer:
No. It is not greater than 3/8
Step-by-step explanation:
3/8 x 100
=> 300/8
=> 37.5
=> 26% < 37.5%
Therefore, 26% is not greater than 3/8 or 37.5
Hoped this helped.
Darryl deposits $1,500 into a savings account that has a simple interest rate of 2.7%.
Lori deposits $1,400 into a savings account that has a simple interest rate of 3.8%.
If no other transactions are made, who will have more money in their account after 10 years? How much more?
Answer:
12
Step-by-step explanation:
the x-coordinate is zero and the y-coordinate is positive choose the location
Answer:
(0,5)
Step-by-step explanation:
A positive number is a number higher than 0. The x-coordinate is the first number, and the y coordinate is the second number. Plug in any random positive y coordinate to get your point.
(x,y)
(0,1)
(0,2)
(0,3)
Find the surface area of this cubiod
Answer:
surface area is 2(lb + bh + lh)
I think this is the right formula
Answer:
Total surface area = 62 cm^2.
Step-by-step explanation:
There are 2 faces each of area 2 * 3 = 6, = 12 cm^2.
There are 2 faces each of area 10, = 20 cm^2.
There are 2 faces each of area 15, = 30 cm^2.
12 + 20 + 30 = 62 cm^2.
68% of what number is 17
Answer:
25
Step-by-step explanation:
We can set up an equation and solve for x (68% of x is 17)
68%*x=17 perform the inverse operation and divide both sides by 68%
dividing both sides by 68% will isolate the x variable
68%*x/68%= 17/68%
x=17/68%
x=25
so, therefore,
68% of 25 is 17
Answer:
[tex]\displaystyle 11\frac{14}{25}[/tex]
Step-by-step explanation:
Whenever you take a percentage of something, you multiply. Turn 68% into a fraction and multiply by 17:
[tex]\displaystyle \frac{289}{25} = [\frac{17}{25}][17] \\ \\ \boxed{11\frac{14}{25}} = \frac{289}{25}[/tex]
I am joyous to assist you at any time.
What decimal is 0.77 %
Answer:
0.0077
Step-by-step explanation:
im giving brainliest to who ever needs it
Answer:
heck ya
Step-by-step explanation:
Each student in Mr. Ricardo's class has one camera that holds
320 pictures. He asks each student to delete 1/4 of the pictures and turn in the rest. Which of the following functions best represents the number of pictures, p that Mr. Ricardo will collect depending on the number of cameras, that his students have?
A) p=80c
B) p=160c
C) p=240c
D) p=320c
Answer:
C) p = 240cStep-by-step explanation:
Each camera has 320 pictures.
If 1/4 of pictures deleted, remaining number is:
320 - 1/4*320 = 320 - 80 = 240Total number of pictures is:
p = 240cCorrect choice is C
In a 2004 poll of 500 cell phone users conducted by the Yankee Group, 20% indicated that they had received commercial messages or ads on their cell phones. Is there sufficient evidence to conclude that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of .13 reported for the previous year
Answer:44÷58+44
Step-by-step explanation:
Let p=x^2+6. Which equation is equivalent to (x^2 + 6)^2 - 21 = 4x^2 + 24 in terms of p?
Answer:
p^2-4p-21=0
Step-by-step explanation:
Where you see (x^2 + 6) you put in p.
p 2 - 21 = 4 ( x 2 + 6 )
p 2 - 21 = 4p
p 2 - 4p - 21 = 0
:)
f(x) = x^3 + 3x^2
What would the graph look like?
Answer: the answer is in the attachment.
Answer:
Hope this helps :)
Step-by-step explanation:
An internet service provider (ISP) has experienced rapid growth in the past five years. As part of its marketing strategy, the company promises fast connections dependable service. To achieve its objectives, the company constantly evaluates the capacity of its servers. One component of its evaluation is an analysis of the average amount of time a customer is connected and actively using the Internet daily. A random sample of 12 customer records shows the following daily usage times, in minutes.
274 347 283 307 327 314
303 285 280 391 359 325
Interpret the confidence interval estimate.
a. Based on the sample data, with 90% confidence, the ISP can conclude that the sample mean daily usage time is between _____ minute(s) and _____ minute(s).
b. Based on the sample data, with 90% confidence, the ISP can conclude that the true population mean daily usage time is between _____ minute(s) and _____ minute(s).
c. Based on the sample data, the ISP can conclude that 90% of daily usage times are between _____ minute(s) and _____ minute(s).
Using the t-distribution, it is found that the correct interpretation is:
b. Based on the sample data, with 90% confidence, the ISP can conclude that the true population mean daily usage time is between 297.75 minute(s) and 334.75 minute(s).
We can find the standard deviation for the sample, which is why the t-distribution is used to solve this question.
We are given a sample size of [tex]n = 64[/tex].Using a calculator, we find that:
The sample mean is [tex]\overline{x} = 316.25[/tex]The sample standard deviation is [tex]s = 35.68[/tex]The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 12 - 1 = 11 df, is t = 1.7959.
Then:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 316.25 - 1.7959\frac{35.68}{\sqrt{12}} = 297.75[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 316.25 + 1.7959\frac{35.68}{\sqrt{12}} = 334.75[/tex]
From the confidence interval, we can infer about the population mean, hence, the correct option is:
b. Based on the sample data, with 90% confidence, the ISP can conclude that the true population mean daily usage time is between 297.75 minute(s) and 334.75 minute(s).
A similar problem is given at https://brainly.com/question/15180581