The rate at which the angle is changing when the angle is 30 degrees is given by the above equation. The specific values of da/dt and db/dt would need to be provided to calculate the numerical value of dθ/dt.
To determine the rate at which the angle is changing when the angle is 30 degrees, we can use the relationship between the rate of change of the area and the rate of change of the angle in a triangle.
Let A be the area of the triangle, and let θ be the angle between the sides of length 8 cm and 12 cm. We are given that the area is changing at a constant rate of 45 sq.m/min. We want to find the rate at which the angle θ is changing, denoted as dθ/dt, when θ is 30 degrees.
The formula for the area of a triangle is A = (1/2) * a * b * sin(θ), where a and b are the lengths of the two sides forming the angle θ.
Differentiating both sides of the equation with respect to time (t), we get:
dA/dt = (1/2) * (da/dt) * b * sin(θ) + (1/2) * a * (db/dt) * sin(θ) + (1/2) * a * b * cos(θ) * (dθ/dt)
Since we know that dA/dt = 45 sq.m/min and a = 8 cm, b = 12 cm, and θ = 30 degrees, we can substitute these values into the equation:
45 = (1/2) * (da/dt) * 12 * sin(30) + (1/2) * 8 * (db/dt) * sin(30) + (1/2) * 8 * 12 * cos(30) * (dθ/dt)
Simplifying and substituting the known values of sin(30) = 1/2 and cos(30) = √3/2, we have:
45 = (1/2) * (da/dt) * 6 + (1/2) * 8 * (db/dt) * 1/2 + (1/2) * 8 * 12 * √3/2 * (dθ/dt)
45 = 3(da/dt) + 2(db/dt) + 24√3(dθ/dt)
15 = (da/dt) + (2/3)(db/dt) + 8√3(dθ/dt)
To find the rate at which the angle θ is changing, we need to solve for dθ/dt. Rearranging the equation, we have:
8√3(dθ/dt) = 15 - (da/dt) - (2/3)(db/dt)
dθ/dt = (15 - (da/dt) - (2/3)(db/dt)) / (8√3)
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write the system first as a vector equation and then as a matrix equation. 5x1 − x2 = 6 7x1 9x2 =
The vector equation is: x1 * (5, 7) + x2 * (-1, 9) = (6, )
- The matrix equation is: | 5 -1 | | x1 | = | 6 | and | 7 9 | | x2 | = | |
To write the given system first as a vector equation and then as a matrix equation, follow these steps:
1. Write the given system of equations:
5x1 - x2 = 6
7x1 + 9x2 =
2. Rewrite the system as a vector equation:
x1 * (5, 7) + x2 * (-1, 9) = (6, )
3. Write the matrix equation:
A * X = B
where A is the matrix of coefficients, X is the matrix of variables, and B is the matrix of constants.
4. Create matrix A using the coefficients of x1 and x2:
A = | 5 -1 |
| 7 9 |
5. Create matrix X using the variables x1 and x2:
X = | x1 |
| x2 |
6. Create matrix B using the constants of the system:
B = | 6 |
| |
So the matrix equation is:
| 5 -1 | | x1 | = | 6 |
| 7 9 | | x2 | = | |
To summarize:
- The vector equation is: x1 * (5, 7) + x2 * (-1, 9) = (6, )
- The matrix equation is: | 5 -1 | | x1 | = | 6 | and | 7 9 | | x2 | = | |
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Caroline spent $63.18 on groceries after using coupons and store discounts. Without the coupons and store discounts, the groceries would have cost $78.00. What is the total discount Caroline received at the grocery store?
Answer:
You're answer would be she saved 14.82 and her discount was 19% off.
Step-by-step explanation:
By my understanding subtracting both 63.18 and 78.00 gives you the amount she saved which is be to exact 14.82 in total
step 1.find the original price
step 2.get the discount percentage
step 3.calculate the savings
step 4.subtract the savings from the original price to get the sale price
step 5.you have your answer.
PLEASE HELP ME ITS REALLY IMPORTANT 30 PTS
The 15 most populous states in the United States have an average population of 14.15 million, with a standard deviation of 8.75 million. Virginia and Washington have populations of 8.38 million and 7.17 million, respectively. Texas and Pennsylvania have z-scores of 1.52 and −0.15, respectively.
Part A: List these four states in order from smallest to largest populations. (4 points)
Part B: Explain your reasoning mathematically and be sure to include all necessary calculations.
Answer:
A.-0.15
1.52
7.17
8.38
8.75
14.15
EASYY ASAPPP!!!!!!
