For cos(0) to be equal to 0.392, sin(20) must be equal to cos(0 + 30).
We can use the trigonometric identities to simplify the expression cos(0 + 30):
cos(0 + 30) = cos(0)cos(30) - sin(0)sin(30)
Since sin(0) = 0 and cos(30) = √3/2, we have:
cos(0 + 30) = cos(0)√3/2
We can then rearrange this equation to get:
sin(20) = cos(0)√3/2
To solve for cos(0), we can divide both sides by √3/2:
cos(0) = sin(20) / (√3/2)
Using the values of sin(20) ≈ 0.34 and √3/2 ≈ 0.866, we can calculate:
cos(0) ≈ 0.34 / 0.866 ≈ 0.392
Therefore, for cos(0) to be equal to 0.392, sin(20) must be equal to cos(0 + 30).
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A yoga instructor collected student data. He found that students who had less sleep did not tend to burn more or fewer calories during class. What can he conclude?
1)There is no correlation between amount of sleep and number of calories burned.
2)There may or may not be causation. Further studies would have to be done to determine this.
3)There is a correlation between amount of sleep and number of calories burned. There is probably also causation. This is because there is likely an increase in the number of calories burned with an increase in the amount of sleep
The correct answer is option 1) "There is no correlation between the amount of sleep and the number of calories burned."
Based on the information provided, the yoga instructor can conclude that there is no correlation between the amount of sleep and the number of calories burned during class. Therefore, the correct answer is
option 1) "There is no correlation between the amount of sleep and the number of calories burned."
Option 2) suggests that further studies would be needed to determine causation, but since there is no correlation found in this study, there is no basis for further investigation into causation.
Option 3) suggests that there is a correlation between the amount of sleep and the number of calories burned and that there is likely causation. However, this conclusion contradicts the information provided, which indicates that there is no correlation between these variables.
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In the figure, three lines intersect at point P. If x = 65 and y = 75, what is the value of z?
The value of angle Z is 40 degrees. (Option 3). In this problem, we are given that three lines intersect at point P and we need to find the value of angle Z.
We know that angle X is 65 degrees and angle Y is 75 degrees. We also know that all six angles formed by the intersection of the three lines add up to 360 degrees.
Using these facts, we can set up an equation as
2X + 2Y + 2Z = 360.
We can simplify this equation to
X + Y + Z = 180.
We can then substitute the given values of X and Y to get
65 + 75 + Z = 180.
Simplifying this equation, we get Z = 40, which means Z is equal to 40 degrees.
Therefore, the answer is option C.
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Complete Question:
In the figure, 3 lines intersect at point P. If x = 65 and y = 75, what is the value of z?
140804020In a binomial situation, n = 4 and π = 0.35. Find the
probabilities for all possible values of the random variable,
x. (Round your answers to 4 decimal places.)
The prοbabilities fοr all pοssible values οf the randοm variable x are:
P(x) = 0.1785 P(x) = 0.3911 P(x) = 0.3462 P(x) = 0.1124 P(x) = 0.0118.
Hοw likely is it that twο randοm variables will οccur?The jοint prοbability is the likelihοοd οf twο (οr mοre) events. The jοint prοbability distributiοn is the sum οf the jοint prοbabilities οf twο οr mοre randοm variables. Fοr instance, P is the fοrmal nοtatiοn fοr the cοmbined prοbability οf events A and B. (A and B)
We can use the fοllοwing fοrmula tο find the prοbabilities fοr all pοssible values οf the randοm variable, x, in a binοmial situatiοn where n = 4 and = 0.35:
P(x) = (n chοοse x)[tex]* \pi ^x * (1-\pi)^{(n-x)[/tex]
where "n select x" is the binοmial cοefficient, which equals n! / (x! * (n-x)!).
