For a right circular cylinder, if the radius is tripled and the height is shrunk down to half its size, then what is the surface area if the original radius is 7 inches and the original height is 17 inches? Round your answer to the nearest hundredth.
A.
3,289.43 in.²
B.
3,298.43 in.²
C.
3,892.43 in.²
D.
3,982.43 in.²
Answers
The surface area of a cylinder that the radius tripled and it height is brought down to half is 3890.46 inches²
How to find the surface area of a cylinder?Surface area of a cylinder = 2πr(r + h)
Therefore,
radius is tripled = 3(7) = 21 inches
height is shrunk half its size = 17 / 2 = 8.5 inches
Therefore,
surface area = 2 × 3.14 × 21 (21 + 8.5)
surface area = 131.88(29.5)
surface area = 3890.46 inches²
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Related Questions
what happens to an inequality sign when the inequality is multiplied or divided by a negative number
Answers
When an inequality is multiplied or divided by a negative number, the inequality sign will flip, meaning it will change its direction. For example, if you have a > b and you multiply or divide both sides by a negative number, the inequality will become a < b. This is because the relationship between the values reverses when multiplied or divided by a negative number.
Explanation:
When an inequality is multiplied or divided by a negative number, the direction of the inequality sign is flipped. This is because multiplication or division by a negative number, results in a reversal of the order of the numbers on the number line.
To see why this happens, consider the following example:
Suppose we have the inequality x < 5. If we multiply both sides of this inequality by -1, we get -x > -5. Notice that we have flipped the inequality sign from "<" to ">". This is because multiplying by -1 changes the sign of x to its opposite, and also changes the sign of 5 to its opposite, resulting in a reversal of the order of the numbers on the number line.
Similarly, if we divide both sides of the inequality x > 3 by -2, we get (-1/2)x < (-3/2). Here, we have again flipped the inequality sign from ">" to "<". This is because dividing by a negative number also changes the order of the numbers on the number line.
In general, if we have an inequality of the form a < b or a > b, where a and b are real numbers, and we multiply or divide both sides by a negative number, we obtain:
If we multiply by a negative number, the inequality sign is flipped. For example, if a < b and c < 0, then ac > bc.
If we divide by a negative number, the inequality sign is also flipped. For example, if a > b and c < 0, then a/c < b/c.
Therefore, it is important to be mindful of the signs of the numbers involved when performing operations on inequalities. If we multiply or divide by a negative number, we must flip the direction of the inequality sign accordingly.
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P (-2,6), Q (9,6), R (7, -1), S (-4, -1) are the vertices of a quadrilateral.
i) Using a scale of 1cm to 1 unit on each axis, plot the quadrilateral.
(5 marks)
ii) Name the type of quadrilateral ..........................................
(1 mark)
iii) Reflect the quadrilateral using the line y = -1
Answers
Step-by-step explanation:
Parallelogram
Reflect y=-1 ;x changes sign
round 387.869911589to 3 decimal places
Answers
387.870
You have to add the zero in order to round it to three places
A novelist writes an average of 0.75 page per hour. Which equation models this unit rate
Answers
Answer: You may have to search it is what it says to me, “no results have been found for “A novelist writes an average of 0.75 page per hour. Which equation models this unit rate.”
Step-by-step explanation:
Factor the trinomial below.
x^2 + 13x + 42
Answers
Answer:
B
Step-by-step explanation:
the gcf of 42 is 1,2,3,6,7,21,42
then we find the number when we add give 13 is 6and 7
x^2+13x+42
x^2+6x+7x+42
x(x+6)+7(x+6)
(x+6)(x+7)
Complete the grouped relative frequency distribution for the data. Write each relative frequency as a decimal rounded to the nearest hundredth.( note that we are using a class width of 5)
Answers
Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario. The formula is given to be:
\(RF=\frac{f}{n}\)where f is the number of times the data occurred and n is the total number of observations.
We have the frequency of the individual groups as shown below:
\(\begin{gathered} 1\text{ to }5\Rightarrow3 \\ 6\text{ to }10\Rightarrow8 \\ 11\text{ to }15\Rightarrow3 \\ 16\text{ to }20\Rightarrow5 \end{gathered}\)The total number of observations is 19.
