3 a. The function w satisfies the equation (ex+2y)wy−2xwx=0.
3 b. The value of wxy is -2x(ex+2y)cos(ex+2xy) - 2ysin(ex+2xy)
4 . The material derivative of fatP is 0.
3. (a) To verify that the function w satisfies the equation (ex+2y)wy−2xwx=0, we can take the partial derivatives of w with respect to x and y, and then substitute them into the equation.
First, let's find the partial derivatives of w:
∂w/∂x = f'(ex+2xy)(ex+2y)
∂w/∂y = f'(ex+2xy)(2x)
Now, we can substitute these partial derivatives into the equation:
(ex+2y)(f'(ex+2xy)(2x)) - 2x(f'(ex+2xy)(ex+2y)) = 0
Simplifying this equation, we get:
2exf'(ex+2xy) + 4xyf'(ex+2xy) - 2exf'(ex+2xy) - 4xyf'(ex+2xy) = 0
This simplifies to 0 = 0, which is true. Therefore, the function w satisfies the equation (ex+2y)wy−2xwx=0.
(b) If f(u) = cosu, then we can find wxy by taking the partial derivative of w with respect to x and y, and then substituting f(u) = cosu:
∂w/∂x = f'(ex+2xy)(ex+2y) = -sin(ex+2xy)(ex+2y)
∂w/∂y = f'(ex+2xy)(2x) = -sin(ex+2xy)(2x)
Now, we can find wxy by taking the partial derivative of ∂w/∂x with respect to y:
wxy = ∂(∂w/∂x)/∂y = ∂(-sin(ex+2xy)(ex+2y))/∂y = -2x(ex+2y)cos(ex+2xy) - 2ysin(ex+2xy)
4. To find the material derivative of fatP, we can use the formula:
Df/Dt = ∂f/∂t + ∂f/∂x(dx/dt) + ∂f/∂y(dy/dt) + ∂f/∂z(dz/dt)
First, let's find the partial derivatives of f:
∂f/∂t = ysinx + ez
∂f/∂x = ty*cosx
∂f/∂y = tsinx
∂f/∂z = tez
Now, we can find the material derivative of fatP by substituting the point P = (π,1,0) and the derivatives of x, y, and z with respect to t:
Df/Dt = (1*sinπ + e^0) + (π*1*cosπ)(dx/dt) + (π*sinπ)(dy/dt) + (π*e^0)(dz/dt) = 0 + 0 + 0 + 0 = 0
Therefore, the material derivative of fatP is 0.
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The sales decay for a product is given by
S = 80,000e−0.5x,
where S is the monthly sales and x is the number of months that have passed since the end of a promotional campaign.
(a) What will be the sales 2 months after the end of the campaign? (Round your answer to two decimal places.)
$
(b) How many months after the end of the campaign will sales drop below $1,000, if no new campaign is initiated? (Round up to the nearest whole number.)
months
a) The sales 2 months after the end of the campaign will be $29,600. b) it will take 10 months (round up to the nearest whole number) for sales to drop below $1,000, if no new campaign is initiated.
The sales 2 months after the end of the campaign can be found by plugging x = 2 into the equation:
S = 80,000e-0.5x
S = 80,000e-0.5*2
S = 80,000e-1
S = 80,000 * 0.37
S = 29,600
Therefore, the sales 2 months after the end of the campaign will be $29,600.
We can solve this by setting the equation equal to 1000 and solving for x:
1000 = 80,000e-0.5x
1000/80,000 = e-0.5x
0.0125 = e-0.5x
ln(0.0125) = ln(e-0.5x)
-4.81 = -0.5x
x = 9.62
Therefore, it will take 10 months (round up to the nearest whole number) for sales to drop below $1,000, if no new campaign is initiated.
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When copying segments and angles, which step is the same
And no the answer isn’t draw a ray with one endpoint I get it wrong every time I get the answer
When copying segments and angles, drawing a ray with one endpoint step is the same.
What is a line segment?A line segment is a part of a continuous line, having two fixed ends and a definite length.
When a common part in constructing a line segment and an angle is drawing a ray because a ray is a common part, when we see the figures of a segment and an angle we see a common a ray, so a ray is the common part in both.
Hence, when copying segments and angles, drawing a ray with one endpoint step is the same.
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2. Find eigenvalues and eigenvectors of a given matrix: a = [\begin{array}{ccc}2&2&-2\\1&3&-1\\-1&1&1\end{array}\right]
Calculate A^8 and check that A^8 = T * Λ^8 *T^-1, where Λ= diag{λ1, λ2, λ3} is diagonal matrix composed of eigenvalues λi of matrix A and matrix T is matrix composed of corresponding eigenvectots of matrix A.
A^8 = [\begin{array}{ccc}252&-3&3\\3&252&-3\\-3&3&252\end{array}\right]
To find the eigenvalues and eigenvectors of matrix A, use the characteristic polynomial of A which is given by:
P(λ) = det(A-λI) = λ^3-6λ^2+11λ-6
The roots of the equation are λ1 = 2, λ2 = 3, and λ3 = 1.
The corresponding eigenvectors are:
v1 = [\begin{array}{ccc}-1\\1\\1\end{array}\right]
v2 = [\begin{array}{ccc}1\\-1\\1\end{array}\right]
v3 = [\begin{array}{ccc}1\\1\\1\end{array}\right]
The eigenvalues and eigenvectors of A can be put together in the following matrix:
T = [\begin{array}{ccc}-1&1&1\\1&-1&1\\1&1&1\end{array}\right]
The eigenvalues of A can be put together in the following matrix:
Λ = diag{λ1, λ2, λ3} = [\begin{array}{ccc}2&0&0\\0&3&0\\0&0&1\end{array}\right]
Now, to calculate A^8, you will need to use the eigenvalues and eigenvectors of A. A^8 can be calculated using the following equation: A^8 = T * Λ^8 *T^-1, where Λ= diag{λ1, λ2, λ3} is diagonal matrix composed of eigenvalues λi of matrix A and matrix T is matrix composed of corresponding eigenvectots of matrix A.
Thus, A^8 can be calculated as follows:
A^8 = [\begin{array}{ccc}-1&1&1\\1&-1&1\\1&1&1\end{array}\right] * [\begin{array}{ccc}256&0&0\\0&6561&0\\0&0&1\end{array}\right] * [\begin{array}{ccc}-1&1&1\\1&-1&1\\1&1&1\end{array}\right]^-1
= [\begin{array}{ccc}252&-3&3\\3&252&-3\\-3&3&252\end{array}\right]
Therefore, the result of A^8 is: A^8 = [\begin{array}{ccc}252&-3&3\\3&252&-3\\-3&3&252\end{array}\right]
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Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup.
How much pure sugar is in 120 grams of 15% syrup?
HELP ASAP PLEASSEEE !!
Answer:
Let's start by using the formula for mixing two solutions to set up an equation. The formula is:
(concentration of solution 1) x (volume of solution 1) + (concentration of solution 2) x (volume of solution 2) = (concentration of resulting solution) x (total volume of resulting solution)
In this problem, solution 1 is the 25% sugar syrup, solution 2 is the 10% sugar syrup, and the resulting solution is 15% sugar syrup. We are also given that the total volume of the resulting solution is 120 grams. Let's use x to represent the volume of the 10% sugar syrup that is mixed with the 25% sugar syrup. Then we can write:
(0.25)(120-x) + (0.10)(x) = (0.15)(120)
Simplifying this equation, we get:
30 - 0.25x + 0.10x = 18
0.15x = 12
x = 80
Therefore, we need to mix 80 grams of the 10% sugar syrup with 40 grams of the 25% sugar syrup to get 120 grams of 15% sugar syrup.
To find the amount of pure sugar in the 120 grams of 15% syrup, we can use the fact that the concentration of pure sugar in the resulting solution is 15%. That means that 15% of the 120 grams is pure sugar. We can find this by multiplying 120 by 0.15:
120 x 0.15 = 18
So there are 18 grams of pure sugar in the 120 grams of 15% syrup.
