When the radius is 10 inches and the height is 20 inches
(a) rate change of the volume of the cylinder is 5340.7 inch²/min.
(b) rate of change of the surface area of the cylinder is 1068.14 inch²/min.
Volume and surface area of the closed cylinder both increase with time.
Let r be the Radius and h be the height of the cylinder in inches at time t.
[tex]\frac{dr}{dt} =5[/tex] inch/min and [tex]\frac{dh}{dt} =-3[/tex] inch/min
Let V be the volume of the cylinder then
Differentiating with respect to t,
[tex]\frac{dV}{dt} =2\pi r(\frac{dr}{dt} )h+\pi r^{2} \frac{dh}{dt}[/tex]
At r=10 inch and h=20 inch,
[tex]\frac{dV}{dt} =1700\pi =[/tex] 5340.7 inch²/min ≈ 5000 inch²/min
Thus, it is increasing with time as it has a positive sign.
Let S be the surface area of a closed cylinder
[tex]\frac{dS}{dt} =2\pi r(\frac{dr}{dt} )h+2\pi r(\frac{dr}{dt} )+4\pi (\frac{dr}{dt} )r[/tex]
At r=20 inch and h=20 inch
[tex]\frac{dS}{dt} =340\pi =[/tex] 1068.14 inch²/min ≈ 1000 inch²/min
It is also increasing with time as it is also having a positive sign.
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what is t - 18 = 6 can you help me
Answer:
[tex]\boxed{\sf{t=24}}[/tex]
Step-by-step explanation:
Find the value of t, to isolate on one side of the equation.
t-18=6
First, add by 18 from both sides.
[tex]\rightarrow \sf{t-18+18=6+18}[/tex]
Solve.
Add the numbers from left to right.
6+18=24
[tex]\Rightarrow \boxed{\sf{t=24}}[/tex]
Therefore, the final answer is t=24.
The answer should have a positive sign.
I hope this helps, let me know if you have any questions.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{t - 18 = 6}[/tex]
[tex]\large\text{ADD \boxed{\textsf{18}} to BOTH SIDES:}[/tex]
[tex]\mathsf{t - 18 + 18 = 6 + 18}[/tex]
[tex]\large\text{CANCEL out: \boxed{\mathsf{-18 + 18}} because it gives you 0.}[/tex]
[tex]\large\text{KEEP: \boxed{\mathsf{6 + 18}} because it gives you the answer of the t-value.}[/tex]
[tex]\large\text{New equation: }\mathsf{t = 6 + 18}[/tex]
[tex]\mathsf{t = 6 + 18}[/tex]
[tex]\mathsf{t = 24}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{t = 24}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
can i gett some help pls
Answer:
26.425
Step-by-step explanation:
For the function f(x)= x^2+4x-1, what is the range of f (x) for the domain {-2,0,1}?
The range of the given function is {-5,-1,4} which is the B option.
Given function:-
[tex]f(x) = x^2+4x-1[/tex]
Domain = {-2,0,1}
We have to find the range of the given function for the given domain.
Putting x = -2 in the given function, we get,
[tex]f(-2) = (-2)^2+4(-2)-1[/tex]
f(-2) = 4 - 8 - 1 = -5
Putting x = 0 in the given function, we get,
[tex]f(0) = (0)^2+4(0)-1[/tex]
f(0) = 0 + 0 -1 = -1
Putting x = 1 in the given function, we get,
[tex]f(1) = (1)^2+4(1)-1[/tex]
f(1) = 1 + 4 - 1 = 4
Hence, the range of the given function is {-5,-1,4}.
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Prealgebra- Write an equation of the line that passes through the points(Question in photo) (Can only attach one photo at time, so for graphing part of question, i will send the photo)
Given:
Point 1 → (-5, 0.6)
Point 2 → (5, -2.4)
Find: the equation of the line and its graph
Solution:
To help us determine the equation of the line passing through the given points, let's use the Two-Point Form formula.
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Let's plug into the formula above the coordinates of the two points.
[tex]y-0.6=\frac{-2.4-0.6}{5-(-5)}(x-(-5))[/tex]Then, solve.
