Evaluate the integral. (Use C for the constant of integration.) integral (x^2 + 2x) cos x dx Evaluate the integral. (Use C for the constant of integration.) integral 11 ln^3 Squareroot x dx Evaluate the integral. (Use C for the constant of integration.) integral sin^-1 x dx Evaluate the integral. (Use C for the constant of integration.) integral arc tan 2t dt
Answers
Substituting back \(u = 1 - x^2,\) we obtain:
\(∫sin^-1(x) dx = x sin^-1(x) - 1/2 ln|1 - x^2| + C,\)
To evaluate the integral\(∫(x^2 + 2x)cos(x)\) dx, we can use integration by parts. Let \(u = x^2 + 2x\)and dv = cos(x) dx. Then du/dx = 2x + 2 and v = sin(x). Applying the integration by parts formula, we get:
\(∫(x^2 + 2x)cos(x) dx = uv - ∫v du/dx dx= (x^2 + 2x)sin(x) - ∫(2x + 2)sin(x) dx= (x^2 + 2x)sin(x) + 2x cos(x) + 2 sin(x) + C,\)
where C is the constant of integration.
To evaluate the integral ∫11ln^3(sqrt(x)) dx, we can use substitution. Let u = ln(sqrt(x)), then du/dx = 1/(2x). Rewriting the integral in terms of u, we get:
\(∫11ln^3(sqrt(x)) dx = ∫11(2u)^3 (1/(2x)) dx\)
\(= 8 ∫11u^3 e^u du\)
We can now use integration by parts, with u = u^3 and dv = e^u du. Then \(du/dx = 3u^2 and v = e^u.\) Applying the integration by parts formula, we get:
\(∫11u^3 e^u du = uv - ∫v du/dx du= u e^u - 3 ∫11u^2 e^u du= u e^u - 3 (uv - ∫v du/dx du)= u e^u - 3e^u u^2 + 6e^u u - 6e^u + C= u(e^u - 3e^u u^2 + 6e^u u - 6e^u) + C\)
Substituting back u = ln(sqrt(x)), we obtain:
\(∫11ln^3(sqrt(x)) dx = 8 ln^3(sqrt(x))(2 ln(sqrt(x)) - 3) + C,\)
where C is the constant of integration.
To evaluate the integral\(∫sin^-1(x) dx,\) we can use integration by parts. Let\(u = sin^-1(x)\), then\(du/dx = 1/sqrt(1 - x^2)\). Rewriting the integral in terms of u, we get:
\(∫sin^-1(x) dx = x sin^-1(x) + ∫(1/sqrt(1 - x^2)) x dx\)
We can now use substitution, with\(u = 1 - x^2.\) Then du/dx = -2x, or x dx = -1/2 du. Substituting x dx with -1/2 du, we get:
\(∫sin^-1(x) dx = x sin^-1(x) - 1/2 ∫(1/u) du\)
\(= x sin^-1(x) - 1/2 ln|u| + C\)
\(= x sin^-1(x) - 1/2 ln|1 - x^2| + C\)
Substituting back \(u = 1 - x^2,\) we obtain:
\(∫sin^-1(x) dx = x sin^-1(x) - 1/2 ln|1 - x^2| + C,\)
where C is the constant of integration.
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Related Questions
"Discuss the relationship that exists amongst the three
short-run total cost curves.
Motivate your answer with the aid of a diagram."
Answers
In the short run, the relationship among the three cost curves shows that as output increases, total variable cost increases, total cost increases at an increasing rate, while total fixed cost remains constant.
1. Total Fixed Cost (TFC):
Total fixed cost remains constant regardless of the level of output. It represents the cost that a firm incurs even when it produces zero units of output. In graphical representation, the TFC curve is a horizontal line parallel to the x-axis. It indicates that fixed costs do not change with changes in output.
