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!
what is another way to solve 8 × 6.98
Answer:
8 × 6.98
Step-by-step explanation:
..............
10 points help asap hurry
Answer:
Betty is right???
Step-by-step explanation:
The circumference of a circle is 6π ft. What is the area, in square feet? Express your answer in terms of
π
Please help
Answer:
Circumference of the circle 2π(radius)=6π ft
Therefore, radius=3 ft
Area=π(radius)²=π×3²=9π ft²
9π ft² is the right answer.
The area of circle is 9π square feet.
What is area?Area is the amount of area occupied by an object's flat (2-D) surface or shape.
The circumference of circle = 2πr
6 = 2πr
r = 3π
And the area of circle is πr².
The area of the circle = 9π
Therefore, the area of the circle is 9π square feet.
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Jeremie bought 5 pounds of bananas for $4.45. How much is 1 pound of bananas? Show or explain your reasoning
what is the strategies for this math problem?
Answer:
1 pound of bananas is 0.89
Step-by-step explanation:
Money over quantity 4.45/5
that means you divide so heres the layout
4.45/5 = x/1 so that is
5x=4.45 divide 5 so that gives us our variable 5÷5 that cancels out five 4.45 divide by 5 is 0.89
so for every pound of bananas is 0.89
And you would use Unite Rate as your strategy
Answer:
for 1 pound of banana...it is 0.89
Step-by-step explanation:
for 5 pound=4.45
for 1 pound =?(x)
5x=4.45×1
x=4.45/5
x=0.89
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Using the order of operations, what should be done first to evaluate 62 +10-(-5)(3) - 5?
A. Subtract 5 from 3
B. Divide 10 by -5
C. Add 6 and 10
D. Evaluate 62
Answer:
can you try and help me with this please? https://brainly.com/question/22223449
Step-by-step explanation:
The order of operations is PEMDAS -
Parenthesis
Exponents
Multiply
Divide
Add
Subtract
So, the first thing would be to solve any parenthesis.
Secondly, you would evaluate the exponent.
From what I can tell, your expression is
(6^2 + 10) / (-5 x 3) - 5
?
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The radius of a circle is 9 centimeters. What is the length of a 96° arc?
Wrong answer but unique technique to consider: i think i inversed the ratio but i think its right
Pi = circumference/diameter
X/18 centimeters =pi
X is whole circumference 18pi cm you need to convert radians to degrees and get partial arc1 pi is 180 degrees so ratio of
Was the error inverse ratio 96/180?
180/96*18
Error here factor of 72 not 96
18*2*3*3*10/2*3*12 [edit factor should be 2 4 12 ]cancel out factors to reduce
180/4 =45cm
Correction
180*3/4*4
So answers i got are 45 cm corrected as 33.75 cm still way more than total circumference of 18pi 56cmapprox and 9.6cm both are wrong according to calculator online
Please note I canceled out pi by using is degree ratio
Double check i may be wrong
Step-by-step explanation:
Answer:
Solution, we have,
Degree measure ([tex]\theeta[/tex][tex]\alpha[/tex]) = 96° = 96[tex]\pi[/tex]/180
Radius (r) = 9cm
Length of arc (l) = ?
Now,
∝ = l /r
or, [tex]\frac{96\pi }{180}[/tex] =[tex]\frac{l}{9}[/tex]
or, l =[tex]\frac{(96\pi )(9)}{180}[/tex] =4.8[tex]\pi[/tex]cm
A bag contains 4 red marbles, 3 blue marbles, and 6 green marbles. What is the probability of choosing a blue marble
Answer:
3/13 or around 23%
Step-by-step explanation:
Add all the marbles together, than your numerator is the amount of blue marbles.
What is the inverse of y= 3/2x -2
Answer:
f^-1(x) = (2x + 4) / 3
Step-by-step explanation:
- switch 'y' with 'x'
x = 3/2y - 2
- solve for 'y'
x + 2 = 3/2y
- multiply each side by 2
y = (2x + 4) / 3
Find the total surface area of the figure shown.
