The radius of the cone is , r = √(154 cm²/π) cm and the slant height is
L = √( 154 /π+ h²) cm.
To find the radius and slant height of the cone, we can use the formula for the total surface area of a cone, which is πr² + πrL, where r is the radius, L is the slant height, and π is pi.
Given that the curved surface area of the cone is 2/3 of its total surface area, we know that the total surface area of the cone is 462 cm², and the curved surface area is (2/3) * 462 cm² = 308 cm².
The formula for the curved surface area of a cone is πrL, where r is the radius, and L is the slant height.
So we know that:
πrL = 308 cm²
We also know that:
πr² + πrL = 462 cm²
Now we can solve for the radius and slant height of the cone by substituting the first equation into the second equation and solving the system of equations.
πrL = 308 cm²
πr² + πrL = 462 cm²
πr² = 462 cm² - 308 cm²
πr² = 154 cm²
r² = 154 cm²/π
Solving for r
r = √(154 cm²/π) cm
Now we can use the radius to find the slant height, by using the formula of slant height L = √(r² + h²) where h is the height of the cone.
Given that we do not have the height of the cone provided, we can't solve for the slant height.
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Step-by-step explanation:
the curved surface area is 2/3 of 462 cm².
462 × 2/3 = 308 cm²
that leaves 1/3 of 462 cm² for the base area, a circle.
462 × 1/3 = 154 cm²
the area of a circle is pi×r²
so, in our case
pi×r² = 154
r² = 154/pi
radius = r = sqrt(154/pi) = 7.001408606... cm
the slant height l
l = sqrt(r² + h²)
with h being the internal height.
to get l we have the total surface area A
A = pi×r(r + sqrt(h² + r²)) = pi×r(r + l)
A/(pi×r) = r + l
l = A/(pi×r) - r = 462/(pi×7.001408606...) - 7.001408606... =
= 14.00281721... cm
the height of a cylinder is increasing at a constant rate of 9 inches per second. the volume remains a constant 1318 cubic inches. at the instant when the radius of the cylinder is 99 inches, what is the rate of change of the radius? the volume of a cylinder can be found with the equation v
The rate of change of the radius is -9/(2π*99) inches/second.
The volume of a cylinder can be found with the equation V = πr^2h, where V is the volume, r is the radius, h is the height and π is a constant. We know that the volume is constant at 1318 cubic inches and we know that the height of the cylinder is increasing at a constant rate of 9 inches per second.
V = πr^2h
1318 = π * 99^2 * h
Now we can differentiate this equation with respect to time.
dV/dt = 2πr*dr/dt * h + πr^2 * dh/dt
where dV/dt is the rate of change of the volume, dr/dt is the rate of change of the radius and dh/dt is the rate of change of the height.
Now we know that dV/dt = 0, dh/dt = 9 and we know the value of r, we can substitute these values in the above equation and solve for dr/dt
0 = 2π * 99 * dr/dt * h + π * 99^2 * 9
dr/dt = -9/(2π*99) inches/second
The rate of change of the radius is -9/(2π*99) inches/second at the instant when the radius of the cylinder is 99 inches.
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Erica is considering moving into a one-bedroom apartment in Hyde Park. The
apartment has a rent of $960 and has the following fees.
- Application fee: 6.5% of one month's rent
Credit application fee: $15
- Security deposit: 2 month's rent
- Lease protection: the last month's rent
Broker's fee: 7% of one year's rent
- First month's rent
How much is Erica expected to pay up front in order to move into this apartment?
PLEASE PLEASE HELP
Graph g(x)=4cosx .
Use 3.14 for π .
Use the sine tool to graph the function. Graph the function by plotting two points. The first point must be on the midline and closest to the origin. The second point must be a maximum or minimum value on the graph closest to the first point.
Answer: The graph of g(x) = 4cosx is a horizontal dilation of the graph of y = cosx by a factor of 4.
To graph the function, we can use the following two points:
(0, 4) which is the point on the midline closest to the origin
(3.14/2, 0) which is the maximum point closest to the first point
We can then use these points to plot the graph of g(x) = 4cosx using the sine tool. It will be horizontal shifted of the graph of y = cos(x) by a factor of 4.
Step-by-step explanation:
a set s of distinct positive integers has the following property: for every integer x in s, the arithmetic mean of the set of values obtained by deleting x from s is an integer. given that 1 belongs to s and that 2002 is the largest element of s, what is the greatest number of elements that s can have?
The greatest number of elements that s can have is 2002, and the set s = {1,2,3,4,5,...,2002}
The property of the set s states that for every element x in s, the arithmetic mean of the set obtained by deleting x from s is an integer.
To understand this property, we can start by considering the case when the set s has only two elements, say x and y. In this case, the arithmetic mean of the set obtained by deleting x from s is y, and the arithmetic mean of the set obtained by deleting y from s is x. As both x and y are integers, this property holds true.
When the set s has three elements, say x, y, and z. The arithmetic mean of the set obtained by deleting x from s is (y+z)/2. as y and z are integers, (y+z) is always even, thus (y+z)/2 is always an integer. The same applies to the arithmetic mean of the set obtained by deleting y and z.
As we can see, this property holds true for any set of distinct positive integers, no matter the number of elements.
Given that 1 belongs to s and that 2002 is the largest element of s, we can use the property of the set to find the greatest number of elements that s can have.
The arithmetic mean of the set obtained by deleting 1 from s is (x+y+z+...+2002)/(n-1) = (x+y+z+...+2002)/n + 1/n. as x, y, z... 2002 are integers, (x+y+z+...+2002) is always an integer, thus (x+y+z+...+2002)/n is always an integer. Then, as 1/n is always an integer, (x+y+z+...+2002)/n + 1/n is always an integer.
Therefore, the greatest number of elements that s can have is 2002, and the set s = {1,2,3,4,5,...,2002}
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Find the remaining zeros of f
Degree 4; zeros: 8i, 6, -6
The reaming zeros of f are ?
Answer:
- 8i
Step-by-step explanation:
the Fundamental theorem of algebra states that
A polynomial of degree n has n roots, some may be complex
• Complex roots occur as conjugate pairs
For this polynomial of degree 4, there are 4 zeros
given 8i , 6 , - 6 , then the fourth root is the conjugate of 8i , that is - 8i
during a recent apple picking at the farm. 169 granny smith and 95 golden delicious apples were picked. how many apple pies and batches of applesauce can be made if every apple is used.
Given that each pie requires 6-8 apples, and each batch of applesauce requires 8 apples, it is possible to make approximately 22 apple pies and 24 batches of applesauce from the 264 apples that were picked.
What is number?Number in math is a symbol or group of symbols used to represent a numerical quantity. Numbers include both rational numbers, such as integers, fractions, and decimals, and irrational numbers, such as pi and e. The use of numbers in mathematics allows us to represent many different types of mathematical objects, such as sets, functions, and equations. Numbers also have numerous applications in everyday life, such as in finance, engineering, and science.
This would leave 4 apples leftover. It is important to note that the exact number of pies and batches of applesauce that can be made will depend on the size of the apples. If smaller apples are used, more pies and batches of applesauce could be made.
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Draw the first through the fifth generations of squares, triangles and trapezoids. count how many of each shape are needed to create each generation. explain the pattern that you have observed. if a pattern does hold for each generation, how many tiles would be required at the 20th generation? how do you determine if the generation you are building is similar (by mathematical definition) to the other generations? what happens to area when you double the dimensions of a given polygon? triple them? describe the pattern and give the value needed for the 20th generation.
At the 20th generation, 400 squares, 400 triangles, and 400 trapezoids are needed.
The pattern for the first through the fifth generations of squares, triangles, and trapezoids is that each generation is made up of the previous generation's shapes, but with each shape having an additional set of smaller shapes attached to each side.
For example, in the first generation, there is only one square. In the second generation, four smaller squares are attached to the sides of the first square. In the third generation, nine smaller squares are attached to the sides of each of the four squares in the second generation, and so on.
The number of shapes needed to create each generation can be found using the formula:
(n^2)
Where n is the generation number.
For example, in the first generation, only 1 square, 1 triangle and 1 trapezoid is needed, in the second generation, 4 of each are needed, in the third generation, 9 of each are needed, and so on.
If this pattern holds for each generation, the number of tiles required at the 20th generation can be found by substituting n = 20 into the formula:
(20^2) = 400
To determine if the generation you are building is similar (by mathematical definition) to the other generations, you would need to check whether the ratio of corresponding sides is the same for each shape in the generation.
When you double the dimensions of a given polygon, the area is multiplied by four. When you triple the dimensions of a given polygon, the area is multiplied by nine.
The pattern for the number of shapes needed to create each generation follows the pattern of a square of n^2. Therefore, the number of tiles required at the 20th generation can be found by substituting n = 20 into the formula, n^2 = 20^2 = 400.
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Suppose an and bn are series with positive terms and bn is known to be convergent. (a) If an > bn for all n, what can you say about an? Why? O a n converges if and only if an < 2bn. Oman converges by the Comparison Test. O an diverges by the Comparison Test. We cannot say anything about an. o a n converges if and only if an 5 4bn. (b) If an
Nothing that we can say regarding an we are unsure of whether the terms of an are rising or falling, a passes the Comparison Test and sequence, Since bn, an also converges.
what is a sequence?A collection of numbers, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence.
We are unable to comment on an.
This is due to the fact that bn converges, causing a to exceed bn, and as a result, we are unable to determine whether the terms of an are increasing or decreasing.
What can you say about an if a bn for all n? a passes the Comparison Test and converges.
This is due to the fact that since bn converges and a converges since bn, we may infer that the terms of an are likewise decreasing and that an also sequence since bn based on the comparison test.
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If the complement of an angle is one-third of its supplement, find the angle
Answer: 45°
Step-by-step explanation:
Let the angle be x and its complement be y
Also,
Complement = 1/3 × Supplement
So,
Supplement = 3 × Complement
= 3y
According to Question:
I. x + y = 90° -----(1)
II. x + 3y = 180° -----(2)
On subtracting eq (1) from (2) we get
2y=90°
y=45°
Now, From eq (1)
x + y = 90°
x = 90° - 45°
x = 45°
∴ The angle is 45°
2 red and 2 overlapping balls in the center are surrounded by a green, fuzzy, circular cloud with a white line running through it. 2 green balls sit on the white line, and a line leading a bracket around the balls is labeled A. A line leading to a bracket overlapping the white line is labeled B.Identify the parts of the atom that are labeled in the diagram.
They describe a model of an atom with two protons, two neutrons, electron density (orbitals), and two electrons. Now suppose we want to know what the labels A and B stand for.
The nucleus is at the center where the protons and neutrons are arranged. This is supported by his three models: the Rutherford model, the Bohr model and the (now accepted) quantum model.
So the red sphere and the two overlapping spheres in the middle represent protons and neutrons.
The line labeled A with the sphere in brackets represents the nucleus, as it signals both protons and neutrons within the nucleus.
The green blurry circular clouds represent the regions where electrons reside. This is blurry according to the quantum model, which states that the electrons are not in a fixed position, but in the region around the atom. This area is called the trajectory. According to the model, the electron's exact position cannot be determined, which means a blurry cloud.
This white line, which in Bohr's model should be circular where the electrons are, represents the electron orbits and shells identified by the letters L, M, N, and K. The first shell was the L shell.
In the quantum model, this line corresponds to the principal quantum number n (principal energy level). Therefore, the lines leading to brackets overlapping the white lines indicate the main energy levels.
Atoms are neutral because they contain as many electrons as protons around the nucleus.
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Answer:
A: nucleus
B: electron cloud
Step-by-step explanation:
what is the slope of y = 17x - 39
Answer:
The slope is 17
Step-by-step explanation:
The slope in a point-slope form equation is always the coefficient of x, which in this case is 17.
marcus is testing a hair sample from the telogen stage. what is likely to be true about this sample?
When Marcus tests a hair sample from the telogen stage. The result likely to be true about this sample is there will be a nuclear DNA present.
DNA (Deoxyribonucleic acid) is a polymer comprised of two polynucleotide chains that loop around each other to form a double helix having genetic instructions for the development, functioning, growth and reproduction of all known organisms and many viruses. DNA and ribonucleic acid both are nucleic acids.
Moreover, DNA is the information molecule. It holds the instructions for creating other large molecules, called proteins. These instructions are kept inside each of our cells, distributed among 46 long structures called chromosomes.
Hence, DNA is made of chemical structures called nucleotides. These structures are made of three parts: a sugar group, a phosphate group, and one of four types of nitrogen bases.
Hence the correct option is c.
--The given question is incomplete, the complete question is
''Marcus is testing a hair sample from the telogen stage. What is likely to be TRUE about this sample?
A. There will be several medullas present.
B. There will be mitochondrial DNA present.
C. There will be nuclear DNA present.
D. There will be very little DNA present."--
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Find the product of the root of 6x^2 = 17x - 42
Solving the provided question, can say can't calculate square root. The solution to this equation could not be determined, quadratic equation can be factorized.
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation we have is ,
[tex]6x^2 = 17x - 42[/tex]
[tex]6x^2 - 17x + 42 = 0\\[/tex]
can't calculate square root. The solution to this equation could not be determined.
so this quadratic equation can be factorized.
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a company has developed a wristband for monitoring blood sugar levels without requiring direct blood samples. it is interested in demonstrating the accuracy of the device. what should the company do first?
Both the wristband and a conventional blood test were used to measure the blood sugar of a random sample selected group of individuals from the neighborhood at random times throughout the day.
what is random sample?selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.
Both the wristband and a conventional blood test were used to measure the blood sugar of a random sample selected group of individuals from the neighborhood at random times throughout the day.
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(0.4)^4 it’s for k12
Answer:
the answer would be
0.0256
a positive integer divisor of $11!$ is chosen at random. what is the probability that this divisor is prime? express your answer as a common fraction.
The probability of a randomly chosen divisor of [tex]$11!$[/tex] being prime is [tex]$\frac{32}{3^{2}\cdot2^{10}} = \frac{1}{243}$[/tex].
COMMON FRACTION EXPRESSIONThe prime factorization of [tex]$11!$[/tex] is 11!=[tex]11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1$[/tex], so there are [tex]$(2+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1) = (3^{2})(2^{10})$[/tex] divisors of [tex]$11!$[/tex]
The prime divisors of [tex]$11!$[/tex] are [tex]$2,3,5,7,11$[/tex], and there are [tex]$(1+1)(1+1)(1+1)(1+1)(1+1) = 2^{5} = 32$[/tex] divisors that are prime.
So the probability of a randomly chosen divisor of [tex]$11!$[/tex] being prime is [tex]$\frac{32}{3^{2}\cdot2^{10}} = \frac{1}{243}$$[/tex]
A common fraction is a way of representing a ratio of two integers, where the numerator (the top part) represents the number of "favorable outcomes" and the denominator (the bottom part) represents the total number of possible outcomes.
In this case, the favorable outcome is a randomly chosen divisor of 11! being prime, and the total number of possible outcomes is the total number of divisors of 11! which is[tex]$(3^{2} )(2^{10})$[/tex]. So the probability of a randomly chosen divisor of 11! being prime can be represented as a common fraction by writing [tex]$\frac{32}{3^{2} \cdot2^{10}}$[/tex], with 32 as the numerator and [tex]$(3^{2})(2^{10})$[/tex] as the denominator.
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What is the imaginary line that divides a shape into two equal halves called?
The imaginary line which divides any shape into two equal halves is known as line of symmetry.
As given in the question,
To divides the given shape into two equal parts :
The imaginary line which is used to divide any given shape into two equal halves is known as line of symmetry.The line of symmetry is also called by another name ' mirror line'.It is called a mirror line as it represents the mirror reflection of the given shape by dividing into two equal parts.Therefore, the imaginary line used to divide the given shape into two equal halves is called line of symmetry.
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Calculate r(-3) Please
Answer: \:y=-3\frac{1}{2}x
Step-by-step explanation:
pls tell me if its wrong so i can fix it
Is √20 greater than, less than, or equal to 4?
Answer: It is greater than 4.
Step-by-step explanation: It is equal to 2 root 5. But if you convert to a decimal you get 4.4721 which is greater than 4.
The formula to find the square root is: y=√a
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Answer: The domain and range is equal to all positive real numbers.
Explanation: The domain and range of the function shown is equal to all positive real numbers because there is no such a value that the function can have an indeterminate situation and also there is no such another positive value that the function cannot have as a result.
I need some help over here
The measure of angle ∠WDY is 89° in problem 20.
What is angle?Two rays (half-lines) that share an endpoint make up an angle. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.
Two angles are said to be congruent by this definition if either of their vertex and side coordinates can be rigidly moved to coincide with the other. The angle may be written as AOB or BOA if O is the vertex and A and B are the points on the two sides (and this for any selection of the two points A and B.)
Given that D is the common point of line segments DW, DX and DY
m∠WDX = 2x - 5
m∠XDY = 52
m∠WDY = 5x - 16
to find m∠WDY
m∠WDY = m∠XDY + m∠WDX
5x - 16 = 52 + 2x - 5
5x - 2x = 52 - 5 + 16
3x = 63
x = 63/3
x = 21
m∠WDY = 5(21) - 16
m∠WDY = 89
Thus, the measure of angle ∠WDY is 89° in problem 20.
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Supposed a family has a credit card balance of -300 ($300 of debt) they spend an average of $33 a day on essential items
Answer: To find out how many days it will take for the family to pay off their credit card balance, we can use the following equation:
Days = (-300) / 33
Solving for Days gives us:
Days = (-300) / 33 = -9
So it will take the family 9 days to pay off their credit card balance, assuming they only spend money on essential items and don't add any more to their debt.
Step-by-step explanation:
Factorise fully x²+X
Answer:
x(x+1)
Step-by-step explanation:
x^2+x=x(x+1)
Answer: x (x + 1)
Step-by-step explanation: Factor out the X
A town with 1800 homes was surveyed. of the 360 who answered the survey, 48 did not have computers at home. On the basis of the survey, estimate how many total homes do not have computers at home.
URGENT!!!!!!!
Answer:
here
Step-by-step explanation:
18000 divided by 360, then multiply that new number with 48. i believe that is the correct math...
Answer:
240
Step-by-step explanation:
48/360*1800
240
What is ½ as a percentage?
Answer:
50%
1 2 = 1 × 50 2 × 50 = 50 100 . . So the answer is 50%.
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bob can drive 50 miles in 40 minutes. sam can drive 90 miles in 105 minutes. if $d$ is the time (in hours) it takes for bob to drive 120 miles and $e$ (in hours) is the time it takes for sam to drive 120 miles, what is the $|d-e|$? express your answer as a decimal to the nearest hundredth.
The required difference in time taken by bob and sam is 0.8 hour.
What is Speed?Speed is defined as. The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
According to question:Bob can drive 50 miles in 40 minutes.
So, Speed of bob = 50×60/40 = 75 miles/hour
And Sam can drive 90 miles in 105 minutes.
Speed of Sam = 90×60/105 = 51.4 miles/hour
Now/
Time taken by bob(d) = 120/75 = 1.6
Similarly,
Time taken by Sam(e) = 120/51.4 = 2.4
So,
d - e
|1.6 - 2.4|
0.8
Thus,required difference in time is 0.8.
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Please see attachment
The fill ups are as follow.
1. vertical Opposite Angle.
2. alternate Interior Angle.
3. b || c, Co- interior angle.
4. a || c, corresponding Angle.
5. Linear pair.
What are parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
First, <3 = <9 because they vertical Opposite Angle.
Second, <2 = <10 are equal because of alternate Interior Angle.
Third, If <9 and <8 are supplementary then line b || line c because they are Co- interior angle.
Fourth, if <11 = <7 then a || c because they corresponding Angle.
Fifth, < and <6 are supplementary because they are Linear pair of Angle.
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what is the probability that their total completion time in the maze for all rats is between 6 and 8 minutes
The probability that their total completion time in the maze for all rats is between 6 and 8 minutes is 0.375, or 37.5%.
The probability that their total completion time in the maze for all rats is between 6 and 8 minutes can be calculated using the Binomial Distribution formula. The formula is P = (nCr) * (p^r) * (1-p)^(n-r), where n is the number of trials, r is the number of successes, and p is the probability of success.
In this case, n = 4 (4 rats), r = 2 (completion time between 6 and 8 minutes), and p = 0.5 (50% chance of success). Therefore, P = (4C2) * (0.5^2) * (1-0.5)^(4-2) = 0.375.
This means that the probability that their total completion time in the maze for all rats is between 6 and 8 minutes is 0.375, or 37.5%.
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two regular hexagons are joined together
work out angle x
Answer:
Step-by-step explanation:
120 degrees per angle - It says that it's a *regular* hexagon
A chord of the circle with centre O and radius 10 cm, subtends an angle
of 120° at the centre of the circle. Find the area of the major sector and
the area of minor segment.
(Use = 3.14 √3 = 1.732
Answer:
Step-by-step explanation:
