g If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at which the diameter decreases when the diameter is 8 cm.
Answers
Answer:
0.0398cm/s
Step-by-step explanation:
The snow ball is spherical in nature.
Total surface area of the spherical ball = 4πr²
= 4π(d/2)²
= 4π(d²/4)
= πd²
S = πd²
dS/dt = dS/dd • dd/dt
dS/dt = 2πd•dd/dt
Given
dS/dt = 2cm²/min
d = 8cm
Substitute and get dd/dt
2 = 2π(8) •dd/dt
2 = 16π•dd/dt
dd/dt = 2/16π
dd/dt = 1/8π
dd/dt = 1/8(3.14)
dd/dt = 1/25.12
dd/dt = 0.0398cm/s
Hence the rate at which the diameter is decreasing is 0.0398cm/s
Related Questions
Please help due at 10
Answers
Answer:
Alternate exterior: 5 and 4
Corresponding: 6 and 8
Alternate Interior: 2 and 7
Step-by-step explanation:
Alternate exterior means the opposite angle on the exterior. Examples are 5 and 4 or 1 and 8.
Corresponding angles are angles that are congruent but one is on the outside and the other on the inside, they're also on the same line. Examples are 6 and 8, 2 and 4, 3 and 1, 7 and 5, etc.
Alternate interior angles are the same as Alternate exterior angles but on the interior. Examples being 6 and 3 or 2 and 7
Which graph represents y as a function of x?
Answers
===========================================================
Reason:
This graph passes the vertical line test, so it is a function.
The vertical line test is where we try to pass a single vertical line through more than one point on the curve. If such a thing is possible, then we say the curve fails the vertical line test and it's not a function.
Graph D for instance can have a vertical line through x = 1 and intersect the curve at (1,4) and (1,-4) simultaneously. The input x = 1 leads to multiple outputs (y = 4 and y = -4). Graph D fails the vertical line test for this very reason, and it is not a function. Graphs A and B are similar stories. Any vertical line itself is automatically not a function.
To have a function, any x input in the domain must lead to exactly one and only one y output in the range.
---------
Notice with graph C it is impossible to have a single vertical line intersect more than one point on the curve. So this is why graph C passes the vertical line test. Each input leads to exactly one output.
i need help with the question
Answers
The intersection points are: (0, -3) and (10, 2)
The bounded area is -20.83 unit²
How to find the intersection points?(a) The intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:
(0, -3) and (10, 2)
(b) The integral terms of y which gives the area bound are:
a = -3, b = 2 (These are the y values of the intersection points)
Since we have x = y² + 3y and x = 2y + 6, we can say:
y² + 3y = 2y + 6
y² + 3y - 2y - 6 = 0
y² + y - 6 = 0
Thus, h(y) =
Using a = -3 and b = 2 with h(y) = y² + y - 6, we have the bounded area as:
\(Area = \int\limits^b_a {y} \, dy\)
\(Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy\)
Integrating the area:
Area = [y³/3 + y²/2 - 6y + C]²₋₃
Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]
Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]
Area = [-22/3] - [27/2]
Area = -125/6
Area = -20.83 unit²
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She has 12 watermelons, 30 pears, and 42 apples
For each basket Kerra makes they must have the same number of fruit.
She must use all the fruit.
What is the greatest number of baskets that Kerra can make?
Answers
12/6=2
30/6=5
42/6=7
Simplify
4c^2+6c-3c^2-2c-3
Answers
Answer:
c^2+4c-3
Step-by-step explanation:
(4c^2-3c^2)+(6c-2c)-3 = c^2+4c-3
Is 4 4/9 + 8 7/9. 13 2/9 the mixed number
Answers
Answer:
Yes
Step-by-step explanation:
Correct
2x² + 5x, what will it a Perfect Square? make
Answers
Answer:
2x² + 5x + c = 0
For this quadratic equation to have one double root, the discriminant must equal 0.
5² - 4(2)(c) = 0
25 - 8c = 0
c = 25/8
2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.
Explanation:2x² + 5x is not a perfect square.
A perfect square is an expression that can be factored into the square of a binomial. To determine if an expression is a perfect square, we can look at the coefficient of x². In this case, the coefficient is 2, which is not a perfect square.Learn more about Perfect Square here:https://brainly.com/question/34063927
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Find the vertex of the graphed function. f(x) = [x - 4] + 3
Answers
The vertex of the graphed function f(x) = [x - 4] + 3 is (4, 3).
