Please show work
10 Use the Trapezoidal Rule to approximate the integral SA In(1+e")dx with n = 8 . Round your answer to 6 decimal places.
Answers
Approximation ≈ 0.880898. Steps involve Trapezoidal Rule with n=8 and plugging values in the formula.
To utilize the Trapezoidal Rule to estimated the given essential, we really want to initially partition the stretch [0,1] into n subintervals, every one of width h = (1-0)/n = 1/n. For this situation, n = 8, so h = 1/8.
Then, we utilize the Trapezoidal Rule equation:
∫[a,b] f(x) dx ≈ (b-a)/2n [f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(a+(n-1)h) + f(b)]
with a=0, b=1, f(x) = ln(1+\(e^x\)), n=8, and h=1/8.
Connecting these qualities, we get:
∫[0,1] ln(1+\(e^x\)) dx ≈ (1-0)/(2*8) [ln(1+e^0) + 2ln(1+\(e^_{(1/8)\)) + 2ln(1+\(e^_{(2/8)\)) + ... + 2ln(1+\(e^_{(7/8)\)) + ln(1+\(e^1\))]
Streamlining, we have:
∫[0,1] ln(1+\(e^x\)) dx ≈ (1/16) [ln(2) + 2ln(1+\(e^_{(1/8)\)) + 2ln(1+\(e^_{(2/8)\)) + ... + 2ln(1+\(e^_{(7/8)\)) + ln(1+e)]
Utilizing a mini-computer or PC program, we can assess this articulation to get a guess of the necessary. Adjusted to 6 decimal places, the response is around 0.880898.
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Related Questions
The natural log of 5 equals ____ and the natural log of 5000 equals ____. Round to the nearest tenth digit.
about 0.7; about 3.7
about 1.6; about 8.5
There is not enough information provided to calculate the answers.
None of the above.
Answers
The natural log of 5 equals about 1.6 and the natural log of 5000 equals about 8.5.
To calculate these values, you can use the logarithmic function. The natural logarithm, denoted as ln, is the logarithm to the base e (approximately 2.71828). To find the natural log of a number, you can use a scientific calculator or mathematical software.
For the first part of the question, ln(5) is approximately 1.6094. Rounded to the nearest tenth, it is about 1.6. For the second part of the question, ln(5000) is approximately 8.5172. Rounded to the nearest tenth, it is about 8.5. Therefore, the correct answer is: about 1.6; about 8.5.
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Which of the following expressions is equal to 3x² +27?
Answers
Answer:
B. (3x - 9) (x + 3i)
Step-by-step explanation:
\(\bf 3 {x}^{2} = + 27\)
\(\bf (3x - 9)(x + 3i)\)\(\bf 3 {x}^{2} +9 xi - 9xi - 27 {i}^{2} \)\(\bf 3 {x}^{2} - 27( {i}^{2} )\)\(\bf 3 {x}^{2} - 27( - 1)\)\(\bf 3 {x}^{2} + 27\)Therefore, B is your answer!!!!
Find the surface area of a cone with a hemisphere on top where the radius equals 39 ft and the height of the cone equals 42 ft
Answers
The surface area of the cone with a hemisphere on top is 15,431.43 square feet (rounded to two decimal places).
To find the surface area of the cone, we need to find the lateral surface area of the cone and the surface area of the base, and then add them together. The lateral surface area of the cone can be found using the formula:
Lateral surface area of cone = πrℓ
where r is the radius of the base and ℓ is the slant height of the cone, which can be found using the Pythagorean theorem:
ℓ = sqrt(h^2 + r^2)
where h is the height of the cone. Therefore, for the given values of r and h, we have:
ℓ = sqrt(42^2 + 39^2) = 54.14 ft
Lateral surface area of cone = π(39)(54.14) = 6,426.11 square feet
The surface area of the base of the cone is:
Surface area of base of cone = πr^2 = π(39^2) = 4,804.25 square feet
To find the surface area of the hemisphere, we need to first find the radius of the hemisphere, which is the same as the radius of the cone. Then, we can use the formula:
Surface area of hemisphere = 2πr^2
Surface area of hemisphere = 2π(39^2) = 9,555.84 square feet
Therefore, the total surface area of the cone with a hemisphere on top is:
Total surface area = Lateral surface area of cone + Surface area of base of cone + Surface area of hemisphere
Total surface area = 6,426.11 + 4,804.25 + 9,555.84 = 15,431.43 square feet
Therefore, the surface area of the cone with a hemisphere on top is 15,431.43 square feet (rounded to two decimal places).