[tex]y-0.6=\frac{-3}{10}(x+5)[/tex]Multiply -3/10 by the terms inside the parenthesis.
[tex]y-0.6=-\frac{3}{10}x-1.5[/tex]Add 0.6 on both sides of the equation.
[tex]y-0.6+0.6=-\frac{3}{10}x-1.5+0.6[/tex][tex]\begin{gathered} y=-\frac{3}{10}x-0.9 \\ or \\ y=-0.3x-0.9 \end{gathered}[/tex]Hence, the equation of the line passing through the given points in slope-intercept form is y = -0.3x - 0.9.
In the equation, the slope is -3/10 while the y-intercept is -0.9.
Since the slope is negative, the line must be leaning to the left. Since the y-intercept is -0.9, the line must cross the y-axis or the vertical line at -0.9. Hence, the graph of the equation is:
A retailer purchases some merchandise with an invoice price of $19,500 and terms of sale of 5/15, n/45. What is the net amount due (in $) on the order if a partial payment of $10,800 is made on the 15th day? (Round your answer to the nearest cent.)
The net amount due on the order after partial payment done is $8700
Given,
A retailer purchases some merchandise;
The invoice price for the merchandise = $19,500
Terms of sale for the merchandise = 5/15, n/45
On 15th day partial payment done = $10,800
We have to find the net amount due on the order after partial payment is done.
Here,
Net amount due = Invoice price - Partial payment
Net amount due = 19,500 - 10,800
Net amount due = 8700
That is,
The net amount due on the order after partial payment done is $8700
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Which brand of granola typically weighs more?
Brand A bags typically weigh more because the median of brand A is higher than that of brand B.
Brand B bags typically weigh more than brand A bags because there is a high outlier at 52.5.
Brand A bags typically weigh more than brand B bags because there are no outliers in the distribution.
Brand B bags typically weigh more because the range of weights is higher than that of brand A.
Brand A bags typically weigh more because the median of brand A is higher than that of brand B and is denoted as option A.
What is Median?This is referred to as the middle value which separates the higher half from the lower half of a data or distribution. This is calculated by first ordering the numbers which could be from the lowest to highest or vice versa.
A data sample which has a higher figure as the median means that it has higher values present in the data distribution. This term provides an insight on certain properties of the values of the data which are given.
In this scenario, the median of brand A is higher than that of brand B which means that it has more weight and is therefore the reason why option A was chosen as the correct choice.
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Evaluate cos 150° without using a calculator.Ο Α.√32B. 2O C. -1/2OD. -32
Note that:
[tex]\begin{gathered} cos(A+B)=cosAcosB-sinAsinB \\ cos(150^0)=cos(90+60) \end{gathered}[/tex]Applying the addition formula given above to cos 150:
[tex]\begin{gathered} cos(150)=cos(90)cos(60)-sin(90)sin(60) \\ \\ cos(150)=0(\frac{1}{2})-1(\frac{\sqrt{3}}{2}) \\ \\ cos(150)=0-\frac{\sqrt{3}}{2} \\ \\ cos \end{gathered}[/tex]Look at this diagram:If KM and NP are parallel lines and m
Answer
Angle NOL = 70°
Explanation
Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines. If the two lines are parallel to each other, then alternate angles are equal.
We can see that Angle MLO and Angle NOL are alternate angles.
And since we have been told that KM and NP are parallel lines,
Angle NOL = Angle MLO = 70°
Hope this Helps!!!
The table shows the cumulative number of minutes Alice practices clarinet for the first part of the school year:The table shows the cumulative number of minutes Alice practices clarinet for the first part of the school year:
The correct option regarding the scale and the origin of the graph are as follows:
D.
x-axis scale: 1 unit = 1 week
y-axis scale: 1 unit = 150 minutes
origin: (0 weeks, 0 minutes)
Scale and originThe scale should be chosen focusing on improving the readability of the data-set by the reader, while the origin should be chosen according to the values assumed by the variables.
In the context of this problem, the values of x, in weeks, are:
2, 3, 4, 5, 6, 7, 8.
They increase by one, hence the scale of x should be of 1 unit = 1 week.
