Answer:
I Can't understand your language !!!!!
Step-by-step explanation:
Please ask it in English Lol !!!!
Water is poured into a conical paper cup at the rate of 3 cubic centimeters
(cm) per second (s). The paper cup measures 8 cm tall and the top has a
radius of 4 cm.
a.) Use similar triangles to express the radius r in terms of the height h.
Be sure to solve your equation for r.
ANSWER: r =
<
b.) Determine how fast the water level is rising at the instant the water is 4
cm deep.(The volume of a cone is V = r2h.) Be sure to round your
answer to 3 Decimal Places.
ANSWER:
dh
dt
m/s
Answer:
The water level is rising at the rate 0.238 cm per second
Step-by-step explanation:
Let the radius and height of water at time t be r and h respectively.
Height of cup =H= 8 cm
Radius of cup = R = 4 cm
By symmetry
[tex]\frac{r}{h}=\frac{4}{8} \\r=\frac{1}{2}h ---1[/tex]
Volume of water at time t , [tex]V= \frac{1}{3} \pi r^2 h[/tex]
[tex]\frac{dV}{dt}=\frac{1}{3}\pi 2r \frac{dr}{dt} h+\frac{1}{3} \pi r^2 \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{3}\pi r (2 \frac{dr}{dt} h+ r \frac{dh}{dt})[/tex]
With 1
[tex]\frac{dr}{dt}=\frac{1}{2} \frac{dh}{dt}[/tex]
So,
[tex]\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) (2 (\frac{1}{2} \frac{dh}{dt}h)+ r \frac{dh}{dt})\\\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) ( \frac{dh}{dt}h+ r \frac{dh}{dt})\\\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) ( h+\frac{1}{2}h) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{6}\pi h(\frac{3h}{2}) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{6}\pi (\frac{3h^2}{2}) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{12}\pi 3h^2 \frac{dh}{dt}[/tex]
We are given that Water is poured into a conical paper cup at the rate of 3 cubic centimeters (cm) per second (s).
We are supposed to find how fast the water level is rising at the instant the water is 4 cm deep.
So,[tex]\frac{1}{12}\pi 3(4)^2 \frac{dh}{dt}=3\\\frac{dh}{dt}=\frac{3 \times 12}{\pi 3(4)^2 }=0.238[/tex]
Hence the water level is rising at the rate 0.238 cm per second
The radius in terms of height is [tex]\mathbf{r =\frac 12h}[/tex], while the water level increases at 0.239 cm per second when the height is 4 cm
(a) Radius in terms of height
The given parameters are:
[tex]\mathbf{h = 8cm}[/tex] --- height
[tex]\mathbf{r = 4cm}[/tex] --- radius
The above parameters can be written as:
[tex]\mathbf{r :h =4cm : 8cm}[/tex]
[tex]\mathbf{r :h =4 : 8}[/tex]
Express as fractions
[tex]\mathbf{\frac rh =\frac 48}[/tex]
[tex]\mathbf{\frac rh =\frac 12}[/tex]
Multiply both sides by h
[tex]\mathbf{r =\frac 12h}[/tex]
(b) How fast the water is rising
The volume of a cone is:
[tex]\mathbf{V = \frac 13 \pi r^2h}[/tex]
Differentiate with respect to time
[tex]\mathbf{V' = \frac 13 \pi(2rh\ \frac{dr}{dt} + r^2\frac{dh}{dt})}[/tex]
When the water is 4cm deep, then the radius is 2cm using [tex]\mathbf{r =\frac 12h}[/tex]
So, we have:
[tex]\mathbf{V' = \frac 13 \pi(2 \times 2 \times 4\times \frac{dr}{dt} + 2^2\frac{dh}{dt})}[/tex]
[tex]\mathbf{V' = \frac 13 \pi(16 \frac{dr}{dt} + 4\frac{dh}{dt})}[/tex]
Also, we have:
[tex]\mathbf{r =\frac 12h}[/tex]
Differentiate with respect to time
[tex]\mathbf{\frac{dr}{dt} = \frac{1}{2}\frac{dh}{dt}}[/tex]
So, we have:
[tex]\mathbf{V' = \frac 13 \pi(16 \times \frac{1}{2}\frac{dh}{dt} + 4\frac{dh}{dt})}[/tex]
[tex]\mathbf{V' = \frac 13 \pi(8\frac{dh}{dt} + 4\frac{dh}{dt})}[/tex]
[tex]\mathbf{V' = \frac 13 \pi(12\frac{dh}{dt})}[/tex]
Expand
[tex]\mathbf{V' = 4\pi\frac{dh}{dt}}[/tex]
The volume increases at 3 cm^3 per second.