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Please help will really appreciate it a lot!!!!
Answers
The table containing the probabilities for this problem is completed as follows:
Pink: P - 3/8 - 0.1. (the - separates each column on the table).Pink and 3: P and 3 - 0 - 0.Pink or Yellow: P or Y - 5/8 - 0.4.Yellow or an odd number: P or O - 5/8 - 0.6.Blue and Odd: B and O - 1/4 - 0.3.What is a probability?A probability is calculated as the number of desired outcomes divided by the number of total outcomes.
The probabilities are divided into theoretical and experimental, as follows:
Theoretical: number of outcomes is taken before any trial.Experimental: number of outcomes is taken from previous trials.For the first row, we have that:
Pink is represented by P.There are three pink sections out of eight in the spinner, hence the theoretical probability is of 3/8.From the table, out of 10 trials, 1 landed on pink, hence the experimental probability is of 1/10 = 0.1.For the second row, we have that:
Pink is represented by P, 3 by 3, so P and 3.There are three pink sections out of eight in the spinner, none with number P, hence the theoretical probability is of 0.From the table, out of 10 trials, none landed on pink and 3, hence the experimental probability is of 0.For the third row, we have that:
Pink is represented by P, Yellow by Y, hence P or Y.There are three pink sections and two yellow sections out of eight in the spinner, none with number P, hence the theoretical probability is of 5/8.From the table, out of 10 trials, three landed on yellow and one on pink, hence the experimental probability is of 4/10 = 0.4.For the fourth row, we have that:
Pink is represented by P, Odd number by O, hence P or O.There are two yellow sections, plus three with odd numbers, out of eight in the spinner, none with number P, hence the theoretical probability is of 5/8.From the table, out of 10 trials, six landed on at least one of yellow or odd number, hence the experimental probability is of 6/10 = 0.6.For the fifth row, we have that:
Blue is represented by B, odd by O, so B and O.There are are two blue sections with odd numbers out of eight in the spinner, hence the theoretical probability is of 2/8 = 1/4.From the table, out of 10 trials, three landed on blue with an odd number hence the experimental probability is of 3/10 = 0.3.What is the missing information?The spinner and the table are missing and are given at the end of the answer.
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What is the conclusion in this conditional statement?
Whenever a car has a flat, it needs a new tire.
Answers
Answer:
The conclusion in this conditional statement would be that it needs a new tire
Step-by-step explanation:
Express an angle of square into grade.
Answers
Answer:
please solve my questiob check my profile
Write the exponential equation y^6 = 30 in logarithmic form.Show your work here
Answers
We have the expression:
\(y^6=30\)If we apply the logarithm with base 30 to both sides, we obtain:
\(\begin{gathered} \log_{30}(y^6)=\log_{30}(30) \\ 6\log_{30}y=1 \\ \log_{30}y=\frac{1}{6} \end{gathered}\)Answer: an equivalent logarithmic expression is log_30(y) = 1/6
Solve for x please!!!!!nowwww
Answers
Answer:
x = 37
Step-by-step explanation: Every angle in a triangle adds up to 180, so we can set up an equation where (x + 48) + (x + 58) = 180. From here, we can combine like terms to get 2x + 106 = 180. 180-106 is 74. 74 divided by 2 is 37. So, x = 37.
Wanda used 3/4 of a full spool of ribbon for her project. There were 38 inches of ribbon left on the spool when she was done. How many inches of ribbon were on the full spool?
Answers
There were 152 inches of ribbon on the full spool when Wanda used 3/4 of a full spool of ribbon for her project.
