Answer:
The digit 6 in 46.12 is in the tenths place. Therefore, 1/10 the value of 6 in 46.12 is simply 6/10 or 0.6.
Can someone help me out?
A multivitamin constaions. 17g of vitamin C. How much vitamin c does 60 tablets contain? answer in milligrams
60 tablets of the multivitamin, with 17g (17,000mg) of vitamin C per tablet, contains 1,020,000mg of vitamin C in total.
If one tablet of the multivitamin contains 17g of vitamin C, then 60 tablets would contain 60 times that amount:
60 tablets x 17g of vitamin C per tablet = 1020g of vitamin C
However, it is more common to express vitamin C (and other nutrients) in milligrams (mg) rather than grams (g). To convert from grams to milligrams, we can multiply by 1000:
1020g of vitamin C x 1000 mg/g = 1,020,000 mg of vitamin C
Therefore, 60 tablets of the multivitamin contain 1,020,000 mg of vitamin C.
Just to clarify, in the answer above, I made a mistake in the units. 17g is actually 17,000mg, not 17mg. So the correct calculation is:
If one tablet of the multivitamin contains 17,000mg of vitamin C, then 60 tablets would contain 60 times that amount:
60 tablets x 17,000mg of vitamin C per tablet = 1,020,000mg of vitamin C
Therefore, 60 tablets of the multivitamin contain 1,020,000mg of vitamin C.
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5) (8 pts) A company’s design of 45-ohm resistors is believed to be manufactured with a standard deviation of 0.12 Ω. To evaluate this, a sample of 15 resistors was collected and the standard deviation of the resistance of these 15 resistors was 0.194 Ω. a) (6 pts) Calculate a 95% two-sided confidence interval for standard deviation of resistance, σ. b) (2 pts) Based on your answer to part (a), is it reasonable to believe that the standard deviation of all resistors produced is 0.12 Ω? Explain your answer using information from part (a).
The true value of the standard deviation may be in the interval of (0.12, 0.3757), it may or may not be 0.12 Ω.
Calculation of a 95% two-sided confidence interval for standard deviation of resistance, σ95% two-sided confidence interval for standard deviation of resistance is given by:\[\left(\sqrt{\frac{\left(n-1\right)s^2}{\chi_{0.025,n-1}^2}},\sqrt{\frac{\left(n-1\right)s^2}{\chi_{0.975,n-1}^2}}\right)\]where s = 0.194 Ω, n = 15, and Χ² distribution with df = 14 at α = 0.05/2 = 0.025/0.975The range of the 95% two-sided confidence interval for the standard deviation of resistance is given as follows:95% two-sided confidence interval for standard deviation of resistance = (0.12, 0.3757)Hence, the 95% two-sided confidence interval for the standard deviation of resistance is given as (0.12, 0.3757).b) Explanation:The standard deviation of the resistance is believed to be 0.12 Ω. From the 95% confidence interval obtained in part (a), 0.12 Ω is not within the 95% confidence interval. This means it is not reasonable to believe that the standard deviation of all resistors produced is 0.12 Ω. Since the true value of the standard deviation may be in the interval of (0.12, 0.3757), it may or may not be 0.12 Ω.
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can someone help me solve the area of this composite figure please
Therefore, the area of the composite figure is 65 square centimeters. Therefore, the area of the composite figure is approximately 150.8 square centimeters.
What is area?In mathematics, the area is the measure of the size of a two-dimensional surface or shape. It is the amount of space inside the boundary of a flat object, such as a triangle, rectangle, circle, or any other polygon. The standard unit of measurement for area is square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²). To calculate the area of a shape, we usually use a formula that depends on the shape's geometry and dimensions, such as its length, width, radius, or height. Area has many applications in everyday life, such as calculating the size of a room, the amount of paint needed to cover a wall, or the area of land required to build a house or grow crops. In mathematics and science, area is also used to solve problems in geometry, physics, engineering, and other fields.
Here,
1. Combination of Square and Rectangle
To find the area of this composite figure, we need to break it down into simpler shapes and add up their areas. The figure consists of a square with sides of 5 cm, a rectangle with sides of 4 cm and 9 cm, and a square with sides of 2 cm.
The area of the square with sides of 5 cm is:
A1 = (side)²
= (5 cm)²
= 25 cm²
The area of the rectangle with sides of 4 cm and 9 cm is:
A2 = length x width
= (9 cm) x (4 cm)
= 36 cm²
The area of the square with sides of 2 cm is:
A3 = (side)²
= (2 cm)²
= 4 cm²
To find the total area of the composite figure, we add up the areas of these three shapes:
A = A1 + A2 + A3
A = 25 cm² + 36 cm² + 4 cm²
A = 65 cm²
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Numeros que multiplicados den 30 y sumados o restados den -11
Los dos números que multiplicados den 30 son 5 y 6. Para encontrar dos números que sumados o restados den -11, debemos verificar todas las posibles combinaciones. Al hacerlo, descubrimos que -5 y -6 sumados dan -11. Por lo tanto, los dos números son 5 y -6.
Maths question. Please explain how you got your answer.
Thank you :)
Answer:5/2=2.5
Step-by-step explanation:
[tex]\sqrt{27}=\sqrt{3^{3}}=3^\frac{3}{2}\\\\we \ can \ show \ \sqrt{3^{3}} \ as \ 3^\frac{3}{2}\\3^{1}*3{\frac{3}{2}}=3^{1+\frac{3}{2}}=3^{\frac{5}{2}}\\n=\frac{5}{2}[/tex]
Answer:
[tex]n=\dfrac{5}{2}[/tex]
Step-by-step explanation:
Rewrite 27 as the product of prime numbers:
[tex]\implies 27 = 3 \cdot 3 \cdot 3 = 3^3[/tex]
Therefore, replace 27 with 3³ in the given equation:
[tex]\implies 3 \times \sqrt{3^3}=3^n[/tex]
[tex]\textsf{Apply the exponent rule:} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]
[tex]\implies 3 \times 3^{\frac{3}{2}}=3^n[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 3^1 \times 3^{\frac{3}{2}}=3^n[/tex]
[tex]\implies 3^{1 +\frac{3}{2}}=3^n[/tex]
[tex]\implies 3^{\frac{2}{2} +\frac{3}{2}}=3^n[/tex]
[tex]\implies 3^{\frac{5}{2}}=3^n[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]\implies \dfrac{5}{2}=n[/tex]
Therefore, the value of n is 5/2.
2000 people lived in a village in the year 1999. By the year 2004 ,the male were increased by 10% and the women decreased by 6%. But the total population remain unchanged. How many males lived in the village by 1999?
The number of males in the village in 1999 was 1200, given that the male to female ratio was 3:5 and the total population was 2000.
Let's assume that in the year 1999, there were M males and W females living in the village, so the total population would be P = M + W = 2000.
Then, in the year 2004, the male population increased by 10%, so the number of males became 1.1M, and the female population decreased by 6%, so the number of females became 0.94W.
The total population remained unchanged, so we have:
1.1M + 0.94W = P = 2000
We also know that P = M + W, so we can substitute this into the above equation:
1.1M + 0.94W = M + W
0.1M = 0.06W
M/W = 3/5
So the ratio of males to females in the village in 1999 was 3:5. Therefore, we can write:
M + W = 2000
3/5 (M + W) = 3/5 (2000)
M = 1200
Therefore, there were 1200 males living in the village in the year 1999.
We can check that this answer is consistent with the information given in the problem. In 1999, there were 2000 people in the village, and the ratio of males to females was 3:5. This means that the number of males is 3/8 of the total population, and the number of females is 5/8 of the total population:
Number of males = 3/8 x 2000 = 750
Number of females = 5/8 x 2000 = 1250
Now let's apply the changes that occurred between 1999 and 2004. The male population increased by 10%, so the new number of males is:
1.1 x 750 = 825
The female population decreased by 6%, so the new number of females is:
0.94 x 1250 = 1175
The total population is:
825 + 1175 = 2000
So the total population remained unchanged, as required by the problem statement. Therefore, our answer of 1200 males in 1999 is consistent with the information given in the problem.
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Identify the multiplication problem that matches the model.