Include 3 examples of each vertical, horizontal, and oblique lines of symmetry that you can find in your house. List them below
Answer:
fridge. door. cabinet. Each line goes from bottom right to top left
Step-by-step explanation:
can someone please help me with this
Step-by-step explanation:
angel on a straight line is 180°
180-140=40°
su=40
st=180-140=40+40=80
Tsu=80
3/10 / p = 4/5 / 1/4
What is the value of people in this proportion?
The value of people in this proportion is equal to 165/10 or 10.67.
What is a proportion?In Mathematics, a proportion can be defined as an equation which is typically used to represent (indicate) the equality of two ratios. This ultimately implies that, proportions can be used to establish that two ratios are equivalent and solve for all unknown quantities.
By applying direct proportion to the given information, we have the following mathematical expression:
3/10/p = 4/5/1/4
3/10 × p = 4/5 × 4
3p/10 = 16/5
Cross-multiplying, we have the following:
15p = 160
People, p = 160/15
People, p = 10.67
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Lin's father is paying for a $20 meal. A 7% sales tax is applied. What does Lin's father pay for the meal
Answer:
$21.40
Step-by-step explanation:
7% is equal to .07
multiply .07 times 20
=1.40
add the $1.40 sales tax to the meal price to get 21.40
f(x)=2x^-6 Find f(7)
Answer: 1/58824.5
Step-by-step explanation: 2x7^-6
2x1/117649
=1/58824.5
The bakers at healthy bakery can make 330 bagels in 5 hours. How many bagels can they bake in 13 hours? what was that rate per hour
Given the homogeneous system of linear equations:
x1 + 2x2 − 2x3 + 2x4 − x5 = 0
x1 + 2x2 − x3 + 3x4 − 2x5 = 0
2x1 + 4x2 − 7x3 + x4 + x5 = 0
4.1. Write out the augmented matrix for the system of equations.
2.2. Solve the system by Gauss elimination method to the augmented matrix and determine a basis and the dimension of the solution space S of the homogeneous system.
The augmented matrix for the system of equations is:
| 1 2 -2 2 -1 | 0 |
| 1 2 -1 3 -2 | 0 |
| 2 4 -7 1 1 | 0 |
A basis for the solution space S is {(-2, 1, 0, 0, 4), (2, 0, 1, 0, -4), (3, 0, 0, 1, -4)}. The dimension of the solution space S is 3, since there are 3 free variables and 3 basis vectors.
To solve the system by Gauss elimination method, we first need to eliminate the x1 term from the second and third equations. To do this, we can subtract the first equation from the second and third equations:
| 1 2 -2 2 -1 | 0 |
| 0 0 1 1 -1 | 0 |
| 0 0 -3 -3 3 | 0 |
Next, we can eliminate the x3 term from the third equation by adding 3 times the second equation to the third equation:
| 1 2 -2 2 -1 | 0 |
| 0 0 1 1 -1 | 0 |
| 0 0 0 0 0 | 0 |
Now, we can see that the third equation is redundant, so we can ignore it. The remaining equations give us:
x1 + 2x2 - 2x3 + 2x4 - x5 = 0
x3 - x4 + x5 = 0
We can solve for x3 and x5 in terms of x1, x2, and x4:
x3 = x4 - x5
x5 = 2x1 + 4x2 - 4x3 - 4x4
Substituting these equations back into the first equation gives us:
x1 + 2x2 - 2(x4 - x5) + 2x4 - (2x1 + 4x2 - 4x3 - 4x4) = 0
Simplifying gives us:
-2x1 - 4x2 + 4x3 + 6x4 = 0
We can solve for x1 in terms of x2, x3, and x4:
x1 = -2x2 + 2x3 + 3x4
Now, we can express the solution space S in terms of the free variables x2, x3, and x4:
S = {(-2x2 + 2x3 + 3x4, x2, x3, x4, 2x1 + 4x2 - 4x3 - 4x4) | x2, x3, x4 ∈ R}
A basis for the solution space S is:
{(-2, 1, 0, 0, 4), (2, 0, 1, 0, -4), (3, 0, 0, 1, -4)}
The dimension of the solution space S is 3, since there are 3 free variables and 3 basis vectors.
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Classify the polynomial 5m^10
Trinomial
Binomial
Monomial
None of these
Answer:
Monomial
Step-by-step explanation:
A polynomial has terms in their equation.
When it is a trinomial, it usually follows the pattern such as x^2+2x+1.
When it is a binomial, it usually is something like x+2
...And finally, when it is a monomial, it can be anything that has just one term. So let's say 4x^8883293483.
The polynomial 5m^10 classifies under a monomial since it only has one term
Let f(x) = sin x and g(x) = x² + 1. Find the following derivatives. d (a) (f(g(x))) (b) = (g(f(x))) dx dx d sin (x²+1) • sin(x²)+1 dx dx = cos(x²+1)(2x)
To find the derivatives of the given expressions, we can apply the chain rule, which states that the derivative of a composition of functions is equal to the derivative of the outer function multiplied by the derivative of the inner function.
(a) To find the derivative of f(g(x)), we start by differentiating the outer function f with respect to the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to x.
df/dx = df/dg * dg/dx
df/dx = cos(g(x)) * (2x)
(b) To find the derivative of g(f(x)), we differentiate the outer function g with respect to the inner function f(x), and then multiply it by the derivative of the inner function f(x) with respect to x.
dg/dx = dg/df * df/dx
dg/dx = 2f(x) * cos(x)
Hence, the derivatives are:
(a) d/dx(f(g(x))) = cos(g(x)) * (2x)
(b) d/dx(g(f(x))) = 2f(x) * cos(x)
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this is a 4 question part which price has the lowest unit per ounce choice a 6 ounces of chocolate chips for $ 2.49 choice b 8 ounces of chocolate chips for $ 3.32 I will ask the other 3 questions soon
For choice (a);
\(\begin{gathered} 6\text{ ounces of chocolate for 2.49} \\ \text{Per ounce=}\frac{2.49}{6} \\ \text{Per ounce=\$0.415} \end{gathered}\)For choice (b);
\(\begin{gathered} 8\text{ ounces of chocolate for 3.32} \\ \text{Per ounce=}\frac{3.32}{8} \\ \text{Per ounce=\$0.415} \end{gathered}\)Both options (a) and (b) have the same price per ounce which is $0.415.
Therefore, none of them is a cheaper option.
An airplane flies 370 miles from point A to point B with a bearing of 24" . It then flies 240 miles from point B to point € with a bearing 0f 37" Draw diagram of the information. Then find the distance from point A to point C and the bearing from point A to point C
The distance from point A to point C and the bearing from point A to point C is 229.5 miles.
Given that:
AB = 370 miles
angle A = 24 degrees
BC = 240 miles
angle B = 37 degrees
To determine the distance from point A to C, we can use the cosine law since we are given two angles and two sides of a regular triangle.
The angle opposite side AC is angle B which is equal to 37 degrees.
(AC)^2 =(AB)^2 + (BC)^2 - 2(AB)(BC)cos(B)
Now we have to solve for AC:
(AC)^2 =(370)^2 + (240)^2 - 2(370)(240)cos(37)
AC = 229.48 miles.
Hence the answer is, the distance from point A to point C and the bearing from point A to point C is 229.5 miles.
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Jess can drive 200 miles on
1/2 tank of gas.
How far can he drive with 3/4 of a tank?
Answer:
300 miles
Step-by-step explanation:
Since Jess can drive 200 miles on a 1/2 of a tank of gas that must mean he can drive 100 miles with his gas tank only 1/4 full. Since he needs to know how far he can drive with his gas 3/4 of the way full he would just add 200 miles to 100 miles and get 300 miles.
You figure this out by dividing 200 miles by 2 since it is a half way full and you just need to half the amount of miles to get how many miles it is for a fourth of the way full. You would need to find out how much it is for a fourth of the way full since it only says Jess can drive 200 miles on a 1/2 tank of gas. However we need to find out how far he can drive with 3/4 tank of gas. Which you know that you need to find out how much it is for a fourth of a tank of gas or 1/4 since 1/2 is also equal to 2/4 and 1/4 plus 2/4 is equal to 3/4.
I hope this helps! If you need any more further help with this question let me know.
All students in Ridgewood Junior High School either got their lunch in the school cafeteria or brought it from home on Tuesday. 5% of students brought their lunch. 49 students brought their lunch. How many students in total are in Ridgewood Junior High School?
Answer:
980
Step-by-step explanation:
A simple way to do this is to do a quick estimate, which I truthfully did.
Since 5% of 1000 is 50, I simply counted back.
5% of 990 is 49.5. Notice the slight change? Use this to your advantage. What would happen if we subtracted 10 from 990, just like we did with 1000? This would be equivalent to removing 0.5 from 49.5.
5% of 980 is 49.
Suppose we apply the Mix Columns operation to a *column* vector [0x19, 0x85, 0x91, 0x02]"
(given with bytes in hex). What are the entries of the resulting column (in decimal)?
The resulting column vector (in decimal) after applying the Mix Columns operation is [50, 283, 313, 4].
The Mix Columns operation in AES (Advanced Encryption Standard) is used to transform the columns of the state matrix in the encryption process. In this case, we are applying the Mix Columns operation to a column vector [0x19, 0x85, 0x91, 0x02].
To perform the Mix Columns operation, we multiply each byte in the column by a fixed polynomial and then take the result modulo x^8 + x^4 + x^3 + x + 1.
Let's go step by step:
1. Multiply 0x19 by 2: 0x19 * 2 = 0x32
2. Multiply 0x85 by 2: 0x85 * 2 = 0x10A. But since this result is greater than 1 byte, we need to reduce it modulo x^8 + x^4 + x^3 + x + 1: 0x10A modulo x^8 + x^4 + x^3 + x + 1 = 0x10A x or 0x11B = 0x11B
3. Multiply 0x91 by 2: 0x91 * 2 = 0x122. Reducing it modulo x^8 + x^4 + x^3 + x + 1, we get: 0x122 modulo x^8 + x^4 + x^3 + x + 1 = 0x122 xor 0x11B = 0x139
4. Multiply 0x02 by 2: 0x02 * 2 = 0x04
Therefore, the resulting column vector (in decimal) after applying the Mix Columns operation is [50, 283, 313, 4].
Please note that this explanation assumes the byte representation is in hexadecimal. Additionally, the multiplication and reduction operations follow specific rules in AES.
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simplify the expression
3x +4 +yxy +7y -10x + 6
Answer:
- 7x + 10 + y² + 7 y
Step-by-step explanation:
Hope this will help
when you reject the null hypothesis that all population means are equal, why do you plot the sample means on a number line?
We plot the means on a number line to see which means are different. Plotting the sample means on a number line serves to illustrate this when the null hypothesis that all population means are equal is rejected.
This criteria, known as (alpha) in null hypothesis testing, is typically set to.05. The null hypothesis is rejected if there is less than a 5% likelihood that a result as dramatic as the sample result would occur if the null hypothesis were true. The outcome is referred to as statistically significant when this occurs.
Plotting scientific data is used to highlight correlations between variables or to visualize variance, but not all data sets need one. If there are only one or two points, it is simple to look at the numbers directly, and adding a graph adds little to nothing.
hence we plot the means on a number line to see which means are different. Plotting the sample means on a number line serves to illustrate this when the null hypothesis that all population means are equal is rejected.
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Amar rakes leaves for his neighbors to earn money. He earned 64 dollars after
8 hours of work.
• How much does Amar make per hour raking leaves?
Answer:
amar makes 8 dollars per hour
Step-by-step explanation:
to find the number of hours of work amar does you have to divide the total amount earned by the number of hours worked
64/8 = 8
every hour amar makes 8 dollars, $8 x 8 hours = $64
What value would you put in
the DENOMINATOR
for this
calibration?
A. 10
B. 5
C. 0.1
D. 1
The value that will be put at the denominator is 10 (optionA)
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
The denominator is the divisor. For example if we have a fraction like 3/5, 3 is the numerator and 5!is the denominator.
Therefore in the above experiment ,the value of the denominator is the no of space between marked value. The number of space between marked value is 10.
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24 and 25 thanks you no links or i report
Answer:
24) D. 5
25) C. $40
Step-by-step explanation:
........
what is the sampling process used on dollar street? in other words, the sample of families on the dollar street page were collected using a sample that is .
The sampling process used on dollar street is stratified sampling.
Given,
Use of dollar street;
Dollar street offers a fresh perspective on families all throughout the world. Every family is arranged down a street, with the wealthiest household on the right and the lowest on the left. Each family's earnings are expressed in US dollars.
Here,
Stratified sampling;
To complete the sampling process, stratified sampling is a form of sampling technique in which the entire population is divided into smaller groups or strata.
Therefore,
Stratified sampling is used in dollar street for sampling process.
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algrebra if8762 a rectangle has a perimeter of 18 cm. its length is 5 cm greater than its width. find the dimensions.
The perimeter of a rectangle is equal to twice the length plus twice the width. Therefore, 18 cm = 2(length + 5) + 2(width). This equation can be solved by subtracting 2(width) from both sides, resulting in 18 - 2(width) = 2(length + 5). Finally, dividing both sides by 2 gives us 9 - width = length + 5. Therefore, width = 4 cm and length = 9 cm.
In this problem, we were given the perimeter of a rectangle, and asked to find its dimensions. We used the formula for the perimeter of a rectangle to set up an equation and solve for the length and width. The width of the rectangle turned out to be 4 cm, and the length was 9 cm, with the length being 5 cm greater than the width.
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"5 more than a number™ translates to an equation.
