The Variation of Parameters is a method used to find a particular solution for ordinary differential equations (ODES). The method involves finding the general solution to the homogeneous equation and then using that to find a particular solution to the non-homogeneous equation.
For the given ODES:
(a) y" - 2y' + y = et^2
First, we need to find the general solution to the homogeneous equation y" - 2y' + y = 0. The characteristic equation is r^2 - 2r + 1 = 0, which has a repeated root r = 1. Therefore, the general solution to the homogeneous equation is yh = c1e^t + c2te^t.
Next, we use the Variation of Parameters to find a particular solution. We assume that the particular solution has the form yp = u1e^t + u2te^t, where u1 and u2 are functions of t. We then find the first and second derivatives of yp and substitute them into the original equation. After simplifying, we obtain a system of equations for u1' and u2'. We solve for u1' and u2' and then integrate to find u1 and u2. Finally, we substitute u1 and u2 back into the equation for yp to find the particular solution.
(b) y" + y = sec(x)
Similarly, we first find the general solution to the homogeneous equation y" + y = 0. The characteristic equation is r^2 + 1 = 0, which has complex roots r = i and r = -i. Therefore, the general solution to the homogeneous equation is yh = c1cos(x) + c2sin(x).
Next, we use the Variation of Parameters to find a particular solution. We assume that the particular solution has the form yp = u1cos(x) + u2sin(x), where u1 and u2 are functions of x. We then find the first and second derivatives of yp and substitute them into the original equation. After simplifying, we obtain a system of equations for u1' and u2'. We solve for u1' and u2' and then integrate to find u1 and u2. Finally, we substitute u1 and u2 back into the equation for yp to find the particular solution.
(c) y" + y = sin^2(x)
The general solution to the homogeneous equation y" + y = 0 is the same as in part (b). We use the Variation of Parameters to find a particular solution in the same way as in part (b), but with the right-hand side of the equation being sin^2(x) instead of sec(x).
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the pythagorean theorem, Please this is due tmrw i need help asap. 76 points and i will mark you as brainliest!!!
The value of the missing sides using Pythagorean theorem are;
1. 15. 81m
2. 24. 08cm
3. 12. 85 ft
4. 4. 58 in
5. 27. 02 yd
6. 18. 14 mm
7. 16. 58 km
8. 6. 24m
9. 9. 85 miles
10. 14.14 feet
11. 14.14 feet
12. 13. 78 feet
How to determine the value of the sides
Using the Pythagorean theorem, which states that the square of the longest side of a triangle which is the hypotenuse leg is the sum of the squares of the other two sides of the triangle, that is, the opposite and adjacent.
Then, we have;
x² = y² + z²
Where the parameters are;
x is the hypotenuse sidey is the opposite sidez is the adjacent sideFrom the figures shown, we have that;
1. Adjacent side = 8m
Opposite side = 9m
Using the Pythagorean theorem, we have;
x² = 13² + 9²
Find the squares and substitute
x² = 169 + 81
x² = 250
find the square root
x =√250 = 15. 81m
2. For the triangle, we have;
x² = 16² + 18²
x² = 256 + 324
x = √580 = 24. 08cm
3. For the third triangle:
y² = 19² - 14²
y² = 361 -196
y = √165 = 12. 85 ft
4. For the fourth triangle
z² = 11² - 10²
z² = 121 - 100
z = √21 = 4. 58 in
5. x² = 21² + 17²
x² = 441 + 289
x = 27. 02 yd
6. z² = 27² - 20²
z² = 729 - 400
z = √329 = 18. 14 mm
7. z² = 30² - 25²
Find the squares
z² = 900 - 625
z² = 275
z = √275 = 16. 58 km
8. y² = 8² - 5²
find the squares
y² = 64 - 25
y = √39 = 6. 24m
9. x² = 9² + 4²
Find the squares
x² = 81 + 16
x = √97 = 9. 85 miles
10. Length of the diagonal is the hypotenuse side
x² = 10² + 10²
x² = 100 + 100
x = √200 = 14.14 feet
11. The height of the pole is the opposite side
y² = 15² - 5²
y² = 225 -25
y = √200 = 14. 14 feet
12. the height of the pole is the opposite side
y² = 14² - 4²
y² = 196 - 16
y = √190 = 13. 78 feet
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Find the monthly payment on a 30-year, $100,000 mortgage if the
interest rate is 6 percent. hundred.