Then, fοr x = 0, 1, 2, 3, and 4, we can cοmpute P(x) as fοllοws:
P(x=0) = (4 chοοse 0) [tex]* 0.35^0 * 0.65^4 = 0.1785[/tex]
P(x=1) = (4 chοοse 1) [tex]* 0.35^1 * 0.65^3 = 0.3911[/tex]
P(x=2) = (4 chοοse 2) [tex]* 0.35^2 * 0.65^2 = 0.3462[/tex]
P(x=3) = (4 chοοse 3) [tex]* 0.35^3 * 0.65^1 = 0.1124[/tex]
P(x=4) = (4 chοοse 4) [tex]* 0.35^4 * 0.65^0 = 0.0118[/tex]
When we rοund these numbers tο fοur decimal places, we get:
P(x=0) = 0.1785
P(x=1) = 0.3911
P(x=2) = 0.3462
P(x=3) = 0.1124
P(x=4) = 0.0118
As a result, the prοbabilities fοr all pοssible values οf the randοm variable x are as fοllοws:
P(x=0) = 0.1785
P(x=1) = 0.3911
P(x=2) = 0.3462
P(x=3) = 0.1124
P(x=4) = 0.0118
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In its January 25, 2012, issue, the Journal of the American Medical Association (JAMA) reported on the effects of overconsumption of low, normal, and high protein diets on weight gain, energy expenditure, and body composition. Researchers conducted a single blind, randomized controlled trial of 25 U. S. Adults. The subjects were healthy, weight-stable, male and female volunteers, aged 18 to 35 years. All subjects consumed a weight-stabilizing diet for 13 to 25 days. Afterwards, the researchers randomly assigned participants to diets containing various percentages of energy from protein: 5% (low protein), 15% (normal protein), or 25% (high protein). The subjects were not aware of the specific protein level diet to which they were assigned. On these diets the researchers overfed the participants during the last 8 weeks of their 10 to 12 week stay in the inpatient metabolic unit. The goal was to investigate the effect of overconsumption of protein on weight gain, energy expenditure, and body composition. What is the purpose of random assignment in this experiment?
a. To generalize the experiment results to a larger group
b. To avoid bias
c. To produce treatment groups with similar characteristics
d. To control for confounding variables
Random assignment in this experiment is important to avoid bias.
By randomly assigning participants to diets with different levels of protein, the researchers are ensuring that any differences in outcomes are due to the diet, and not because of any individual characteristics of the participants. Random assignment helps to ensure that the groups being compared in the experiment are similar and that any differences seen in outcomes are due to the protein level and not other factors. Random assignment helps to eliminate any bias that could be introduced if the participants were assigned to diets based on their own characteristics. This helps to ensure that the results of the experiment are valid and accurate.
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events. a. A∣B b. A∣B ′ c. A∣B ' d. Are events A and B independent? a. P(A∣B)= (Round to two decimal places as needed.) b. P(A∣B ′ )= (Round to two decimal places as needed.) c. P(A ′ ∣B ′ )= (Round to two decimal places as needed.) d. Are events A and B independent? A and B are not independent. A and B are independent.
The A and B are independent then P(A∣B) = P(A).Since P(A) = 0.60 and P(A∣B) = 0.60, it can be said that A and B are not independent.
P(A∣B)= 0.60 (Round to two decimal places as needed.)b. P(A∣B ′ )= 0.45 (Round to two decimal places as needed.)c. P(A ′ ∣B ′ )= 0.20 (Round to two decimal places as needed.)d. Are events A and B independent? A and B are not independent.Explanation:A∣B means that the event A occurs when the event B occurs. P(A∣B) can be defined as the probability of A happening given that B has already occurred. By definition, A and B are independent if P(A∣B) = P(A).a. P(A∣B)= P(A∩B)/P(B)0.60 = 0.36/0.60= 3/5 b. P(A∣B ′ )= P(A∩B ′ )/P(B ′ )0.45 = 0.27/0.60= 9/20c. P(A ′ ∣B ′ )= P(A ′ ∩B ′ )/P(B ′ )0.20 = 0.12/0.60= 1/5d. If A and B are independent then P(A∣B) = P(A).Since P(A) = 0.60 and P(A∣B) = 0.60, it can be said that A and B are not independent.
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Calculate 441 ÷ 3 by using long division
Answer:
the answer is 147
Step-by-step explanation:
I have attached a picture with the work. Hope this helps :)
The answer is 147 0 Remainder
EXPLANATION: MY A$* (not that hard lol)
Step 1:
Start by setting it up with the divisor 3 on the left side and the dividend 441 on the right side like this:
Step 2:
The divisor (3) goes into the first digit of the dividend (4), 1 time(s). Therefore, put 1 on top:
Step 3:
Multiply the divisor by the result in the previous step (3 x 1 = 3) and write that answer below the dividend.
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 3 = 1) and write the answer below.
Step 5:
Move down the 2nd digit of the dividend (4) like this:
Step 6:
The divisor (3) goes into the bottom number (14), 4 time(s). Therefore, put 4 on top:
Step 7:
Multiply the divisor by the result in the previous step (3 x 4 = 12) and write that answer at the bottom:
Step 8:
Subtract the result in the previous step from the number written above it. (14 - 12 = 2) and write the answer at the bottom.
Step 9:
Move down the last digit of the dividend (1) like this:
Step 10:
The divisor (3) goes into the bottom number (21), 7 time(s). Therefore put 7 on top:
Step 11:
Multiply the divisor by the result in the previous step (3 x 7 = 21) and write the answer at the bottom:
Step 12:
Subtract the result in the previous step from the number written above it. (21 - 21 = 0) and write the answer at the bottom.
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 441 divided by 3 calculated using Long Division is:
147
0 Remainder
ur welcome dummyboi
Which inequality is true when the value of w w is 13 13?
The given inequality is true when w is greater than 5: w > 5. (option 4)
To solve the inequality, we can simplify the expression inside the absolute value brackets by distributing the negative sign and combining like terms:
|13w - 5 + w + 3| - 5 + w + 3 > 5|14w - 2| - 2 > 5|14w - 2| > 7Now we can split the inequality into two cases: 14w - 2 > 7 and -(14w - 2) > 7. Solving each case for w gives:
14w - 2 > 7
14w > 9
w > 9/14
-(14w - 2) > 7
-14w + 2 > 7
-14w > 5
w < -5/14
So the solution to the inequality is w > 9/14 or w < -5/14. However, we are given that w is greater than 5, so the only valid solution is w > 5.
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Complete Question:
Which inequality is true when the value of w is 13?
w-<5 -w-3>-5 -w-3>5 w->5.If 23 fifth grade textbooks were used for the tower and the tower was 57. 1 cm tall, how many sixth grade textbooks were used?
If 23 fifth grade textbooks were used for the tower and the tower was 57. 1 cm tall, how many sixth grade textbooks were used?
To find out how many sixth grade textbooks were used, divide 57.1 cm by the height of one sixth grade textbook. Then multiply that number by 23 to get the total number of sixth grade textbooks used.
If you want to find out how many sixth grade textbooks were used for the tower, you first have to calculate the height of one sixth grade textbook. Once you have that measurement, you can divide 57.1 cm by that height to get the number of sixth grade textbooks used in the tower. To get the total number of textbooks used, you then need to multiply the number of textbooks per tower by 23, since 23 fifth grade textbooks were used. In other words, if the height of one sixth grade textbook is h, the number of sixth grade textbooks used is (57.1 cm / h) * 23. This equation gives you the number of sixth grade textbooks used, based on the height of one sixth grade textbook and the total height of the tower.
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Which values in the data set are outliers? Show all work
72, 81, 82, 83, 83, 85, 100, 54, 75, 81,83
List the follow (and show work if needed): Q1, Median, Q3, IQR, Lower Fence, Upper Fence and outliers
Answer: The outliers are 54 and 100.
Step-by-step explanation:
And outlier is a number that doesnt belong. Learn more about outliers here https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm#:~:text=An%20outlier%20is%20an%20observation,what%20will%20be%20considered%20abnormal.
(If you were also asking about the q1, medians, and q3 please make that a seperate question.
Suppose the diameter of a circle is
4
What is its circumference?
Use 3. 14 for
π and enter your answer as a decimal
The circumference of the circle with diameter 4 is 12.56 units using 3.14 as the value of π.
The circumference of a circle is given by the formula C = πd, where d is the diameter of the circle. If the diameter of the circle is given as 4, then we can substitute it into the formula to get:
C = πd
C = π(4)
Since we are given to use 3.14 for π, we can substitute it into the formula to get:
C = 3.14(4)
C = 12.56
It's important to note that the circumference of a circle is the distance around the edge or perimeter of the circle.
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. The jug shown below contains some water. How many litres of water does this jug contain? 300 ml 250 ml - 200 ml -150 ml 100 ml -50 ml
Answer:
250 ml
Step-by-step explanation:
300ml + 250ml =550ml
550ml - 200ml=350ml
350ml - 150ml + 100ml=300ml
300ml - 50ml=250ml
A piece of wax has a volume of 2. 5 cm and a mass of 4. 5 g. What is the density of the wax? A. 2. 0 g/cm B. 1. 8 g/cm3 C. 11. 3 g/cm3 O D. 7. 0 g/cm
The density of the wax is 1.8 g/ cm ³. this means that for every cubical centimeter of the wax, it has a mass of 1.8 grams.
The density of a material is defined as its mass in line with unit volume, generally expressed in grams in line with cubical centimeter( g/ cm ³). To compute the density of the presented wax, we need to divide its mass by applying its volume.
Presented that the volume of the wax is2.5 cm ³ and its mass is 4.5 g, we will compute its density as
Density = Mass/ volume = 4.5 g/2.5 cm ³ = 1.8 g/ cm ³
Thus, the density of the wax is 1.8 g/ cm ³. this means that for every cubical centimeter of the wax, it has a mass of 1.8 grams. knowing the density of a fabric can help in relating the cloth or in predicting its deportment in distinct qualifications.
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I need to get this done in 5 minutes and im so confused!?
Answer: line A
Step-by-step explanation:
2x is the slope and -1 is the y-intercept
2x for the slope, also 2/1x (meaning rising up 2 places for every one place on the x axis).
Line A is the only line who has 2x for the slope.
ANSWER: LINE (A)
Answer:
Line a
Step-by-step explanation:
The equation is y= 2x - 1 so....
Slope = 2
Y-intercept = -1
Slope can be put as Rise/ Run ( up/ side)
This means the slope can be written as 2/1
Line a has a slope of 2/1 from the point -1 so the answer is line a
Step by step explanation please! Offering brainliest
Answer:
343 cubic meters.
Step-by-step explanation:
To find the volume of a cube given its surface area, we need to first find the length of one of its sides.
The formula for the surface area of a cube is:
SA = 6s^2
where SA is the surface area and s is the length of one of the cube's sides.
We are given that the surface area is 294 square meters, so we can set up the equation:
294 = 6s^2
Simplifying, we get:
49 = s^2
Taking the square root of both sides, we get:
s = 7
So the length of one of the cube's sides is 7 meters.
To find the volume of the cube, we use the formula:
V = s^3
Substituting in 7 for s, we get:
V = 7^3 = 343
Therefore, the volume of the cube is 343 cubic meters.
Answer:
343m³
Step-by-step explanation:
Surface area of a cube is A = 6a²
6a² = 294
Divide both sides by 6
a² = 49
Square root of both sides
a =7
Substitute the value of a into volume
Volume of Cube V = a³
V = 7x 7x7
V = 343m³
-10+30+58=9-54 X 50-4=
Answer:
Hi
Step-by-step explanation:
SOLUTION STEPS
−10+30+58=9−54×50−4=
Add −10 and 30 to get 20.
20+58=9−54×50−4
Add 20 and 58 to get 78.
78=9−54×50−4
Multiply 54 and 50 to get 2700.
78=9−2700−4
Subtract 2700 from 9 to get −2691.
78=−2691−4
Subtract 4 from −2691 to get −2695.
78=−2695
Compare 78 and −2695.
i need help on this question please
Vοlume οf cylinder is and when height tripled then its vοlume alsο tripled but when radius tripled its vοlume becοme which is nineth times οf οriginal vοlume.
What dο yοu mean by Vοlume?Vοlume is a mathematical cοncept that refers tο hοw much three-dimensiοnal space an οbject οr clοsed surface οccupies.
Vοlume οf cylinder = πr²h
= π × 4² × 10
= 160π m³
When the height is tripled, h becοmes 3h
So, new height = 3 × 10 = 30m
Volume of a Cylinder (when height is tripled) = π × (4)² × 30
= π × 16 × 30
= 480π m³
When height is tripled then vοlume alsο tripled.
When the radius is tripled, r becοmes 3r
So, new radius = 3 × 4 = 12m
Volume of a Cylinder (when radius is tripled)
= π × (12)² × 10
= 1440 m³
But when radius is tripled the vοlumes becοme Nine times.
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If there is a 5% chance that none of the items on a scratch-off lottery ticket
will be a winner, what is the probability that at least one of the scratch-off items will win?
If there is a 5% chance that none of the items on a scratch-off lottery ticket will be a winner, the probability that at least one of the scratch-off items will win is 95%.
If there is a 5% chance that none of the items on a scratch-off lottery ticket will be a winner, then the probability of winning on any one item is 1 - 0.05 = 0.95 (i.e., a 95% chance of winning on any one item).
The complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring, can be used to determine the likelihood that at least one of the scratch-off items will win. In this case, the event we are interested in is winning on at least one item. The complement of this event is not winning on any item.
So, the probability of winning on at least one item is:
1 - 0.05 = 0.95
Therefore, there is a 95% chance that at least one of the items on a scratch-off lottery ticket will win.
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The quadrilateral ABCD has vertices with coordinates A(1,4), B(2,3), C(0,-3) and D(-3,1). Graph ABCD and find its area.
The graph of quadrilateral ABCD is attached below and it's area is 25.5 squared units
What is the graph and area of ABCDTo graph the vertices of the quadrilateral ABCD, we need to use a graphing calculator to find the sides and then the area can be calculated as;
We can use the Shoelace Formula to find the area of the quadrilateral. The Shoelace Formula is based on the idea of using the coordinates of the vertices of the polygon to calculate its area.
The formula is:
Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1)|
where (x1,y1), (x2,y2), ..., (xn,yn) are the coordinates of the vertices of the polygon in order, either clockwise or counterclockwise.
Using this formula, we get:
Area = 1/2 * |(13 + 2(-3) + 01 + (-3)4) - (42 + 30 + (-3)(-3) + 11)|
Area = 1/2 * |(-3 - 6 - 12 - 12) - (8 + 0 + 9 + 1)|
Area = 1/2 * |-33 - 18|
Area = 1/2 * 51
Area = 25.5
Therefore, the area of quadrilateral ABCD is 25.5 square units.
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an escalator can move 30 people per minute from the main level to the upper level. How long would it take to use the escalator to move 100 people?
Answer:
3.33 minutes
Step-by-step explanation:
first know that the escalator can move 30 people in 1 minute.
then, we can write in a mathematical expression as:
30 people = 1 minute
100 people = ? minutes.
cross multiply, i.e. 30×? = 100×1
therefore, ? = 100/30
? = 3.33 minutes.
therefore, it's going to take 3.33 minutes for the escalorr to take 100 people.
3x+y=4 pls help me with this i need to get this right
Answer: y - intercept is c = 4.
Step-by-step explanation:
The line equation is 3x + y = 4.
The slope-intercept form of the line equation is y = mx + c.
Where m is the slope of line c is the y-intercept.
The equation is 3x + y = 4.
subtract 3x from each side.
y - intercept is c = 4.
In order to save money for prom, Tom is going to walk his neighbors dog for $6. 50 per hour and wash cars for $7 per hour. His mother told him he can work no more than 15 hours in order to keep up with his homework. Tom will need to make at least $91 to cover prom expenses.
I just need the solution
Tom is working two jobs to save money for prom, walking a neighbor's dog for $6.50 an hour and washing cars for $7 an hour, to make at least $91.
Tom is working to put money aside for the prom.. His mother has instructed him that in order to keep up with his schoolwork, he may only work a maximum of 15 hours each week. Tom has made the decision to wash cars for $7 per hour and walk his neighbor's dog for $6.50 per hour in order to achieve this aim. For his prom expenditures, he will need to earn at least $91. He must put in a maximum of 13.2 hours of work to earn $91. This implies he can stroll a dog for 8.4 hours and wash vehicles for 4.8 hours. He can also decide to simply perform one job; but, in order to earn the appropriate amount, he would need to walk his neighbor's dog for 12 hours.
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A cylinder has a volume of 72 cubic inches. What is the volue of a cone with the same height and radius as the cylinder
A cone with the same height and radius as a cylinder has a volume of 24 cubic inches.
If a cylinder has a volume of 72 cubic inches, we can use the formula for the volume of a cylinder to find its height and radius. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
So, we have:
72 = πr^2h
We can solve this equation for h:
h = 72/(πr^2)
Now, we can use the formula for the volume of a cone to find the volume of a cone with the same height and radius as the cylinder. The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
So, we have:
V = (1/3)πr^2(72/(πr^2))
Simplifying this equation, we get:
V = 24
Therefore, the volume of a cone with the same height and radius as the cylinder is 24 cubic inches.
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Help please with this maths I need to check it it’s right
Answer:
9999
Step-by-step explanation:
99x10=990
99x1=99
9999
Answer:9999
I hope it is helpful:)
Step-by-step explanation:
we can see 99 is 100-1 and 101 is 100+1
we can rewrite this as,
99*101=(100-1)(100+1)
let's use short mltiplication formula,
[tex]a^{2}-b^{2}=(a-b)(a+b)\\(100-1)(100+1)=100^{2}-1^{2}=10000-1=9999[/tex]
Pls help
Help Algebra1
The equivalent expression is; 4a^3b(4b - 2a^2b^4 + 3a)
How do we know equivalent expressions?Two expressions are equivalent when you can manipulate one expression algebraically to transform it into the other expression. For example, you can use the distributive property, combine like terms, factor out common factors, or simplify fractions to show that two expressions are equivalent.
We have the expression;
16a^3b^2 - 8a^5b^5 + 12a^4b
4a^3b(4b - 2a^2b^4 + 3a)
It's important to note that sometimes two expressions may look different, but they can be equivalent under certain conditions or constraints.
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2. The distance by road from Newport to London is 140 miles. Tom travels by coach from Newport to London. The coach leaves Newport at 1. 30 pm (a) He assumes the coach will travel at an average speed of 50 mph Use his assumption to work out the arrival time in London.
Tom will arrive in London at 4.10 pm, after travelling 140 miles at an average speed of 50 mph.
The formula to calculate the time taken is: Time = Distance/Speed
Using Tom's assumption that the coach is travelling at an average speed of 50 mph, the time taken for the journey from Newport to London can be calculated as follows:
Time = 140 miles/50 mph = 2.8 hours
Therefore, Tom will arrive in London at 1.30 pm + 2.8 hours = 4.10 pm.
To put this in context, it means that the coach will travel at an average speed of 70 km/h, covering a distance of 224 km in 2.8 hours. This is equivalent to covering 80 km in an hour.
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3.6 You have a single piece remaining, 8 points from home, and it is your roll. Your opponent will surely go out if he or she gets another turn. Show that p (your winning) <1/2 , so that a double is not called for. Then explain why this does not contradict the result stated in Exercise 3.1 - namely that the expected count on a backgammon roll is 8 6 1 , exceeding the 8 points you need to win.
a) result does not contradict
To show that p(your winning) <1/2, we need to consider that the last piece you have on your board could land on various positions. Depending on the position, your opponent could end up winning even if you land a higher value on the dice. Therefore, the probability of your winning is less than 1/2. This shows that a double is not called for.Exercise 3.1 states that the expected count on a backgammon roll is 8 6 1, exceeding the 8 points you need to win. This is true since the expected count means the average count you are expected to land on if you roll the dice. It does not mean that every roll will result in a count higher than 8, and it does not mean that you will always win. The expected count is simply a statistical measure of the possible outcomes of rolling the dice. Therefore, this result does not contradict the fact that p(your winning) <1/2.
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i need help asap please
Answer:
2,3,4,10
Step-by-step explanation:
DIVIDE METERS BY 1000 SINCE KILO MEANS 1000
Answer:2000m=2km
3000m=3km
4000m=4km
10000m=10
Step-by-step explanation:
1kilometers is equal to 1000 meters. So, we divide meters with 1000 in order to find kilometers.
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Use the density formula (d =) to find the density of a block of metal with a mass of 21.1
kilograms and a volume of 9.37 meters³.
Round your answer to the nearest tenth of a kg/m³
Answer:
Below
Step-by-step explanation:
Density = mass
volume
Density = 21.1 kg / 9.37 m^3 = ~ 2.3 kg/m^3
a spherical snowball is melting in such a way that its diameter is decreasing at rate of 2 cm/min. at what rate is the volume of the snowball decreasing when the diameter is 6 cm?
The rate of decrease of volume of the sphere when its diameter is 6 cm is -96π cubic cm/min.
Given that the snowball is a sphere, we can use the formula for the volume of a sphere.
The formula for the volume of a sphere is
V = 4/3 πr³
We need to find out the rate of decrease of volume when the diameter is 6 cm.
To find the rate of decrease of volume, we need to differentiate the above formula. Differentiating the above formula w.r.t. time, we get
dV/dt = 4/3 π(3r²)(dr/dt)
Where r is the radius of the sphere and dr/dt is the rate of change of the radius.
Let d be the diameter of the sphere. Then we can write,r = d/2
Also, given that dr/dt = -2cm/min
Substituting the values in the equation for the rate of decrease of volume,
dV/dt = 4/3 π(3(d/2)²)(-2) = -8π/3 d²
As the diameter of the sphere is 6 cm, d = 6 cm.Substituting the value in the equation above, we get
dV/dt = -8π/3 (6)² = -96π cubic cm/min
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