What is the smallest lateral surface are of a cone if I want the volume of the cone to be 10π cubic inches? The volume of a cone is 1/3πr^2h. The surface area of a cone is πr√(r^2+h^2)
Answers
To find the smallest lateral surface area of a cone with a given volume, we can use the formulas for the volume and surface area of a cone and optimize the lateral surface area with respect to the radius and height of the cone.
Given that the volume of the cone is 10π cubic inches, we have the equation:
(1/3)πr^2h = 10π
Simplifying, we find r^2h = 30.
To find the surface area, we use the formula πr√(r^2+h^2). Substituting the value of r^2h from the volume equation, we have:
Surface area = πr√(r^2 + (30/r)^2)
To find the smallest lateral surface area, we can minimize the surface area function. Taking the derivative of the surface area function with respect to r, setting it equal to zero, and solving for r will give us the radius that minimizes the surface area.
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Related Questions
Dylan was saving to buy a video game console that cost $249. He already saved $60 and plans to save $22 per week. After how many weeks will she have saved enough money for the video game console?
Answers
5.5.4 (TST) - Systems of Linear Equations
Answers
Answer:
I dont see a
Step-by-step explanation:
Simplify: 4(3−4x) −4x negative 4 x 7−8x 7 minus 8 x 12−16x 12 minus 16 x i don't know.
Answers
The simplified form of the expression 4(3 - 4x) - 4x + 7 - 8x + 12 - 16x is \(16x^2\) - 52x + 31.
Simplify the given expression, we apply the distributive property first. We multiply 4 with each term inside the parentheses:
4(3 - 4x) - 4x + 7 - 8x + 12 - 16x
This simplifies to:
12 - 16x - 16x + 16x^2 - 4x + 7 - 8x + 12 - 16x
We combine like terms by grouping the variables and constants together:
(-16x - 16x - 4x - 8x - 16x) + (12 + 7 + 12)
This simplifies to:
-52x + 31
Hence, the simplified form of the expression is 16x^2 - 52x + 31. It is a quadratic expression with a coefficient of 16 for the x^2 term.
The -52x term represents the combined coefficient of all the x terms, and the constant term is 31.
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Lilly likes to collect records. Last year she had 10 records in her collection. Now she has 13 records. What is the percent increase in her collection?
Answers
The percentage increase is 30%
Here, we want to calculate percentage increase
Mathematicall, this is;
\(\text{percentage increase = }\frac{new\text{ value -old value}}{\text{old value}}\text{ }\times\text{ 100}\)From the question, the old value is 10 and the new value is 13
Substituting these values, we have that;
\(\text{Percentage increase = }\frac{13-10}{10}\text{ }\times\text{ 100 = }\frac{3}{10}\text{ }\times\text{ 100 = 30\%}\)Gerry wants to have a cover made for his swimming pool which consists of two parallel lines that are connected at each end by the curved boundary of a semicircle. The parallel lines are 12 feet long and 10 feet apart. Find the area of the swimming pool cover. Round to the nearest hundredth.
Answers
The area of the swimming pool cover is approximately 159.27 square feet, rounded to the nearest hundredth.
To find the area of the swimming pool cover, we can calculate the area of the rectangle and the area of the semicircle separately.
Area of the rectangle:
The length of the rectangle is 12 feet and the width is 10 feet. The formula to calculate the area of a rectangle is:
Area_rectangle = length × width
Area_rectangle = 12 × 10
Area_rectangle = 120 square feet
Area of the semicircle:
The radius of the semicircle is half the distance between the parallel lines, which is 10/2 = 5 feet. The formula to calculate the area of a semicircle is:
Area_semicircle = (π × radius²) / 2
Area_semicircle = (π × 5²) / 2
Area_semicircle = (π × 25) / 2
Area_semicircle ≈ 39.27 square feet
The total area of the swimming pool cover:
To find the total area, we add the area of the rectangle and the area of the semicircle:
Total_area = Area_rectangle + Area_semicircle
Total_area = 120 + 39.27
Total_area ≈ 159.27 square feet
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How many and what type of solutions does 5x2−2x+6 have?
1 rational solution
2 rational solutions
2 irrational solutions
2 nonreal solutions
Answers
Answer:
2 nonreal solutions
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 (a ≠ 0 )
then the nature of the roots are determined by the discriminant
b² - 4ac
• if b² - 4ac > 0 then 2 real and irrational solutions
• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions
• if b² - 4ac = 0 then 2 real and equal solutions
• if b² - 4ac < 0 then no real solutions
5x² - 2x + 6 = 0 ← in standard form
with a = 5 , b = - 2 , c = 6
b² - 4ac
= (- 2)² - (4 × 5 × 6)
= 4 - 120
= - 116
since b² - 4ac < 0
then there are 2 nonreal solutions to the equation
I would love if someone helps me w this one
Answers
Answer:
2,7 is where the lines intersect
X=2
Y=7
correct me if i am wrong
Step-by-step explanation:
Find the derivative of the function.
f(t) = (2t3 + 3t2 - 2t + 4)-3
Answers
The derivative of the function is:
f'(t) = \(-6(2t^3 + 3t^2 - 2t + 4)^-4 * (3t^2 + 3t - 1)\)
How can we find the derivative of the function?We can use the chain rule and the power rule of differentiation to find the derivative of the function.
First, we can rewrite the function as:
f(t) = \((2t^3 + 3t^2 - 2t + 4)^-^3\)
Then, using the chain rule, we have:
f'(t) = -\(-3(2t^3 + 3t^2 - 2t + 4)^-4 * (6t^2 + 6t - 2)\)
Simplifying the expression, we get:
f'(t) = \(-6(2t^3 + 3t^2 - 2t + 4)^-4 * (3t^2 + 3t - 1)\)
Therefore, the derivative of the function is:
f'(t) = \(-6(2t^3 + 3t^2 - 2t + 4)^-4 * (3t^2 + 3t - 1)\)
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simplify |4+ (-9)|
The simplified form of the expression is ?_________
Answers
Answer:
5
Step-by-step explanation:
l4+(-9)l
l4-9l
l-5l
5
HELP pls will mark you the brainliest
Answers
Answer:
One solution: \((-8,1)\)No solutionOne solution: \((1,3)\)Infinitely many solutionsStep-by-step explanation:
If the graphs intersect at one point, the solution is the point of intersection.
If the graphs are parallel, there is no solution.
If the graphs are identical, there are infinitely many solutions.
multiple choice question:
simplify √-72 .
A) -6√2
B) 3√-2
C) 3√2i
D) 3i√2
Answers
Answer:
im really not to sure on this one. sorry dude
Step-by-step explanation:
Closest one to the answer is A
15 Points !! Write an inequality
The science club is going on a field trip to the science museum. The club has at most $800 to špend on the trip. The bus for the trip costs $100, and meals at the museum cost $4.50 per student. If admission to the museum is $12 per student and $16 per adult, and there are six chaperones attending, how many students can go on the trip?
Answers
Answer:
38 students
Step-by-step explanation:
100+(16x6)=196
800-196=631
4.50+12=16.5
A differential equation is given:
y''+ 2y' + 3y =0 is:
a. linear
b. second order nonlinear
c. first order linear
d. first order nonlinear
e. second order
Answers
The differential equation y''+2y'+3y=0 is a second order linear differential equation. Therefore, option a is the correct answer.
What is a linear differential equation?
A differential equation is said to be linear if its dependent variable and all its derivatives occur only in the first degree and are not multiplied together. This means that the dependent variable and its derivatives appear as separate variables.
For example, the following differential equation is linear:
y′′(x) + xy′(x) + y(x) = 0
On the other hand, a nonlinear differential equation is one that involves powers or products of the dependent variable or its derivatives. For example:
y′′(x) + (y(x))² = 0
What is a second order differential equation?
A differential equation is said to be of the second order if it contains two derivatives of the dependent variable. For example, the differential equation:
3y′′(x) + 2y′(x) + y(x) = 0
is a second order differential equation.
What is the solution to a second order linear differential equation?
The general solution to a second order linear differential equation of the form:
y′′(x) + p(x)y′(x) + q(x)y(x) = 0 is given by:
y(x) = c₁y₁(x) + c₂y₂(x)
where y₁(x) and y₂(x) are two linearly independent solutions of the differential equation.
The constants c₁ and c₂ are found by applying initial or boundary conditions that specify the values of y and its derivative at one or more points in the domain of the differential equation.
Hence, the differential equation y''+2y'+3y=0 is a second order linear differential equation. Therefore, option a is the correct answer.
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1. You have learned about inductive and deductive reasoning this week. You will be using these lessons in your assignment. The bike Target Segments are the Mountain, Recreation, and Speed segments you chose for your company to build and will be the basis of your responses. 2. Describe your critical thinking decision-making as if you used inductive critical reasoning in choosing the bike Target Segments’ for your company. Comment on your chosen sample and the data analysis you would have used in making your choice(s).
3. Describe your critical thinking decision-making process as if you used deductive critical reasoning in choosing the bike Target Segments' for your company. Comment on the major and minor premises you woud have used to reach your choice(s).
Answers
The concept of inductive reasoning is based on the fact that people generate information through general observations and evidence. In the decision-making process, inductive reasoning involves selecting the bike segments based on observations. On the other hand, the deductive approach would involve starting with a general idea and creating specific conclusions based on it.
Inductive Reasoning: Inductive reasoning involves using specific pieces of evidence or observations to generate general conclusions. In the decision-making process, inductive reasoning can be used to select the most suitable bike segments for a company. This is based on a combination of observations and a general idea of the characteristics that the company is looking for. To select the bike segments, an inductive approach would begin with the observation of different bike segments in the market and the characteristics of the potential customers that the company is targeting. The company would then use this information to develop an understanding of the key features that are important to these customers. After generating the initial set of ideas, the company would then narrow down the bike segments that meet these criteria to arrive at a final decision.
Deductive Reasoning: Deductive reasoning involves starting with general ideas and then using specific evidence to create specific conclusions. In the decision-making process, a deductive approach can be used to select bike segments based on specific premises. This would involve starting with a general idea of what the company is looking for and then breaking this down into specific criteria. The company would then use these criteria to evaluate the different bike segments in the market and select the most suitable segments based on their specific characteristics. The major premise would be the initial idea of what the company is looking for, while the minor premise would be the specific characteristics that the company is evaluating. The company would then use these two premises to arrive at a final decision.
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a class has 30 students. what is the probability that at least two people in this class share the same birthday?
Answers
To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.
If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:
365/365 * 364/365 * 363/365 * ... * 336/365
This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).
Calculating this probability gives us:
(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937
So the probability that no two people in the class share the same birthday is approximately 0.2937.
Using the complement rule, the probability that at least two people in the class share the same birthday is:
1 - 0.2937 = 0.7063
Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.
Find the probability of rolling a sum of 10 or a sum that is an odd number when two number cubes are rolled.
Answers
Answer:
7/12 chance
Step-by-step explanation:
(1 2 3 4 5 6)
(1 2 3 4 5 6)
All the possibilities:
(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)
(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)
(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)
(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)
(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)
(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)
There are 18 odd sums.
(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)
(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)
(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)
(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)
(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)
(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)
There are 3 possibilities whose sums add up to 10.
Since there are 36 total possibilities and 21 numbers that fit the rule of having an odd sum or a sum of 10. There is a 21/36 chance or simplified, 7/12 chance.
Parker puts 25 $ of her earnings
each month into a savings
account. If Parker put $300 into
savings How many months did it take for
she earn?
Answers
Answer:
12 months or a year
Step-by-step explanation:
300÷25=12
fifteen percent means fifteen out of
Answers
Answer:
15 out of 100
Step-by-step explanation:
15 %= 15/100 it means 15 out of 100
A classifier has portioned a set of 8 biomedical documents into
C = { mentions the IL-2R a-promoter} (6 documents), and C (the rest).
The gold standard indicates that only 3 documents actually mention the Interleukin-2 receptor alpha promoter (IL-2R a-promoter), and we determine that exactly one of them is (incorrectly) in C. In testing a post-processing heuristic, we select a document at random from C and move it in the class C.
Next, we randomly select a document from C.
a. What is the probability that the document we selected from C mentions the IL-2R a-promoter (according to the gold standard)?
Answers
The probability that the document we selected from C mentions the IL-2R a-promoter (according to the gold standard) is 0.375 or 37.5%.Hence, the required answer is 37.5% or 0.375.
Given that a classifier has portioned a set of 8 biomedical documents into C = {mentions the IL-2R a-promoter} (6 documents), and C (the rest).The gold standard indicates that only 3 documents actually mention the Interleukin-2 receptor alpha promoter (IL-2R a-promoter), and exactly one of them is (incorrectly) in C. In testing a post-processing heuristic, we select a document at random from C and move it in the class C. Next, we randomly select a document from C.To determine the probability that the document we selected from C mentions the IL-2R a-promoter (according to the gold standard),
we can use Bayes' theorem.Bayes' theorem is represented as:P(A|B) = P(B|A) * P(A) / P(B)Where;P(A|B) = Posterior ProbabilityP(B|A) = LikelihoodP(A) = Prior ProbabilityP(B) = Marginal ProbabilityGiven that, the prior probability that the document is in class C is 6/8 = 3/4. Also, one of the documents has been incorrectly classified into C. So the probability of selecting a document from C is 5/7.To calculate the probability that the document selected from C mentions the IL-2R a-promoter according to the gold standard,
we can use Bayes' theorem as follows:P(document mentions IL-2R a-promoter | selected document from C) = P(selected document from C | document mentions IL-2R a-promoter) * P(document mentions IL-2R a-promoter) / P(selected document from C)Given that the gold standard indicates that only 3 documents actually mention the IL-2R a-promoter, the probability that a document mentions the IL-2R a-promoter is P(document mentions IL-2R a-promoter) = 3/8 = 0.375.Likelihood = P(selected document from C | document mentions IL-2R a-promoter) = 5/7Posterior Probability = P(document mentions IL-2R a-promoter | selected document from C)Marginal Probability = P(selected document from C) = 5/7P(document mentions IL-2R a-promoter | selected document from C) = (5/7 * 0.375) / (5/7) = 0.375Therefore, the probability that the document we selected from C mentions the IL-2R a-promoter (according to the gold standard) is 0.375 or 37.5%.Hence, the required answer is 37.5% or 0.375.
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HELP
Identify a pair of parallel lines in the given figure.
OA) s and t
OB) p and r
OC) s and a
OD) q and t
Answers
Answer:
A) s and t.
Step-by-step explanation:
just trust me. Plus lines s and t are the only pair of lines that don't touch each other and can go on forever not touching each other.
c) (-1,2) m = -4
What is the equation of the line?
Answers
Answer:
Point-slope form:
\(y - 2 = - 4(x + 1)\)
Slope-intercept form:
\(y = - 4x - 2\)
Standard form:
\(4x + y = - 2\)
Step-by-step explanation:
\(y - 2 = - 4(x + 1)\)
\(y - 2 = - 4x - 4\)
\(y = - 4x - 2\)
\(4x + y = - 2\)
1. What is the probability the marble is yellow? The probability it is blue? The
probability
it is red?
Answers
Answer:
What is the probability the marble is yellow? = 1/3
The probability it is blue? = 1/3
The probability it is red? = 1/3
Daniel has 54/3 CUPS of ice in the ice maker to use to make smoothies for his friends. He uses 2/3 of ice for each smoothie. How 3 cups many friends can have a smoothie?
Answers
Answer:
27
Step-by-step explanation:
i might be wrong if I'm wrong try 9 as the answer
Answer:
i think 9 i might be wrong
Step-by-step explanation:
In which triangle is the measure of the unknown angle, x, equal to the value of sinâ€"1(startfraction 5 over 8.3 endfraction)?
Answers
Answer:
A right triangle is shown. The length of the hypotenuse is 8.3 and the length of another side is 5.
Answer: B
Step-by-step explanation:
Hereee +13 points + the star
Answers
Someone PLEASE help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly
Answers
Answer:
8/25
Step-by-step explanation:
Since there are only three possible outcomes on the spinner (1, 2, or 3), we can find the probability of spinning a 2 by subtracting the probabilities of spinning a 1 or a 3 from 1
P(2) = 1 - P(1) - P(3)
P(2) = 1 - 7/25 - 2/5
P(2) = 1 - 35/125 - 50/125
P(2) = 1 - 85/125
P(2) = 40/125
P(2) = 8/25
Therefore, the experimental probability of spinning a 2 is 8/25 or 0.32.
Which triangle congruence is this a picture of?
SSS
SAS
AAS
HL
Answers
Answer:
sas
Step-by-step explanation:
Answer:
SAS
Step-by-step explanation:
SAS
calculate the molecular weight of a gas with a density of 1.524 g/l at stp.
Answers
To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.
Rearranging the equation, we get n = PV/RT.
Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.
Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.
To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:
1. Recall the ideal gas equation: PV = nRT
2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).
3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):
n/V = (1.524 g/L) / (22.4 L/mol)
4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):
M = (n/V) * (RT/P)
5. Substitute the values and solve for M:
M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)
6. Calculate the molecular weight of the gas:
M ≈ 32.0 g/mol
Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.
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Consider the following polynomial expression: 4x^5-16x^2+13x^8. Part B: What is the degree of the polynomial
Answers
Answer:
8
Step-by-step explanation:
Step 1: Write polynomial
4x⁵ - 16x² + 13x⁸
Step 2: Rearrange
13x⁸ + 4x⁵ - 16x²
The degree of a polynomial is the highest power. In this case, our degree would be 8 because of the x⁸ term being the largest exponent.
setting up squares of known dimension over the entire pattern describes what method of documentation?
Answers
The method of documentation that describes the setting up of squares of known dimension over the entire pattern is known as grid method.
Grid method is a method of documentation that involves the setting up of squares of known dimensions over the entire pattern to document a site. This method is commonly used in archaeological surveys and historical preservation.
Grids are used to help maintain a sense of orientation and scale in the documentation process, and they provide a reference point for mapping and recording data. Grids can be set up on maps or site plans, as well as on the ground using physical markers such as stakes or string.Grids can also be used to help facilitate excavation by allowing archaeologists to isolate specific areas of a site and keep track of their findings in a consistent and organized manner.Therefore, grid method is a simple and effective way of recording data, and it is still widely used in the field of archaeology today.
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