Therefore, the relative frequencies are calculated below:
\(\begin{gathered} 1\text{ to }5\Rightarrow\frac{3}{19}=0.16 \\ 6\text{ to }10\Rightarrow\frac{8}{19}=0.42 \\ 11\text{ to }15\Rightarrow\frac{3}{19}=0.16 \\ 16\text{ to }20\Rightarrow\frac{5}{19}=0.26 \end{gathered}\)ANSWER
\(\begin{gathered} 1\text{ to }5\Rightarrow0.16 \\ 6\text{ to }10\Rightarrow0.42 \\ 11\text{ to }15\Rightarrow0.16 \\ 16\text{ to }20\Rightarrow0.26 \end{gathered}\)T
The angles of a triangle are in the ratio 2:8:5 find the size of each side
Answers
Answer:
24° , 60° , 96°
Step-by-step explanation:
sum the parts of the ratio, 2 + 8 + 5 = 15 parts
divide the sum of the angles in a triangle by 15 to find the value of one part of the ratio.
180° ÷ 15 = 12° , then
2 parts = 2 × 12° = 24°
5 parts = 5 × 12° = 60°
8 parts = 8 × 12° = 96°
the 3 angles in the triangle are 24° , 60° , 96°
line 0 ≤ x ≤ 10 cm, y = 3, z = 0 carries current 4 a along az. calculate h at the point (-1, 6, 0)
Answers
The value of h at the point (-1, 6, 0) is approximately 0.149 mm.
To calculate the value of h at the point (-1, 6, 0), we need to use the Biot-Savart Law which states that the magnetic field at a point due to a current-carrying conductor is proportional to the current and the length of the conductor.
Given that the current-carrying conductor is a line along az with current 4 A and coordinates 0 ≤ x ≤ 10 cm, y = 3, z = 0, we can express the position vector of any point on the conductor as r = xi + 3j, where i, j, and k are the unit vectors in the x, y, and z directions, respectively.
The magnetic field at the point (-1, 6, 0) due to the current-carrying conductor is given by the equation:
B = (μ₀/4π) * ∫(I dl x ẑ)/r²
where μ₀ is the magnetic constant, I is the current, dl is a small element of the conductor, ẑ is the unit vector in the z direction, and r is the distance from the element dl to the point (-1, 6, 0).
To calculate the integral, we need to express dl in terms of x and find the limits of integration. Since the conductor is along az, we have dl = dzk, where k is the unit vector in the z direction. Thus, the limits of integration are from z = 0 to z = 10 cm.
Substituting dl = dzk and r = |r - xi - 3j| into the equation above, we get:
B = (μ₀/4π) * ∫(I dz ẑ x ẑ)/(x² + (y - 3)² + z²)^(3/2)
Since the conductor is infinitely long, we can ignore the x-dependence in the denominator and integrate over z from 0 to 10 cm. The cross product of two unit vectors is zero, so we get:
B = (μ₀/4π) * ∫(I dz)/(y - 3)²
Plugging in the values of μ₀, I, and y = 3, we get:
B = (2 × 10^-7 Tm/A) * (4 A) * ln(10/3) ≈ 2.67 × 10^-6 T
Finally, we can use the formula for the magnetic field of a long straight wire to find h at the point (-1, 6, 0):
B = μ₀I/(2πh)
Solving for h, we get:
h = μ₀I/(2πB) ≈ 1.49 × 10^-4 m or 0.149 mm
Therefore, the value of h at the point (-1, 6, 0) is approximately 0.149 mm.
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If anyone knows about definite integrals for calculus then please I request help! I
Will award 100 points to anyone who can figure out the answer in RED! THANKS AND GOOD LUCK!!
Answers
Answer:
\(\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)\)
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]: \(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)
Integration Property [Multiplied Constant]: \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)
U-Substitution
Step-by-step explanation:
Step 1: Define
Identify
\(\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx\)
Step 2: Integrate Pt. 1
Identify variables for u-substitution.
Set u: \(\displaystyle u = 4x^{-2}\)[u] Differentiate [Basic Power Rule, Derivative Properties]: \(\displaystyle du = \frac{-8}{x^3} \ dx\)[Bounds] Switch: \(\displaystyle \left \{ {{x = 9 ,\ u = 4(9)^{-2} = \frac{4}{81}} \atop {x = 5 ,\ u = 4(5)^{-2} = \frac{4}{25}}} \right.\)Step 3: Integrate Pt. 2
[Integral] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^9_5 {\frac{-8}{x^3}e^\big{4x^{-2}}} \, dx\)[Integral] U-Substitution: \(\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^{\frac{4}{81}}_{\frac{4}{25}} {e^\big{u}} \, du\)[Integral] Exponential Integration: \(\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}(e^\big{u}) \bigg| \limits^{\frac{4}{81}}_{\frac{4}{25}}\)Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: \(\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8} \bigg( e^\Big{\frac{4}{81}} - e^\Big{\frac{4}{25}} \bigg)\)Simplify: \(\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)\)Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
how many hexadecimal numbers begin with one of the digits 4 through d, end with one of the digits 2 through e, and are 6 digits long?
Answers
There are 8,519,680 hexadecimal numbers. The result is obtained by using the multiplication principle.
What is hexadecimal number system?Hexadecimal number system is a numbering system with the base of 16. The 16-digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. They are usually denoted by the subscript 16. For example, 429AD₍₁₆₎.
How many combination of hexadecimal numbers that can be made if:
They begin with one of the digits 4 - D.They end with one of the digits 2 - E.They are 6 digits long.Let's broke the problem into 3 cases.
The first digit is from 4 to D. They are 4, 5, 6, 7, 8, 9, A, B, C, D. There are 10 choices.The last digit is from 2 to E. They are 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E. They are 13 choices.The three digits in the middle are 16³ choices.Using the multiplication principle, we can multiply them all.
The combination of hexadecimal numbers is
= 10 × 13 × 16³
= 8,519,680
Hence, the combination that can be made is 8,519,680 hexadecimal numbers.
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PLEASE HELP ASAP!! EXPLANATION = BRAINLIEST! THANK YOU SO SO MUCH
A model of Spaceship Earth, a major tourist attraction at Epcot Center in Florida, is a sphere whose diameter is approximately 5 inches.
The volume of the model sphere is approximately ___ cubic inches.
Use 3.14 for pi. Round only your final answer to the nearest hundredth.
Answers
Answer:
See below.
Step-by-step explanation:
As the diameter is 5 inches, the radius “r” is 5/2 = 2.5 inches.
We calculate the volume of a sphere as follows: \(V = 4/3 \pi r^3\)
As we have to use 3.14 for pi, we’ll use that instead of “true” pi.
The formula becomes:
\(V = 4/3*3.14*2.5^3 = 65.42\)
The volume of the sphere is 65.42 cubic inches.
help please am stuck tap on picture for full question
Answers
Answer:
h = 9n
Step-by-step explanation:
Since h (height) is a function of number of DVDs then we can express in the form of:
\(\displaystyle{h = an+b}\)
where h is height, a is rate of change, n is number of DVD and b is the initial height which of course is 0 (proportional). Henceforth, we will be with the equation:
\(\displaystyle{h = an}\)
Next, we will be finding the rate of change of how much the dependent values change with respect to the independent values. That can be expressed as:
\(\displaystyle{a = \dfrac{h_2 - h_1}{n_2-n_1} = \dfrac{\Delta h}{\Delta n}}\)
delta means "change of/in"
We will pick \(\displaystyle{(n_1,h_1) = (2,18)}\) and \(\displaystyle{(n_2, h_2) = (3,27)}\). Therefore, substitute in the rate of change formula:
\(\displaystyle{a = \dfrac{27-18}{3-2}}\\\\\displaystyle{a = \dfrac{9}{1}}\\\\\displaystyle{a = 9}\)
Therefore, the rate of change is 9. Substitute a = 9 in and therefore, the equation for the table is:
\(\displaystyle{h = 9n}\)
Find the product of 85 and 25
Answers
Answer: The product of 85 and 25 is 2125 .
85x25 = 2125
Step-by-step explanation:
Hope it works out !SM 7 – 8 On Monday, 329 students went on a trip to the zoo. All 8 buses were filled, and 9 students had to travel in cars. How many students were in each bus?
Answers
Answer:
40 students
Step-by-step explanation:
you have to minus 9 because of the cars then you have 320 divide 8 and you get 40.
4. (6 pts) Find the partial fraction decomposition. Show all steps/supporting work. No calculators. -12x - 29 2x² + 11x + 15
Answers
The decomposition of the partial fraction is 2 / (2x + 5) - 7 / (x + 3)
Given data ,
To find the partial fraction decomposition of the expression (-12x - 29) / (2x² + 11x + 15), we need to factor the denominator first.
The denominator, 2x² + 11x + 15, can be factored as follows:
2x² + 11x + 15 = (2x + 5)(x + 3)
Now, we can write the expression as:
(-12x - 29) / (2x + 5)(x + 3)
Next, we express the given expression as a sum of two fractions with unknown numerators and the factored denominator:
(-12x - 29) / (2x + 5)(x + 3) = A / (2x + 5) + B / (x + 3)
To determine the values of A and B, we need to find the common denominator on the right side:
A(x + 3) + B(2x + 5) = -12x - 29
Expanding and simplifying:
Ax + 3A + 2Bx + 5B = -12x - 29
Matching the coefficients of x terms on both sides:
A + 2B = -12
Matching the constant terms on both sides:
3A + 5B = -29
We now have a system of linear equations:
A + 2B = -12
3A + 5B = -29
To solve this system, we can use any method such as substitution or elimination. Let's use the substitution method:
From the first equation, we have:
A = -12 - 2B
Substituting this value of A into the second equation:
3(-12 - 2B) + 5B = -29
-36 - 6B + 5B = -29
-B = 7
B = -7
Substituting the value of B into the first equation:
A + 2(-7) = -12
A - 14 = -12
A = 2
So, we have found that A = 2 and B = -7.
Hence , the partial fraction is (-12x - 29) / (2x² + 11x + 15) = 2 / (2x + 5) - 7 / (x + 3)
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What is the value of new_list?
my_list = [1, 2, 3, 4]
new_list = [i**2 for i in my_list]
a.
[1, 2, 3, 4, 1, 2, 3, 4]
b.
[2, 4, 6, 8]
c.
[1, 2, 3, 4]
d.
[1, 4, 9, 16]
Answers
The value of `new_list` will be [1, 4, 9, 16]. In the given code, a new list `new_list` is created using a list comprehension.
The list comprehension iterates over each element `i` in the original list `my_list` and computes the square of each element using the expression `i**2`. The resulting squared values are then added to the new list.
Therefore, for each element in `my_list`, the corresponding squared value is appended to `new_list`. Since `my_list` contains the elements [1, 2, 3, 4], the squared values would be [1**2, 2**2, 3**2, 4**2], which simplifies to [1, 4, 9, 16]. Hence, the value of `new_list` is [1, 4, 9, 16].
The correct option is d. [1, 4, 9, 16].
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Edgar said 3/5 is equivalent to 18/32. Check his work by making a
table of equivalent ratios.
Answers
Answer:
In a nutshell, \(\frac{3}{5}\) is not equivalent to \(\frac{18}{32}\).
Step-by-step explanation:
Now we proceed to demonstrate that Edgar's statement is false:
1) \(\frac{3}{5}\) Given
2) \(\frac{3}{5} \times \frac{2}{2}\) Modulative property/Existence of multiplicative inverse
3) \(\frac{6}{10}\) \(\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot b}{c\cdot d}\)
4) \(\frac{6}{10}\times \frac{3}{3}\) Modulative property/Existence of multiplicative inverse
5) \(\frac{18}{30}\) \(\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot b}{c\cdot d}\)/Result
In a nutshell, \(\frac{3}{5}\) is not equivalent to \(\frac{18}{32}\).
Solve the following system of equations. -5x - 4y= -11 7x + 3y = 18
Answers
Step-by-step explanation:
-5x - 4y= -117x + 3y = 18
-5x +117x = 3y + 4y = 18
112x = 7y = 18
Alejandro buys 4 bottles of pineapple juice at the corner store for a total cost of
$2.64. If each bottle costs the same amount, how much is 15 bottles of juice?
Answers
Answer:
$9.9
Step-by-step explanation:
4 = $2.64
15= ?
15 × $2.64 = 39.6
39.6 ÷ 4 = $9.9
Help me please Solve for x.
Answers
B.
I assume this is a trapezium.
Since SR = PQ, the trapezium is isosceles.
[51+(4x-3)] x 2 = 360 (angle sum of a quadrilateral)
4x - 3 = 129
x = 33 i.e. B
A farmer grows vegetables on seven acres, fruit on six acres, and flowers on two acres. Out in his fields, he finds a ladybug. To the nearest tenth of a percent, what is the theoretical probability that the ladybug was not found within the acres of flowers? 13.3% 15.4% 84.6% 86.7%
Answers
Answer:
86.7
Step-by-step explanation:
Answer:
86.7%
Step-by-step explanation:
Correct on Edge2020
Please Help 100 POINTS!!!
Answers
Answer:
B
Step-by-step explanation:
Answer:
B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)
Step-by-step explanation:
one bucket of gravel has a mass of 7.05 kilograms. what is the mass for 20 buckets of gravel in kilograms
Answers
Answer:
tell me if am wrong.
Step-by-step explanation:
1 bucket=7.05kg
20 bucket=20*7.05=141 kg
the mass of 20 bucket is 141 kilogram(kg)
Which of the following functions matches this graph?
Answers
Answer:
a. y=x^2
Step-by-step explanation:
desmos graphing calculator
NEED HELP ASAP! THANK YOU!
To get to Checkpoint C, Helena needs to run north 6 units, crawl through a 4-unit-long tube to the east, hopscotch south 3 units, jump 1 unit to the east, and run south 3 units.
1. Since she began at Checkpoint B, what are the coordinates for Checkpoint C?
2. What would be an easier way to get from Checkpoint B to Checkpoint C?
3. How might you be able to figure this out just by reading the description of the translations? (Hint: It may help you to plot these points on a graph or draw a picture.)
Answers
Helena's motions, including the 6 units north, 4 and 1, east, 3 and 3 south gives;
(5, 0)5 units to the southAdding the motions based on their directionsHow can the position of Helena be found?1. Let the coordinates of checkpoint B be (0, 0), using vectors, we have;
\(6 \times j \: + 4 \times i - 3 \times j \: + i - 3 \times j = 0 \times j \: + 5 \times i\)
The coordinates of checkpoint C is therefore; (5, 0)
2. The easier way to get to checkpoint C from point B is to go south 5 units.
3. How it is possible to figure out the shortest route is by taking the northwards and eastwards motions as positive numbers, and the motions to the south as negative.
The motions to the north can only be added to the motions to the south (motions in the same straight line) and the motions towards east are to be added to themselves.
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Answer:
5, 0
5 units south
adding motions based on direction
Step-by-step explanation:
Need help with 2 and 3 ASAP PLEASE SHOW WORK it’s due soon please
Answers
Answer:
The volume of the cone is 25.13, the other one is 167.55
Step-by-step explanation:
v = 1/3pi(2)^2(6)
simplify and divide the above.
v = 25.13
1/3pi(4)^2(10)
= 167.55
what is r + 3/4 = 7/8
Answers
Answer:
r + ¾ = ⁷/₈
r = ⁷/₈ - ¾
⁷/₈ - ⁶₈ = ¹/₈
r = ¹/₈
Step-by-step explanation:
but my original answer was 4/4
Assume that aduls have scores that are nomaly distribued with a mean of *105 and a standard deviation o15. Find the probability that a randomly selected adut has an 10 between 94 and 116
Answers
The probability that a randomly selected adult has an IQ between 94 and 116 is approximately 0.4176, or 41.76%. This implies that there is a relatively high chance of encountering individuals within this IQ range in the adult population.
To find the probability that a randomly selected adult has an IQ between 94 and 116, we need to standardize the values using the mean and standard deviation provided. We can then use the standard normal distribution table or a calculator to find the area under the curve between the z-scores corresponding to these values.
First, we calculate the z-scores for the IQ values:
z1 = (94 - 105) / 20 = -0.55
z2 = (116 - 105) / 20 = 0.55
Using the standard normal distribution table or a calculator, we find the corresponding probabilities for these z-scores.
P(-0.55 < Z < 0.55) ≈ P(Z < 0.55) - P(Z < -0.55)
Consulting the standard normal distribution table, we find that P(Z < 0.55) is approximately 0.7088, and P(Z < -0.55) is approximately 0.2912.
P(-0.55 < Z < 0.55) ≈ 0.7088 - 0.2912 ≈ 0.4176
Therefore, the probability that a randomly selected adult has an IQ between 94 and 116 is approximately 0.4176, or 41.76%.
Conclusion: Based on the given mean and standard deviation for the normal distribution of IQ scores, we calculated the probability that a randomly selected adult has an IQ between 94 and 116 to be approximately 0.4176, or 41.76%. This implies that there is a relatively high chance of encountering individuals within this IQ range in the adult population.
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A new car costs $18,000. It is expected to depreciate at an average rate of 12% per year. Find the value of the car in 8 years
Answers
The value of the car in 8 years after it has depreciated is $8,348.
To find the value of the car in 8 years, we can use the formula for the future value of a depreciating asset:
future value = original value * (1 - rate of depreciation)^number of years
In this case, the original value is $18,000, the rate of depreciation is 12% per year (or 0.12), and the number of years is 8. Plugging these values into the formula, we get:
future value = 18,000 * (1 - 0.12)^8
future value = 18,000 * 0.4630
future value = $8,348
So the value of the car in 8 years is $8,348.
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Gianna invested \$750$750 in an account in the year 2010, and the value has been growing exponentially at a constant rate. The value of the account reached \$1,060$1,060 in the year 2015. Determine the value of the account, to the nearest dollar, in the year 2019
Answers
The value of the account in 2019 is $1398.
What is the rate of growth of the account?The formula that can be used to determine the growth rate is:
g = (FV / PV)^1/n - 1
Where:
g = growth rate FV = future value PV = present value n = number of years(1060 / 750)^1/5 - 1 = 7.164%
What is the value of the account in 2019?The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value P = Present value R = interest rate N = number of years$750 x ( 1.07164)^9 = 1398
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