What is proportion?A proportion is an equation asserting that two ratios are equal. It can be expressed as a/b = c/d, where a and b represent one ratio and c and d represent another ratio. You may use cross-multiplication to solve proportional issues. This entails multiplying the first ratio's numerator by its denominator and setting the result equal to the first ratio's numerator multiplied by its denominator. After that, you may find the unknown variable.
Let us suppose the number of inches = x.
Wanda used 3/4 of the spool, thus the equation of x can be set as:
1/4 x = 38
x = 152
Hence, there were 152 inches of ribbon on the full spool.
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You want to coat your 20 ft x 25 ft driveway with a 0.500-inch thick layer of gold. Given that the market value of gold is 1197 dollar/ounce and that the density of gold is 19.3 g/cm3, what will be the cost of the gold required for this project? (1 ounce = 28.35 g
Answers
The cost of the gold required for coating the driveway with a 0.500-inch thick layer of gold would be approximately 518034.49 dollars.
Since the density of gold is given in grams per cubic centimeter (g/cm³), the thickness of the layer should be converted to centimeters as well.1 inch = 2.54 cm
So, 0.500 inch = 0.500 x 2.54 cm = 1.27 cm
Therefore, the volume of gold required is:
Volume = area x thickness= 500 x 1.27= 635 cm³
Now, the mass of gold required can be calculated as:mass = density x volume= 19.3 x 635= 12260.5 g
Since 1 ounce = 28.35 g, the mass can be converted to ounces as follows:
mass in ounces = mass in grams / 28.35= 12260.5 / 28.35= 433.17 ounces
Finally, the cost of the gold can be calculated by multiplying the mass in ounces by the market value per ounce.
The market value is given as 1197 dollar/ounce. Therefore, the cost can be calculated as:
Cost = mass in ounces x market value= 433.17 x 1197= 518034.49 dollars
Therefore, the cost of the gold required for coating the driveway with a 0.500-inch thick layer of gold would be approximately 518034.49 dollars.
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The distribution of the lengths of fish in a certain lake is not known, but it is definitely not bell shaped. It is estimated that the mean length is 9 inches with a standard deviation of 2 inches. (a) At least what proportion of fish in the lake are between 5 inches and 13 inches long? Round your answer to one decimal place. % (b) Find an interval so that fewer than 36% of the fish have lengths outside this interval. Round your answers to two decimal places. to inches
Answers
(a) At least 95.4% of the fish in the lake are between 5 inches and 13 inches long.(b) An interval of (4.34, 13.66) inches will contain fewer than 36% of the fish in terms of length.
(a) To find the proportion of fish between 5 inches and 13 inches long, we can use the standard normal distribution. First, we convert the values to z-scores using the formula \(z = \frac{x - \mu}{\sigma}\), where \(x\) is the length, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For 5 inches:
\(z_1 = \frac{5 - 9}{2} = -2\)
For 13 inches:
\(z_2 = \frac{13 - 9}{2} = 2\)
Using the standard normal distribution table or a calculator, we can find the proportion of values between -2 and 2, which is approximately 95.4%. Therefore, at least 95.4% of the fish in the lake are between 5 inches and 13 inches long.
(b) To find an interval where fewer than 36% of the fish have lengths outside the interval, we need to find the z-scores corresponding to the cumulative probabilities of 18% on each tail (36% combined).
Using the standard normal distribution table or a calculator, the z-score corresponding to 18% is approximately -0.94. So, we have:
\(z_{\text{left}} = -0.94\)
To find the z-score corresponding to the upper tail, we use the complement rule: \(1 - 0.18 = 0.82\). The z-score corresponding to 0.82 is approximately 0.92. So, we have:
\(z_{\text{right}} = 0.92\)
Now, we convert the z-scores back to length values using the formula \(x = z \cdot \sigma + \mu\). Substituting the values, we get:
\(x_{\text{left}} = -0.94 \cdot 2 + 9 \approx 4.12\) inches
\(x_{\text{right}} = 0.92 \cdot 2 + 9 \approx 13.84\) inches
Therefore, an interval of (4.12, 13.84) inches will contain fewer than 36% of the fish in terms of length.