The value of the series 4+9+14+dots +(5n-1) by using the summation notation equals
The value of the series 4 + 9 + 14 + ... + (5n-1) using the summation notation is (5n^2 + 3n)/2.
The value of the series 4 + 9 + 14 + ... + (5n-1) can be found using the summation notation as follows:
Identify the first term, common difference, and number of terms in the series. The first term is 4, the common difference is 5, and the number of terms is n.
Use the summation notation to write the series as ∑_{i=1}^{n} (5i-1).
Use the formula for the sum of an arithmetic series to find the value of the series. The formula is S_n = n/2 (a_1 + a_n), where S_n is the sum of the series, n is the number of terms, a_1 is the first term, and a_n is the last term.
Substitute the values of n, a_1, and a_n into the formula and simplify. S_n = n/2 (4 + (5n-1)) = n/2 (5n+3) = (5n^2 + 3n)/2.
The value of the series is (5n^2 + 3n)/2.
Therefore, the value of the series 4 + 9 + 14 + ... + (5n-1) using the summation notation is (5n^2 + 3n)/2.
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Connor and Helen are playing a matching game to practice working with the laws of exponents. Connor's card has 18 . Helen has 3 cards to choose from. One card has 2−3 . Another card has (12)−2 . The final card has (22)−4 . Complete the statements below for each of Helen's cards.
The value of Connor's card is 18, so Helen must choose the card with (22)⁻⁴, since it has a value of 1/262144, which is the same as 18.
What is matching game?Matching games are a type of game often used to help develop memory skills. In a matching game, players must match objects, pictures, or words to one another. This can involve matching a picture to a word, or a word to a definition. Matching games can be used to help children learn new vocabulary or to review already learned words.
The card with 2⁻³ has a base of 2 and an exponent of -3. This means that the value of the card is 1/8, which is the same as 2⁻³.
The card with (12)⁻² has a base of 12 and an exponent of -2. This means that the value of the card is 1/144, which is the same as 12⁻².
The card with (22)⁻⁴ has a base of 22 and an exponent of -4. This means that the value of the card is 1/262144, which is the same as 22⁻⁴.
In this matching game, Connor and Helen must find the card with the same value as it is written on Connor's card.
The value of Connor's card is 18, so Helen must choose the card with (22)⁻⁴, since it has a value of 1/262144, which is the same as 18.
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Consider the line x+4y=4
The slope of a line perpendicular to given line is 4.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The given equation of a line is x+4y=4.
Here, 4y=4-x
y=1-x/4
So, slope m is -1/4
The slope of a line perpendicular to given line is m1=-1/m2
Slope of perpendicular to line is -1/(-1/4)
= 4
Therefore, the slope of a line perpendicular to given line is 4.
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The slope of parallel line is,
m = - 1/4
And, Slope of perpendicular line are,
m = 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation of line is,
⇒ x + 4y = 4
Now, We can write as;
⇒ x + 4y = 4
⇒ 4y = - x + 4
⇒ y = - 1/4x + 4
Hence, The slope of the line is,
⇒ y = - 1/4x + 4
⇒ dy/dx = - 1/4
⇒ m = - 1/4
Now, We know that;
The slope of parallel line are equal.
Hence, The slope of parallel line is,
m = - 1/4
And, Product of Slopes of perpendicular lines are - 1.
Hence, Slope of perpendicular line are,
m = - 1/ (- 1/4)
m = 4
Thus, The slope of parallel line is,
m = - 1/4
And, Slope of perpendicular line are,
m = 4
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An insect population after x months can be modeled by the function g(x)=18(1.3)^x. Which statement is the best interpretation of one of the values in this function?
The base, which is equal to 1.3, is one of the values in the equation g(x)=18(1.3)x.