The function f(x) = [x - 4] + 3 is in the form of an absolute value function, where the expression inside the absolute value brackets represents the input value shifted horizontally by 4 units to the right.
The constant term of 3 represents a vertical shift upwards by 3 units.
To find the vertex of this function, we need to determine the x-coordinate that corresponds to the minimum value of the absolute value function.
In this case, since the absolute value function is within brackets and not being multiplied or divided by a coefficient, the minimum value occurs at the point where the expression inside the brackets equals zero.
Therefore, setting x - 4 = 0, we find x = 4.
Substituting this x-value into the function, we find f(4) = [4 - 4] + 3 = 3. So the vertex of the graphed function is located at the point (4, 3), where x = 4 and y = 3. This means that the graph is shifted 4 units to the right and 3 units upward from the origin.
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Evaluate each expression and order them from least to greatest.
Answers
We want to evaluate each expression and order from the least to the greatest.
let's firstly evaluate the expressions;
\(\begin{gathered} 6+5=11 \\ 4+(-6)=4-6=-2 \\ -3-(4)=-7 \\ 7-(-2)=7+2=9 \\ -6-(-1)=-6+1=-5 \\ 0-9=-9 \end{gathered}\)From the value of each expression we can now arrange it from the smallest to the greatest;
\(-9,-7,-5,-2,9,11\)Writing the expression in order we have;
\(0-9,-3-(4),\text{ }-6-(-1),\text{ }4+(-6),\text{ }7-(-2),\text{ }6+5\)Note; 0-9 is the least and 6+5 is the greatest.
heeeeeeeeeeeeeeeeeeelp plssssss
Answers
To solve this problem, we need to first convert the distance on the map to actual distance using the map scale.
1 cm on the map represents 50,000 cm (or 500m) in actual distance.
So, 8.5 cm on the map represents 8.5 x 500m = 4,250m in actual distance.
Now, we can use the formula: time = distance ÷ speed
Here, distance = 4,250m and speed = 10km/h = 10,000m/h
So, time = 4,250m ÷ 10,000m/h = 0.425 hours
To convert hours to minutes, we can multiply by 60:
time = 0.425 x 60 = 25.5 minutes
Therefore, it will take Myra 25.5 minutes to run from the park entrance to the beach.
***PLZ PLZ HELP*** Find m < GEH if segment FH is a diameter of O E and m FG = 64
options:
120°
123°
126°
116°
Answers
Angles at the center of a circle add up to 360 degrees.
The measure of angle GEH in the circle is (d) 116 degrees
The given parameters are:
\(\mathbf{\angle FEG = 64^o}\)
Since line FH is the diameter of the circle;
It means that:
\(\mathbf{\angle FEG + \angle GEH = 180^o}\) --- By angle on a straight line theorem
Substitute 64 for FEG
\(\mathbf{64 + \angle GEH = 180^o}\)
Subtract 64 from both sides
\(\mathbf{\angle GEH = 180^o - 64}\)
Evaluate like terms
\(\mathbf{\angle GEH = 116^o}\)
Hence, the measure of angle GEH in the circle is (d) 116 degrees
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Please answer this question
Answers
Answer:
the third one
Step-by-step explanation:
Answer:
I think the 3rd one
Step-by-step explanation:
Norma and Jane go to the store to buy stocking stuffers. Norma spends $8 more than Jane. Total, Norma and Jane spend $52. How much did each girl spend?
Answers
Answer:
Norma spent $30
Jane spent $22
simplify each algrebraic expression. drag tiles to correct boxes to complete the pairs.
-5x-2 5x+2 5x-2 -5x+2
Answers
(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.
(b) The algebraic expression, 5x -2 - (5x + 2) is simplified as -4.
What is the simplification of the algebraic expression?The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.
The given algebraic expressions are;
-5x - 2 + 5x + 2
5x -2 - (5x + 2)
The first algebraic expression is simplified as follows;
-5x - 2 + 5x + 2
collect similar terms;
(-5x + 5x) + (-2 + 2)
= 0 + 0
= 0
The second algebraic expression is simplified as follows;
5x - 2 - (5x + 2)
= 5x - 2 - 5x - 2
collect similar terms;
= (5x - 5x) + (-2 - 2)
= 0 - 4
= - 4
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The sum of two numbers is 49 and the difference between these two numbers is 9.
What are these two numbers?
Answers
Answer:
the answer is 39 and 14.