The multiplication problem that matches the model is: 5 * 1/2
How to identify the multiplication model?A representation is a way of showing multiplication. A model for multiplication is slightly more sophisticated and it is comprised of several related representations that all have the same structure. There are two models for multiplication namely repeated addition and arrays.
From the attached file, we see that there are 5 images. Now, each image depicts a triangle that is shaded in half.
Thus, it means that each triangle represents the fraction 1/2.
Thus, the model will be expressed as a multiplication model as;
5 * 1/2
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Matt collects classic stamps. For his birthday this year his grandma gave him a stamp’s worth $40. He expected the stamps value to double every decade. Assuming Matt is right you can use a function to approximate the stamp’s value x decades from now.
Write an equation for the function. If it is linear write in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)^x
She walked 30 minutes a day for 5 days. The next 3 days she walked an average of 46 minutes. What was the average time she spent walking?
She took five days of daily 30-minute walks. She walked for 46 minutes each day for the following three days. 36 minutes per day was the average time she spent walking.
To find the average time she spent walking, we need to add up the total time she spent walking and divide it by the number of days she walked.
For the first 5 days, she walked for a total of:
30 minutes/day x 5 days = 150 minutes
For the next 3 days, she walked for an average of 46 minutes/day, so she walked a total of:
46 minutes/day x 3 days = 138 minutes
The total time she spent walking over 8 days is:
150 minutes + 138 minutes = 288 minutes
The average time she spent walking is:
288 minutes / 8 days = 36 minutes/day
Therefore, the average time she spent walking is 36 minutes per day.
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In a class of 100 students, 60 like sports, 50 like music and 25 like both. show it in Venn-diagram and find the number of students who do not like any of them. find the number of students who like only one item
Answer:
Step-by-step explanation:
n(u)=100
n(s)=60
n(m)=50
n(snm)=25
n(sum)=85
n(sum)compliment = n(u)-n(sum)
= 100-85
= 15
Benjamin owns a food truck that sells tacos and burritos. He only has enough supplies to make 120 tacos or burritos. He sells each taco for $3.75 and each burrito for $8.25. Benjamin must sell at least $660 worth of tacos and burritos each day. If � x represents the number of tacos sold and � y represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
one possible solution is to sell 60 tacos and 60 burritos. To graph these inequalities, we can start by graphing the boundary lines for each inequality, which are obtained by replacing the inequality signs with equal signs.
Let x be the number of tacos sold and y be the number of burritos sold. Then we can write the following system of inequalities:
x + y ≤ 120 (since Benjamin only has enough supplies to make 120 tacos or burritos)
3.75x + 8.25y ≥ 660 (since Benjamin must sell at least $660 worth of tacos and burritos each day)
To graph these inequalities, we can start by graphing the boundary lines for each inequality, which are obtained by replacing the inequality signs with equal signs.
For the first inequality, we have:
x + y = 120
This is the equation of a straight line passing through the points (0, 120) and (120, 0). We can graph this line by plotting these two points and connecting them with a straight line.
For the second inequality, we have:
3.75x + 8.25y = 660
This is the equation of a straight line in slope-intercept form, y = (-3.75/8.25)x + 80. We can graph this line by plotting the y-intercept (0, 80) and using the slope (-3.75/8.25) to find additional points on the line.
Next, we need to shade the feasible region, which is the region that satisfies both inequalities. This is the region below the line x + y = 120 and above the line 3.75x + 8.25y = 660.
One possible solution is the point where these two lines intersect, which we can find by solving the system of equations:
x + y = 120
3.75x + 8.25y = 660
Solving for x and y, we get:
x = 60
y = 60
Therefore, one possible solution is to sell 60 tacos and 60 burritos.
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100 points please help
Answer:
(x-6)(x-2)
Step-by-step explanation:
To factor, we use the quadratic formula, which gives us the roots of the equation. In an equation as ax²+ bx + c, we can use (-b±√(b^2-4ac))/2a. Since we have x² - 8x +12, a will be 1, b will be -8, and c will be 12.
(-(-8)±√((-8)²-4(1)(12))/2(1)
(8±√(64-48)/2
(8±√16)/2
(8±4)/2
We now have two cases: (8+4)/2 and (8-4)/2. We can solve these:
(8+4)/2 = 12/2 = 6
(8-4)/2 = 4/2 = 2
Since we have to factor this, we have to write it in the form of
(x-z)(x-y)
for z, we have 6, and for y, we have 2
(x-6)(x-2) is our final answer.
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pls help on this for math
Answer: 1/6 x 3, 1/6 of 3
Step-by-step explanation: i did this in iready one time and got it write :))))))
have a great day/night or whatever ididdkk
Write the function in the form f(x) = (x − k)q(x) + r for the given value of k. F(x) = x3 − x2 − 10x + 5, k = 3
The formula for the function f(x): (x- k)q(x) + r for the specified value of k. F(x) = x3 − x2 − 10x + 5, k = 3 is f(x) = (x - 3)([tex]x^2[/tex] + 2x - 1) - (4x - 5).
To write the function in form f(x) = (x − k)q(x) + r, we need to divide the given polynomial by (x-k) using long division. Here's the long division process:
[tex]x^2[/tex] + 2x - 1
----------------------
x - 3 | [tex]x^3[/tex] - [tex]x^2[/tex] - 10x + 5
- [tex]x^3[/tex] + [tex]3x^2[/tex]
---------------
- [tex]2x^2[/tex] - 10x
+ [tex]2x^2[/tex] - 6x
------------
- 4x + 5
Therefore, we have:
f(x) = (x - 3)([tex]x^2[/tex] + 2x - 1) - (4x - 5)
Thus, the function with the formula f(x)= (x-k)q(x) + r for k= 3 is:
f(x) = (x - 3)([tex]x^2[/tex] + 2x - 1) - (4x - 5)
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Linda and Imani are each traveling in a car to the beach. Linda's travel is modeled by a table. Imani's travel is modeled by a graph.
Did Linda or Imani travel faster? How do you know?
Linda traveled faster than Imani because when t =1 , linda traveled 65 miles and Imani traveled 60 miles and linda travelled at a faster rate because when t=0,
She travelled 10 miles and Imani travelled 0 miles these are cοrrect answer. The prοvided graph's cοοrdinates are (2, 120) and (4, 240).
What is graph ?A graph is a structure that amοunts tο a set οf items where sοme pairs οf the οbjects are in sοme manner "cοnnected" in discrete mathematics, mοre specifically in graph theοry. The items are represented by mathematical abstractiοns knοwn as vertices (sοmetimes knοwn as nοdes οr pοints), and each pair οf cοnnected vertices is knοwn as an edge. Generally, a graph is represented diagrammatically as a cοllectiοn οf dοts οr circles fοr the vertices cοnnected by lines οr curves fοr the edges. Graphs are οne οf the tοpics studied in discrete mathematics.
Slοpe with (2, 120) and (4, 240) is
Slοpe (y2-y1)/(x2-x1)
= (240-120)/(4-2)
= 120/2
= 60
Put m=60 and (x, y)=(2, 120) in y=mx+c, we get
120=60(2)+c
c=0
Sο, equatiοn is y=60x
Put x=0, 1, 2, 3 and 4, we get
y= 0, 60, 120, 180, 240
(0, 0), (1, 60), (2, 120), (3, 180) and (4, 240)
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Two bags contain white and yellow balls. Bag 1 contains two white balls and four yellow balls. Bag 2 contains four white balls and five yellow balls. A ball is drawn at random from each container. What is the probability that both balls are white?
A. 1/9
B. 1/6
C. 4/27
D. 10/201
Answer:
C. 4/27
Step-by-step explanation:
Let's use the multiplication rule of probability to calculate the probability that both balls drawn are white:
P(white ball from Bag 1) = 2/6 = 1/3
P(white ball from Bag 2) = 4/9
Therefore, the probability of drawing a white ball from each bag is:
P(white from Bag 1 and white from Bag 2) = P(white from Bag 1) * P(white from Bag 2)
= (1/3) * (4/9)
= 4/27
So, the answer is C. The probability that both balls are white is 4/27.
Levi Hempke wants to buy a car costing $21,000. He will finance the pu rchase with an installment loan from the bank, but he would like to finance no more than$14,280. What percent of the car's total cost should his down payment be?
Therefore , the solution of the given problem of percentage comes out to be down payment is 32% of the overall cost of the vehicle.
What is percentage, exactly?In statistics, a% is a number or value that is expressed as a fraction of 100. The terms "pct.," "pct.," but also "pc" are also infrequently used. Nevertheless, the symbol "%" is frequently used to indicate it. The percentage sum is flat; there are no dimensions. Since the numerator of a percentage is always 100, percentages truly constitute integers. Either the percent symbol (%) or the word "percent" must come before a number to denote that it is a percentage.
Here,
Levi Hempke wishes to borrow a maximum of $14,280 to finance a $21,000 vehicle. Consequently, he intends to put down:
=> $21,000 - $14,280 = $6,720
We must divide his down payment by the total cost of the car, multiply by 100 to convert to a percentage, and
then determine the percentage of the total cost of the car that he should put down:
=> ($6,720 ÷ $21,000) × 100 = 32%
Levi's down payment should therefore equal 32% of the overall cost of the vehicle.
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In particular, you will compare the AVERAGE PROFITABILITY for customers with INCOME < 40,000 with customers whose income > = 40,000. Ignore missing values in this analysis (leave them as they are as you complete this analysis and do NOT eliminate records with INCOME missing) and let the EXCEL IF function treat missing values by default. Which of the following is a FIRST STEP towards completing this analysis?
The formulas will calculate the average profitability for customers with income < 40,000 and those with income >= 40,000 respectively.
The first step towards completing the given analysis is to create two groups of customers based on their income levels. The groups should consist of customers with income < 40,000 and those with income > = 40,000. The detailed explanation is provided below:Step-by-step explanation:Here, we need to compare the average profitability of two groups of customers based on their income levels, one with income less than 40,000 and the other with income greater than or equal to 40,000.The first step towards completing this analysis is to create two groups of customers based on their income levels. The groups should consist of customers with income < 40,000 and those with income > = 40,000. This can be achieved using the following steps:1. Open a new Excel workbook and import the dataset that needs to be analyzed.2. Once the data is imported, create a new column named 'Income Group' that will classify customers into the two groups based on their income level. To do this, we can use the following formula: =IF(B2<40000,"<40,000",">=40,000")Here, B2 is the cell that contains the income value of the first customer.3. Drag the formula down to the last cell in the column to apply it to all customers. This will create two groups of customers based on their income levels.4. Now, we need to calculate the average profitability of each group. To do this, we can use the following formula: =AVERAGEIF(C2:C11,"<40,000",D2:D11) and =AVERAGEIF(C2:C11,">=40,000",D2:D11)Here, C2:C11 contains the income group values, D2:D11 contains the profitability values, and "<40,000" and ">=40,000" are the criteria for each group. These formulas will calculate the average profitability for customers with income < 40,000 and those with income >= 40,000 respectively.
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A jar of dimes and quarters contains $2. 55. There are 15 coins in all. How many of each coin are there?
Which term best describes a figure that is made up of two or more shapes?
composite shape
becuse thats what its called
An account with an initial balance of $1250 earns interest that is compounded quarterly. If no other deposits or withdrawals are made, the
account will have a balance of $1406.08 after 9 months. Find the annual interest rate.
Answer:
If no other deposits or withdrawals are made, the account will have a balance of $1406.08 after 9 months. Find the annual interest rate. Expert Answer.
1 answer
·
Top answer:
Given that P=1,250A=1,406.08n=9 month
Step-by-step explanation:
A(n)_is a two-dimensional boundary of a three-dimensional figure
Answer:
429
Step-by-step explanation:
He following data points represent the number of quesadillas each person at Toby's Tacos ate.
Sort the data from least to greatest.
00
0
0
12\dfrac12
2
1
start fraction, 1, divided by, 2, end fraction
00
0
0
11
1
1
12\dfrac12
2
1
start fraction, 1, divided by, 2, end fraction
22
2
2
11
1
1
14\dfrac14
4
1
start fraction, 1, divided by, 4, end fraction
54\dfrac54
4
5
start fraction, 5, divided by, 4, end fraction
22
2
2
11
1
1
Find the interquartile range (IQR) of the data set
To get the interquartile range (IQR) of the data set, we must first determine the median [tex](Q2). 00 0 0 12\dfrac12 2 1 begin fraction,[/tex] divide by 2, end fraction.
[tex]00 0 011 1 1 12\dfrac12 2 1 begin fraction,[/tex]divide by 2, end fraction 22 2 2 11 1 1 14\dfrac14 4 1 begin fraction, divide by 4, end fraction 54\dfrac 5 4 5 end fraction, 5, divided by 4, start fractio When the data is sorted in order, the median is the middle value, thus we must locate the value that is exactly in the centre[tex]0 0 0 11] 1 12\dfrac12 2 1 begin fraction,[/tex] divide by 2, end fraction 22 2 11 1 1 14\dfrac14 4 1 begin fraction, divide by 4, end fraction 54\dfrac54 4 5 end fraction, 5, divided by 4, start fraction The median is (1 + 1)/2 = 1 since the middle two numbers are 1 and 1. The median of the lower half of the data (Q1) and the median of the upper half of the data (Q2) must then be determined (Q3) For the bottom half: 00 0 0 11 1 1 Q1 = 0 since the intermediate value is 0. For the top half: 12\dfrac12.
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An initial investment of $5000 grows at 7% per year. Write the function represents the
value of the investment after t years.
Answer: V(t) = 5000 * (1.07)^t
Step-by-step explanation:
Write a quadratic function for the area of the figure. Then, find the area for the given value of x.
x=6
Answer:
Area = π*r^2
Area = 113.1 units^2
Step-by-step explanation:
The figure drawn is a circle. The ancient Greeks devised an approximation of the area of circles by dividing the circle into a series of small triangles with their peaks at the center of the circle and their bases are formed by the curve of the circle. Although this means there is an error because the circumference is not a straight line, they made the triangles small enough so that the error would be minimized. They found that the area of the circle was related to it's radius by the expression: Area = π*r^2.
Without retracing their steps, let's simply use the formula that is now the accepted measure of the area of a circle. Pi (π) is 3.14 to 3 decimal places. Far more accurate values are known, but 3.14 offers reasonable accuracy, assuming this is not intended for space flight.
Area = π*r^2
Area = 3.34*(6)^2
Area = 113.1 units^2
2. Verify the following identity, using the elementary trigonometric identities you have learned. Carefully lay out all steps in your computation. cos 2θ−cotθsin 2θ−tanθ=tan 2θ
The trigonometric identities cos 2θ − cotθ sin 2θ − tanθ= tan 2θ, is verified below with the help of elementary trigonometric identities.
Describe Trigonometric Identities?Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables in the equation. They are useful in solving trigonometric equations, simplifying expressions involving trigonometric functions, and evaluating integrals in calculus.
There are several types of trigonometric identities, including:
Pythagorean identities: These involve the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The Pythagorean identities express this relationship in terms of trigonometric functions, such as sin²θ + cos²θ = 1.
Reciprocal identities: These involve the reciprocals of trigonometric functions, such as csc θ = 1/sin θ and sec θ = 1/cos θ.
We will start with the left-hand side of the identity and simplify it using the trigonometric identities:
cos 2θ − cotθ sin 2θ − tanθ
= cos 2θ − (cosθ/sinθ)(2sinθcosθ) − (sinθ/cosθ)
= cos 2θ − 2cosθsinθ − sin²θ/cosθ
= cos²θ − sin²θ − 2cosθsinθ − sin²θ/cosθ
= (cos²θ - sin²θ) - (sin²θ/cosθ) - 2cosθsinθ
= cos²θ - sin²θ - sin²θ/cosθ - 2sinθcosθ
= cos²θ - sin²θ - sin²θ/cos²θ - 2sinθcosθ/cos²θ (since cosθ ≠ 0)
= cos²θ - sin²θ - (sin²θ + 2sinθcosθ)/cos²θ
= cos²θ - sin²θ - sin(2θ)/cos²θ
= (cos²θ - sin²θ)/cos²θ - sin(2θ)/cos²θ
= (cos²θ/cos²θ) - (sin²θ/cos²θ) - sin(2θ)/cos²θ
= 1 - tan²θ - sin(2θ)/cos²θ
= (1 - tan²θ) - sin(2θ)/cos²θ
= (sec²θ) - (2sinθcosθ)/cos²θ
= (sec²θ) - (2sinθ/cosθ)
= (sec²θ) - 2tanθ
= tanθ + 1 - 2tanθ - 2tanθ (using the identity sec²θ = tan²θ + 1)
= tan²θ - 4tanθ + 1
= (tanθ - 1)²
= tan²θ - 2tanθ + 1
Therefore, we have shown that:
cos 2θ − cotθ sin 2θ − tanθ = tan 2θ
This verifies the given identity.
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Find the area of the triangle with vertices (10, 1), (7, 11), and (7, 1).
The area of the triangle is 15 square units.
What is area of triangle?The area of a triangle is a measure of the size of the region enclosed by the three sides of the triangle. The formula for finding the area of a triangle depends on the length of its base and height, which are usually denoted by "b" and "h", respectively.
We can find the area of the triangle with vertices (10, 1), (7, 11), and (7, 1) by using the formula for the area of a triangle:
area = (1/2) * base * height
where the base is the distance between the two points with the same y-coordinate, and the height is the distance from the third point to the line that contains the base.
The base is a vertical line segment with length 11 - 1 = 10, since the two points (7, 11) and (7, 1) have the same y-coordinate.
The height is the distance from the point (10, 1) to the line that contains the base. Since the line is vertical and passes through the point (7, 1), the distance is simply the difference between the x-coordinates of the two points: 10 - 7 = 3.
Substituting these values into the formula, we get:
area = (1/2) * 10 * 3
= 15
Therefore, the area of the triangle is 15 square units.
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Brianna bought two pounds of strawberries for 4.80 What is the price of dollars ounce per strawberries 1 pound = 16 ounces
Answer:
There are 16 ounces in 1 pound, so Brianna bought 2 x 16 = <<2*16=32>>32 ounces of strawberries.
The total cost was 4.80 dollars for 32 ounces.
To find the price per ounce, we divide the total cost by the number of ounces:
4.80 / 32 = 0.15
Therefore, the price of dollars per ounce for strawberries is $0.15.
Step-by-step explanation:
as a special case in which the error of the backward euler method can be analyzed directly, we consider the model problem (4.3) again, with x an arbitrary real constant. the backward euler solution of the problem is given by the formula (4.10).
This equation can be used to analyze the error of the backward Euler method directly for the model problem (4.3) with x an arbitrary real constant. The backward Euler method is a numerical method for solving ordinary differential equations (ODEs). It is an implicit method, meaning that it requires the solution of a nonlinear equation at each time step.
The error of the backward Euler method can be analyzed directly for the model problem (4.3) with x an arbitrary real constant. The backward Euler solution of the problem is given by the formula (4.10).
The backward Euler method is given by:
y_n+1 = y_n + h*f(t_n+1, y_n+1)
Where h is the time step, f is the function defining the ODE, t_n is the current time, and y_n is the current solution. The backward Euler method is an implicit method because it requires the solution of the nonlinear equation f(t_n+1, y_n+1) = 0 at each time step.
The error of the backward Euler method can be analyzed directly for the model problem (4.3) with x an arbitrary real constant. The model problem is given by:
y' = x*y
The exact solution of this problem is given by:
y(t) = y_0*exp(x*t)
The backward Euler solution of the problem is given by the formula (4.10):
y_n+1 = y_n/(1 - h*x)
The error of the backward Euler method is given by the difference between the exact solution and the numerical solution:
e_n = y(t_n) - y_n
By substituting the exact solution and the numerical solution into the error equation, we can analyze the error of the backward Euler method directly:
e_n = y_0*exp(x*t_n) - y_n
By rearranging the terms and using the formula for the numerical solution, we can obtain an equation for the error:
e_n = (y_0*exp(x*t_n) - y_n)/(1 - h*x)
This equation can be used to analyze the error of the backward Euler method directly for the model problem (4.3) with x an arbitrary real constant.
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