The values of y, in minutes are given as follows:
300, 450, 600, 750, 900, 1050, 1200.
They increase by 150, hence the scale of y should be of 1 unit = 150 minutes, which is the rate of change of the problem.
As the measures are both positive values, the origin should be of (0,0), hence the correct option for the scales and the origin is option D.
Complete problemThe table is:
Weeks Minutes
2 300
3 450
4 600
5 750
6 900
7 1,050
8 1,200
The options are:
A. x-axis scale: 1 unit = 2 weeks
y-axis scale: 1 unit = 50 minutes
origin: (0 weeks, 0 minutes)
B. x-axis scale: 1 unit = 2 weeks
y-axis scale: 1 unit = 150 minutes
origin: (2 weeks, 300 minutes)
C. x-axis scale: 1 unit = 1 week
y-axis scale: 1 unit = 50 minutes
origin: (2 weeks, 300 minutes)
D. x-axis scale: 1 unit = 1 week
y-axis scale: 1 unit = 150 minutes
origin: (0 weeks, 0 minutes)
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If the sum of a number and seven is tripled, the result is eight times a number.
Step 1: Represent a with an unknown
Let a number be x
Step 2: Represent the given information with an equation
From the first statement, the sum of a number and seven is tripled can be represented with the equation below:
[tex](x+7)\times3[/tex]The second statement reflects that the result of the first statement is eight times a number. Eight times a number is
[tex]8\times x=8x[/tex]The result of the first statement and the second statement is
[tex](x+7)\times3=8x[/tex][tex]3x+21=8x[/tex]Step 3: Solve for the unknown
The solution of the unknown is as shown below:
[tex]\begin{gathered} 3x+21=8x \\ \text{collect like-terms} \\ 21=8x-3x \\ 21=5x \\ \text{divide through by 5} \\ \frac{21}{5}=\frac{5x}{5} \\ \frac{21}{5}=x \end{gathered}[/tex][tex]\begin{gathered} \frac{21}{5}=x \\ x=\frac{21}{5} \\ \operatorname{Re}-\text{write as a mixed fraction} \\ x=4\frac{1}{5} \end{gathered}[/tex]Hence, the number is 4 1/5
An adult elephant weighs 2 2/5 tons. An adult hippo weighs 1 4/5 tons. How much will the animals weigh together?
Answer: If you want the result as a fraction it should be 3.7/5. but if you want a whole number it's 4.2. if you want a mixed number its 4 1/5
Step-by-step explanation:
What is the simple interest rate on an account that earned $56.25 in interest after two and one-half years on a principal balance of $300? please show work
The rate of interest on the given principal is 7.5%.
Given that, simple interest = $56.25, principal = $300 and time period = [tex]2\frac{1}{2}[/tex] years.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Now, 56.26 = (300 × R × 2.5)/100
⇒ 5625 = 750R
⇒ R = 7.5%
Therefore, the rate of interest on the given principal is 7.5%.
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Determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
The solution of x in the mathematical statement is 11.73
How to determine the value of x?From the question, the mathematical statement is given as
x over 5 and 7 tenths equals 2 and 3 tenths.
When represented as an algebraic equation, we have
x/5.10 = 2.30
To start with, we multiply both sides of the equation by 5.10
This is represented as
5.10 * x/5.10 = 2.30 * 5.10
Evaluate the product on the left-hand side
So, we have
x = 2.30 * 5.10
Evaluate the product on the right-hand side
So, we have
x = 11.73
Hence, the value of x is 11.73
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The required simplified value of the given numeral is given as 13.11.
As given in the question, to determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
The statment given in the word string, first transform the equation in the mathematical inscription,
So,
x / 5.7 = 2.3
Simplifying,
x = 5.7 × 2.3
x = 13.11
Thus, the required simplified value of the given numeral is given as 13.11.
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9 The 11th term of an A.P. is -31 and
21st term is -71, find the (a) 1st term
(b) common difference (c) 15th term
(a) The 1st term of the arithmetic progression is 9
(b) The common difference of the arithmetic progression is -4
(c) The 15th term of the arithmetic progression is -47
Calculating the terms of an Arithmetic ProgressionThe nth term of an arithmetic progression is given by
aₙ = a + (n - 1)d
Where a is the first term
and d is the common difference
From the given information,
a₁₁ = -31
and
a₂₁ = -71
But
a₁₁ = a + 10d
and
a₂₁ = a + 20d
Thus,
a + 10d = -31 ------------ (1)
a + 20d = -71 ------------ (2)
Subtract equation (1) from equation (2)
a + 20d = -71
a + 10d = -31
---------------------------
10d = -40
d = -40/10
d = -4
Substitute the value of d into equation (1)
a + 10d = -31
a + 10(-4) = -31
a - 40 = -31
a = -31 + 40
a = 9
Also,
a₁₅ = a + 14d
Substitute the values of a and d
a₁₅ = 9 + 14(-4)
a₁₅ = 9 - 56
a₁₅ = -47
Hence, the first term is 9, the common difference is -4 and the 15th term is -47
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Adriel is going to invest in an account paying an interest rate of 2.4% compounded monthly. How much would Adriel need to invest, to the nearest ten dollars, for the value of the account to reach $120,000 in 8 years?
The principal amount is $99,055.82.
What is Compound interest?When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits. Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.
Given:
Amount = 120,000
r = R/100
r = 2.4/100
r = 0.024 per year,
Then, solve the equation for P
P = A / [tex](1 + r/n)^{nt}[/tex]
P = 120,000.00 /[tex](1 + 0.024/12)^{(12)(8)[/tex]
P = 120,000.00 / [tex](1 + 0.002)^{(96)[/tex]
P = $99,055.82
Hence, the principal amount is $99,055.82.
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Which are the solutions of the equation x^4-5x^2-14=0? Use factoring to solve.
Answer:
x = ±√7 and x=±i√2
Step-by-step explanation:
x^4-5x^2-14=0
Factor
(x^2 - 7) ( x^2 +2) =0
Using the zero product property
x^2 -7 =0 x^2 + 2 =0
x^2 =7 x^2 = -2
Taking the square root of each side
(x^2)^1/2 =7^1/2 ( x^2)^1/2 = (-2)^1/2
x = ±√7 x=±i√2
Please help, i really need help
Answer: m<1 = 146 degrees, m<3 =146 degrees, m<4 = 34 degrees
Step-by-step explanation:
Since m<2 and m<4 are vertical angles, they will be equal to each other.
By using straight lines, we can easily find out that m<1 = 180-34 = 146
Since m<1 and m<3 are vertical angles, they are equal to each other.
Hope this helped :))
X AND Y (PLEASE HELP)
Answer:
HERE YOU GO HOPE IT HELPS
someone please help me please
Graph
[tex]-2x+y\ge-2[/tex]
Procedure
A line passes through the point (–2, 7) and has a slope of –5.
A coordinate plane.
What is the value of a if the point (a, 2) is also on the line?
–7
–1
1
7
Based on the fact that the line passes through (-2, 7) and the slope, the value of a can be found to be -1
How to find the value of a?To find the value of a, you first need to find the y-intercept to complete the linear equation which takes the form:
y = slope (x) + y-intercept
7 = -5(-2) + y-intercept
7 = 10 + y-intercept
y-intercept = 7 - 10
y-intercept = -3
The line equation is:
y = -5x - 3
The line y = -5x - 3 is passing through the point (a,2) is:
2 = -5(a) - 3
3 + 2 = -5a
a = 5 / -5
a = -1
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Answer:
the answer is -1
Step-by-step explanation:
Point A(3, 5) was dilated, and the point after dilation was A'(6, 10). What was the scale factor used?
Answer:2 is the scale factor
Step-by-step explanation:
What is the slope that passes through these points?
(0, -4) and (-5, -5)
Answer: m=1/5
Step-by-step explanation:
Find the inverse of the given function.
5. f= {(1,3), (2,-5), (3,6)}
Check the picture below.
The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute.
How does the rate for Printer B compare to the rate for Printer A? Use the drop-down menus to explain your answer.
The unit rate of Printer B = 25 pages per minute, which is greater than the unit rate of Printer A that is 15 pages per minute.