The solution is, the numbers are 20 and 29.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Here, we have,
given that,
The sum of two numbers is 49
and the difference between these two numbers is 9.
let, the numbers are x & y
so, we get,
according to question:
x+y = 49 ...1
x-y = 9 ....2
so, simplifying we get,
2x = 58
or, x = 29
so, we get,
y = 20
Hence, The solution is, the numbers are 20 and 29.
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Determine the measure of angle Q.
Not possible
20°
30°
25°
Answers
The angle that is marked as Q has a value of 30°
What is cosine rule?The cosine rule, also known as the law of cosines, is a mathematical formula used to calculate the length of a side or the measure of an angle of a triangle.
Cosine rule useful in solving triangles when you know the lengths of two sides and the measure of the angle between them, or when you know the lengths of three sides.
By the use of the cosine rule, we have that;
7^2 = 12^2 + 14^2 - 2(12 * 14)Cos Q
49 = 144 + 196 -336CosQ
49- 340 = -336CosQ
-291= -336CosQ
Q = Cos-1 (-291/-336)
Q = 30
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Question 14 (Essay Worth 12 points)
(Comparing Data HC)
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Sky View School
9, 7, 2,0
8, 7, 6, 5, 5, 5, 4, 3, 1, 0
0
1
South Lake School
5,8
0, 1, 2, 6, 6, 8
2
0 3
Key: 2|1|0 means 12 for Sky View and 10 for South Lake
5, 5, 6, 7, 8
0,6
Part A: Calculate the measures of center. Show all work. (5 points)
Part B: Calculate the measures of variability. Show all work. (5 points)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (2 points)
7
Answers
To find the measures of center, we need to determine the median for each school.
For Sky View School:
Arrange the data in order: 0, 0, 1, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9
The median is the middle value, which is 5.
For South Lake School:
Arrange the data in order: 0, 0, 1, 2, 2, 5, 6, 6, 8
The median is the middle value, which is also 5.
Therefore, the median class size for both schools is 5.
Part B: Measures of variability
To find the measures of variability, we need to determine the range and interquartile range (IQR) for each school.
For Sky View School:
The smallest value is 0 and the largest value is 9, so the range is 9 - 0 = 9.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 1 + 2 + 3 + 4)/5 = 2. The third quartile is the median of the upper half, which is (6 + 7 + 8 +9)/4 = 7.25 (rounded to two decimal places).
Therefore, the IQR is 7.25 - 2 = 5.25.
For South Lake School:
The smallest value is 0 and the largest value is 8, so the range is 8 - 0 = 8.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 0 + 1 + 2)/4 = 0.75 (rounded to two decimal places). The third quartile is the median of the upper half, which is (6 + 6 + 8)/3 = 6.67 (rounded to two decimal places).
Therefore, the IQR is 6.67 - 0.75 = 5.92 (rounded to two decimal places).
Part C: Choosing a school based on class size
If you are interested in a smaller class size, South Lake School is the better choice. This is because the range and IQR for South Lake School are smaller than those for Sky View School, indicating that the class sizes at South Lake School are more consistent and less variable. Additionally, the largest class size at South Lake School is 8, while the largest class size at Sky View School is 9, further indicating that South Lake School may have smaller class sizes overall.
Measures of center for Sky View School:
Mean = (0+1+2+3+4+5+5+5+6+7+7+8+9)/13
Mean = 4.8
Median = 5
Measures of center for South Lake School:
Mean = (0+1+2+2+3+5+6+6+8+8)/10
Mean = 4.1
Median = 5
Part B:
Measures of variability for Sky View School:
Range = 9 - 0 = 9
Interquartile Range (IQR) = Q3 - Q1 = 7 - 2 = 5
Variance = [(0-4.8)^2 + (1-4.8)^2 + (2-4.8)^2 + (3-4.8)^2 + (4-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (6-4.8)^2 + (7-4.8)^2 + (7-4.8)^2 + (8-4.8)^2 + (9-4.8)^2]/12
Variance = 7.6
Standard Deviation = √7.6
Standard Deviation = 2.76
Measures of variability for South Lake School:
Range = 8 - 0 = 8
Interquartile Range (IQR) = Q3 - Q1 = 6 - 1 = 5
Variance = [(0-4.1)^2 + (1-4.1)^2 + (2-4.1)^2 + (2-4.1)^2 + (3-4.1)^2 + (5-4.1)^2 + (6-4.1)^2 + (6-4.1)^2 + (8-4.1)^2 + (8-4.1)^2]/9
Variance = 6.45
Standard Deviation = √6.45
Standard Deviation = 2.54
Part C:
If you are interested in a smaller class size, South Lake School is a better choice for you. This is because the measures of center and variability for South Lake School are both smaller than those for Sky View School.