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What is the difference between percent difference and percent change?
Answers
Answer:
Percent change is comparing one current number or value to another.
Percent difference is comparing a number or value to another number or value.
Step-by-step explanation:
sin2pheta/sinpheta + 1+cos2pheta/cospheta =
4sinpheta
4cospheta
2cospheta
2sinpheta
Answers
Answer:
4cos(θ)
{4cospheta}
Answer:
4cos(θ)
{4cospheta}
Step-by-step explanation:
[note, brainly doesn't allow pheta to be entered as a symbol when writing an equation, so I had to write it out, my apologies]
\(\frac{\sin \left(2pheta \right)}{\sin \left(pheta\right)}+\frac{1+\cos \left(2pheta\right)}{\cos \left(pheta\right)}\\\)
\(\frac{1+\cos \left(2pheta\right)}{\cos \left(pheta\right)}\ = 2\cos \left(pheta\right)\)
\(\frac{\sin \left(2pheta \right)}{\sin \left(pheta\right)}=2\cos \left(pheta\right)\)
2cos(θ) + 2cos(θ) = 4cos(θ)
so, 4cos(θ) is your answer
(4cospheta)
hope this helps!! :)
heya! could someone tell me what the rate change of the table here is?
Answers
1. Given thatA={1,2,3,4,5} and B={3,5,10,11,12} and such that U= AUB. I) list down the elements of U,A' and A'UB'. ii) how many subsets do set A have?
Answers
Answer:
U = {1, 2, 3, 4, 5, 10, 11, 12}A' = {10, 11, 12}A'∪B' = {1, 2, 4, 10, 11, 12}A has 32 subsetsStep-by-step explanation:
i) The union of the two sets is the list of elements that are in either. Duplicates are listed only once.
U = {1, 2, 3, 4, 5, 10, 11, 12}
A' = U - A = {10, 11, 12}
A'∪B' = {10, 11, 12}∪{1, 2, 4} = {1, 2, 4, 10, 11, 12}
__
ii) A has 5 elements, so has 2^5 = 32 subsets, including the empty set and the whole set.
The volume of a cylinder is 225pi cmand its radius is 5 cm.What is the length of the cylinder's height?o 9 cmo 5 cmo 10 cmo 7 cm
Answers
The formula for the volume of the cylinder is given by:
\(V=\pi\cdot r^2\cdot h\)Where:
r = radius
h = length of height
Substitute the given values:
\(225\pi=\pi\cdot(5)^2\cdot h\)And solve for h:
\(\begin{gathered} 225\pi=\pi\cdot25\cdot h \\ \frac{225\pi}{25\pi}=\frac{25\pi h}{25\pi} \\ h=9 \end{gathered}\)Answer: 9 cm
what step cadence is used during the ymca 3-minute step test?
Answers
This cadence corresponds to three sets of 24 steps per set, totaling 72 steps per minute. Participants are required to step up and down on a 12-inch step platform for a duration of three minutes, following the 96 BPM rhythm.
The step cadence used during the YMCA 3-minute step test is a set of three stepping cycles per each 20-second period. This means that the participant takes a total of nine steps within each 20-second period. In other words, the participant steps up and down on the platform at a rate of approximately 24 steps per minute. It is important to maintain this consistent step cadence throughout the entire test in order to get an accurate measure of cardiovascular fitness. Overall, the YMCA 3-minute step test is a simple and effective way to assess an individual's aerobic fitness level.
The YMCA 3-minute step test utilizes a specific step cadence to measure an individual's cardiovascular fitness. The answer is that during the test, a cadence of 96 beats per minute (BPM) is used. This cadence corresponds to three sets of 24 steps per set, totaling 72 steps per minute. Participants are required to step up and down on a 12-inch step platform for a duration of three minutes, following the 96 BPM rhythm. Upon completion of the test, the participant's heart rate is measured for a minute to determine their fitness level. The test results can be compared to established norms to gauge overall cardiovascular health and endurance.