How to Find the Unit Rate of a Linear Graph?The unit rate of a graph can b determined by using any point, (x, y), on the graph and solve by finding, m, which is the ratio of y to x, if x and y represents the variables of the relationship that is graphed.
Thus, unit rate (m) = y/x.
The printing rate for Printer A is represented by the graph. To find the unit rate for Printer A, use a point on the graph, (2, 30) to find the unit rate, m.
Printer A's Unit rate (m) = y/x = 30/2
Printer A's unit rate (m) = 15 pages per minute.
The printing rate for Printer B is given as 25 pages per minute. 25 pages per minute is a greater unit rate compared to 15 pages per minute.
Therefore, we can conclude that Printer B has a greater printing rate than Printer A, because the unit rate of 25 pages per minute is greater than 15 pages per minute.
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Claire scheduled a taxi to pick her up at her house. The taxi service says it will take 15 minutes to get to her house based on normal traffic routines. However, due to either no traffic or more traffic than normal, the time could vary by as much as 4 minutes. Which inequality and solution show the range of possible minutes, t, it will take for the taxi to get to Claire's house?
The inequality would be 15 ≤ t ≤ 19 showing the range of possible minutes it will take for the taxi to get to Claire's house.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The time could vary by as much as 4 minutes.
Let t be the range of possible minutes
The taxi service says it will take 15 minutes to get to her house based on normal traffic routines.
So the inequality as 15 ≤ t
The time could vary by as much as 4 minutes.
So the inequality as 15 ≤ t ≤ 15 + 4
⇒ 15 ≤ t ≤ 19
Therefore, the inequality would be 15 ≤ t ≤ 19 showing the range of possible minutes.
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given angle 1 is congruent toangle 3 and angle 12 is congruent to angle 8 prove l is parallel to m
Given that;
[tex]\angle1\cong\angle3,\angle12\cong\angle8[/tex]Line a and b are two straight lines cut by two transversal lines l and m.
The tranversal line l shows that;
[tex]\begin{gathered} \angle8\cong\angle6 \\ \end{gathered}[/tex]But also;
[tex]\angle8\cong\angle12[/tex]Thus,
[tex]\angle6\cong\angle12[/tex]Then, if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
Thus, line l is parallel to m
Question 10 !!
Help me please
letter A = C
letter B = B
Letter C= B
Answer:
(a) Figure C
(b) Figures B and C
(c) Figures B and C
Step-by-step explanation:
Figure A does not apply to any of the 3 questions
Hope this helps
Your mom Paid $8 for 10 Granny Smithapples and bought 15 Golden Delicious at60 cents an apple. What is her average costper apple?
First, let's find the total cost of all the apples:
[tex]8+(0.6\cdot15)=17[/tex]Now, we divide this by the total amount of apples bought. In our case, we know that there were 10 Granny Smith apples and 15 Golden Delicious, for a total of 25 apples.
[tex]\frac{17}{25}\rightarrow0.68[/tex]Therfore, we can conclude that the average cost per apple was $0.68
Order the fractions from smallest to largest. 3/4, 4/6, 1/2, 5/8
To solve the exercise you can rewrite the fractions in decimal form and then we order.
To write them in decimal form divide the numerator by the denominator, then we have
[tex]\begin{gathered} \frac{3}{4}=0.75 \\ \frac{4}{6}=0.67 \\ \frac{1}{2}= \end{gathered}[/tex]The dot plot shows predictions for the winning time in the 200-meter sprint. The winner finished the race in 22.3 seconds. What is the greatest percent error among the predictions?
2.69%, is the required maximum percent error among the predictions.
Given,
The predicted winning time in 200 meter sprint shows in the dot plot
The winner finished the race in 22.3 seconds
We have to find the greatest percent error among the predictions;
Here,
The actual time to complete is 22.3 seconds.
22.9 seconds is the prediction that is the most off.
The difference is, 22.9 - 22.3 = 0.6 seconds
To obtain a prediction, divide this by the actual time value.
= 0.6/22.3 = 0.0269 = 2.69
Therefore, 2.69%, is the required maximum percent error among the predictions.
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