The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.
What is the rate of change of the surface area of a cone?
In this question we find a formula for the surface area of a cone, of which we must estimate its rate of change by applying derivative rules and the concept of rate of change. The rate of change is the first derivative of the equation:
ds / dt = 2π · r · (dr / dt) + π · √(r² + h²) · (dr / dt) + π · r · [0.5 / √(r² + h²)] · [2 · r · (dr / dt) + 2 · h · (dh / dt)]
If we know that r = 3 m, h = 4 m, dr / dt = 0.5 m / s and dh / dt = 0.2 m / s, then the rate of change of the surface area of the cone is:
ds / dt = 2π · (3 m) · (0.5 m / s) + π · √[(3 m)² + (4 m)²] · (0.5 m / s) + π · (3 m) · [0.5 / √[(3 m)² + (4 m)²] · [2 · (3 m) · (0.5 m / s) + 2 · (4 m) · (0.2 m / s)]
ds / dt ≈ 18.473 m² /s
The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.
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Which equation represents the line with slope −2/3 that passes through (3, 0)?
The following equation [tex]y=\frac{-2x}{3}+2[/tex] represents the given line.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=3x+1. Where:
a= the slope. It can be calculated for [tex]a=\frac{\Delta y}{\Delta x}[/tex].
b= the constant term that represents the y-intercept.
For solving linear equations, you should organize variables on one side of the equation and the numbers on the other side. When a number or variables change side, its signal also is changed.
For the given example: a=3 and b=1
The question gives:
the value of the slope (a) = -2/3the coordinates of a point = (3,0)Thus, you can write from the question information :
y=ax+b
0= -2/3*(3)+b
0= -2 + b
b=2
Now, you know the value of the slope and the constant term.
Therefore, the standard form for the linear equation is:
[tex]y=\frac{-2x}{3}+2[/tex]
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4 divided by 8/9 - 1/2
Answer:
-0.28
Step-by-step explanation:
4 ÷ 8/9 -1/2
BODMAS
8/9 ÷ 4
8/9 x 1/4
2/9 x 1
2/9 - 1/2
= -0.2777
= -0.28
janice wants to put a fire at the mid point between two of her trees in her backyard. the coordinates of tree A are (3, 5) and the coordinates of tree b are (-3,-3). How far is the fire from tree b?
Answer:
janice wants to put a fire at the mid point between two of her trees in her backyard. the coordinates of tree A are (3, 5) and the coordinates of tree b are (-3,-3). step by step thinking we want tree A is coordinat at 35. three b coordinate is -3-3 .janice stand between centre that from A mark 6feet so At B is 3
Simplify.
[tex]\sqrt{20+5}[/tex]
Answer: 5
Step-by-step explanation:
[tex]\sqrt{20+5}[/tex]=
[tex]\sqrt{25}[/tex]=5
Answer:
√(20 + 5) = 5
Step-by-step explanation:
Let's solve the problem,
→ x = √(20 + 5)
→ x = √25
→ [ x = 5 ]
Hence, the answer is 5.
what is the diffrence between irregular and irrational numbers?
Answer:
Numbers that can be expressed as a ratio of two number (p/q form) are termed as a rational number. Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number.
Step-by-step explanation:
please make my answer as brainelist
25 POINTS AND BRAINLIEST
NO EXPLANATION NEEDED JUST ANSWER
Answer: 35.
Step-by-step explanation: 33 + 34 + 35 is 102. Your 35 is the largest of the three.
A restaurant earns $1073 on friday and $1108 on saturday. Write and solve an equation to find the amount x(in dollars) the restaurant needs to earn in Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day
The amount the restaurant needs to earn on Sunday to average $1000 per day over the three-day period is $819.
What is average ?
The average is the ratio of the sum of the number of a given set of values to the total number of values present in the set.
It is given that restaurant earns $1073 on Friday and $1108 on Saturday.
The amount which restaurant needs to earn on Sunday to average $1000 per day over the three-day period can be calculated by finding the average.
The average is given by ratio of sum of amount on each day from Friday to Sunday and divide it by number of days.
Let's assume amount earn on Sunday is $x.
So ,
[tex]\frac{1073 + 1108 + x}{3}[/tex] = 1000
1073 + 1108 + x = (1000 × 3)
2181 + x = 3000
Let's solve this equation to get the value of x.
x = 3000 - 2181
x = $819
So , amount earn by restaurant is $819.
Therefore , the amount the restaurant needs to earn on Sunday to average $1000 per day over the three-day period is $819.
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During a snowstorm, Snowfill an a constant rate for a number of hours. Then it stoped snowing for a number of hours. then it started Up again at a different constant rate Andrew Madie graph showing the edges of the snow on the ground over time using the data he collected. After how many hours were there 7 inches of snow on the ground
Answer: Unable to answer
Step-by-step explanation: If you do not show what the constant rate is, I am unable to solve it for you.
To win the annual read-a-thon at his school, Ronald has to read more books than any of his
classmates over winter break. He starts by reading a lot of sports books. Then, he reads 7
mystery books. In all, Ronald reads 25 books for the read-a-thon.
Which equation can you use to find the number of sports books n Ronald reads?
n+ 7 = 25
n - 7 = 25
Submit
7n = 25
7
= 25
Solve this equation for n to find the number of sports books Ronald reads.
sports books
Answer:
The equation for this question should be n+7=25
where n=18
Step-by-step explanation:
What is this 6/x-5/-7=11
help needed ASAP. high school geometry
Answer:
9 u^2
Step-by-step explanation:
there's 2 ways to solve this problem
easy way
plot every coordinate and youll see it's a square
square area = side^2
3^2 = 9 answer
and this method
working with 3 points (triangle)
W - X - Y
0 0
0 3
-3 3
0 0
--------------
2
--------------------------------------
0 0
0 -9
0 0
-----------
l-9/2l
4.5
since a square is made of 2 triangles
4.5 * 2 = 9 u^2
a company makes widgets from three machines. machine m1 makes 3000/hour, and 80% are good. machine m2 makes 4000/hour, and 90% are good. machine m3 makes 3000/hour, and 60% are good. all widgets are mixed together. what is the probability that a widget drawn at random is good
If all the widgets from the three machines are mixed together, then the probability that a good widget will be drawn at random is 0.78 or 78%.
Probability is defined as how likely an event is to occur, or how likely it is that a proposition is true.
If machine 1 makes 3000/hour and 80% are good, then the chances of it being good is 80% also or, 2400 out of 3000.
80% of 3000 is 2400
If machine 2 makes 4000/hour and 90% are good, then the chances of it being good is 90% also or, 3600 out of 4000.
90% of 4000 is 3600
If machine 3 makes 3000/hour and 60% are good, then the chances of it being good is 60% also or, 1800 out of 3000.
60% of 3000 is 1800
Mixing together the widgets from the three machines, use the formula to calculate the probability of an event which is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Probability(good) = (2400 + 3600 + 1800)/(3000 + 4000 + 3000)
Probability(good) = 7800/10000
Probability(good) = 0.78 or 78%
Hence, the probability that a good widget drawn at random is 0.78 or 78%.
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answer the question in the image
Answer:
[tex]\frac{211}{500}[/tex]
Step-by-step explanation:
[tex].4\bar{2}[/tex] means the 2 repeats till infinity
[tex].4\bar{2}[/tex] = .4222222222.....
To convert to fraction just take the first three decimal place digits 422 and divide by 1000 to convert to fraction
[tex].4\bar{2} = \frac{422}{1000}[/tex]
Dividing numerator and denominator of this fraction by 2 gives
[tex]\frac{422/2}{1000/2} =\frac{211}{500}[/tex]
This cannot be simplified further and therefore
[tex].4\bar{2} = \frac{211}{500}[/tex]
If we had chosen first 4 decimal digits then it would be[tex].4\bar{2} = \frac{4222}{10000} = \frac{2111}{5000}[/tex]
i.e. we divide by 10,000
help a real one out i need help with this
1. A(2,8) A'(6,7)
2. B(5,2) B'(9,1)
3. C(2,2) C'(6,1)
4. P(x,y) P'(x ₊ 4 , y ₋ 1)
5. x units to x ₊ 4 units.
y units to y ₋ 1 units.
6. triangle A'B'C' (6 , 4)
7. triangle A'B'C' (7 , 5)
8. triangle ABC ( 3,2)
9. triangle ABC (4 , 4)
Given,
A set of values called coordinates helps to display a point's precise location in the coordinate plane.
we can observe the points from the graph we get the values for B' and C'.
P(x,y) P'(x₊,y₋)
P(2,5) P'=(6,4) ⇒(2₊4,5₋1)
P(3,6) P' = (3₊x' , 6₋y') ⇒ (3₊4 , 6₋1) = (7,5)
P'(7,1) P = (x'₋4 , y'₊1) ⇒ (7₋4 , 1₊1) = (3,2)
P'(8,3) P = (x'₋4 , y'₊1) ⇒ (8₋4 , 3₊1) = (4,4)
hence we acquired the desired values of the points from the graph given.
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Although it is much larger in reality, when we
see Saturn from Earth, it looks like it has a
diameter of 20 μm. Through a telescope, the
diameter looks 9,000 um long. What
magnification scale was used?
The magnification scale used was 450:1
Saturn from Earth, it looks like it has a diameter of 20 μm.
d₁=20μm
Through a telescope, the diameter looks 9,000 μm long.
d₂= 9,000 μm
magnification scale = d₂/d₁
= 9,000 μm/20μm
= 450/1
magnification scale used was 450:1
A scale factor is a number that can be used to adjust the size of any geometrical figure or object in relation to its original size. It's used to draw the enlarged or reduced shape of any given figure, as well as to calculate the missing length, area, or volume of an enlarged or reduced figure. It should be noted that the scale factor only affects the figure's size and not its shape.
A scale factor is a number or conversion factor used to adjust the size of a figure without changing its shape. It is used to enlarge or reduce the size of an object. If the dimensions of the original figure and the dimensions of the dilated (increased or lowered) figure are known, the scale factor can be determined. A rectangle, for example, has a length of 5 units and a width of 2 units. If we raise the size of this rectangle by a factor of two, the sides will become 10 and 4, respectively. As a result, we can use the scale factor to determine the dimensions of the altered figures.
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Evaluate the expression if m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5 , and t = − 2 . − | 10 − 7 r + 8 m + 2 p |
Answer:
-53
Step-by-step explanation:
if m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5 , and t = − 2
-| 10 - 7r + 8m + 2p |
Substitute the given values into the equation.
-| 10 - 7(5) + 8(-4) + 2(2) |
Simplify
-| 10 - 35 + -32 + 4) |
-| -53 |
= -53
Absolute value of -53 is 53 however there is a negative sign outside of it, so the answer is -53
A rectangular swimming pool is 15 meters long, 14 1/2 meters wide, and 5 1/2 meters deep. What is its volume?
Answer:
length x width x height (or depth) = volume
Step-by-step explanation:
761.25 or 761 1/4 is the answer
Mr.letter has 80 sheets of colored paper. seven of his students need the paper for a project. how many sheets does each student get. how many sheets are left over?
Answer:
11
Step-by-step explanation:
80 /7=11.428
so each gets 11 so 77 so u do 80-77=3 so u would have 3 left over
1) 2 + x = 22 3) -6 + p = -18 5) -29 = -20 + n 7) -5 + r = -23 9) 11 = x + 13 11) 101 = n +55 2) -15 = -18 + n 4) -18 + v = -9 6) -19 = n - 13 8) -12 = k +5 10) 11 = -1 + x 12) x - 36 = -68
Answer:
1)x=20
3)p=−12
5)n=−9
7)r=−18
9)x=−2
11)n=46
2)n = 3
4)v=9
6)n=−6
8)k=−17
10)x=12
12)x=−32
Step-by-step explanation:
Let's solve your equation step-by-step.
1) 2+x=22
Step 1: Simplify both sides of the equation.
x+2=22
Step 2: Subtract 2 from both sides.
x+2−2=22−2
x=20
3) −6+p=−18
Step 1: Simplify both sides of the equation.
p−6=−18
Step 2: Add 6 to both sides.
p−6+6=−18+6
p=−12
5) −29=−20+n
Step 1: Simplify both sides of the equation.
−29=n−20
Step 2: Flip the equation.
n−20=−29
Step 3: Add 20 to both sides.
n−20+20=−29+20
n=−9
7) −5+r=−23
Step 1: Simplify both sides of the equation.
r−5=−23
Step 2: Add 5 to both sides.
r−5+5=−23+5
r=−18
9) 11=x+13
Step 1: Flip the equation.
x+13=11
Step 2: Subtract 13 from both sides.
x+13−13=11−13
x=−2
11) 101=n+55
Step 1: Flip the equation.
n+55=101
Step 2: Subtract 55 from both sides.
n+55−55=101−55
n=46
2) −15=−18+n
Step 1: Simplify both sides of the equation.
−15=n−18
Step 2: Flip the equation.
n−18=−15
Step 3: Add 18 to both sides.
n−18+18=−15+18
n=3
4) −18+v=−9
Step 1: Simplify both sides of the equation.
v−18=−9
Step 2: Add 18 to both sides.
v−18+18=−9+18
v=9
6) −19=n−13
Step 1: Flip the equation.
n−13=−19
Step 2: Add 13 to both sides.
n−13+13=−19+13
n=−6
8) −12=k+5
Step 1: Flip the equation.
k+5=−12
Step 2: Subtract 5 from both sides.
k+5−5=−12−5
k=−17
10) 11=−1+x
Step 1: Simplify both sides of the equation.
11=x−1
Step 2: Flip the equation.
x−1=11
Step 3: Add 1 to both sides.
x−1+1=11+1
x=12
12) x−36=−68
Step 1: Add 36 to both sides.
x−36+36=−68+36
x=−32
(Adding and Subtracting Rational Numbers MC)
Solve negative four minus one and three fifths.
five and three fifths
one and three fifths
four fifths
negative five and three fifths
Answer:
negative 5 and 3/5
Step-by-step explanation:
-4-1&3/5
-5&3/5
negative 5 and 3/5(three fifths)
don't forget to mark as brainliest
Answer:
negative 5 and 3/5
Step-by-step explanation:
-4-1&3/5
-5&3/5
negative 5 and 3/5(three fifths)
don't forget to mark as brainliest
Step-by-step explanation:
3 charles can type 675 words in 9 minutes how many words can charles type in 3 minutes
In one minute, Charles can type in 3-minute 225 words.
How many words can Charles type in 3 minutesIn one minute, Charles can type
675/9 = 75 words.
Hence, in 3 minutes Charles can tape [tex]75\times3[/tex] = 225 words (if works with the same rate).
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a real-valued function f (x) is said to be increasing on the closed interval [a, b] if for all x1, x2 ∈ [a, b], if x1 < x2, then f (x1) < f (x2) write the negation of this definition
A real valued function f(x) is said to be decreasing on the interval [a,b] for all x1,x2 if x1 < x2, And f(x1) > f(x2)
What are increasing and decreasing function ?A function is said to be increasing if we increase the value of the independent variable the function also increases and a function is said to be decreasing if we increase the value of the independent variable the function decreases.
According to the given question real-valued function f (x) is said to be increasing on the closed interval [a, b] if for all x1, x2 ∈ [a, b], if x1 < x2, then f (x1) < f (x2).
A real valued function f(x) is said to be increasing on the interval [a,b] if a < b, And f(a) < f(b).
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Solve for x. 7x - 3 = 2x - 18
Answer:
x = -3Step-by-step explanation:
7x - 3 = 2x - 18
5x = -15
x = -15 : 5
x = -3
-----------------------------
check
7 * (-3) - 3 = 2 * (-3) - 18
-24 = -24
the answer is good
On a map with a scale of 1 inch to 12 feet, the area of a restaurant is 60 in². Han says that the actual area of the restaurant is 720 ft²
O True
O False
Answer:
False
Step-by-step explanation:
The scale is for length only, when converting to area scale, you have to square both sides of the scale.
1 in² = 144 ft²
Calvin’s toy airplane flew to an elevation of 168 feet then landed back onto the flat sidewalk from where it was launched. What is the change in elevation?
The change in elevation will be 0.
What is the change in elevation?It should be noted that from the information, Calvin’s toy airplane flew to an elevation of 168 feet then landed back onto the flat sidewalk from where it was launched.
Therefore, when it flew, the expression will be +168.
When it came down, the expression will be -168.
Therefore, the change in elevation will be:
= +168 - 168.
= 0
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-4x+1.5x-2.5x-2 x-6.5= evaluate the expression when x=4
could someone do this :(
Answer:
-34.5
Step-by-step explanation:
Put together like terms:
-7x-6.5
-28-6.5
-34.5
5| c + 7 | = -45
Absolute Volume
Answer:c=16
Step-by-step explanation:5c+35=-45=5c=-45-35=5c=-80. C=16
A survey was carried out among 120 school children looked at which type of meat they preferred. 55%said they preferred lamb,20% said they preferred chicken, 15% preferred duck and 10% turkey . calculate the number of children in each category
No. of children in lamb, chicken, duck, and turkey category is 66, 24, 18 and 12 respectively.
What is percentage ?Percentage is the value per hundredth.
According to the given question a survey was carried out among 120 school children looked at which type of meat they preferred. 55% said they preferred lamb,20% said they preferred chicken, 15% preferred duck and 10% turkey and we have to calculate no. of children in each category.
55% said they preferred lamb, So the no. of students i this category is
= (55/100)×120
= 66 children.
20% said they preferred chicken, So the no. of children in this category is
= (20/100)×120
= 24 children.
15% said they preferred duck, So the no. of children in this category is
= (15/100)×120
= 18 children.
10% said they preferred turkey, So the no. of children in this category is
= (10/100)×120
= 12 children.
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First 4 solve for x
Last 4 solve for x AND y
Step-by-step explanation:
find the value of 8x³-y³if 2x-y and xy=-1
HELP...............................! !
Answer:
-1 31/65
Step-by-step explanation:
I did this before trust me
Answer:
[tex] \sf \large - 1 \frac{31}{65} [/tex]
Step-by-step explanation:
6 2/5/-4 1/3
6 2/5/−4 1/3
=32/5/−4 1/3
= 32/5 −13/3
=32/5/−13/3
=−96/65
= −1 /31/65