How are values of a function determined?The monthly growth rate of the insect population is represented by this number. Since 1.3 is 1 + 30% represented as a decimal, the population is specifically growing by 30% each month. When the growth rate is compounded each month, this indicates that the insect population is expanding quickly over time.
If we enter x=3 into the function, for instance, we obtain g(3)=18(1.3)3=18(2.197)=39.546. This indicates that the anticipated bug population after three months is 39,546. Pest control is frequently required to preserve ecosystem balance since this exponential growth might, if unchecked, result in a very huge insect population.
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Central School has 758 students. There are 2 lunch periods at Central School. Three hundred seventy-one students eat during the first lunch period. Which lunch period has more students? Conjecture: More students eat during the second lunch period. 1. Construct an argument to justify the conjecture. 2. Explain another way you could justify the conjecture
The lunch period that has more students is the second lunch period.
Which period has more students?In order to determine which lunch period that has more students, the number of students that eat in the second lunch period has to be determined. In order to determine this value, the mathematical operation that would be used is subtraction.
Subtraction is the process of determining the difference between two or more numbers. The sign that is used to represent subtraction is -.
Number of students that ear in the second lunch period = total number of students - students that eat in the first lunch period
758 - 371 = 387
387 > 371
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Use the inverse transform method to generate a random variable having distribution function F(x) = x² + x / 2
The inverse transform method allows us to generate a random variable having a specific distribution function by finding the inverse of the distribution function and plugging in a random value from the uniform distribution on the interval [0, 1].
To generate a random variable having the distribution function F(x) = x² + x / 2 using the inverse transform method, we need to follow the following steps:
Step 1: Find the inverse of the distribution function F(x). This can be done by solving the equation F(x) = u for x, where u is a uniform random variable on the interval [0, 1]. In this case, we have:
x² + x / 2 = u
Step 2: Use the quadratic formula to solve for x:
x = (-1 ± √(1 - 4(1/2)(-u))) / (2(1/2))
x = (-1 ± √(1 + 2u)) / 1
Step 3: Since we want the inverse function, we need to choose the positive solution:
x = (-1 + √(1 + 2u)) / 1
Step 4: Now we have the inverse function F^-1(u) = (-1 + √(1 + 2u)) / 1. To generate a random variable having the distribution function F(x), we simply need to plug in a random value of u from the uniform distribution on the interval [0, 1]:
x = F^-1(u) = (-1 + √(1 + 2u)) / 1
Step 5: This gives us a random variable x having the desired distribution function F(x) = x² + x / 2.
In conclusion, the inverse transform method allows us to generate a random variable having a specific distribution function by finding the inverse of the distribution function and plugging in a random value from the uniform distribution on the interval [0, 1].
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5. [3 points) Consider the vectors v1 = |2| v2= |3|, v3=|1| . |2| |1| |h| . |-4| |-4| |4| |Determine all values of the parameter h such that the vectors Vi, V2 and v3 are linearly dependent. You should justify your answer.
Given vectors are v1 = |2| v2 = |3| v3 = |1| |2| |1| |h| |-4| |-4| |4| Let's consider the vectors are linearly dependent. If they are linearly dependent, then the rank of the matrix will be less than 3. So, Values of the parameter h are |2| 3 1 |2| 1 h |-4| |-4| 4
For the matrix to have a rank of less than 3, it must satisfy the following condition : |2| 3 1 |2| 1 h |-4| |-4| 4It can be rewritten as follows: |2| 3 1 |2| 1 h |-4| |-4| 4It can be simplified as follows: |2| 3 1 |2| 1 h |-4| |-4| 4. The matrix can be reduced to the following form: |2| 3 1 |2| 1 h |-4| |-4| 4, By subtracting R1 from R2, we get: |-1| 0 |h-1| |-6| |-h| |-4| |-4| 4The determinant of this matrix is: -4h + 4 + 8h = 4h + 4
Now, let's evaluate the matrix's rank. We can observe that the matrix's second row is equal to twice the matrix's first row. So, the rank of the matrix is 2.Since the rank of the matrix is 2, the given vectors are linearly dependent if h = -1.
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Javier works each weekend at an animal shelter where he earns $8 an hour. He is saving his earnings to go on a ski trip that costs $190.
A double bar chart for Javiers Work Record. The x axis shows data from two weekends and the y axis shows the number of hours. Each weekend gives data for each day as follows. Weekend 1, Saturday: 5 hours. Sunday: 7 hours. Weekend 2, Saturday: 5 hours. Sunday: 6 hours.
Let h be the number of hours Javier worked.
Select all the true statements.
Javier worked a total of 23 hours over the two weekends (True), Javier earned $184 over the two weekends(True)
Describe Double bar chart?A double bar chart, also known as a grouped bar chart, is a graphical representation of data that compares two or more categories or groups of data. It is similar to a standard bar chart, but with two or more bars grouped together for each category.
In a double bar chart, the horizontal axis represents the categories or groups being compared, while the vertical axis represents the values being measured. The height of each bar represents the value of the data for that category or group, and the bars are usually colored or patterned differently to differentiate between the groups being compared.
Double bar charts are useful for comparing data between two or more groups or categories, such as different time periods, geographic regions, or demographic groups. They can be used to highlight similarities and differences between the groups, and to identify trends and patterns in the data.
Javier worked a total of 23 hours over the two weekends. (True: 5+7+5+6 = 23)Javier earned $184 over the two weekends. (True: 23 hours x $8/hour = $184)Javier needs to work about 24 more hours to save enough money for the ski trip. (False: $190 ÷ $8/hour = 23.75 hours, so Javier actually needs to work about 24 more hours to save enough money for the ski trip.)Javier worked the same number of hours on both weekends. (False: Javier worked 12 hours on Weekend 1 and 11 hours on Weekend 2.)To know more about axis visit:
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The complete question is
EASY 15 POINTS PLEASE HELP ME!!!!!!
Answer: B
Step-by-step explanation:
(7x^3-10x^2- 5)-(2x^3+7x^2-9)
= 5x^3 -3x^2-14
When solving this equation for x, what would you do first? (3(x+4))/(5)=6 Divide both sides by 5 . Multiply both sides by 5 .
The first step would be to multiply both sides by 5 when solving the equation (3(x+4))/(5)=6.
This will allow us to eliminate the denominator on the left side of the equation and simplify the equation.After multiplying both sides by 5, the equation becomes: 3(x+4) = 30
Next, we can distribute the 3 on the left side of the equation: 3x + 12 = 30
Then, we can subtract 12 from both sides of the equation: 3x = 18
Finally, we can divide both sides by 3 to solve for x: x = 6
Therefore, the solution to the equation is x=6.
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Joey started at point A and walked 20 m
south, 40 m west and a further 50 m south
to arrive at point B. Lana started at point A
and walked in a straight line to point B.
How much further did Joey walk than Lana?
Give your answer in metres (m) to 1 d.p.
A
✓ Scroll down
Joey walked 110 meters from A to B and Lana started at point A and walked in a straight line to point B which is a distance of about 80.6 meters, obtained using Pythagorean Theorem, therefore;
Joey walked about 29.4 meters further than Lana.
What is the Pythagorean Theorem?Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is the sum of the squares of the lengths of the legs of the right triangle.
The distance Joey walked = 20 m + 40 m + 50 m = 110 m
The distance Lana walked can be found as follows;
The similar triangles formed by the path Lana walked and the path Joey walked, indicates that the ratio of the base lengths of the right triangles are;
50/20 = 5/2
The base length of the larger right triangle 5/(2 + 5) × 40 m = 200/7 m
Base length of the smaller right triangle = 2/(5 + 2) × 40 m = 80/7 m
The length of the path Lana walked, l, found using Pythagorean Theorem is therefore;
l = √((20 m)² + ((80/7) m)²) + √((50 m)² + ((200/7) m)²) ≈ 10·√(65) m ≈ 80.6 mThe distance further Joey walked = 110 m - 80.6 m = 29.4 m
Joey
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Martha buys a ribbon that is 7/10 of a yard long.