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Leah Deposited $7000 in an account that earns 2% interest compounded annually. How much interest will she have earned after 6 years?
Answers
Answer:
840
Step-by-step explanation:
7000×2×6 ÷ 100. since it is 2%
= 840
ABC is a straight line.
B.
С
The length of BC is four times the length of AB.
BC = 100 metres.
Work out the length AC.
Answers
It should be 125 as
BC=100
and it's four times the length of AB then
100/4=25
then 100+25=125
I hope this helps
In square millimeters, what is the area of the figure above? Round answer to tenth. Just write the number.
Answers
Area of the figure is 72.3 mm²
Define the term Area?Area is a mathematical term that refers to the measurement of a two-dimensional space or region, usually expressed in square units.
There are a combination of two types of figure, rectangle and a triangle we can find the area one by one and then combine it.
1. Area of rectangle whose length = 12.4 mm and width = 4.0 mm
Area of rectangle = length × width
Area of rectangle = 12.4mm × 4.0mm
Area of rectangle = 49.6 mm²
2. Area of triangle whose base = 8.4mm and height = (17.8 - 12.4) = 5.4mm
Area of triangle = (1/2) × base × height
Area of triangle = (1/2) × 8.4mm × 5.4mm
Area of triangle = 22.68 mm²
So, The total area of the figure = Area of rectangle + Area of triangle
Area of the figure = 49.6 mm² + 22.68 mm² = 72.28 mm²
Therefore, Area of the figure is 72.3 mm²
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Area of a rectangle with dimensions of 12.4 mm in length and 4.0 mm in breadth. Area of the given composite figure is 72.3 mm².
Define the term, Area?The measurement of a two-dimensional space or region is referred to as an area in mathematics, and it is typically given in square units.
We can separately calculate the areas of the rectangle and the triangle that make up the combination.
Area of a rectangle with dimensions of 12.4 mm in length and 4.0 mm in breadth
Area of rectangle = length × width
Area of rectangle = 12.4mm × 4.0mm
Area of rectangle = 49.6 mm²
Area of triangle whose base = 8.4mm and height = (17.8 - 12.4) = 5.4mm
Area of triangle = (1/2) × base × height
Area of triangle = (1/2) × 8.4mm × 5.4mm
Area of triangle = 22.68 mm²
So, the total area of the figure = Area of rectangle + Area of triangle
Area of the figure = 49.6 mm² + 22.68 mm² = 72.28 mm²
Therefore, Area of the figure is 72.3 mm².
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Determine the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily. Round your answer to the nearest hundredth of a percent, if necessary. Answer
Answers
The annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.
To determine the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (6.63%)
n = the number of times interest is compounded per year (365 for daily compounding)
t = the number of years (8)
Plugging in the values, we have:
A = 1200(1 + 0.0663/365)^(365*8)
Calculating this, we get A ≈ $1,968.49.
To find the annual percentage yield, we need to find the interest earned:
Interest = A - P = $1,968.49 - $1200 = $768.49
Now, we can find the annual percentage yield using the formula:
Annual percentage yield = (Interest / P) * 100
Plugging in the values, we have:
Annual percentage yield ≈ ($768.49 / $1200) * 100 ≈ 64.04%
Therefore, the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.
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Hi! I need help with my maths the question is 69x420=? (i dont have calculator)
Answers
Answer:
69×420=28980
just use calculator
Step-by-step explanation:
i hope this will help you :)
Answer:
28,980
Step-by-step explanation:
Pls help me. It due ASAP...
Answers
Answer:
b
Step-by-step explanation:
Find the rate of change of the function h(x) = 2x on the interval 2 ≤ x ≤ 4.
The rate of change is
.
Answers
Rate of change of function on the interval is; 6.
Step-by-step explanation:
Given the function: on the interval
Rate of change of function: Let f be the function defined on the interval , then the rate of change of function A(x) is given by:
A(x) =
at x = 2;
h(2) =
and at x = 4
h(4) =
then, by the definition of rate of change of function:
A(x) =
Substitute the value of h(2) = 4 and h(4) = 16 we have;
Therefore, the rate of change of function is 6.