O
True
M
w
O False
True
5 more than a number is an equation because you are adding two values.
Answer:
n+5
Step-by-step explanation:
If we choose the number to be n then 5 more than is 5 added to the number.
hence: n + 5
What is the first step to solve this equation?
4x +1 = 2x – 5
Answer: I divided but clearly that's not a choice
Step-by-step explanation:
Following are the numbers of hospitals in each of the 50 U. S. States plus the District of Columbia that won Patient Safety Excellence Awards. 1 22 1 9 7 9 0 2 5 2 9 3 6 14 1 2 9 0 5
5 2 3 10 12 6 1 11 0 9 9 5 6 3 2 12 20 12 1 6
12 8 20 3 8 3 11 0 11 3 (a) Construct a dotplot for these data
To construct a dot plot for the given data, follow these steps in RStudio:Make sure to have the ggplot2 package installed and loaded in order to create the dot plot.
Create a vector containing the data:
data <- c(1, 22, 1, 9, 7, 9, 0, 2, 5, 2, 9, 3, 6, 14, 1, 2, 9, 0, 5, 5, 2, 3, 10, 12, 6, 1, 11, 0, 9, 9, 5, 6, 3, 2, 12, 20, 12, 1, 6, 12, 8, 20, 3, 8, 3, 11, 0, 11, 3)
Install and load the ggplot2 package: install.packages("ggplot2")
library(ggplot2)
Create the dot plot:
dotplot <- ggplot(data = data, aes(x = data)) + geom_dotplot(binaxis = "y", stackdir = "center", dotsize = 0.5) + labs(x = "Number of Patient Safety Excellence Awards", y = "Frequency")
Display the dot plot: print(dotplot)
This will create a dot plot with the x-axis representing the number of Patient Safety Excellence Awards and the y-axis representing the frequency of each number in the data. The dots will be stacked in the center and have a size of 0.5. Note: Make sure to have the ggplot2 package installed and loaded in order to create the dot plot.
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Paula bought a ski jacket on sale for $8 less than half its original price. She paid $84 for the jacket. What was the original price?
The original price of the ski jacket is $184.
What is price?
The sum of money paid or the amount of compensation offered by one party to another in exchange for goods or services is known as a price. The cost of production can take on different names depending on the circumstance. If the item is a "good" in a commercial transaction, the cost of the item will probably be referred to as its "price".
Given:
Paula bought a ski jacket on sale for $8 less than half its original price.
She paid $84 for the jacket.
We have to find the original price of the ski jacket.
Let
The original price = x
The amount she bought it = x/2 - 8
She paid $84 for the jacket
Therefore,
84 = x/2 - 8
Add 8 on both sides,
84 + 8 = x/2 - 8 + 8
92 = x/2
x = 184
Hence, the original price of the ski jacket is $184.
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let z be a standard normal variable. find the value of z if z satisfies p(z < z) = 0.9525.a. 1.60b. -1.67c. -2.00d. -1.60e. 1.67f. None of the above
The question is asking for the value of z that satisfies the probability that a standard normal variable z is less than z to be 0.9525. In other words, we want to find the z-score that corresponds to the 95.25th percentile of the standard normal distribution. Option (b) is the closest to the correct answer (-1.67). However, this could be due to rounding errors or differences in the table used. Therefore, the correct answer is (f) None of the above.
To solve this problem, we can use a standard normal distribution table or a calculator with a normal distribution function. Using a standard normal distribution table, we can look up the closest value to 0.9525 in the body of the table, which is 0.9515. The corresponding z-score is 1.65.
However, since the table only gives us values for the area to the left of a positive z-score, we need to subtract 1.65 from 0 (the mean of the standard normal distribution) to get the z-score that corresponds to the 95.25th percentile on the left tail. Therefore, the answer is -1.65. So none of above is correct.
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in goal programming, deviation variables allow for the possibility of not meeting the target value exactly.
T/F
It is true that in goal programming, deviation variables allow for the possibility of not meeting the target value exactly.
In goal programming, deviation variables are used to measure the deviation or distance from the target values or goals for different objectives. These deviation variables allow for the possibility of not meeting the target value exactly, as they represent the degree of deviation from the desired goals.
Goal programming recognizes that in real-world situations, it may not always be possible or practical to achieve the target values exactly due to various constraints or limitations. Therefore, deviation variables are introduced to capture the extent to which the objectives can deviate from their targets, allowing for a more realistic representation of the decision-making process.
By minimizing the deviations or finding a solution that minimizes the overall deviations from the goals, goal programming seeks to find the best compromise or trade-off between conflicting objectives while considering the flexibility of not meeting the target values exactly.
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