The conic water vessel of height 40 cm and radius 8 cm filled at 20 cm^3/s gives;
The rate at which the water level is rising when the water level is 12 cm from the vertex is approximately 1.1 cm/s.When the vessel is one-quarter filled the rate at which the water level is rising is approximately 0.21 cm/s.How can the water level rate be found?The volume of the vessel, v = π•r^2•h/3
[tex] \frac{h}{r} = \frac{40}{8} = 5[/tex]
h = 5•r
Therefore;
v = π•r^2•(h)/3 = π•(h/5)^2•h/3
v = π•h^3/75
By chain rule of differentiation, we have;
[tex] \frac{dv}{dh} = \frac{dv}{dt} \times \frac{dt}{dh} [/tex]
Which gives;
[tex]π• \frac{ {h}^{2} }{25} = 20 × \frac{dt}{dh} [/tex]
[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {h}^{2} }{25} } [/tex]
When the height is 12 cm from the vertex, we have;
[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {12}^{2} }{25} } = 1.1 [/tex]
The rate at which the water level is rising when the water level is 12 cm from the vertex is approximately 1.1 cm/s.When the vessel is one-quarter filled, we have;
v = π•h^3/75
π•(40)^3/(75×4) = π•h^3/75
10•(40)^2 = 16,000 = h^3
h = (16,000)^(1/3) = 25 (approx)
Which gives;
[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {25}^{2} }{25} } = 0.21 [/tex]
When the vessel is one-quarter filled the rate at which the water level is rising is approximately 0.21 cm/s.
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9,000 were divided equally among a certain no of persons . had there been 20 more person each would have got rupees 160 . find the original no of persons
Answer:
let the number of persons be " x "
and , let each person get [tex]\frac{9000}{x}\\[/tex]rupees.
______________________________________
let's first see why each person got [tex]\frac{9000}{x}\\[/tex] rupees ,
let us suppose each person gets an amount of " r " rupees.
then ,
[tex]x \times r = amount \: we \: have \: with \: us \\ \dashrightarrow{xr = 9000} \\ \dashrightarrow{ r = \frac{9000}{x}} [/tex]
_____________________________________
According to Question ,
hαd thєrє вєєn 20 mσrє pєrѕσnѕ, єαch pєrѕσn wσuld'vє gσt rupєєѕ 160 lєѕѕ.
hєncє, wє αrє nσw ín α ѕtαtє tσ frαmє αn єquαtíσn whích íѕ αѕ fσllσwѕ -
[tex]\fbox{(x + 20)(r - 160) = 9000}[/tex]
lєt'ѕ nσw plug ín thє vαluє σf r αѕ [tex]\frac{9000}{x}\\[/tex]
[tex](x + 20)( \frac{9000}{x} - 160) = 900 0\\ \\ \cancel{9000} + \frac{180000}{x} - 160x - 3200 =\cancel{ 9000} \\ \\ taking\:LCM, \\ \\ - 160x {}^{2} - 3200x + 180000 = 0 [/tex]
on dividing the complete equation by (- 160)
[tex]x { }^{2} + 20x - 1125 = 0[/tex]
now , use the method of splitting the middle term so that we get the value of x.
[tex]x {}^{2} + 45x - 25x - 1125 = 0 \\ \\ x(x + 45) - 25(x + 45) \\ \\ (x + 45)(x - 25) = 0 \\ \\ \fbox{x = - 45 \: \: or \: \: 25}[/tex]
since number of persons can't be negative. therefore ,
number of persons = x = 25
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hope helpful :D
The length and width of the park are measured in linear units. inches, miles, meters, etc the area is measured in square units. explain the reason for using square units for area of the park. (please hurry and make it not too long please )
The area is measured in square units because it is the product of two units which gives square unit.
What is area?Area is the amount of space occupied by a two dimensional shape or object.
The area of a rectangular park is gotten from the productiif the width and length, hence:
Area = length * width
The area is measured in square units because it is the product of two units which gives square unit.
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based on the experimental probability about how many times will yosef draw a green marble if he draws a total of 75 marbles
0.17 + (0.68—0.17)* （20- -14.4)/-21.3- -14.4)
Answer:
See the steps below
Step-by-step explanation:
[tex]0.17 + \cfrac{(0.68-0.17)(20- (-14.4))}{-21.3- (-14.4)} =[/tex]
[tex]0.17 + \cfrac{0.51(20+14.4)}{-21.3+14.4} =[/tex]
[tex]0.17 + \cfrac{0.51*34.4}{-6.9} =[/tex]
[tex]0.17 - \cfrac{17.544}{6.9} =[/tex]
[tex]\cfrac{17}{100} - \cfrac{17544}{6900} =[/tex]
[tex]\cfrac{17*69-17544}{6900} =\\[/tex]
[tex]-\cfrac{16371}{6900} =[/tex]
[tex]-\cfrac{5457}{2300} =[/tex]
[tex]-2\cfrac{857}{2300}[/tex]
who ever can help ill give brainlist
Answer:
?=2
Step-by-step explanation:
1. Solve
?/10+8/100=28/100
?/10+8/100-8/100=28/100-8/100
?/10=20/100
2. Simplify
20/100=2/10
so, ?/10=2/10
3. Check
2/10+8/100=28/100
20/100+8/100=28/100
28/100=28/100
Correct !
4. Answer
Simplify the following variable expressions
The half-life of a particular radioactive substance is 10 seconds. If you started with 100 grams of this substance, how much of it would remain after 60 seconds?
There are 1.5625 grams of the radioactive substance that would remain after 60 seconds.
What is an exponent?The exponent of a number represents the total time required to multiply that number. 8 8 8 may be stated as 83 since 8 is multiplied by itself three times. In this case, 3 is the 'exponent' or 'power' that indicates how many times 8 is multiplied by itself, and 8 is the 'base' that represents the integer being multiplied.
The exponent is given as:
y = a (1 - r)ˣ
As per the question, we have
a = 100, and r = 0.50 and x = 6
Substitute the known values in the above formula, and we get
y = 100 × (1-0.50)⁶
y = 100 × (0.50)⁶
y = 100 × 0.015625
Apply the multiplication operation, a
y = 1.5625
So, after 60 seconds, 1.5625 grams of the radioactive substance would remain.
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I need help with number 13 please hurry
Answer:
a+b
-------
4
Step-by-step explanation:
Which set of ordered pairs does not represent a function?
O {(8,-4), (-5,6), (-5,7), (-3,-5)}
O{(-1,0), (1,0), (3,-2), (2, -9)}
O {(3,-7), (-2, -9), (9,3), (7, - 7)}
O {(8, –9), (-3,9), (-9,2), (-2,0)}
keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.
find the volume of a right circular cone that has a height of 3.2 m and a base with a radius of 14.1 m
Answer: 666.22 m^3
Step-by-step explanation:
The formula for the volume of a right circular cone is: V = π*r^2*(h/
3)
Therefore, plugging in 14.1 for "r" and 3.2 for "h" yields 666.22
Is -2 a whole number or irrational number?
Answer:
It is neither.
Step-by-step explanation:
A whole number is all numbers is 0, 1, 2, 3, 4.... you get it
An irrational number is a number that cannot be written as a fraction and -2 can be written as -2/1
Select the reason that best supports Statement 7 in the given proof.
Answer:
the guy above if right it is D
Step-by-step explanation:
I did the work on Acellus and pick D IT GAVE ME A CHECK MARK
The reason that supports the statement 7 in the given proof is D. Subtraction property of equality.
What is Subtraction property of equality?Subtraction property of equality is defined as, if an equation is of the form,
a = b,
then any number subtracted from both sides makes the equation same.
a - c = b - c
Here, given a proof for the value of x.
In the 6th step, by substitution,
55 = 5x + 10
This is an equation.
We need term in x on one side and a constant term on other side.
For that, if we subtract both sides by 10,
55 - 10 = 5x + 10 - 10
45 = 5x
So here the subtraction property of equality is used.
Hence the correct option is D.
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A rectangle is 2/5 (fraction) inches long and 1/3 inches wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form by filling in the boxes
in2
__/__ in2
Answer:
A = 2/15 in^2
Step-by-step explanation:
To find the area of a rectangle, we multiply length times width
A = l*w
A = 2/5 * 1/3
A = 2/15 in^2
Answer:
[tex]\sf area=\dfrac{2}{15} \ in^2[/tex]
Step-by-step explanation:
Area of a rectangle = width x length
Given:
[tex]\sf length=\dfrac25[/tex][tex]\sf width=\dfrac13[/tex]Substitute these values into the equation are solve:
[tex]\sf \implies area=\dfrac13 \times \dfrac25[/tex]
[tex]\sf \implies area=\dfrac{1 \times 2}{3 \times 5}[/tex]
[tex]\sf \implies area=\dfrac{2}{15} \ in^2[/tex]
find the value of x
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{11 + x}\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{17}\\ \end{cases}\implies (11+x)^2=x^2+17^2 \\\\\\ (11+x)(11+x)=x^2+17^2\implies \stackrel{F~O~I~L}{121+22x+x^2}~~ = ~~x^2+289 \\\\\\ 121+22x=289\implies 22x=168\implies x=\cfrac{168}{22}\implies x=\cfrac{84}{11}\implies x=7\frac{7}{11}[/tex]
Find the measure of angle M in the paralellogram. ANSWER QUICK PLS, LOTS OF POINTS, WILL GIVE BRAINLIEST WILL REPORT!!
Opposite angles are equal in parallelogram
7x-4=5x+127x-5x=12+42x=16x=8<M:-
7(8)-456-452°x=8. The steps are in the attachment.
Answer number 8 please. Thank you.
Answer:
The answer is C. A triangle is made up of a total angle of 180°, therefore C. is more than 180°
There are a total of 12 bicycles and tricycles in a parking lot. If there are 31 wheels in all, how many of them are bicycles?
Answer:
5 bicycles
Step-by-step explanation:
5 * 2 = 10 wheels
7 * 3 = 21 wheels
10 + 21 = 31
Hope this helped! Brainliest :)
Please help i am confused
Answer:
18 +2
Step-by-step explanation:
it's like 3x you just add each side 3 then you will get the answer. and the (+2) stays the same.