20 cm
16 cm
10 cm
12 cm
Answer:
672
Step-by-step explanation:
(1/2×16×12)×2 + (10×12) + (10×16) + (20×10)
The total surface area of the figure is S = 672 cm²
What is the surface area of the prism?The surface area of the prism is calculated as
The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism
Surface Area of the prism = 2B + ph
The area of the triangular prism is A = ph + ( 1/2 ) bh
Given data ,
Let the area of the 2 triangles be T
Let the area of the 2 rectangles be R
Let the area of the third side be U
Now , the total surface area of the prism = T + R + U
where T = 2 x ( 1/2 ) ( 16 x 12 )
T = 192 cm²
R = ( 16 x 10 ) + ( 12 x 10 )
R = 280 cm²
And , U = 20 x 10
U = 200 cm²
Therefore , the total surface area of prism S = 192 cm² + 280 cm² + 200 cm²
S = 672 cm²
Hence , the surface area of prism is S = 672 cm²
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In a random sample of 60 computers, the mean repair cost was $150. Assume the population standard deviation is $36. Construct a 95% confidence interval for the population mean.
Answer:
The 95% confidence interval for the population mean is between $140.89 and $159.11.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{36}{\sqrt{150}} = 9.11[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 150 - 9.11 = $140.89
The upper end of the interval is the sample mean added to M. So it is 150 + 9.11 = $159.11
The 95% confidence interval for the population mean is between $140.89 and $159.11.
Select the line that represents y=3x
Answer:
The first one is correct
Step-by-step explanation:
hope it helps ^^
Answer:
Graph C
Is the correct.
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what is 4/5 ( 10x - 25) + 25
Answer:
8x+5
Step-by-step explanation:
Answer:
8x +5
Step-by-step explanation:
Which of the following is true? Group of answer choices Pie charts can generally be used instead of bar charts. Line charts are not used for cross-sectional data. Pyramid charts are generally preferred instead of column charts. Line charts are useful for visualizing categorical data.
Answer:
Pie charts can generally be used instead of bar graphs
Step-by-step explanation:
A pie chart can be used instead of a bar chart. A pie chart is an alternative to the bar chart. Both of these can be regarded as data visualization tools. The pie chart shoes us generally how several parts makes up a whole. While the bar chart uses rectangular bars to show us the proportion of each of the categories of data
The statement which is true among the given group of options is; Pie charts can generally be used instead of bar charts.
Data visualization toolsPie charts can be used as substitutes for bar charts. This stemmed from.the fact that both tools are data visualization tools.
On this note, pie charts can be used to replace the bar charts even though pie charts entails dividing the 360° angle in a circle in respective ratios.
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Can someone answer this?
Answer:
Length of mammoth's tusk in poster = 15.33
Step-by-step explanation:
Actual height of mammoth = 10 feet 5 inches = 126 inches
Height on the poster of mammoth = 14 inches
Actual length of mammoth's tusk = 11.5 feet = 138 inches
Length of mammoth's tusk in poster = x
126 : 14 :: 138 : x
Product of mean = product of extremes
x * 126 = 14 * 138
[tex]x = \frac{14*138}{126}[/tex]
x = 15.33
What is the area of an rectangle with sides lengths of 5/12 foot and 2/3 foot
Answer:
The area of given rectangle is 5/18 square feet.
Step-by-step explanation:
Let l be the length of rectangle and w be the width of the rectangle.
Given information is:
Length = l = 5/12 foot
Width = w = 2/3 foot
The area of a rectangle is given by the formula
[tex]Area = Length*Width\\A = l*w[/tex]
Putting the values for width and length
[tex]A = \frac{5}{12} * \frac{2}{3}\\= \frac{10}{36}\\=\frac{5}{18}[/tex]
The area is 5/18 square feet.
Hence,
The area of given rectangle is 5/18 square feet.
on sale, boxes of cereal cost $11 for 4 boxes, $24.75 for 9 boxes, and $33 for 12 boxes. Predict the cost of twelve boxes.
Answer:
omg this is so eaasy like u need tia tammera
Step-by-step explanation:
Answer:
$33(the answer is $33)
PLEASE ANSWER THIS QUESTION RIGHT Name the x-intercept(s)?
A:0 and 4,B:2,C:4,D:0.
Answer:
A. 0 and 4
Step-by-step explanation:
The x-intercepts are simply the values of x when y = 0. In other words it is the points where the line curve intercepts or cuts across the x-axis.
Form the graph given, we can see that at x = 0 and x = 4, the value of y = 0. Simply put, the curve cuts the x-axis at x = 0 and x = 4.
x-intercepts are 0 and 4.
Need help ASAP will mark Brainly
Answer:
115°
Step-by-step explanation:
its in the middle of 60° and 70°
Emergency plsssssssssssss answer this what is 0.43 rounded to the nearest hundredth
Answer:
0.430
Step-by-step explanation:
I GIVEEEEEEEEEEE BRAINLIST
Answer:
Step-by-step explanation:
B
get brainliest please help
Answer:
2
Step-by-step explanation:
9514 1404 393
Answer:
-3/2
Step-by-step explanation:
The line crosses grid intersections at (-1, 2), (1, -1) and (3, -4). These points are separated by 2 units horizontally and 3 units vertically.
The rise (vertical change) is -3 for each run (horizontal change) of +2, so the ratio rise/run is -3/2. That is the slope of the line: -3/2.
Need help fast!!!
Point P has coordinates (1, 3). Point Q has coordinates (4, 8). How long is the line segment? Round to the nearest tenth if necessary.
Answer:
0
Step-by-step explanation:
0
Please answer ASAP will give brainliest!!!!!!!
Answer: No he is not correct the answer is 6 3/8
Step-by-step explanation: so what you have to do is add the 2 numbers you it should look like this(2 3/4+ 3 5/8) then you want to add the 2 and the 3 and add the 3/4 and 5/8 it should look like this (5+11/8) then you want to converse the number to a mixed number it should look like this (5+1+3/8) then you should add the
Answer:
No. Total distance = 6 3/8.
Step-by-step explanation:
[tex]2\frac{3}{4}+3\frac{5}{8}=\frac{11}{4}+\frac{29}{8}\\\\[/tex]
[tex]=\frac{11*2}{4*2}+\frac{29}{8}\\\\=\frac{22}{8}+\frac{29}{8}\\\\=\frac{22+29}{8}\\\\=\frac{51}{8}\\\\=6\frac{3}{8}[/tex]
Evaluate the function for the given value: y=8x0.7^x for x=3
Answer:
y= 8(5 * 0.7) ^ 5
Step-by-step explanation:
13/14% of a quantity is equal to what fraction of the quantity. simplify your answer
Answer:
=1
Step-by-step explanation:
multiply the numerator and denominator by common integer
Please help easy math equation. Make sure it give the answer first then explain why. Don't lie
1/4x+2=-4 how do you do this step by step?
Answer: Solution
=
−
2
4
Step-by-step explanation: Combine multiplied terms into a single fraction
1
4
+
2
=
−
4
1
4
+
2
=
−
4
Multiply by 1
1
4
+
2
=
−
4
4
+
2
=
−
4
Subtract
2
2
2
from both sides of the equation
The total weight of 15 containers on a freight train is 330 tonnes. What is the mean weight of the containers?
Answer:
the mean weight is 22 tonnes
Step-by-step explanation:
mean=total sum/number of numbers you added
in this case the question already gave you the total so just divide right away
mean weight= 330/15 = 22 tonnes
Help please...........................
Answer:
1st one is 16.
2nd one is 5.
Step-by-step explanation:
Multiply 4x4 and you get 16.
Multiply 5x1 and you get 5.
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