QUESTION 1
A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm/sec. How fast (in cm/sec) is the water level dropping
when the height of the water is 3 cm?(Round your answer two (2) decimal places)
Answers
The water level will be dropping at the rate of [tex]0.64 cm/sec[/tex] when the height of the water reaches [tex]3cm[/tex]
We are give a cone with dimensions as seen in the diagram in the attached image.
The volume changes at the rate
[tex]\frac{dV}{dt}=-2cm^2/sec[/tex]
the negative sign is used because the volume of water is reducing.
what we need to know is the rate the height is changing when [tex]h=3cm[/tex]. That is, we need to evaluate
[tex]\frac{dh}{dt}|_{h=3cm}[/tex]
The relationship between the volume and the height is given by
[tex]V=\frac{1}{3}\pi r^2h[/tex]
but both [tex]h[/tex] and [tex]r[/tex] are changing when [tex]V[/tex] changes. So we need to eliminate [tex]r[/tex] somehow. From the diagram, we can use the similar triangle property to accomplish this
[tex]\frac{r}{2}=\frac{h}{6}\\\\\implies r=\frac{h}{3}[/tex]
substitute into the volume formula to eliminate [tex]r[/tex]
[tex]V=\frac{\pi h^3}{27}[/tex]
differentiate both sides with respect to time, [tex]t[/tex], since both the volume and height are functions of time. They will both be differentiated implicitly
[tex]\frac{dV}{dt}=\frac{\pi h^2}{9}\frac{dh}{dt}[/tex]
to find [tex]\frac{dh}{dt}|_{h=3cm}[/tex], substitute the values for [tex]\frac{dV}{dt}[/tex] and [tex]h[/tex]
[tex]-2=\frac{\pi 3^2}{9}\frac{dh}{dt}\\\\\frac{dh}{dt}=-\frac{2}{\pi}\\\\\approx -0.64 cm/sec[/tex]
So the rate at which the height is reducing when it reaches [tex]3cm[/tex] is [tex]0.64cm/sec[/tex]
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Related Questions
What is the value of x and y?
Answers
Answer:
x = 90y = 43Step-by-step explanation:
The angle bisector in this isosceles triangle is also its altitude. It meets the base segment at right angles.
x° = 90°
__
The acute angles in a right triangle are complementary.
y° = 90° -47°
y° = 43°
Classify the following polynomial by its degree value. -x + x26 - 104
Answers
[tex] \: \: \: \: \: \: [/tex]
[tex] = 25x - 104[/tex]
Step-by-step explanation:
[tex] - x + x26 - 104[/tex]
use the commutative property to reorder the terms[tex] - x + 26x - 104[/tex]
collect like terms[tex] = 25x - 104[/tex]
hope it helpsFind the results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.
Answers
Answer:
[tex]\huge\boxed{\overrightarrow{u}-\overrightarrow{v}=\left<-10;\ -3\right>}[/tex]
Step-by-step explanation:
[tex]\overrightarrow{u}=\left<-8;\ 4\right>;\ \overrightarrow{v}=\left<2;\ 7\right>\\\\\overrightarrow{u}-\overrightarrow{v}=\left<-8;\ 4\right>-\left<2;\ 7\right>=\left<-8-2;\ 4-7\right>=\left<-10;\ -3\right>[/tex]
Answer:
Step-by-step explanation:
-u-v = 6,-11
u-v = -10,-3
v-u = 10,3
litterally nobody answers my questions
my question is the image
Answers
Nam
20. Carol bought 5 pork chops and 3 steaks.
Each pork chop weighed 0.32 pound
and each steak weighed 0.8 pound. How
Temand
many pounds of meat did Carol buy in
telall?
Answers
Answer: Carol bought 4 pounds(lb) of meat.
Explanation: 0.32 x 5 = 1.60, and 0.8 x 3 = 2.40, and 1.60 + 2.40 = 4.
The weight of the meat bought by Carol is 4 pounds.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Given that Carol bought 5 pork chops and 3 steaks. Each pork chop weighed 0.32 pounds and each steak weighed 0.8 pounds.
The weight of the meat will be calculated as:-
0.32 x 5 = 1.60,
0.8 x 3 = 2.40,
Total weight,
1.60 + 2.40 = 4 pounds
Therefore, the weight of the meat bought by Carol will be 4 pounds.
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Simplify the expression
3+4·10 – 8
Answers
Answer:
35
Step-by-step explanation:
one word: PEMDAS. technically they are all a bunch of words but whatever...
P: parentheses
e: exponents
m: multiply
d: divide
a: add
s: subtract
first we multiply 4*10 since that's first on the list
4*10=40
we have
3+40-8
then we add
3+40
which is 43
then we subtract 8 from it as we have 43-8
which is in the end:
35
Step by step equation
A county has constructed a conical building to store sand. The cone has a height of 101 m and a diameter of 330 m. Find the volume of this building to the nearest hundredth. Use 3.14 for π.
Answers
Answer:
2878045.500 cubed metres
Step-by-step explanation:
volume = 1/3* pie* r*r*h
= 1/3 *3.14*165*165*101
=2878045.5 cubed metres
i hope it's helpful
Find the equation of the line that is parallel to x=5y-8 and pass through (6, -5) in slope intercept form
Answers
Answer:
y=1/5x-31/5 (or y=0.2x-6.2 in decimals)
Step-by-step explanation:
x=5y-8 (original equation)
x+8=5y (Addition Property of Equality)
1/5x+8/5=y (Division Property of Equality, slope of original equation is 1/5)
y-y1=m(x-x1) (point-slope formula)
y-(-5))=1/5(x-(6)) (plug in the slope that was found earlier and the point given in the question)
y+5=1/5(x-6)
y+5=1/5x-6/5 (Distributive Property of Multiplication) Note: 5 = 25/5
y=1/5x-31/5 (Subtraction Property of Equality, and there's your answer)
y=0.2x-6.2 (This is the same answer, but written with decimals)
At noon, a tank contained 8 in. of water. After several hours, it contained 6 in. of water. What is the percent decrease of water in the tank?
Answers
Answer:
25%
Step-by-step explanation:
8-6=2
2/8=0.25
0.25×100=25%
What is the mathematical formula of ligma
Answers
Who's Joe? I am in dire need of therapy.
There is a group of 5 turtles near the playground. More turtles joined. Now there are 13 turtles. How many turtles joined the group?
Answers
Answer:
8 turtles joined the group
Step-by-step explanation:
13-5=8
Write the equation of the line perpendicular to y = 8 - 5z that contains the point (0, 0) . Fill in the slope and y-intercept
Answers
The equation of the line perpendicular to y = 8 - 5z is 5x+8y=16.
8y=-5x+16
y=-5/8x+2.
To be perpendicular, the slope has to be 8/5.
What is the slope-intercept form of the line?
The slope-intercept form is y=mx+c
Where m is the slope and c is the y-intercept.
So y=8/5x+b.
We can plug in the given coordinates to get
7=8/5*-5+b
7=-8+b
b=15.
So eqn is y=8/5x+15 or in point-slope form, y=8/5x+15
5y=8x+75
5y-8x=75
The equation of the line perpendicular to y = 8 - 5z is 5x+8y=16.
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A bag of mixed nuts has 18 almonds, 8 cashews, and 14 peanuts. If one nut is selected, what is the probability that a peanut is chosen?
Provide the answer as a simplified fraction.
Answers
Answer:
7/20
Step-by-step explanation:
Answer:
ok so here is answer option no1
1/8 + 1/4 = 3/8
or you could do
18 plus 14 equals 32divided into 8 equals 4
Step-by-step explanation:
if this is wrong I'm very very very really really really sorry.
Please help me solve this problem, thank you.
Answers
Step-by-step explanation:
first you need to find the 17 and 8 triangles missing sides length so we do a squared plus b squared equals c square and since we have c which is 17 we subtract 8 squared or 64 from 17 square and we get 225. next the missing line from the next one is done the same way 225 minus 9 squared or 81 and we get 144 and the square root of that is 12 we do 12 squared 144 minus 6 squared because we already know that the side is six because it gives it to us and we get 10.392
Expand and simplify: (x - 7)(x+7)
Answers
Answer:
[tex]x^{2} -49[/tex]
Step-by-step explanation:
Answer:
[tex](x-7)(x+7) =x^2 -7^2 = x^2 -49[/tex]
Step-by-step explanation:
single simplified fraction
X/3+X/5
Answers
hope this helps:)
A certain function multiplies Each input number by three to produce an output number given that X represents the input numbers and Y represents the output numbers which graph represents the function.
Please answer
No links
Picture is included
Answers
Answer:
The answer is A. Hope this helped!!!!!!
Answer:
answer C because is x is input and is multiplied by 3 so the function would have been y=3x so that is C
please help!! easy but i don't understand <3
Answers
in essence it's just asking on getting the equation of that line in more or less slope-intercept form, hmmm well, it's a line, so all we need is two points to get it, hmmm let's see let's use the starting point and terminal point, so we know it goes through the origin, (0,0) and also goes through (1, 0.7), let's change 0.7 to a fraction, so its 7/10, ok, let's use those two points from it.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{\frac{7}{10}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{7}{10}}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{~~ \frac{7}{10}~~}{1}\implies \cfrac{7}{10}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{\cfrac{7}{10}}(x-\stackrel{x_1}{0})\implies y = \cfrac{7}{10}x[/tex]
What is the slope of the line?
1/2 2 1 -2
Answers
Answer:
the slope of the line is 2
Step-by-step explanation:
Answer:
The slope of the line is 2.