The monthly payment on a 30-year, $100,000 mortgage with an interest rate of 6 percent is $599.55.
To find the monthly payment on a 30-year, $100,000 mortgage with an interest rate of 6 percent, we need to use the following formula:
Monthly Payment = (Loan Amount * Interest Rate) / (1 - (1 + Interest Rate)^(-Number of Payments))
First, we need to convert the interest rate from a percentage to a decimal by dividing it by 100:
Interest Rate = 6 / 100 = 0.06
Next, we need to calculate the number of payments over the life of the loan. Since there are 12 months in a year, and the loan is for 30 years, the number of payments is:
Number of Payments = 12 * 30 = 360
Now we can plug these values into the formula:
Monthly Payment = ($100,000 * 0.06) / (1 - (1 + 0.06)^(-360)) = $599.55
Therefore, A $100,000 mortgage with a 30 year term and a 6% interest rate has a $599.55 monthly payment.
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URGENT!!! A dolphin swims 665,280 feet in 3 hours. Use the formula d = rt, where d represents distance, r represents rate, and t represents time, to answer the following questions. Show your work.
Rearrange the distance formula, d = rt, to solve for time.
Answer:
Step-by-step explanation:
665,280 dived by 3 = 221760
221760 = distance
221760 = per 1 hour
I tried my best :}
Shan used a surveying tool to map a region of land for his science class. To determine the height of a vertical rock formation, he measured the distance from the base of the formation to his position and the angle between the ground and the line of sight to the top of the formation. The distance was 43 meters, and the angle was 36°. What is the height of the formation to the nearest meter?
The height of the formation is [tex]31meter[/tex], to the nearest meter.
How is height defined?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base but something above it. Height is used to describe everything that may be measured vertically, high or low.
What types of heights are there?In essence, height relates to elevation, which is the height above a certain level. Furthermore, height refers to any quantifiable distance above a particular level as well as extend upwards (as it is from foot to head). For instance, the elevation of a tower, tree, person, mountain, etc.
We can use the tangent function to calculate the formation's height.
[tex]tan(36^{0} )=\frac{h}{3}[/tex]
Here, we have to multiply both sides by [tex]43[/tex] we get,
[tex]43tan(36^{0} )=h[/tex]
[tex]h=31meter[/tex]
Therefore, the height of the formation to the nearest meter is [tex]31meter[/tex].
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give the new coordinates of the ordered pair(7,-4) after a 180 degree rotation
The new coordinates of the point (7, -4) after a 180-degree rotation are (-7, 4).
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
To find the new coordinates of the ordered pair (7, -4) after a 180-degree rotation,
Following the trasformation of 180-degree rotation,
(x, y) ⇒ (-x, -y)
So,
(7, -4) ⇒ (-7, 4)
Therefore, the new coordinates of the point (7, -4) after a 180-degree rotation are (-7, 4).
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Zachary earned scores of 20, 25, 22, 18, and 24 on his last five math quizzes. What score will he need to earn on the sixth quiz in order to have a mean score of 22?
Zachary will need to earn a score of 23 on his sixth quiz to have a mean score of 22 for all six quizzes.
How to determine his possible scoreTo find out what score Zachary needs to earn on his sixth quiz to have a mean score of 22,
We need to use the formula for the mean (or average) of a set of numbers:
Mean = (sum of all the scores) / (number of tests)
Zachary's mean score for the first five quizzes is 22.
Using the above as a guide, we have the following:
(20 + 25 + 22 + 18 + 24 + x) / 6 = 22
Evaluate the like terms
(109 + x) / 6 = 22
So, we have
109 + x = 132
Evaluate the like terms
x = 23
Hence, the score must be 23
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Suppose you own a large grocery store and are trying to save money by controlling
your inventory costs for beans, which you order by the whole case. Each year you
order a total of 675 cases. Suppose that you know that your yearly inventory cost
if you order Q cases of beans at a time is given by , where C is
yearly inventory cost measured in dollars.
a) What is your yearly inventory cost if you order one case at a time? Explain in
context what your answer means.
b) How many cases should you order at a time to minimize your annual inventory
cost? [Be sure to provide evidence supporting your answer.]
c) How much money will you save each year by ordering based on your answer to
part b) instead of ordering one case at a time?
d) When you are minimizing your annual inventory cost as in part b), about how
often should you place your orders? [Be sure to provide evidence supporting
675 cases divided by 135 cases per order equals five orders each year
a) If you order one case at a time, your yearly inventory cost is $6,750. This means that if you order one case of beans each year, it will cost you a total of $6,750.
b) To minimize your annual inventory cost, you should order 135 cases at a time. This is the number of cases that produces the minimum value for the cost equation, C = 200Q + 5,750.
c) By ordering 135 cases at a time instead of one, you will save $3,750 each year in inventory costs.
d) When you are minimizing your annual inventory cost, you should place your orders every five years. This is because 675 cases divided by 135 cases per order equals five orders each year.
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t \( \vec{u}=\left[\begin{array}{c}1 \\ -3 \\ 2\end{array}\right] \) and \( \vec{v}=\left[\begin{array}{c}2 \\ 0 \\ -1\end{array}\right] \) Compute the cross product: \[ \vec{u} \times \vec{v}=\left[\
1 & -3 & 2
2 & 0 & -1
The cross product of two vectors can be calculated using the formula:
\[ \vec{u} \times \vec{v} = \left[ \begin{array}{ccc}
\vec{i} & \vec{j} & \vec{k}\\
u_{1} & u_{2} & u_{3} \\
v_{1} & v_{2} & v_{3}
\end{array} \right] \]
For your given vectors, we can calculate the cross product as follows:
\[ \vec{u} \times \vec{v} = \left[ \begin{array}{ccc}
\vec{i} & \vec{j} & \vec{k}\\
1 & -3 & 2 \\
2 & 0 & -1
\end{array} \right] \]
Which simplifies to:
\[ \vec{u} \times \vec{v} = \left[ \begin{array}{c} 6 \\ 2 \\ -1 \end{array} \right] \]
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Find the volume of each figure and round awnsers to the nearest tenth if needed
The volume of cylinder is 3799.4 cubic feet when diameter is 22 ft and height is 10 feet.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Let us find the volume of the cylinder which has diameter of 22 ft and height of 10 feet.
Diameter=2radius
Radius=22/2=11 feet.
V=πr²h
=3.14×11²×10
=3799.4 cubic feet.
Hence, the volume of cylinder is 3799.4 cubic feet when diameter is 22 ft and height is 10 feet.
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Someone remind me what is the rule for reflecting both x and y on a coordinate plane when you reflect on the x do you change the y or and on the y do you change the x and how would this work on negative example:( -x,y ) and ( x,-y ) *can you show me how to do that using reflection on both x and y* much appreciated (middle school math i don’t why it’s says high school)
Therefore, for the first coordinate point (-x, y), the ultimate reflected points are (-x, -y) and (-x, -y), and for the second point, they are (x, -y) and (-x, -y) .
Describe coordinate plane.A coordinate system is a technique used to precisely find points or additional mathematical objects on a distance, such as Euclidean space, by using one or so more values or coordinates. To find a point or item on a double plane, one uses coordinates, which are pairs of numbers. Two numbers called the y and x matrices are used to describe a point's location on a two-dimensional plane. a set of numbers used to identify specific locations.
Here,
The x-coordinate remains constant and the y-coordinate is cancelled when a point on the coordinate plane is reflected over the x-axis (i.e. multiplied by -1). The y-coordinate remains constant and the x-coordinate is cancelled when a point is reflected over the y-axis.
Let's mirror the point (-2, 3) first over the x-axis and then over the y-axis as an illustration:
The x-coordinate remains constant while the y-coordinate is cancelled when reflecting over the x-axis. In light of this, the argument is (-2, -3).
The x-coordinate is cancelled while the y-coordinate remains constant when reflecting over the y-axis. In light of this, the argument is (2, -3).