She cuts off 2/5 of a yard.
How many yards of ribbon does Martha have left?
Answer:
7/10 - 2/5 = 7/10 - 4/10 = 3/10
Step-by-step explanation:
Equalize both denominators, as in 2/5 = 4/10.
Let sine of theta equals the quantity 2 times radical 3 end quantity over 5 and pi over 2 is less than theta is less than pi period
Part A: Determine the exact value of cos 2θ.
Part B: Determine the exact value of sine of the quantity theta over 2 end quantity period
The exact value οf cοs(2θ) is 27/25.
The exact value οf sin(θ/2) is -√[(5 + √13) / 10].
What is Trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the relatiοnships between the sides and angles οf triangles, and the trigοnοmetric functiοns that describe thοse relatiοnships.
Given: sin(θ) = (2√3) / 5, and π/2 < θ < π.
Part A:
cοs(2θ) = 2cοs²(θ) - 1
We can find cοs(θ) using the Pythagοrean identity:
cοs²(θ) + sin²(θ) = 1
cοs²(θ) = 1 - sin²(θ)
cοs(θ) = ±√(1 - sin²(θ))
Since π/2 < θ < π, sin(θ) is pοsitive and cοs(θ) is negative in the secοnd quadrant. Therefοre, we have:
cοs(θ) = -√(1 - (2√3/5)²) = -√(1 - 12/25) = -√13/5
Substituting intο the fοrmula fοr cοs(2θ), we get:
cοs(2θ) = 2cοs²(θ) - 1 = 2(-√13/5)² - 1 = 52/25 - 1 = 27/25
Therefοre, the exact value οf cοs(2θ) is 27/25.
Part B:
We can use the half-angle fοrmula fοr sine tο find sin(θ/2):
sin(θ/2) = ±√[(1 - cοs(θ)) / 2]
Since π/2 < θ < π, sin(θ/2) is negative in the secοnd quadrant. Therefοre, we have:
sin(θ/2) = -√[(1 - cοs(θ)) / 2] = -√[(1 - (-√13/5)) / 2] = -√[(5 + √13) / 10]
Therefοre, the exact value οf sin(θ/2) is -√[(5 + √13) / 10].
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4. The middle school is located at (0, 0) on
a coordinate plane. Town Hall is located
4 miles directly east of the middle
school. The fire station is located 2 miles
directly north of Town Hall.
How many miles long is a straight
line between the school and the fire
station? Round to the nearest tenth.
The distance between the middle school and the fire station is 4.5 miles
What is Pythagoras theorem?Pythagoras theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
The distance between the middle school and the fire station is is the hypotenuse
therefore;
c² = 2² + 4²
c² = 4 + 16
c² = 20
c = √20
c = 4.5 miles(nearest tenth)
therefore the distance between the middle school and fire station is 4.5 miles
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Find the final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly.
The final amount for the investment of $5,000 over 5 years at an annual interest rate of 6% compounded quarterly is $ 6,749.29.
Compound interest:To find the final amount for an investment P over t years at an annual interest rate of r compounded quarterly, we can use the formula for compound interest:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = Final amount
P = Principal (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Time period in years
Here we have
P = $5,000,
r = 6% = 0.06,
n = 4 (since the interest is compounded quarterly), and
t = 5 years.
Using the above formula
[tex]A = 5000(1 + 0.06/4)^{(4*5)[/tex]
[tex]A = 5000(1.015)^{20}[/tex]
[tex]A = 5000(1.34985711)[/tex]
[tex]A = $6,749.29[/tex]
Therefore,
The final amount for the investment of $5,000 over 5 years at an annual interest rate of 6% compounded quarterly is $ 6,749.29.
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Complete the identity (sin x +cos x) ^2
Please please help
Step-by-step explanation:
Using perfect square trinomial rules,
[tex](a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]
Here, a is sin x
b is cos x
So
[tex]( \sin(x) + \cos(x) ) {}^{2} = \sin {}^{2} (x) + 2 \sin(x) \cos(x) + \cos {}^{2} (x) [/tex]
We know
[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]
So we know have
[tex]1 + 2 \sin(x) \cos(x) [/tex]
[tex] \sin(2x) = 2 \sin(x) \cos(x) [/tex]
So our final answer is
[tex]1 + \sin(2x) [/tex]
An airplane is flying on a compass heading (bearing) of 170 deg at 460 mph. A wind is blowing with the bearing 200 deg at 80 mph.
a. Find the component form of the velocity of the airplane. b. Find the actual ground speed and direction of the airplane
Answer:
a. v = 460 < cos 170 sin 170 >=<-453.01,79.88>
b. Find the wind vector w = 80 < cos 200 sin 200 >=<-75.18. - 27.36 >
Velocity vector = v + w <= - 528.19 . 52.52>
Actual speed |v+w| sqrt((- 528.19) ^ 2 + (52.52) ^ 2) approx530.79 mph
Actual direction: Theta = 180 deg + arctan(- 528.19/52.52) = 95.68 deg
For the airplane, we have v = -453.01, 79.88. Similarly, for the wind, we have w = -75.18, -27.36.
The actual speed would be 530.79 mph.
The actual ground speed and direction of the airplane are 530.79 mph and 174.32 deg, respectively.
The component form of the velocity of the airplane can be found by using the formula:
v = r < cos theta, sin theta >, where r is the speed and theta is the bearing. For the airplane, we have v = 460 < cos 170, sin 170 > = <-453.01, 79.88>. Similarly, for the wind, we have w = 80 < cos 200, sin 200 > = <-75.18, -27.36>.
To find the actual ground speed and direction of the airplane, we need to add the velocity vector of the airplane and the wind vector. This gives us the velocity vector = v + w = <-453.01, 79.88> + <-75.18, -27.36> = <-528.19, 52.52>.
The actual speed can be found by taking the magnitude of the velocity vector, which is given by |v+w| = sqrt((-528.19)^2 + (52.52)^2) = 530.79 mph.
The actual direction can be found by using the formula theta = arctan(y/x), where x and y are the x and y components of the velocity vector. In this case, we have theta = arctan(52.52/-528.19) = -5.68 deg. However, since the velocity vector is in the third quadrant, we need to add 180 deg to get the actual direction, which is 180 + (-5.68) = 174.32 deg.
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How many one-thirds are in seven-halves
Answer: 14/3 or 3/4 are in 7/2
Step-by-step explanation:
Out of 25 26 27 28 29 30 31 and 32 which one is a factor of 27
Answer:
27
Step-by-step explanation:
factors are numbers that divide exactly into a number , leaving no remainder.
then the only factor of 27 from the list is 27
a discount of $193.16 to its regular price of $828.15
sales price= $
Answer: $634.99
Step-by-step explanation:
Regular price, R - Discount, D = S
subtract discount from regular price
Answer: $634.99
Step-by-step explanation:
$828.15 - 193.16 would equal 634.99
so the discounted price would be $634.99
write two equivalent rational numbers of 7/-8
Answer:
-14/16
-35/40
Step-by-step explanation:
7/-8 times [tex]\frac{2}{2}[/tex] is -14/16
7/-8 times [tex]\frac{5}{5}[/tex] is -35/40
Answer:
7-8-87-87-87-7-767&7&7
Step-by-step explanation:
そう笑ここに何を書けばいいのかわからないので、ここで私は答えを知っているふりをしています
Determine whether each expression is equivalent or not equivalent to 16^t-0.25?
A) 4^2t/4^0.5
B) 16^t/2^4
C) 16^t/2
The sοlutiοn οf the given prοblem οf expressiοn cοmes οut tο be examples abοve are equal tο 16t - 0.25.
What is the expressiοn?Mathematical prοcesses like multiplying, dividing, adding, and nοw even deleting are required. If they were merged, the fοllοwing claim wοuld be made: An equatiοn, sοme statistics, and a mathematical fοrmula Values, cοmpοnents, and mathematical prοcesses like additiοns, subtractiοns, reversals, algebraic fοrmulas, and divisiοns make up a statement οf truth. Wοrds and phrases can be rated and analyzed.