2. Total Variable Cost (TVC):
Total variable cost varies with the level of output. It represents the cost associated with variable factors of production, such as labor and raw materials, which change as production levels change. As output increases, TVC also increases. In graphical representation, the TVC curve slopes upward, indicating that variable costs increase with higher levels of output.
3. Total Cost (TC):
Total cost is the sum of total fixed cost and total variable cost. It represents the overall cost incurred by the firm at different levels of output. The TC curve is obtained by adding the TFC and TVC curves together. In graphical representation, the TC curve starts from the same point as the TFC curve (since TFC is constant) and then slopes upward at an increasing rate due to the upward slope of the TVC curve.
The relationship among these three cost curves can be summarized as follows:
- TFC remains constant and does not change with changes in output.
- TVC increases with higher levels of output.
- TC is the sum of TFC and TVC, and its rate of increase is steeper than the TVC curve.
This relationship can be illustrated using a diagram:
```
| /|
| / |
| / |
Cost | / |
| / |
| / |
| / |
| / |
|________/________|
Output
```
In the diagram, the horizontal line represents TFC, the upward-sloping line represents TVC, and the steeper line represents TC. As output increases, TVC increases, and the gap between the TC and TVC curves widens. This is because TC includes both fixed and variable costs, and as output increases, variable costs contribute more to the total cost.
Therefore, in the short run, the relationship among the three cost curves shows that as output increases, total variable cost increases, total cost increases at an increasing rate, while total fixed cost remains constant.
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A knight travels in a straight line from the starting point to Token 1. The knight can only make right-angle turns to get to
Tokens 2 and 3. Answer parts (a) to (c) below.
a. Since the knight can only make right-angle turns, what are the slopes of the straight line paths the knight can travel?
Answers
The slope of the straight line paths the knight can travel is 1.
What is slope?Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line.
To calculate the slope of the straight paths, we use the formula below.
Formula:
s = (y₂-y₁)/(x₂-x₁)............ Equation 1Where:
s = Slope of the straight line pathsFrom the question,
Given:
y₂ = 5y₁ = 2x₂ = 6x₁ = 3Substitute these values into equation 1
s = (5-2)/(6-3)s = 3/3s = 1hence, the slope of the straight line part is 1.
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If apples are $1.87 per pound, how much does 3 pounds of
apples cost?
Answers
Answer:
$5.61
Step-by-step explanation:
Just multiply 1.87 and 3
If you really need a step by step ex take out the decimal and multiply 187 and 3 and put the decimal back in
Question 5. (14 Points)
A message g(t)=16x10³ sinc(16000zt) + 10×10³ sinc(10000zt) +20×10³ sinc(10000zt) cos(30000ft) is sampled at a sampling rate 25% above the Nyquist rate and quantized into L levels. The maximum acceptable error in sample amplitudes is not more than 0.1% of the peak signal amplitude.
1. Sketch the amplitude spectrum of g(t) with the horizontal axis as "f".
2. Sketch the amplitude spectrum of the sampled signal in the range - 50 kHz < f <30 kHz. Label all amplitudes and frequencies.
3. What is the minimum required bandwidth if binary transmission is used?
4. What is the minimum M if the available channel bandwidth is 50 kHz and M-ary multi-amplitude signaling is used to transmit this signal?
5. What is the pulse shape that satisfies M to be minimum?
6. If raised cosine pulse is used in part 4, what is the roll off factor? What is the required M?
7. If delta modulation is used with five times the Nyquist rate, find the number of levels L and the corresponding bit rate.
Answers
It is sampled at a rate 25% higher than the Nyquist rate and quantized into L levels. The maximum acceptable error in sample amplitudes is limited to 0.1% of the peak signal amplitude.
To sketch the amplitude spectrum of g(t), we observe that sinc functions centered at 16 kHz and 10 kHz contribute amplitudes of 16x10³ and 10x10³, respectively, while the cosine component centered at 30 kHz has an amplitude of 20x10³. The horizontal axis represents the frequency (f).
The amplitude spectrum of the sampled signal, within the range -50 kHz to 30 kHz, will exhibit replicas of the original spectrum centered at multiples of the sampling frequency. The amplitudes and frequencies should be labeled according to the replicated components.
The minimum required bandwidth for binary transmission can be determined by considering the highest frequency component in g(t), which is 30 kHz. Therefore, the minimum required bandwidth will be 30 kHz.
For M-ary multi-amplitude signaling within a channel bandwidth of 50 kHz, we need to find the minimum value of M. It can be determined by comparing the available bandwidth with the required bandwidth for each amplitude component of g(t). The minimum M will be the smallest number of levels needed to represent all the significant amplitude components without violating the bandwidth constraint.
To minimize M, we need to select a pulse shape that achieves the narrowest bandwidth while maintaining an acceptable level of distortion. Different pulse shapes can be considered, such as rectangular, triangular, or raised cosine pulses.
If a raised cosine pulse is used, the roll-off factor determines the pulse shape's bandwidth efficiency. The roll-off factor is defined as the excess bandwidth beyond the Nyquist bandwidth. The required M can be calculated based on the available channel bandwidth, the roll-off factor, and the distortion tolerance.
When using delta modulation with a sampling rate of five times the Nyquist rate, the number of levels (L) and corresponding bit rate can be determined by considering the quantization error and the maximum acceptable error in sample amplitudes. The bit rate will be determined based on the number of bits required to represent each level and the sampling rate.
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the standard deviation is the square root of the variance T/F
Answers
The statement "the standard deviation is the square root of the variance" is TRUE.What is the standard deviation?The standard deviation is a statistical measure that calculates the amount of variability or dispersion in a set of data.
It quantifies the distribution's spread by measuring the average distance of each point from the mean. In other words, it's a measure of how much the values in a data set deviate from the mean.What is the variance?Variance is a statistical measure that quantifies the distribution's dispersion.
It is defined as the average of the squared distances of each data point from the mean of the data set. It provides information on how spread out the data is with regard to the mean.Standard Deviation vs VarianceThe variance and standard deviation are two closely related statistical measures.
The variance is computed by squaring the standard deviation. To calculate the standard deviation, take the square root of the variance. In simpler terms, the standard deviation is the square root of the variance.Therefore, the statement "the standard deviation is the square root of the variance" is TRUE.
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Amy is six years older than her brother Leo. Leo is seven years old.
If n stands for Amy’s age, which of these sentences could be used to find her age?
Answers
please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Area = 7.853981 in^2 (2.5 Pi)
Perimeter = 11.42478 in (3.63Pi)
Step-by-step explanation:
Area
Lg semi circle area = Pi(2^2)(0.5) = 3.141593(4)0.5) = 6.283185 in^2
Sm semi circle area = Pi(1^2)(0.5) = 3.141593(2)(0.5) = 1.570796 in^2
added together = 7.853981 in^2
Perimeter
Lg semi circle perimeter = Pi(4)(0.5) + 2 = 8.283185 in
Sm semi circle perimeter = Pi(2)(0.5) = 3.141593 in
added together = 11.42478 in
explain how a scientist can target a specific gene or region of the dna in a pcr reaction. explain how a thermal cycler helps with the process of pcr. brainstorm how you could run a pcr reaction
Answers
To target a specific gene or region of DNA in a PCR (Polymerase Chain Reaction) reaction, scientists use specific primers that are designed to bind to the DNA sequence flanking the target region.
Primers are short, single-stranded DNA sequences that act as starting points for DNA replication during PCR. By designing primers that are complementary to the target gene or region, scientists can selectively amplify and target that specific sequence. The process involves selecting the target DNA sequence and designing two primers: one that anneals to the forward strand (5' to 3' direction) and another that anneals to the reverse strand (3' to 5' direction). These primers define the region of DNA that will be amplified. When added to the PCR reaction mixture, the primers specifically bind to their complementary sequences on the DNA template strands, allowing DNA polymerase to extend and synthesize new DNA strands from the primers.
A thermal cycler is a crucial instrument in the PCR process. It helps automate and control the temperature changes required for the different steps of PCR. The thermal cycler allows precise temperature cycling, which is essential for denaturation of the DNA template (separation of the double-stranded DNA into single strands), annealing of primers to the template DNA, and extension (synthesis of new DNA strands). The thermal cycler ensures that the reactions occur at specific temperatures and for specific durations, optimizing the efficiency and specificity of DNA amplification. To run a PCR reaction, you would need the following components and steps: DNA template: The DNA sample containing the target gene or region you want to amplify. Primers: Design and obtain forward and reverse primers that are complementary to the target DNA sequence.
PCR reaction mixture: Prepare a reaction mixture containing DNA template, primers, nucleotides (dNTPs), DNA polymerase, and buffer solution. The buffer solution provides the necessary pH and ionic conditions for optimal enzymatic activity. Thermal cycling: Load the reaction mixture into the thermal cycler. The thermal cycler will then undergo a series of temperature changes, including: Denaturation: Heating the reaction mixture to around 95°C to denature the DNA, separating the double-stranded DNA into single strands. Annealing: Cooling the reaction mixture to a temperature (typically 50-65°C) suitable for the primers to bind (anneal) to their complementary sequences on the DNA template.
Extension: Raising the temperature to the optimal range (usually around 72°C) for DNA polymerase to extend and synthesize new DNA strands from the primers. This allows replication of the target DNA sequence. Repeat cycles: The thermal cycler will repeat the denaturation, annealing, and extension steps for a predetermined number of cycles, typically 20-40 cycles. Each cycle exponentially amplifies the target DNA sequence, resulting in a significant increase in DNA quantity. Final extension: After the desired number of cycles, a final extension step is performed at 72°C for a few minutes to ensure the completion of DNA synthesis and finalize the PCR process. By following these steps and using a thermal cycler, scientists can successfully amplify and target specific genes or regions of DNA through the PCR technique.
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Jackie obtains a 30-year 4/2 ARM at 5% with a 4/7 cap structure in the amount of $313,500. What is the monthly payment during the initial period? (3 points)
$1,832. 69
$1,496. 70
$1,682. 94
$870. 83
Answers
The monthly payment during the initial period is about $1,682.94
The type of loan Jackie obtains is an Adjustable Rate Mortgage, ARM, loan, which is a 4/2 ARM
The introductory interest rate of 5% is fixed for the first 4 years, and will be adjusted every 2 years after the first four years.
Let us assume that m represents the initial monthly payment.
\(M=\frac{P.(\frac{r}{12} ).(1+\frac{r}{12} )^n}{(1+\frac{r}{12} )^n - 1}\)
where, M is the monthly payment during the initial period
P is the amount on loan
r is the interest rate = 5% = 0.05
n is period = 30 × 12 = 360
Here, P = $313,500
r = 5%
r = 0.05
n = 30 × 12
n = 360
Substituting these values in the above formula we get,
\(M=\frac{313500\times (\frac{0.05}{12} ).(1+\frac{0.05}{12} )^{360}}{(1+\frac{0.05}{12} )^{360} - 1}\)
M ≈ 1,682.94
Therefore, the monthly payment is about $1,682.94
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A dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 6 feet in length. How many 12-inch pieces can the dressmaker cut from 10 of these rolls of ribbon?
Before you try that problem, answer the question below.
How many inches of ribbon does the dressmaker have, in total?
Answers
Answer:
he can cut 60 strips or ribbon
Step-by-step explanation:
The dressmaker has 720 inches of ribbon
from each roll of ribbon, he can make 6 12-inch pieces or ribbon
she has 10 rolls
so 6(strips per roll) x 10(amount of rolls) = 60 strips :)
If 24 boxes of equal size can be prepared by 54 kilos of pages of books. What amount of the pages of the books are required for each box?
Answers
Answer:
2.25 kilos of pages of books
Step-by-step explanation:
This is a division question.
54/24 = 2.25 kilos
the distance between the earth and the moon is approximately feet, and a rocket can travel there at a speed of about 1,540,000 ft/min. how long will it take the rocket ship to travel to the moon and back, in minutes? express your final answer in minutes and round to the nearest minute.
Answers
The average distance between the Earth and the Moon is about 238,855 miles or 1.28 light-seconds.
To convert miles to feet, multiply by 5,280, giving us approximately 1.27 million feet. A rocket traveling at a speed of 1,540,000 ft/min would take approximately 82.5 minutes to travel to the Moon. The round trip to the Moon and back would take approximately 165 minutes, or about 2 hours and 45 minutes.
It's important to note that this is an estimate and the actual time it takes may vary due to various factors such as the rocket's trajectory, speed, and other environmental conditions. Also, it's worth noting that this speed is significantly faster than current spacecraft speeds, so the actual time it would take a rocket to travel to the Moon and back is likely to be much longer.
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5/16=x/64 what is x.
Answers
Answer:
5/16=x/64
Step-by-step explanation:
the x is 1280 that is the answer
Answer:
20 even though its not an answer option?
Step-by-step explanation:
It should be since 16x4=64 5x4=20
. What is 20% as a decimal?
Answers
Answer:
20% as a decimal is 0.2.
Answer:
0.20
Step-by-step explanation:
You take the percent and divide by 100
4b) Solve each equation.
Answers
Answer:
x = 6
Step-by-step explanation:
Given equation,
→ 5x + 6 = 2x + 24
Now we have to,
→ Find the required value of x.
Then the value of x will be,
→ 5x + 6 = 2x + 24
→ 5x - 2x = 24 - 6
→ 3x = 18
Dividing RHS with number 3:
→ x = 18/3
→ [ x = 6 ]
Hence, the value of x is 6.
i have absolutely no idea what this answer is i worked on it for 15 minutes could i get some help please
Answers
Answer:
40
Step-by-step explanation:
m<1 = (1/2)(50 deg + 30 deg)
m<1 = (1/2)(80 deg)
m<1 = 40 deg
Answer: 40
Which graphs represent functions? Graph A plots rise and decline curves intersecting at (negative 3, 0). Graph B plots example (negative 1, 1) and (1, 5), Graph C plots example (negative 2, negative 2) and (1, 5). Graph D plots rise and decline curves through (1, negative 2). A. Graph B and Graph D B. Graph A only C. Graph D only D. Graph C and Graph D
Answers
The graphs that represent functions are Graph B and Graph D.The correct answer is option A.
A function is a mathematical relationship where each input value (x-coordinate) corresponds to exactly one output value (y-coordinate). In Graph B, the plotted points (negative 1, 1) and (1, 5) satisfy this condition, as each x-value has a unique y-value associated with it.
Similarly, Graph D represents a function because it has a rise and decline curve passing through the point (1, negative 2). This means that for any given x-value, there is only one corresponding y-value.
On the other hand, Graph A does not represent a function because it shows multiple y-values for the same x-value. This violates the definition of a function, where each x-value must have a unique y-value.
Graph C also does not represent a function because it fails the vertical line test. The vertical line passing through x = -2 intersects the graph at two different points, violating the uniqueness requirement of a function.
In conclusion, Graph B and Graph D are the only ones that represent functions, making option A. Graph B and Graph D the correct answer.
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What is the surface area?
in
- 5 in
Answers
Answer:
94 ft
Step-by-step explanation:
adam, benin, chiang, deshawn, esther, and fiona have internet accounts. some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. each of them has the same number of internet friends. in how many different ways can this happen?