We can reflect the coordinates (-x, y) and (x, -y) over the x-axis and then over the y-axis:
Therefore, for the first point (-x, y), the ultimate reflected points are
(-x, -y) and (-x, -y), and for the second point, they are (x, -y) and (-x, -y) .
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given a line and a point not on the line , find a plane
containing the point and parallel to the given line
Geometry
To find a plane containing a point P not on a given line l and parallel to l, we can follow these steps:
Choose any point Q on the line l.
Find the vector v that connects point Q to point P, i.e., v = P - Q.
Find the direction vector d of the line l.
Take the cross product of the direction vector d and the vector v, denoted by d x v.
The plane that contains point P and is parallel to line l can be represented by the equation ax + by + cz = d, where (a, b, c) is the vector d x v, and x, y, and z are the coordinates of any point on the plane.
Here's an example to illustrate the process:
Let's say we have a line l that passes through points A(1, 2, 3) and B(4, 5, 6), and a point P(7, 8, 9) not on the line. We want to find a plane containing point P and parallel to line l.
Choose any point Q on the line l. Let's choose Q(1, 2, 3) for convenience.
Find the vector v that connects point Q to point P: v = P - Q = (7-1, 8-2, 9-3) = (6, 6, 6).
Find the direction vector d of the line l: d = (4-1, 5-2, 6-3) = (3, 3, 3).
Take the cross product of the direction vector d and the vector v: d x v = <3, 3, 3> x <6, 6, 6> = <0, 18, -18>.
Write the equation of the plane: 0x + 18y - 18z = d. Since the plane is parallel to line l, we know that the coefficients of x, y, and z are all 0, except for the coefficients of y and z, which are the components of the vector d x v. Therefore, the equation simplifies to 18y - 18z = 0, or y - z = 0.
So the plane containing point P(7, 8, 9) and parallel to the line passing through points A(1, 2, 3) and B(4, 5, 6) can be represented by the equation y - z = 0.
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Solve x^2 + 7= 43 using square roots
Answer: 6
Step-by-step explanation:
Let's start with what we know. We have the following equation:
x^2 + 7 = 43
Now, we subtract 7 from both sides.
x^2 = 36
Then we take the square root of both sides giving our final answer:
x = 6.
Math part 3 question 1
The value of (g - f) (x) is -3x² + 2x - 4
The value of (f + g) (x) is 3x² + 6x - 6.
The value of (g / f) (x) is (4x - 5) / (3x² + 2x - 1).
The value of (fg) (x) is 12x³ - 7x² -14x + 5.
The solution has been obtained by using operations on functions.
What are operations on functions?
Similar to how we operate on the terms of the functions, we can add, subtract, multiply, and divide functions with overlapping domains using the operations on functions.
We are given f(x) = 3x² + 2x - 1 and g(x) = 4x - 5
(g - f) (x)
⇒(g - f) (x) = g(x) - f(x)
⇒(g - f) (x) = (4x - 5) - (3x² + 2x - 1)
⇒(g - f) (x) = 4x - 5 - 3x² - 2x + 1
⇒(g - f) (x) = 2x - 4 - 3x²
⇒(g - f) (x) = -3x² + 2x - 4
(f + g) (x)
⇒(f + g) (x) = f(x) + g(x)
⇒(f + g) (x) = (3x² + 2x - 1) + (4x - 5)
⇒(f + g) (x) = 3x² + 2x - 1 + 4x - 5
⇒(f + g) (x) = 3x² + 6x - 6
(g / f) (x)
⇒(g / f) (x) = g(x) / f(x)
⇒(g / f) (x) = (4x - 5) / (3x² + 2x - 1)
(fg) (x)
⇒(fg) (x) = f(x) * g(x)
⇒(fg) (x) = (3x² + 2x - 1) * (4x - 5)
⇒(fg) (x) = 12x³ - 7x² -14x + 5
Hence, the required solutions have been obtained.
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HELP PLEASE Roberto needs 6 feet and 8 inches of lumber to repair the deck. He has 54 inches of lumber. How many more inches of lumber does he need?
134 inches
80 inches
26 inches
18 inches
Therefore, Roberto needs 26 more inches of lumber. Answer: 26 inches.