Graph the equation y=-X – 2 using the intercepts.
Answer:
y intercept = (0,-2)
x intercept = (-2,0)
Step-by-step explanation:
For y intercept, plug 0 for x
y = (0) - 2
y = -2
y intercept = -2
For x intercept, plug 0 for y
(0) = -x - 2
Move -2 to other side
-x = 2
Since x is negitave, make 2 negitave
x = -2
x intercept = -2
Your younger brother is getting stickers from a vending machine at the local supermarket. A proportion of stickers have the
phrase "Girls Rule!" If there are eight stickers with this message in a sample of 36 stickers, what is the 95% confidence interval
for this proportion? (1 point)
0 (0.0864, 0.3580)
0 (0.0862, 0.3578)
0 (0.0847, 0.3553)
0 (0.0812, 0.3256)
Answer:
p^=368=0.2222.95%CI=(0.2222−1.960.2222(1−0.2222)36,0.2222+1.960.2222(1−0.2222)36)=95%CI=(0.2222−1.96360.2222(1−0.2222),0.2222+1.96360.2222(1−0.2222))==(0.0864,0.3580).
=(0.0864,0.3580).
Step-by-step explanation:
flvs?
The 95% confidence interval for the given proportion is (0.864, 0.3580).
What is a confidence interval?In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of predicted observations are frequently used by analysts.
Given total samples = E = 36
number of outcomes = 8
probability = p = 8/36 = 0.2222
value of z for 95% confidence interval = 1.96
intervals = p ± z([tex]\sqrt{\frac{p(1 - p)}{E} }[/tex])
taking positive sign
= 0.2222 + 1.96[tex](\sqrt{\frac{0.2222(1 - 0.2222)}{36} })[/tex] = 0.3580
taking negative sign
= 0.2222 - 1.96[tex](\sqrt{\frac{0.2222(1 - 0.2222)}{36} })[/tex] = 0.0864
Hence, the intervals are (0.864, 0.3580), and option A is a suitable answer.
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The figure below is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point, and two regions between the smaller circles have been shaded. Each small circle has a radius of 5 cm.
The figure below is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point, and two regions between the smaller circles have been shaded. Each small circle has a radius of 5 cm.
1 of 39 men is chosen at random. 27 men passed the test. 12 men failed. What is the probability that the man failed his test
Answer:
30.7%, 0.3, or 4/13
Step-by-step explanation:
The correct procedure for this problem is:
The number of men that passed the test and the number of men should be located as the numerator and denominator of the fractional number.12/39 is our fraction, which we can reduce to 4/13We can change it to a percent and a decimal, which would be 30.7% and 0.3.A 20-inch pizza has an area of 314 in? That pizza is
divided into eight equal slices. What is the area of two slices of
that pizza?
A. 3114 in2
B. 78.5 in2
C. 39.25 in2
D. 314 in2
The area of each pizza is gotten by dividing the total area by the number of slices. Therefore, the area of two slices of that pizza is 31.4 inches².
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words the area is the space occupied by a flat shape or the surface of an object.
Therefore, 20 inch pizza has an area of 314 inches². The pizza is divided into 8 equal slices.
Each area of the slices = 314 / 20
Each area of the slices = 15.7 inches²
Therefore, the area of two slices of the pizza is as follows:
area of two slices = 15.7 + 15.7 = 31.4 inches²
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will give brainliest!!
Evaluate [(40 + 5) – 321 = 9.2
- 9.3
- 8.6
- 8
- 2
Answer:
The answer should be 9.2
Step-by-step explanation:
Im lowkey kinda lost in this one ngl
find perimeter of a semicircle that has radius of 6cm (give answer in 2 d.p)
Answer:
30.84 cm
Step-by-step explanation:
Formula for perimeter of semi-circle = πr + 2r
Radius (r) = 6 cm
π = 3.14
Perimeter
= πr + 2r
= 3.14(6) + 2(6)
= 3.14(6) + 12
= 18.84 + 12
= 30.84 cm
_________
Hope it helps ⚜
Answer:
30.85 cm to 2 d.p.
Step-by-step explanation:
The perimeter is made up of the diameter ( = 2*radius) and half a full circle
= 6*2 + 1/2 * π* 6
= 12 + 3π
= 30.849
Helpppppp!!!
(Show work)
Answer:
Step-by-step explanation:
Which expression is equivalent to 125 x 15,??
y
O 5x®y3z
0 5x²y5z
O 25x²y3z
O 25x²y5z
Answer:
25²×3is the equivalent answer
What is the image of (-1, -2) after a reflection over the y-axis?
Answer:
(1, -2)
Step-by-step explanation:
Since (-1, -2) is in quadrant 3 and reflected to quadrant 4, the values become (+, -)
Hope this helps :)
Please help its decimals
Each line they are adding 4.96
11.72 + 4.96 = 16.68
Answer:
the correct answer is 16.68
what numbers can you make ?
Answer:
196
Step-by-step explanation: