Answer:
The volume is increasing at a rate of 16286 in³/min.
Step-by-step explanation:
a) The volume of a cone is given by:
[tex] V = \frac{1}{3}h\pi r^{2} [/tex]
Where:
r: is the radius
h: is the height
The rate of change of the volume can be calculated by using the chain rule:
[tex] \frac{dV}{dt} = \frac{\pi}{3}[\frac{dh}{dt}r^{2} + h\frac{d(r^{2})}{dt}] [/tex]
Since h = 4/3 r we have:
[tex] \frac{dV}{dt} = \frac{\pi}{3}[\frac{d(\frac{4r}{3})}{dt}r^{2} + \frac{4r}{3}\frac{d(r^{2})}{dt}] [/tex]
[tex] \frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + r\frac{d(r^{2})}{dt}] [/tex]
[tex] \frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + 2r^{2}\frac{dr}{dt}] [/tex] (1)
With:
[tex]\frac{dr}{dt}[/tex] = 3 in/min
[tex]r = 3 ft*\frac{12 in}{1 ft} = 36 in[/tex]
And by entering the above values into equation (1) we have:
[tex] \frac{dV}{dt} = \frac{4\pi}{9}[(3 in/min)*(36 in)^{2} + 2*(36 in)^{2}*3 in/min] [/tex]
[tex]\frac{dV}{dt} = 16286 in^{3}/min[/tex]
Therefore, the volume is increasing at a rate of 16286 in³/min.
I hope it helps you!
Find the volume of this cylinder 9cm 20cm give answer to 1 decimal place
Answer:
the answer is 5,087 or 5,086.8
Answer:
5086.8
Step-by-step explanation:
The size of a cylinder changes with time. If r increases at the rate of 2 cm/min and h decreases at the rate of 7 cm/min, at what rate is the volume changing at the instant when r
Answer:
The volume of the cylinder with time is increasing approximately at a rate of 16.493 cubic centimeters per minute.
Step-by-step explanation:
The statement is incomplete: The size of a cylinder changes with time. If r increases at the rate of 2 cm/min and h decreases at the rate of 7 cm/min. ¿At what rate is the volume changing at the instant when r = 1 cm and h = 7 cm?
The volume of the cylinder ([tex]V[/tex]), measured in cubic centimeters, is expressed by the following formula:
[tex]V = \frac{\pi}{4}\cdot r^{2}\cdot h[/tex] (1)
Where:
[tex]r[/tex] - Radius, measured in centimeters.
[tex]h[/tex] - Height, measured in centimeters.
The rate of change of the volume ([tex]\frac{dV}{dt}[/tex]), measured in cubic centimeters is obtained by deriving (1) in time:
[tex]\frac{dV}{dt} = \frac{\pi}{2} \cdot r\cdot h\cdot \frac{dr}{dt} + \frac{\pi}{4}\cdot r^{2}\cdot \frac{dh}{dt}[/tex] (2)
Where:
[tex]\frac{dr}{dt}[/tex] - Rate of change of the radius, measured in centimeters per minute.
[tex]\frac{dh}{dt}[/tex] - Rate of change of the height, measured in centimeters per minute.
If we know that [tex]r = 1\,cm[/tex], [tex]h = 7\,cm[/tex], [tex]\frac{dr}{dt} = 2\,\frac{cm}{min}[/tex] and [tex]\frac{dh}{dt} = -7\,\frac{cm}{min}[/tex], then the rate of change of the volume is:
[tex]\frac{dV}{dt} = \frac{\pi}{2}\cdot (1\,cm)\cdot (7\,cm)\cdot \left(2\,\frac{cm}{min} \right) + \frac{\pi}{4}\cdot (1\,cm)^{2}\cdot \left(-7\,\frac{cm}{min} \right)[/tex]
[tex]\frac{dV}{dt} \approx 16.493\,\frac{cm^{3}}{min}[/tex]
The volume of the cylinder with time is increasing approximately at a rate of 16.493 cubic centimeters per minute.
A yard is 3.1 meters long and 1.4 meters wide. What is the area of the yard? Group of answer choices
Answer:
The area of the yard is 4.34.
Step-by-step explanation:
a = l x w
a = 3.1 x 1.4
a = 4.34
Deer ticks can be carriers of either Lyme disease or human granulocytic ehrlichiosis (HGE). Based on a recent study, suppose that 16% of all ticks in a certain location carry Lyme disease, 10% carry HGE, and 10% of the ticks that carry at least one of these diseases in fact carry both of them. If a randomly selected tick is found to have carried HGE, what is the probability that the selected tick is also a carrier of Lyme disease
Answer:
0.2364
Step-by-step explanation:
We will take
Lyme = L
HGE = H
P(L) = 16% = 0.16
P(H) = 10% = 0.10
P(L ∩ H) = 0.10 x p(L U H)
Using the addition theorem
P(L U H) = p(L) + P(H) - P(L ∩ H)
P(L U H) = 0.16 + 0.10 - 0.10 * p(L u H)
P(L U H) = 0.26 - 0.10p(L u H)
We collect like terms
P(L U H) + 0.10P(L U H) = 0.26
This can be rewritten as:
P(L U H)[1 +0.1] = 0.26
Then we have,
1.1p(L U H) = 0.26
We divide through by 1.1
P(L U H) = 0.26/1.1
= 0.2364
Therefore
P(L ∩ H) = 0.10 x 0.2364
The probability of tick also carrying lyme disease
P(L|H) = p(L ∩ H)/P(H)
= 0.1x0.2364/0.1
= 0.2364
Select the correct simulations
Identify the simulations that correctly use numbers to represent a situation in which 55% of store shoppers already have store credit cards.
shoppers with store credit
cards: 1 through 11
shoppers without store credit
cards: 12 througe 20
shoppers with store credit
cards: 1 through 21
shoppers without store credit
cards: 22 through 40
shoppers without store credit
cards: 1 through 33
shoppers with store credit
cards: 34 through 60
shoppers without store credit
cards: 1 through 18
shoppers with store credit
cards: 19 through 40
shoppers with store credit
cards: 1 through 24
shoppers without store credit
cards: 25 through 40
shoppers without store credit
cards: 1 through 36
shoppers with store credit
cards: 37 through 80
Answer: a) and b)
Step-by-step explanation: Lets find the percentages for each option.
a). with 1-11 without 12-20
Here there are 20 shopers. From 1 to 11, there are 11 shoppers. From 12 to 20, there are 9 shoppers. 11 of 20 have credit cards, and 11/20 = 0.55. So this option is correct
b). with 1-33 without 34-60
Here there are 60 shoppers. 1 to 33 there are 33 shoppers with store credit cards. 33/60 = 0.55. So this is also a simulation which represents this situation.
c). with 1-24 without 25-40
Here there are 40 shoppers. 1 to 24, so there are 24 shoppers with the store credit card. 24/40 = 0.6. So this is not a correct option.
d). with 1-21 without 22-40
Here there are 40 shoppers, of which 21 have the credit card. 21/40 = 0.525, so this is not one of the options
e). with 1-18 without 19-40
Here there are 40 shoppers, of which 18 have the credit card. 18/40 = 0.45, so this is not one of the options.
f). with 1-36 without 37-80
Here there are 80 shoppers, of which 36 have the credit card. 36/80 = 0.45,
so this is not one of the options.
Answer:
answers are A, D, and F
Step-by-step explanation:
PLATO
Evaluate the expression, showing work please
5((8+2)+3(6-3))
Answer:
The answer is 59
Step-by-step explanation:
5(8+2)+3(6-3)
5*8=40
5*2=10
3*6=18
3*-3=-9
(40+10)+(18-9)
50+9=59
How can these fractions be rewritten so they can be added together?
2
3
+
3
12
Answer:
8/12 + 3/12
Step-by-step explanation: multiply 2 and 3 by 4 to add these two fractions correctly.
For what values of x is the inequality below true?
6x-2 ≥ 10
Answer:
x[tex]\geq[/tex]2
Step-by-step explanation:
You add 2 to both sides. Then you divide everything by 6. Hope this helps!
write the expression in expanded form that is equivalent to 3(7d +4e)
Answer:
21+4
Step-by-step explanation:
3 times 7=21
3 times4=12
21d+4e
Answer:
21d+12e
Step-by-step explanation:
I'm pretty sure thats it if its expanding.
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter. To the nearest inch, how many inches are in 11 meters?
Answer:
3937.01 Inch are in 100 meter
HURRY PLSS
Solve for x
x=1 or x= 12
Step-by-step explanation:
x²-13x+12=0
x²-12x-x+12=0
x(x-12)-1(x-12)=0
(x-1)(x-12)=0
x-1=0 or x-12=0
x=1 or x=12
The tree in Mary’s backyard is 7.1 m high. How high is it in centimeters?
Answer:
701 cm
Step-by-step explanation:
cm =m * 100.0000
cm =7.1 * 100.0000
cm =710.0000
history on our 50% of 32 less than a hundred greater than 100 but less than 150 or greater than 150
Answer:
I'm not sure I understand this. elaborate a bit more and I can help tho :)
Which pair of sides in this shape are parallel? R S P T RS and ST RS and PT QR and QP QR and ST
Answer:
RS and PT
Step-by-step explanation:
Judging by looks, RS and PT are going the exact same direction, and look like they don't touch. Also, if RSTP is a square, then those two are definitely parallel.
Find the acute angle between the lines. Round your answer to the nearest degree. 9x − y = 4, 8x + y = 6
Answer:
[tex]\approx 13^\circ[/tex]
Step-by-step explanation:
Given two lines with the equations:
[tex]9x - y = 4\\ 8x + y = 6[/tex]
First of all, let us learn the formula for finding the angle between the two lines with given equations:
[tex]tan\theta = \dfrac{m_1-m_2}{1+m_1m_2}[/tex]
[tex]m_1, m_2[/tex] are the slopes of the two lines respectively.
Let us convert the given equation to point intercept form.
Point intercept form of a line is given as:
[tex]y = mx+c[/tex]
[tex]y = 9x-4\\y =-8x+6[/tex]
Comparing with slope intercept form, we get:
[tex]m_1 = 9\\m_2 = -8[/tex]
Using the above formula:
[tex]tan\theta =\dfrac{9 -(-8)}{1+9(-8)}\\\Rightarrow tan\theta = -\dfrac{17}{71}\\\Rightarrow \theta = -13.46^\circ\\[/tex]
Therefore, the acute angle between the two lines is [tex]\approx 13^\circ[/tex]
The acute angles between the equations is 13.46 degree.
To find the acute angles between the two equation, let's write out the individual slope of each equation.
Given Data
9x - y = 48x + y = 6Equation of lineThe given equations can be rearranged into equation of line.
[tex]9x-y=4\\ y=9x-4\\ slope=m_1=9[/tex]
The second equation can also be rearranged as and solving for the slope
[tex]8x+y=6\\ y=6-8x\\ y=-8x+6\\ slope = m_2 = -8[/tex]
Since we have the slopes of the two equation, we can now find the acute angle between them.
θ = [tex]tan^-^1[\frac{m_1-m_2}{1+m_1m_2}]\\ [/tex]
substituting the values and solving for the angle
[tex]x = tan^-^1[\frac{9-(-8)}{1+(9*-8)}]\\ x = tan^-^1[17/-71]\\ x=-13.46 = 13.46^0[/tex]
The acute angle between the equations is 13.46 degree
Learn more about acute angle in equations here;
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HELP FAST WILL MARK BRAINLYIST
Answer:
pq = st and qu = tr
the last option
Please I really need help!
Answer:
26 if we not adding then -12
Step-by-step explanation:
What is the area of the obtuse triangle below?
The area of the triangle is 126 square units. Then the correct option is D.
What is the area of the triangle?Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
A = (1/2) × h·b
The height of the triangle will be 12 units and the base of the triangle will be 21 units. Then the area of the triangle is calculated as,
A = 1/2 x 21 x 12
A = 21 x 6
A = 126 square units
Thus, the correct option is D.
More about the area of the triangle link is given below.
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#13
Write the following equation in slope-intercept form.
Equation
DE
-8y- 6x = 32
Answer:
y = -3/4x - 4
Step-by-step explanation:
-8y -6x = 32
-8y = 32 + 6x -- isolate the y variable.
(-1) -8y = 32 + 6x (-1) -- the y has to be a positive number so multiply every single number by -1
8y/8 = -32/8 - 6x/8 -- divide both sides by 8
y = - 4 - 6/8x
y = -3/4x -4 - simplify the fraction and that is your answer
Determine whether the graph shown to the right represents a function.
Choose the correct answer below.