How does this simple equation translate?an explanation of the relationship between the two phrases on either side of a sign. A single variable and an equal sign are typically present. It is equivalent to this 2. 2x - 4 Equals 2. The variable x is present in the earlier instance.
To solve this problem, we need to convert all the measurements to the same units. Let's convert 6 feet and 8 inches to inches:
6 feet = 6 x 12 inches = 72 inches
6 feet and 8 inches = 72 + 8 = 80 inches
So Roberto needs 80 inches of lumber to repair the deck.
He has 54 inches of lumber, so he needs:
80 - 54 = 26 inches
Therefore, Roberto needs 26 more inches of lumber. Answer: 26 inches.
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Help me giving brainliest
Answer:
277
Step-by-step explanation:
Just add lol
help me solve this homework
The correct answer to the listed problems above in their correct scientific notation would be :
1.) 76,450,000 =7.645×10⁷
2.) 0.000327 = 3.27 × 10^-4
3.) 34,000 = 2.4 × 10⁴
4.) 116,000,000,000, = 1.16 × 10¹¹
5.) 0.024= 2.4× 10^-2
6.) 2,800= 2.8× 10³
7.) 100= 1 × 10²
8.) 0.00000qq= q.q × 10^-6
9.) q00,000= q × 10⁵
10.) 0.00633= 6.33 × 10^-3
How to determine the scientific notation of a value?Scientific notation is defined as a form that can be used to represent cumbersome numbers or very small numbers in a way that is most convenient.
The correct scientific notation of the given values are listed below with reasons:
1.) 76,450,000 =7.645×10⁷ and not =7.645×10⁸ when the decimal point is moved so that there is 1 non-zero value in front of the decimal point, the number of zero is 8 not 7.
2.) 0.000327 = 3.27 × 10^-4 and not 3.27 × 10⁴ as the value is less than 1.
3.) 34,000 = 3.4 × 10⁴. Correctly written.
4.) 116,000,000,000, = 1.16 × 10¹¹. Should be 11 not q.
5.) 0.024= 2.4× 10^-2 and not 24 × 10^-2
6.) 2,800= 2.8× 10³. Correctly written.
7.) 100= 1 × 10² and not 1 × 10³
8.) 0.00000qq= q.q × 10^-6. Correctly written.
9.) q00,000= q × 10⁵ and not q × 10^-5
10.) 0.00633= 6.33 × 10^-3 and not 63.3 × 10^-3. This is because the decimal point should be placed immediate after the first whole number.
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Determine the y-intercept.
Answer:
y=-x-2
Step-by-step explanation:
All of them are solved, but I will help to find the relationship.
I found the pattern in my head as I thought about absolute value and proportionality.
Feel free to ask more questions.
Find the equation of the line perpendicular to y = 35 x − 4 and
passing through the point (1, 2). Write your answer in
slope-intercept form (i.e., y = mx + b)
Answer:
y = -1/35x + 71/35
Step-by-step explanation:
slope of the perpendicular line = -1/35 (the negative reciprocal of 35)
use the point (1,2) and the point-slope form:
y - 2 = -1/35(x - 1) now put it in slope-intercept form
y = -1/35x + 1/35 + 2
y = -1/35x + 71/35
0r, y = -1/35(x - 71)
The equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.
To find the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2), we need to follow these steps:
1. Find the slope of the given line: The slope of the line y = 35x − 4 is 35.2. Find the slope of the perpendicular line: The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. So, the slope of the perpendicular line is -1/35.3. Use the point-slope form of a line equation to find the equation of the perpendicular line: The point-slope form of a line equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values we have, we get:y - 2 = (-1/35)(x - 1)
4. Solve for y to get the equation in slope-intercept form: Distribute the -1/35 and then add 2 to both sides of the equation to get y on one side:y - 2 = (-1/35)x + 1/35
y = (-1/35)x + 1/35 + 2
y = (-1/35)x + 71/35
So, the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.
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The terminal side of θ in standard position contains the
given point. Find the values of the six trigonometric functions of
θ.