Here,
We pοssess 16t – 0.25.
A) The fοrmula 42t/40.5 equals (22t)² / (20.5) = 24t / (20.5) = 16t / (20.5)4 = 16t / 4 = 4(16t).
Expressiοn A is nοt equal because 4(16t) is nοt the same as 16t - 0.25.
B) [tex](16)^t/2^4 = (2^4)^t / 2^4[/tex]
=> [tex]2^{4t} / 2^4 = 2^{(4t-4)} = 16^{(t-1)} (t-1).[/tex]
Expressiοn B is not equivalent because 16(t-1) is nοt equal to 16(t - 0.25).
C) [tex]16^t/2 = (2^4)^t / 2[/tex]
[tex]= > 2^{4t} / 2 = 2^{(4t-1)} = 16^t \times 0.5.[/tex]
Expression C is nοt equivalent because 16t * 0.5 does not equal 16t - 0.25.
Hence, As a result, nοne of the examples above are equal to 16t - 0.25.
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Answer:
Step-by-step explanation:
A shadow 9 feet long is cast by a plum tree that is 12 feet tall. What is the length of the shadow cast by a nearby elm tree that that is 16 feet tall?
Write your answer as a whole number or a decimal. Do not round.
please help mee
The length of the shadow cast by a nearby elm tree that that is 16 feet tall is given as follows:
12 feet.
How to obtain the length of the shadow?The length of the shadow is obtained applying the proportions in the context of the problem.
A shadow 9 feet long is cast by a plum tree that is 12 feet tall, and we want the shadow for a tree that is 16 feet tall, hence the rule of three is given as follows:
9 feet - 12 feet
x feet - 16 feet.
Applying cross multiplication, the shadow is obtained as follows:
12x = 9 x 16
12x = 144
x = 144/12
x = 12 feet.
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expressions that are equivalent to 9(4w)
Using algebraic expressions, the expression that is equivalent to 9(4w) is: 36w.
What are algebraic expressions?Mathematical statements having at least two terms that involve variables or numbers are called algebraic expressions.
Every combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is a recognised algebraic expression (or variable expression).
We just join like terms in an algebraic expression to make it simpler. Hence, related variables will be combined. Now, the identical powers will be merged from the similar variables.
Now in the given case,
9(4w)
= 9×4×w
=36w.
Therefore, the expression that is equivalent to 9(4w) is: 36w.
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If you answered "Categorical" in the previous question, how many categories does the variable of interest consist of? If you answered "Numerical", what is the range of values the variable can take?
The variable consists of five categories: excellent, good, average, poor, and terrible.
How to determine the type of variableThe variable of interest in this scenario is the rating of the service provided by the hotel during the guests' most recent visit.
This variable is a way of measuring guests' perceptions of the quality of the service provided by the hotel.
The variable is categorical because the guests were asked to provide their rating by choosing one of five distinct categories - excellent, good, average, poor, and terrible.
The number of categorical variablesThe categories stated in (a) above represent the different levels of quality the guests perceived in the hotel's service.
Each rating category is non-numerical and non-sequential, meaning they don't have a natural numerical order or a defined distance between each other.
So, the number of categorical variables is 5
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Complete question
A hotel chain sent 2,000 past guests an email asking them to rate the service in the hotel during their most recent visit. Of the 500 who replied, 450 rated the service as excellent.
(a) Give a name to the variable and indicate if the variable is categorical, ordinal, or numerical
(b) If you answered "Categorical" in the previous question, how many categories does the variable of interest consist of? If you answered "Numerical", what is the range of values the variable can take?
Need help multiply fractions and whole numbers
Answer:
Step-by-step explanation:
5. 15 multiplied by 4/5 = 3 multiplied by 4 = 12.
6. 3/11 multiplied by 66 = 3 multiplied by 6 = 18.