Step-by-step explanation:
The point where the line crosses the y-axis, also known as the y-intercept, is (0,1). The next clear point is (1,3).
We can use the formula for finding slope here.
[tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]
If we plug in the points, with (0,1) being the first and (1,3) being the second, we'll get this:
[tex]\frac{3-1}{1-0} --> \frac{2}{1} --> 2[/tex]
Therefore, the slope is 2.
Below the function h (x) ang g (x) are graphes. At which values of x is true that h (x) > g (x)? Select all that apply.
Answers
Answer:
25
Step-by-step explanation:
At x = 10 and 31 the value of the function h(x) is greater than g(x) thus options (A) and (D) are correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given graph of the function,
At x = 10 the h(x) > g(x)
At x = 31 the h(x) > g(x)
Hence "The value of the function h(x) is bigger than g(x) at x = 10 and 31".
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With the last of your gold, you decide to buy a Ferrari F50 GT1. It has a maximum speed of 380 km/hour. How fast is that in MPH (miles per hour)
Answers
Answer:
237.5 miles / hour
Step-by-step explanation:
The conversion factor is 1.6 km = 1 mile.
1 mile / 1.6 km = x / 380 km / hour Multiply both sides by 380 km/hour
380 km/hr * 1 mile / 1.6km = x
237.5 miles / hour = x
A typical tip in a restaurant is 15% of the total bill. If the bill is $90, what would the typical tip be?
Answers
Answer:
Step-by-step explanation:
Let the tip be x.
You have to take 15% of 90 to get x.
The equation looks like
15/100 * 90 = x Multiply the numerator of the fraction by 90
1350/100 = x Divide by 100
x = 13.50
So the tip is 13.50
There are other ways you could do this problem, but I think this is the most easily understood.
A typical tip in a restaurant is 15% of the total bill. If the bill is $90, what would the typical tip be?
Answer:-$13.50
Explanation:-Let the tip be x.
→ x = [tex] 90 \times \frac{15}{100} [/tex]
→ x = [tex] \frac{1350}{100} [/tex]
→ x = $13.50
Explain how to find the distance between two integers using the difference.
Answers
Answer:
read explanation for answer
Step-by-step explanation: Finding the distance between any two integers is obtained by;
Taking the absolute value of the difference between the two integer values.
For instance :
Point A = - 10
Point B = 5
The distance between the two integer points is :
Difference = Point A - Point B = - 10 - 5 = - 15
Absolute value = |-15| = 15
Therefore, This procedure works for any pair of integer distances.
Answer:Find the difference between two integers by adding the additive inverse. The distance is the absolute value of the difference. Check the distance by plotting the original two integers on a number line and counting the units between them.
Step-by-step explanation:
The vertices of a triangle are A(0,0),B(3,8) and C(9,0). What is the area of this triangle?
Answers
Answer:
9
Step-by-step explanation:
To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.
Fill in the numbers for each corresponding letter combination within the formula.
Fill in your formula like this: 0(8-10) + 3(0-0) + 9(0-8).
Subtract the numbers within the parentheses.
0 from 8 = 8, 0 from 0 = 0 and 8 from 10 = 2.
Multiply that result by the number to the left of the parentheses.
0 by 8 = 0, 3 by 0 = 0 and 9 by 2 = 18.
Add the three products together.
0 + 0 + 18 = 18
Divide the sum of the three products by 2.
18 ÷ 2 = 9
Answer:36
Step-by-step explanation:
Help help help help math math
Answers
Angle 53 and angle 5, are supplementary angles therefore
53 + 5 = 180
5 = 127
Simplify completely
(192x^12/3x^3)^1/3
Show all work for full credit
Answers
Answer and Explanation: The answer and explanation is in the image.
whats 3-6h if h = -1
Answers
Answer:
9 is the answer.
Step-by-step explanation:
Given:
h = -1=> 3-6h
=> 3 - 6(-1)
=> 3 + 6
=> 9
Therefore, 9 is the answer.
Hoped this helped.
You use substitution to solve a system of equations and, after simplifying, end with a statement that says 7 7. Describe what this statement means about the number of solutions and about the graph of the system.
Answers
Answer:
Sample Response: Since the statement is true, there are an infinite number of solutions to the system. This statement also indicates that the lines are equivalent.
Write an equation in slope-intercept form for the line with y-intercept −8 and slope 1/3
Answers
Answer:
y=1/3x-8
Step-by-step explanation:
The slope intercept form of a line is y=mx+b
m stands for slope and b stands for y intercept
So ... simply put 1/3 in for m and -8 in for b
(4x 2 − 2x + 10) + (−2x 2 + 4x − 2)
Answers
Answer:
2x²+2x+8
Step-by-step explanation:
4x²-2x+10-2x²+4x-2
=4x²-2x²-2x+4x+10-2
=2x²+2x+8