Answers
(a) Therefore, the range of possible values for "x" is 1 to 5. (b) Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31. Therefore, there are 31 different ways this can happen
To find the number of different ways this can happen, we can consider the number of internet friends each person can have. Since each person has the same number of internet friends, let's denote that number as "x". We can then create equations based on the given information:
1. Some, but not all, of them are internet friends with each other: This means that at least two people are internet friends with each other, but not everyone is friends with each other. This implies that the minimum number of internet friends any person can have is 1, and the maximum number is 5 (since there are 6 people in total).
Therefore, the range of possible values for "x" is 1 to 5.
2. None of them has an internet friend outside this group: This means that each person's internet friends must be within this group of 6 people. So, the number of internet friends each person can have is limited to the remaining 5 people.
To find the number of different ways this can happen, we need to sum up the possible values of "x" and calculate the corresponding combinations. For "x = 1", we choose 1 person out of 5 remaining people, giving us C(5, 1) = 5. For "x = 2", we choose 2 people out of 5 remaining people, giving us C(5, 2) = 10.
Similarly, for "x = 3", "x = 4", and "x = 5", we have C(5, 3) = 10, C(5, 4) = 5, and C(5, 5) = 1 respectively. Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.
Therefore, there are 31 different ways this can happen
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Which of the following functions maps 3 to -5?
O f(x) = -x + 2
O f(x) = x-5
O f(x) = x + 8
O f(x) = 4 – x²
Answers
Answer:
F(x)=x-5
Step-by-step explanation:3 to -5.... x values the 3 and then the -5 is already there. PLUS I DID THE TEST
Simplify (24)−1. please help me find out
Answers
Step-by-step explanation:
24×-1=
-24ans
and that's the answer
solve the equation A-X=B-A for X.
Answers
Answer:
X= -B+2A
Step-by-step explanation:
Hope this helps and sorry if I'm wrong
1 in 10,000 white tailed deer on the east coast of the united states carries the lyme disease bacteria. you randomly select a white-tailed deer from a population on the east coast. what is the probability that the deer you select carries the lyme disease bacteria?
Answers
The probability of selecting a white-tailed deer that carries the Lyme disease bacteria is 1 in 10,000, or 0.0001. This means that out of every 10,000 white-tailed deer on the east coast, only one is expected to carry the Lyme disease bacteria.
If we assume that each deer in the population has an equal chance of carrying the bacteria, then the probability of selecting a deer that carries the bacteria can be calculated using the formula for probability:
Probability = Number of desired outcomes / Total number of possible outcomes
In this case, the number of desired outcomes is one (since we want to select a deer that carries the bacteria), and the total number of possible outcomes is the total number of white-tailed deer in the population. Since we don't know the exact number of deer in the population, we can assume that it is very large, so we can use an approximation:
Probability ≈ 1 / (Very large number)
Therefore, the probability of selecting a white-tailed deer from the east coast population that carries the Lyme disease bacteria is very close to 0.0001 or 1 in 10,000.
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Michael is building a fence around his garden to keep the rabbits out. The perimeter of his garden is 42 feet. If the length of the garden is 5 more than the width, what are the dimensions of the fence? Hint: draw a rectangle, and label all 4 sides for the length and width, given what you know this is the last question on my test please help me
Answers
Here are the steps
In ratio analysis, a single value has little meaning. Therefore analysts use trend and comparative analyses to help "interpret the numbers." T/F
Answers
True, analysts use trend and comparative analyses to help "interpret the numbers.
What is Ratio Analysis?
a) Ratio analysis is a financial analysis tool that helps to evaluate the financial performance and health of a business by comparing different financial figures
b) There are three categories of ratios in ratio analysis: liquidity ratios, profitability ratios, and solvency ratios.
c) Ratio analysis is important because it helps to provide a quick snapshot of a company's financial health and performance.
In ratio analysis, a single value may not provide sufficient context or insight into a company's financial performance.
To draw meaningful conclusions, analysts use trend and comparative analysis to effectively interpret numbers.
Trend analysis involves examining financial ratios over multiple periods to identify patterns and determine whether performance is improving, deteriorating, or remaining stable over time.
This helps identify potential trends or anomalies that may affect decision making. Benchmarking, on the other hand, involves comparing a company's ratios to industry standards, competitor performance, or historical data to assess its relative performance and identify areas of strength or weakness.
By comparing ratios over different time periods or with external benchmarks, analysts gain a more comprehensive picture of a company's financial health and can make more informed judgments and recommendations.
Trend and comparative analyzes are therefore essential tools for analysts to effectively interpret ratio analysis and gain valuable insights into a company's financial performance.
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Help PLease! PLease explainn how to do these types of equations!
Answers
The simplified form of the expression, 6x² / 5y ÷ 3x / 10y² is 4xy.
How to solve an expression?The expression can be simplified as follows:
To simplify an expression means to write an equivalent expression which contains no similar terms.
Therefore,
6x² / 5y ÷ 3x / 10y²
Therefore,
6x² / 5y ÷ 3x / 10y² = 6x² / 5y × 10y²/ 3x
Hence,
6x² / 5y × 10y²/ 3x = 60x²y² / 15xy
60x²y² / 15xy = 4xy
Therefore,
6x² / 5y ÷ 3x / 10y² = 4xy
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I really need help with this mind lending a hand?
Answers
Answer:
A. -4 ≤ x ≤ 3
Step-by-step explanation:
The domain is the horizontal extent of the graph.
The solid dot at the extreme left of the graph indicates x=-4 is in the domain of the graph. The solid dot at the extreme right indicates x=3 is in the domain of the graph. The continuous line between those points indicates all values of x between -4 and +3 are in the domain.
The domain is -4 ≤ x ≤ 3.
solve by using elimtation
Answers
Answer:
1. x = 5, y = 13/2
2. x = 15 , y = 24
Step-by-step explanation:
Solve the following system:
{8 y + 6 x = 82 | (equation 1)
{6 y + 9 x = 84 | (equation 2)
Swap equation 1 with equation 2:
{9 x + 6 y = 84 | (equation 1)
{6 x + 8 y = 82 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{9 x + 6 y = 84 | (equation 1)
{0 x + 4 y = 26 | (equation 2)
Divide equation 1 by 3:
{3 x + 2 y = 28 | (equation 1)
{0 x + 4 y = 26 | (equation 2)
Divide equation 2 by 2:
{3 x + 2 y = 28 | (equation 1)
{0 x + 2 y = 13 | (equation 2)
Divide equation 2 by 2:
{3 x + 2 y = 28 | (equation 1)
{0 x + y = 13/2 | (equation 2)
Subtract 2 × (equation 2) from equation 1:
{3 x + 0 y = 15 | (equation 1)
{0 x + y = 13/2 | (equation 2)
Divide equation 1 by 3:
{x + 0 y = 5 | (equation 1)
{0 x + y = 13/2 | (equation 2)
Collect results:
Answer: {x = 5, y = 13/2
_____________________________________
Solve the following system:
{8 y + 3 x = 237 | (equation 1)
{3 y + 5 x = 147 | (equation 2)
Swap equation 1 with equation 2:
{5 x + 3 y = 147 | (equation 1)
{3 x + 8 y = 237 | (equation 2)
Subtract 3/5 × (equation 1) from equation 2:
{5 x + 3 y = 147 | (equation 1)
{0 x + (31 y)/5 = 744/5 | (equation 2)
Multiply equation 2 by 5/31:
{5 x + 3 y = 147 | (equation 1)
{0 x + y = 24 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{5 x + 0 y = 75 | (equation 1)
{0 x + y = 24 | (equation 2)
Divide equation 1 by 5:
{x + 0 y = 15 | (equation 1)
{0 x + y = 24 | (equation 2)
Collect results:
Answer: {x = 15 , y = 24
HELP PLEASEE ASPA 30 points
Answers
Answer:
\(x = 75\)
Step-by-step explanation:
\(hope \: it \: helps\)
Pls I need help thank you
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Answer:
angleLMK and angleQPR