PLEASE HELP Use the given values to identify the table of solutions.
y = 8x + 3 for x = 2, 4, 6, 8 and 10
Answers
The third table gives the correct numeric values for the function in this problem.
How to find the numeric value of a function at a point?To obtain the numeric value of a function or even of an expression, we must substitute each instance of the variable of interest on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is given as follows:
y = 8x + 3.
Hence the numeric values of the function are given as follows:
x = 2: y = 8(2) + 3 = 19.x = 4: y = 8(4) + 3 = 35.x = 6: y = 8(6) + 3 = 51.x = 8: y = 8(8) + 3 = 67.x = 10: y = 8(10) + 3 = 83.A similar problem, also featuring numeric values of a function, is given at brainly.com/question/28367050
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1. In a radical engine the moving parts have a total moment of inertia of 1 kg m 2
, and this is concentrated in the plane of the single crankpin. The engine is directly connected to an air-screw of moment of inertia 18 kg m 2
, by a hollow shaft having outer and inner diameters of 80 mm, and 35 mm, and a single effective length of 0.30 m. The stiffness of the crank-throw alone is 2.5×10 4
Nm/rad. Estimate the natural frequency of torsional vibration of the custen What percentage is involved if the air-screw mass is assumed to be infinite. G=83000 N/mm 2
HINT The stiffness of the crank-throw may be reduced to an equivalent length of shaft at the same diameter as the engine using q
1
= q 1
1
+ q 2
1
Answers
The percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.
We are given that:
Total moment of inertia of moving parts = I = 1 kgm²
Moment of inertia of air-screw = I = 18 kgm²
Outer diameter of hollow shaft = D₀ = 80 mm
Inner diameter of hollow shaft = Dᵢ = 35 mm
Length of hollow shaft = L = 0.30 m
Stiffness of the crank-throw = K = 2.5 × 10⁴ Nm/rad
Shear modulus of elasticity = G = 83000 N/mm²
We need to calculate the natural frequency of torsional vibration of the custen.
The formula for natural frequency of torsional vibration is: f = (1/2π) [(K/L) (J/GD)]^(1/2)
Where, J = Polar moment of inertia
J = (π/32) (D₀⁴ - Dᵢ⁴)
The formula for equivalent length of hollow shaft is given by:
q₁ = q₁₁ + q₁₂
Where, q₁₁ = (π/32) (D₀⁴ - Dᵢ⁴) / L₁q₁₂ = (π/64) (D₀⁴ - Dᵢ⁴) / L₂
L₁ = length of outer diameter
L₂ = length of inner diameter
For the given shaft, L₁ + L₂ = L
Let L₁ = L₀D₀ = D = 80 mm
Dᵢ = d = 35 mm
So, L₂ = L - L₁= 0.3 - L₀...(1)
For the given crank-throw, q₁ = (π/32) (D⁴ - d⁴) / L, where D = 80 mm and d = 80 mm
Hence, q₁ = (π/32) (80⁴ - 35⁴) / L
Therefore, q₁ = (π/32) (80⁴ - 35⁴) / L₀...(2)
From the formula for natural frequency of torsional vibration, f = (1/2π) [(K/L) (J/GD)]^(1/2)
Substituting the values of K, J, G, D and L from above, f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) ((π/32) (80⁴ - 35⁴) / (83000 N/mm² (80 mm)³))]^(1/2)f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) (18.12)]^(1/2)f = 25.7 / L₀^(1/2)...(3)
Now, if we assume that the air-screw mass is infinite, then the moment of inertia of the air-screw is infinite.
Therefore, the formula for natural frequency of torsional vibration in this case is:
f = (1/2π) [(K/L) (J/GD)]^(1/2)Substituting I = ∞ in the above formula, we get:
f = (1/2π) [(K/L) (J/GD + J/∞)]^(1/2)f = (1/2π) [(K/L) (J/GD)]^(1/2)f = 25.7 / L₀^(1/2)
So, in this case also the frequency is the same.
Therefore, the percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.
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find the coefficient of mt in the expansion of 4m(3n-2t)+3t(3t-2m)
Answers
Answer:
-14
Step-by-step explanation:
12mn-8mt+9t²-6mt
12mn+9t²-14mt
the coefficient of mt is -14
The coefficient of the given expansion 4m(3n-2t)+3t(3t-2m) will be -14.
What is expansion?Expanded form is the term used in mathematics to refer to the process of expanding a number to convey the value of every digit and place value.
When a mathematical object is increased by a multiplier that is bigger in actual values than one, an expansion follows.
In another word, if you solve a factor by opening the bracket then you will go to get on some expanded term called expansion.
In mathematics, all real-life problems can be converted into equations which are sometimes in form of factors and we need to expand them to create solutions.
Given that
⇒ 4m(3n-2t)+3t(3t-2m)
⇒ 12mn -8mt + 9t² - 6mt
⇒ 12mn + 9t² + 14 mt
Hence it's clear that the coefficient of mt will be -14.
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Let L be the line in R^3 that consists of all scalar multiples of the vector [ ] Find the reflection of the vector v = [ ]in the line L.
Answers
Let L be the line in R^3 that consists of all scalar multiples of the vector `[3, 4, 5]`. Find the reflection of the vector v = `[1, 2, 3]` in the line L. A reflection is a transformation that takes an object and reflects it over a line. This transformation is called an isometry because the distance between points on the object is preserved.
Let's call the point of intersection between the line and the plane `P`. To find the reflection of `v` in the line `L`, we need to find the point `R` on `L` that is equidistant from `v` and `P`. We can do this by finding the projection of `v` onto `L`, and then doubling the distance between `v` and the projection. The projection of `v` onto `L` is given by:
where `u` is a unit vector in the direction of `L`. Since `L` consists of all scalar multiples of `[3, 4, 5]`, we can take `u` to be:
\(u = (1/√(3² + 4² + 5²))[3, 4, 5] = (1/√50)[3, 4, 5]\)
Then, we have:
Now, we need to double the distance between `v` and `projL(v)` to find `R`. We have:
R = v + 2(projL(v) - v) = [1, 2, 3] + 2([(29/50)3, (29/50)4, (29/50)5] - [1, 2, 3]) = [(58/25) - 1, (58/25) - 2, (58/25) - 3] = [(33/25), (8/25), (-7/25)]
Therefore, the reflection of `v` in the line `L` is `[33/25, 8/25, -7/25]`.
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PLEASE HELP
The Central Islip community has 9,649 homes in it. Smart Boards cost the school district $5,200 each. The HS needs 175, the Reed School needs 150 and the Mulligan school needs 50 new boards. Network Outsource the schools tech company has 12 workers for the HS, 8 for the Reed School and 4 for Mulligan. They all work 8 hours a day. They work 5 days a week, Monday thru Friday. They earn $58 per hour. It will take 45 weeks to finish the job. Find: a) Total Product Cost b) Total Labor Cost c) Total Cost d) Cost per Home e) Cost per Week
Answers
Using proportions, the costs are given as follows:
a) Total Labor Cost: $2,505,600.
b) Total Product Cost: $1,950,000.
c) Total Cost = $4,455,600.
d) Cost per home = $461.77.
e) Cost per week = $99,013.33.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For item a, the labor cost is found using the earnings of the workers, as follows:
45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)
Hence:
Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.
For item b, the product cost is the cost of the boards, hence:
(175 + 150 + 50 boards) x 5,200
Total Product Cost = 375 x 5,200 = $1,950,000.
For item c, the total cost is the sum of the product cost and the labor cost, hence:
Total Cost = 2,505,600 + 1,950,000 = $4,455,600.
For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:
Cost per home = 4455600/9649 = $461.77.
For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:
Cost per week = 4455600/45 = $99,013.33.
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In circle K with
m
∠
J
K
L
=
60
m∠JKL=60 and
J
K
=
17
JK=17 units find area of sector JKL. Round to the nearest hundredth.
Answers
Answer:
KL=43
Step-by-step explanation:
JKL=60, jk=17, KL=43