O A. No, because no vertical line can be drawn that intersects the graph more than once.
B. Yes, because a vertical line can be drawn that intersects the graph more than once.
C. No, because a vertical line can be drawn that intersects the graph more than once.
D. Yes because no vertical line can be drawn that intersects the graph more than once.
Using the function definition, it is found that the correct option is:
C. No, because a vertical line can be drawn that intersects the graph more than once.
--------------------------
In a function, each value of the input x can have only one respective output y.In a graph, for a value of x, there can only be one value of y.To verify this, we trace a vertical line, and if it intercepts the function more than once, the graph is not a function.In the picture at the end, it can be seen that multiple vertical lines intersect the function twice, thus, not a function, and the correct option is C.A similar problem is given at https://brainly.com/question/12463448
Use the scale factor from Part I and a proportion to find the length of RT. Show your work.
Similar triangles are those triangles whose corresponding sides are in the same ratio. The length of the sides ST and RT are 5 units and 3 units, respectively.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same. It is denoted by ‘~’ symbol.
Given that the two triangles are similar because the two have the same ratio. Therefore, the ratio of the corresponding sides in the triangle can be written as,
Ratio = AB/RS = BC/ST = AC/RT
Ratio = 18/6 = 15/ST = 9/RT
Now, using the ratio the length of the sides can be written as,
18/6 = 15/ST
ST = (15 × 6)/18
ST = 5 units
18/6 = 9/RT
RT = (9 × 6)/18
RT = 3 units
Hence, the length of the sides ST and RT are 5 units and 3 units, respectively.
Learn more about Similar Triangles:
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Solve log x = 2 by changing it to exponential form.
a. X = -20
C. X=20
B x=10^2
D x=2^10
Answer:
Option B
Step-by-step explanation:
log x=2
x = 10^2
Therefore, the exponential form is the one in option B
Answer:
B
Step-by-step explanation:
Convert to Exponential Form log of x=-2. log(x)=−2 log ( x ) = - 2. For logarithmic equations, logb(x)=y log b ( x ) = y is equivalent to by=x b y = x such that x>0 x
Find the unknown angle measure by solving for the given variable.
Answer:
10 1/2
Step-by-step explanation:
What is a watt, which is a unit of power, equal to?
Answer: a joule divided by a second
Step-by-step explanation:
can somebody help me with these, i will mark you brainliest :)
Answer:
1). sin 30°=5/x
1/2=5/x
x=10
2)sin 30°=y/18
1/2=y/18
y=9°
cos 30°=x/18
√3/2=x/18
x=9√3
3) option D is correct
because cosine ratio is base / hypotenuse.
4) option c is correct.
Which shape has parallel lines and at least one acute angle
Answer:
A Parallelogram.
Step-by-step explanation:
Hope this helps! :)
In the diagram below of triangle KLM, N is a midpoint of K L and P is a midpoint
of LM. If NP + 3, and KM = 36 - 4x, what is the measure of NP?
The graph shows the number of paintballs, y, a machine launches in x seconds. Which expression can be used to calculate the rate per second at which the machine launches the balls? (1 point)
120 over 5
5 over 120
5 over 30
30 over 5
Answer:
Option B.) 12/2 (´⌣`ʃƪ)
Step-by-step explanation:
The rate of a linear equation is equal to the slope m
The slope is equal to
points (2,12) and (4,24)
m=(24-12)/(4-2)
m=12/2
m=6 balls/sec
Which equations passes through point (5, 1) with an x-intercept of 4?
O y=x-4
O y = 5x + 1
Oy - 4x + 1
O y = x + 5
What is the total area, in square inches, of the shaded sections of the trapezoid below?
Help test
Total area of shaded region in trapezoid is 54.4in²
What is trapezoid?A trapezoid is a four-sided, quadrilateral shape with two parallel sides, which are called the bases, and two non-parallel sides, which are called the legs.
here, we have,
The formula for the area of a trapezoid is:
Area = (1/2) × (sum of the bases) × (height)
The Shaded region in trapezoid form right angled triangle.
Area of 1st shaded region=area of right triangle
=1/2×b×h
=1/2×6.8×7.4
=25.16in²
Area of 2nd shaded region=area of right triangle
=1/2×b×h
=1/2×6.8×8.6
=29.24in²
Hence, total area of shaded region in trapezoid is 54.4in²
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