So, we have:
[tex]\mathbf{3 = 4\pi\frac{dh}{dt}}[/tex]
Divide both sides by 4
[tex]\mathbf{0.75 = \pi\frac{dh}{dt}}[/tex]
Divide both sides by pi
[tex]\mathbf{0.239 = \frac{dh}{dt}}[/tex]
Rewrite as:
[tex]\mathbf{\frac{dh}{dt} = 0.239}[/tex]
Hence, the water level increases at 0.239 cm per second when the height is 4 cm
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6. Find the value of r in the following triangle.
Answer:
Helpppppp
Step-by-step explanation:
Question is on attached photograph.
Answer:
Here you go sorry.
Step-by-step explanation:
Question 1.
y = 4x - 8 has a slope of 4. Since parallel lines have equal slopes, the slope of your new line will also be 4.
Now, you have a point (3,9) and a slope 4. Use the Point-Slope Form for the equation of a line.
y - y1 = m(x - x1)
y - 9 = 4(x - 3)
y - 9 = 4x - 12
y = 4x - 3
Question 2.
Since it is parallel, it must have the same slope.
y = (1/2)x + b
Find b from the given point.
4 = (1/2)(2) + b
b = 3
y = (1/2)x + 3
The table and the graph show the height and weight of ten basketball players. Which
statement is true?
Answer: the data point for player G is an outlier.
Step-by-step explanation:
Answer:
The data point for player G is an outlier.
Express the solution of, x^3 + 3x^2 < x + 3, using interval notation.
Answer:
Step-by-step explanation:
x^3+3x^2<x+3
(-∞,-3)∪(-1,1)
alice arranges 42 blocks in 7 equal rows how many blocks are in each row
I NEED THIS ACAP
Answer:
There are 6 blocks in each row
Step-by-step explanation:
The total number of blocks is 42 and the number of rows is 7. So the equation would be 42 ÷ 7.
So, 42 ÷ 7 = 6. There are 6 blocks in each row.
Hope this Helps!
Total number of row is 6 row.
Given that;
Total number of block = 42 block
Total number i=of block in each row = 7
Find:
Total number of row
Computation:
Total number of row = Total number of block / Total number i=of block in each row
Total number of row = 42 / 7
Total number of row = 6
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What expression is equivalent to (-4y-x)-(3y-9x
Answer:
-7y+8x
Step-by-step explanation:
-7y+8x
This is trigonometry please answer it :)
I'll give a ♡ if you answer it
Answer:
2(a) 30°
(b) 48,59°
(c) 31,4485°
(d) 33,005565°
is b intersection c = to b union c
Answer:
no.
Step-by-step explanation:
b ∩ c is the values that appear in both b and c.
b ∪ c is all the values in b and c.
While Brayden is in
training, he has to drink 650
milliliters of water per day.
How many liters of water will
that be for one week?
Answer:
4,550
Step-by-step explanation: 7 x 650 is 4,550
Suppose the area of a rectangular paper parachute used for disaster relief is 260 square feet. If one side of the parachute measures 2x + 4 and another side measures 8x + 2, what is the value of x?
Answer:
x= 2.6ftStep-by-step explanation:
Step one:
given
A= 260ft^2
W= 2x + 4
B=8x + 2
Step two:
A=L*W
260=(2x+4)*(8x + 2)
open bracket
260=16x^24x+32x+8
16x^2+56x-252=0
Solving using quadratic formula
the roots are
x=-6.0
x= 2.6
Hence the value of x= 2.6ft
how do u write hundredths like I literally forgot
Answer:
its the second number to the right of the decimal
Answer:
two zeroes at the end and if it is a number like 2400 the hundreths place is the 400
Step-by-step explanation:
In how many ways can the numbers 3,4,5,6,7,8,9, and 10 b
divided into two sets A and B such that the sum of the numbers in B is three times the sum of the numbers in A?
pls help quick! will mark brainliest!
Answer:
4 times
Step-by-step explanation:
Given that the sum of all the numbers => 3+4+5+6+7+8+9+10 = 52
And we are to divide it into two sets such that the sum of set B is three times the number of sum of set A => Sum B = 3 * Sum A
Hence Total sum = Sum B + Sum A
Total sum ÷ 4 = 52 ÷ 4 = 13.
Since Sum B = (3 * Sum A) => (3 * 13 ) = 39
Therefore Sum B = 39 and Sum A = 13
To divide them into two sets
Sum A = (10, 3) = 13: Sum B = ( 4, 5, 6, 7, 8, 9) = 39
Sum A = (9, 4) = 13: Sum B = (3, 5, 6, 7, 8, 10) = 39
Sum A = (8, 5) = 13: Sum B = (3, 4, 6, 7, 9, 10) = 39
Sum A = (7, 6) = 13: Sum B = (3, 4, 5, 8, 9, 10) = 39
Hence, the correct answer is 4 times
Error Analysis A contractor purchases 7 dozen pairs of padded work gloves for $93.24. He incorrectly calculates the unit price as $13.32 per pair for the expense report. What is the correct unit price? What is the error
Answer:
Step-by-step explanation:
i hopes this helps
Solve -4.m - 6 + 6-m = -5 + 2m - 1
Answer:
m= 6/7
decimal form m= 0.857
Step-by-step explanation:
hope this helps
Answer:
m=6/7
m=0.857...
Step-by-step explanation:
-4m - 6 + 6-m = -5 + 2m - 1
-5m-6+6=-5+2m-1
-5m=-5+2m-1
-5m=2m-5-1
-5m=2m-6
-5m-2m=2m-6-2m
-7m=-6
divide both sides by -7
x=6/7
Which expression can be used to check the answer to 56-(-14)=-4?
O-14x-4
O4(-14)
O 56x(-14)
O-4-56
Answer:
B
Step-by-step explanation:
The cost of 6 books is $20.46. What is the cost of 1 book
Answer:
3.41
Step-by-step explanation:
divided 20.46 by 6
Answer:
$3.41
Step-by-step explanation:
You divided the total cost by number of books.
20.46 divided by 6 = 3.41.
Find the slope of each line
Answer:
y= -1/2x
Step-by-step explanation:
The price of a new car is $42,500. If sales tax is 9%, then how much will you pay in total for the car?
Answer:
$46325 in total for the car
Step-by-step explanation:
Seth has two similar ice cream cones, Cone A and Cone B. The height of Cone A is 16 inches, and the height of Cone B is 4 inches. What is the ratio of the volume of Cone A to the volume of Cone B?
Answer:
64 : 1.
Step-by-step explanation:
Ratio of the volumes is 16^3 to 4^3
= 4096 : 64
= 64 : 1.
HELP ill give brailist
Answer:
x = 4.25 (A. 4.25)
Step-by-step explanation:
(For, 4x + 39) 4 times 4.25 = 17, then add 17 + 39, which gets you to 56.
( for 16x - 12) multiply 16 times 4.25 = 68. subtract 12 from 68 to equal 56.
how many kg are equal to 325 grams
Answer:
0.325
Step-by-step explanation:
thats it
Answer:
0.325 kg
Step-by-step explanation:
You move the decimal point three places to the left, and end up with 0.325 kg. :)
grandfathers age is 4 times abduls age. 10 years ago his age was 7 times abduls age. find their present ages
Answer:
20,80
Step-by-step explanation:
[tex]Let\ Abduls\ present\ age\ be\ x\\His\ Grandfather's\ present\ age\ = 4x\\\\Abdul's\ age\ before\ 10\ years=x-10\\His\ Grandfather's\ age\ before\ 10\ years =4x-10\\\\We\ are\ given\ that\ ,\\Abdul's\ Grandfather's\ age\ before\ 10\ years = 7 * Abdul's\ age\ before\ 10\ years\\Hence, \\4x-10=7(x-10)\\4x-10=7x-70\\-10+70=7x-4x\\60=3x\\x=20\\Hence,\\Abduls\ present\ age\ =20\\His\ grandfather's\ present\ age\ = 4*20=80[/tex]
Answer:
Abdul's age=20 y/o
Grandpa's age=80y/o
Step-by-step explanation:
let Abdul's age be 'x'
so, grandpa's age=4x
Grandpa's age 10 yrs ago= 4x-10
according to the question, grandpa's age 1o yrs ago=7(x-10)
so, 4x-10=7(x-10)
4x-10=7x-70
by substituting,
70-10=7x-3x
60=3x
60/3=x
20y/o=x
so, 4x=20*4=80 y/o
Maggie is making a necklace using a 13-inch string and identical beads.
Maggie has placed 12 beads next to each other starting at the left end of the string as shown in the
figure
The 12 beads fill 3 inches of the string. How many total beads will completely fill the 13-inch string
Answer:
52
Step-by-step explanation:
First find out how many beads cover 1 inch of the string which is 4 beads then multiply that number, 4, by the length of the string, 13. You should get 52.
Answer: 52
Part A
Why?
So for this question. You can write a ratio what will the balance be what information do they give you that you can register as a ratio? Well, what will the ratio be?
OK, THE WORK IS HERE!--v
So 12 beads are the ratio.
Now what do we want to know? Well, we want to know how to solve it.
1. 12b= __
3in= 13in <---------well-known way people use it to solve
--------------------------------------------------------------------------------------------------------------------------------
2. 12b divided by 12 = 1b
3in divided by 12= ____->ANSWER: 0.25 <----- Not that many people do it this way
for 2. solve-v
1b = ___ ANSWER: 52
0.25 13in 1 We can do this 13 divided by 0.25 which is 52
SO FOR PART A THE ANSWER IS 52
--------------------------------------------------------------------------------------------------------------------------------
ANSWER: Part B is __
Why?
-1in off here----------------------------1in off here-
And she wants to keep The middle part and we know this whole thing is 13 but the middle part = 11. Sooooooo...
1b = ___ANSWER 8
0.25 = 2in so now we can do this: 2 divided by 0.25 which we get 8
ANSWER FOR PART B IS 8
cos²30° + cos²60° + cos²90° + 2 cos 30° cos 60° cos 90°
Answer:
1
Step-by-step explanation:
[tex]cos²30° + cos²60° + cos²90°\\ + 2 cos 30° cos 60° cos 90° \\ \\ = \bigg( \frac{ \sqrt{3} }{2} \bigg) ^{2} + \bigg( \frac{ 1 }{2} \bigg) ^{2} + \bigg( 0\bigg) ^{2} \\ + 2 \times \frac{ \sqrt{3} }{2} \times \frac{ 1 }{2} \times 0 \\ \\ = \frac{3}{4} + \frac{1}{4} + 0 + 0 \\ \\ = \frac{3 + 1}{4} \\ \\ = \frac{4}{4} \\ \\ = 1[/tex]
A store is having a sale where movies are 40% off their original price. A movie is on sale for $26.00. What was the original price of the movie?
−2(x + 3 − 4x) = 3x − 18
How many solutions for x does this equation have?
Answer:
3
Step-by-step explanation:
because there are 3 x's
NEED HELP FAST MARKING PEOPLE AS BRAINLIST
Answer:
sss
Step-by-step explanation:
since the problem dosent give angles its most likes sss
Answer:
so i cant really see it but it looks as if the two triangles are right angles and are congruent.
Step-by-step explanation:
so i hope this helps a little if so mark as brainleist pls have a nice day
question 10 pls help
Answer:
D
Step-by-step explanation:
Pls help me on this one.
Which statement describes the graph of the system of equations below?
1.5x + 0.2y = 2.68
1.6x + 0.3y = 2.98
A. The lines are parallel.
B. The lines overlap at all points.
C. The lines intersect at (1.6,1.4).
D. The lines intersect at (3.1,0.5).
The statement that describes the graph of the system of equations is:
C. The lines intersect at (1.6, 1.4).
Here, we have,
To determine the description of the graph of the system of equations:
1.5x + 0.2y = 2.68
1.6x + 0.3y = 2.98
We can start by comparing the slopes of the two lines.
The equations are in the form y = mx + b, where m represents the slope.
In the first equation, the slope is 0.2, and in the second equation, the slope is 0.3.
Since the slopes are different, we can conclude that the lines are not parallel (option A) or overlapping at all points (option B).
To determine the point of intersection, we can solve the system of equations.
By using any appropriate method, we find that the lines intersect at (1.6, 1.4) (option C).
Therefore, the statement that describes the graph of the system of equations is:
C. The lines intersect at (1.6, 1.4).
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