( 4 , 3 )
Answer: Read the step by step explanation for the answer
Step-by-step explanation:
We can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the given point (4, 3) and the origin (0, 0):
r = √(4² + 3²) = 5
Then we can use the coordinates of the point (4, 3) to determine the values of the trigonometric functions:
sin(θ) = opposite/hypotenuse = 3/5
cos(θ) = adjacent/hypotenuse = 4/5
tan(θ) = opposite/adjacent = 3/4
csc(θ) = hypotenuse/opposite = 5/3
sec(θ) = hypotenuse/adjacent = 5/4
cot(θ) = adjacent/opposite = 4/3
Therefore, the values of the six trigonometric functions of θ are:
sin(θ) = 3/5
cos(θ) = 4/5
tan(θ) = 3/4
csc(θ) = 5/3
sec(θ) = 5/4
cot(θ) = 4/3
Using Gaussian Elimination to solve an inconsistent system Try & Check: Solve the following system of equati using Gaussian Elimination. x-3y+z=4 -x+2y-5z=3 5x-13y+13z=8
The solution for this system is (x,y,z) = (4,3,-2).
To solve this system of equations using Gaussian Elimination, start by adding 3 times the first equation to the second equation, then add 5 times the first equation to the third equation. This will give you a new set of equations in the following form:
x-3y+z=4
0+y-2z=5
0-8y+10z=24
Now, you can use Gaussian Elimination to solve for y and z. Subtract the second equation from the third equation to solve for z, then use that answer to solve for y in the second equation.
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A large pickup truck can hold up to 26.4 gallons
of fuel. Which inequality shows this, using g for
the amount of fuel the truck can hold?
Inequality g ≤ 26.4 means that the amount of fuel the truck can hold (represented by g) is at most 26.4 gallons.
What is Inequality ?
In mathematics, an inequality is a comparison between two values that shows whether they are larger than, less than, equal, or greater than or equal to each other.
Common symbols for inequalities include (less than), > (greater than), (less than or equal to), and (greater than or equal to).
The inequality that shows this would be:
g ≤ 26.4
This reads as "g is less than or equal to 26.4".
Therefore, g ≤ 26.4 means that the amount of fuel the truck can hold (represented by g) is at most 26.4 gallons.
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Solve for w. (w+7)/(w-1)=(w+5)/(w+2)+1 If there is more than one solution. separa If there is no solution, click on "No solutio
The solution is w = 9/5.
Solve for w.
Start by multiplying both sides by (w-1)(w+2):
(w+7)(w+2) = (w+5)(w-1) + (w-1)(w+2)
Simplifying:
w² + 9w + 14 = w² + 4w + 5
Subtracting w² + 9w + 14 from both sides:
0 = -5w - 9
Dividing by -5:
w = 9/5
The solution is w = 9/5.
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Write an explicit formula for an, the nth term of the sequence 7, -14,28,..
The explicit formula for an, the nth term of the sequence is a(n) = 7(2)^n-1
How to determine the explicit formula of the sequenceFrom the question, we have the following parameters that can be used in our computation:
7, -14,28,..
The above definitions imply that we simply multiply -2 to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
First term, a = 7
Common ratio, r = -2
The sequence is represented as
a(n) = a(r)^n-1
So, we have
a(n) = 7(2)^n-1
Hence, the sequence is a(n) = 7(2)^n-1
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I need help with pre calc
The trigonometric equation [tex]\frac{2tanx}{1+tan^2x}[/tex] is equivalent to sin2x
What is an equation?An equation is an expression that shows how numbers and variables are related using mathematical operators like exponent, addition, multiplication, subtraction and division.
Trigonometric identity is used to show relationship between trigonometric functions. Some examples are:
1 + tan²x = 1/cos²x; tanx = cosx/sinx; sin2x = 2sinxcosx
Given:
[tex]\frac{2tanx}{1+tan^2x} \\\\but\ 1+tan^2x=\frac{1}{cos^2x};substituting:\\ \\= \frac{2tanx}{\frac{1}{cos^2x} } \\\\=2tanx*cos^2x\\\\=2*\frac{sinx}{cosx}*cos^2x\\ \\=2sinxcosx[/tex]
= sin2x
The trigonometric equation are equivalent.
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please help me I am solving sequences of algebra 1
The value of a₄ is,
⇒ a₄ = 108
What is mean by Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The value is,
⇒ a₁ = - 4
And, [tex]a_{n} = - 3a_{n - 1}[/tex]
Now, We can put n = 2;
⇒ a₂ = - 3 a₁
⇒ a₂ = - 3 x - 4
⇒ a₂ = 12
Put n = 3;
⇒ a₃ = - 3 a₂
⇒ a₃ = - 3 x 12
⇒ a₃ = - 36
Put n = 4;
⇒ a₄ = - 3 a₃
⇒ a₄ = - 3 x - 36
⇒ a₄ = 108
Thus, The value of a₄ is,
⇒ a₄ = 108
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Value of a₄ in sequence is -108.
What is geometric sequence?In mathematics, geometric sequence, also known as a a geometric progression, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Given,
a₁ = 4 and aₙ = -3aₙ₋₁
a₂ = -3a₂₋₁
a₂ = -3a₁
a₂ = -3(4)
a₂ = -12
a₃ = -3(-12)
a₃ = 36
a₄ = -3a₄₋₁
a₄ = -3a₃
a₄ = -3(36)
a₄ = -108
Hence, -108 is value of a₄ of the sequence.
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what time is 4 hours and 47 mins before 3.08pm
Answer:
10:21 AM
Step-by-step explanation:
To get the answer you subtract 4 hours and 47 mins from 3:08 pm
4 hours and 47 minutes before 3:08 pm is 10:21 am.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the time 4 hours and 47 minutes before 3:08 pm, we can subtract 4 hours and 47 minutes from 3:08 pm.
First, let's convert 3:08 pm to 24-hour format:
3:08 pm = 15:08
Now we can subtract 4 hours and 47 minutes:
15:08 - 4:47 = 10:21
Therefore,
4 hours and 47 minutes before 3:08 pm is 10:21 am.
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In a neighborhood,
out of every
houses participate in a yard sale. What percent of the neighborhood participate in the yard sale?
Let's assume, if 10 out of 20 houses in the neighborhood are participating in the yard sale, the percentage of the neighborhood participating in the yard sale would be 50%.
What is percentage?A number or ratio that can be stated as a fraction of 100 is a percentage. If we need to compute a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent implies. The letter "%" stands for it.
To calculate the percentage of the neighborhood participating in the yard sale, divide the number of houses participating by the total number of houses in the neighborhood and multiply by 100. For example, if 10 out of 20 houses in the neighborhood are participating in the yard sale, the percentage of the neighborhood participating in the yard sale would be 50%.
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Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
The values of x in the given equation, (x-7)^2=36, are x = 13 and x = 1. The correct options are the first and second options - x = 13 and x = 1
Quadratic equation: Calculating the value of xFrom the question, we are to determine the values of x in the given equation. The given equation is:
(x-7)^2=36
To solve the equation (x-7)^2=36, we can take the square root of both sides and solve for x:
(x-7)^2 = 36
Taking the square root of both sides:
x - 7 = ±6
Adding 7 to both sides:
x = 7 ± 6
So we get two possible values of x:
x = 7 + 6 or x = 7 - 6
x = 13 or x = 1
Hence, the correct values of x are:
x = 13
x = 1
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Marco bought a pair of jeans on sale for 30% off the regular price of $54.00. What was the discount he
received at the cash register and what was the sale price (not including tax)?
Answer:
Step-by-step explanation:
He received $16.20
because 30% of $54.00 is $16.20
Measure the height of the tin in the mm and write down the real height in mm
The measure of the height of the tin in mm can be found using the steps below.
What are Measurements?Measurement is the method of comparing the properties of a quantity or object using a standard quantity.
Measurement is essential to determine the quantity of any object.
Here, the activity is to measure the height of a tin.
Height of the tin is the vertical distance from the base of the tin to the top of the tin.
The height of the tin is the exact straight line measurement when the tin is placed upright on a flat surface.
The measurement has to be in millimeters.
So the best tool is the ruler.
Place the ruler vertically with the point 0 at the base line of the tin.
Mark the point in millimeters that the ruler coincides with the top of the tin.
Read the height to the nearest millimeter.
Hence the height of the tin can be measured as above.
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