Given the table below, what is the x-intercept of the linear function?
Answers
Answer:
-6
Step-by-step explanation:
I need help with geometry! I need to find x and y, please help asp
Answers
Check the picture below.
What is the expression equivalent too?
Answers
Answer:
x+5
Step-by-step explanation:
3(x+4)-(2x+7)
1. Distribute 3 to x and 4
3x+12-2x+7
2. Distribute the "-" to 2x and 7
2x+12-2x-7
3. Subtract 7 from 12
3x+12-2x-7
3x+5-2x
4. Combine like terms
3x+5-2x
1x+5
Answer:
x+5
which of the following rational numbers is larger than 3/4?
5/6
4/10
3/6
1/3
HELP
Answers
—3/4 is the same as 75% and the rest are less than that. 1/3 is 33%. 3/6 is 50%. 4/10 is 40%.
Justin has $500 in a savings account at the beginning of the summer. He wants to have at least $300 in the account by the end of the summer. Justin withdraws $20 each week for food, clothes, and movie tickets. How many weeks (w) can Justin withdraw money from his account?
Answers
Answer:
10 weeks
Step-by-step explanation:
1 because 20 times 10 is 200 and if he starts with 500 then he can withdraw 20 dollars a week for 10 weeks to have 300 left by the end of the summer, hope this helps :)
The value of a car decreases by 20 percent per year. Mr. Sing purchases a $22,000 automobile. What is the value of the car at the end of the second year?$14,080$17,600$19,800$26,400
Answers
Answer:
$14,080
Step-by Step Explanation:
Answer:
$14,080
Step-by-step explanation:
Hope this helps.
Which of the following pairs consists of equivalent fractions? 3/9 and 5/15 ,12/20 and 20/25,5/6 and 6/5,6/12 and3/4
Answers
Answer:
\(The\) \(Answer\) \(Is:\) \(\frac{3}{9}\) \(&\)& \(\frac{5}{15}\)
Step-by-step explanation:
Divide by 4 , 2nd fraction Divide by 5:
3/4 ≠ 4/5
5/6 ≠ 6/5 We can already see it.
Divide by 3. . .
2/4 ≠ 3/4
Divide by 3 , 2nd fraction Divide by 5:
1/3 = 1/3 \(Perfect!\)
The answer is, \(\frac{3}{9}\) & \(\frac{5}{15}\)
Which ones right ????
Answers
What is the solution to 4 x + 6 less-than-or-equal-to 18?
Answers
Answer:
a
Step-by-step explanation:
edge 2020-2021 <3333
(have an amazing day lovely)
Question 3 A 44-metres long fire-fighting ladder is leaned against a building, as shown in the diagram. The base of the ladder is 7 metres from the building and 3 metres above the ground. How high on the building will the ladder reach?
Answers
The ladder will reach a Height of approximately 43.46 meters on the building.
To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.
Using the Pythagorean theorem, we can set up the equation:
(Height of the building)^2 + 7^2 = 44^2
Simplifying the equation, we have:
(Height of the building)^2 + 49 = 1936
Subtracting 49 from both sides, we get:
(Height of the building)^2 = 1887
To find the height of the building, we take the square root of both sides:
Height of the building = √1887
Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.
Therefore, the ladder will reach a height of approximately 43.46 meters on the building.
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Tom exercise a total of 150 minutes in two days he exercise 20 minutes less on the first day then on the second day how many minutes did he exercise each day?
Answers
Answer:
60 on the first day and 80 on the second
Step-by-step explanation:
the first day was lesser than the second day by 20 minutes.
so the second day was more than the first day by 20 minutes.
Reason
We know he exercised for 2 days
We know the second day was -20
We know the total minutes = 150
We don’t know x
Equation is 2x -20 = 150. Solve for x
Isolate x by subtracting (-20) from both sides.
2x = 170. Solve for x by dividing both sides by 2.
X= 85
Now we know the first day was (-20)
85-20= 65
Answer 85 + 65 = 150
A rectangular garden has an area of 63ft2. The length of the garden is 2 feet more than the width. Find the length and the width of the garden.
Answers
Answers:
L = 64
W= 62
Explanation:
51. التي سجل 16 لاعبا للاشتراك في دروس التنس. ويخطط المدرب لاستخدام 50 كرة تنس لكل لاعب وامتلاك
200 إضافية كك عدد كرات التنس اللازمة للدروس
Answers
Answer:
no islamic state propaganda in my country
Step-by-step explanation: