In a case whereby a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, the number of miles from earth the star is can be expressed as [tex]3.4 * 5.87 * 10^12 miles[/tex]
How can the number of miles be calculated?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given that star=3.4 light years from earth
1 light years= [tex]5.87*10x^{12} miles[/tex]
The number of miles from earth is
[tex]3.4 * 5.87 *10^{12} miles\\\\=3.4 * 5.87 * 10^12 miles[/tex]
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The indicated function y1(x) is a solution of the given differential equation. use reduction of order or formula (5) in section 4.2, y2 = y1(x) e−∫p(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). 9y'' − 12y' + 4y = 0; y1 = e2x/3
The indicated function y1(x) is a solution of the given differential equation.The general solution is [tex]y = c_1 e^{2x}- c_2e^{-6x}/8[/tex]
What is a differential equation?An equation containing derivatives of a variable with respect to some other variable quantity is called differential equations.
The derivatives might be of any order, some terms might contain the product of derivatives and the variable itself, or with derivatives themselves. They can also be for multiple variables.
Given differential equation is
y''-4y'+4y=0
and
[tex]y_1(x) = e^{2x}[/tex]
[tex]y_2(x) = y_1(x) \int\limits^a_b {e^{\int pdx} \, / y_1 ^2(x)dx[/tex]
The general form of equation
y''+P(x)y'+Q(x)y=0
Comparing both the equation
So, P(x)= - 4
[tex]y_2(x) = y_1(x) \int\limits^a_b {e^{\int pdx} \, / y_1 ^2(x)dx\\\\\\[/tex]
[tex]y_2(x) = e^{2x}\int e^{-4x} \, / e^{4x}dx[/tex]
[tex]y_2(x) = e^{2x}\int e^{-8x}dx\\\\y_2(x) = -e^{-6x}/8[/tex]
The general solution is
[tex]y = c_1 e^{2x}- c_2e^{-6x}/8[/tex]
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write the smallest numeral possible using the digits 9, 3 and 6
The smallest numeral that can be created from the digits 9, 3, and 6 is 369. This is achieved by arranging the digits in ascending order.
Explanation:The smallest numeral that can be formed using the digits 9, 3, and 6 is 369. In mathematics, when we are to create the smallest possible numeral from a given set of digits, we arrange the digits in increasing order from left to right, that means the smallest digit will be on the left-most side and the largest digit will be on the right-most side.
So, with the digits 9, 3, and 6, we place 3 first as it's the smallest, then 6 as it's the next smallest, and finally 9, resulting in the smallest numeral 369.
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The smallest numeral possible using the digits 9, 3, and 6 is 369, arranged in ascending order.
To write the smallest numeral possible using the digits 9, 3, and 6, we arrange the digits in ascending order. The smallest digit is placed at the beginning, followed by the larger ones. Therefore, the smallest numeral we can create is 369.
The average score on a standardized test is 500 points with a standard deviation of 50 points. If 2,000 students take the test at a local school, how many students do you expect to score between 500 and 600 points?
To solve this problem, we use the z statistic. The formula for z score is given as:
z = (x – u) / s
Where,
x = sample score
u = the average score = 500
s = standard deviation = 50
First, we calculate for z when x = 500
z = (500 – 500) / 50
z = 0 / 50
z = 0
Using the standard z table, at z = 0, the value of P is: (P = proportion)
P (z = 0)= 0.5
Secondly, we calculate for z when x = 600
z = (600 – 500) / 50
z = 100 / 50
z = 2
Using the standard z table, at z = 2, the value of P is: (P = proportion)
P (z = 2) = 0.9772
Since we want to find the proportion between 500 and 600, therefore we subtract the two:
P (500 ≥ x ≥ 600) = 0.9772 – 0.5
P (500 ≥ x ≥ 600) = 0.4772
Answer:
Around 47.72% of students have score from 500 to 600.
Answer:
To solve this problem, we use the z statistic. The formula for z score is given as:
z = (x – u) / s
Where,
x = sample score
u = the average score = 500
s = standard deviation = 50
First, we calculate for z when x = 500
z = (500 – 500) / 50
z = 0 / 50
z = 0
Using the standard z table, at z = 0, the value of P is: (P = proportion)
P (z = 0)= 0.5
Secondly, we calculate for z when x = 600
z = (600 – 500) / 50
z = 100 / 50
z = 2
Using the standard z table, at z = 2, the value of P is: (P = proportion)
P (z = 2) = 0.9772
Since we want to find the proportion between 500 and 600, therefore we subtract the two:
P (500 ≥ x ≥ 600) = 0.9772 – 0.5
P (500 ≥ x ≥ 600) = 0.4772
Answer:
Around 47.72% of students have score from 500 to 600.
Step-by-step explanation:
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −1 1 s2 − 720 s7
The inverse Laplace transform of [tex]\( \frac{1}{s^2 - 720s^7} \) is \( (1 - \frac{1}{720})t + e^{720t} \).[/tex]
To find the inverse Laplace transform of [tex]\( \frac{1}{s^2 - 720s^7} \),[/tex] we can use the method of partial fraction decomposition. First, factor the denominator:
[tex]\[ s^2 - 720s^7 = s^2(1 - 720s^5) \][/tex]
Now, we can write the partial fraction decomposition as:
[tex]\[ \frac{1}{s^2(1 - 720s^5)} = \frac{A}{s} + \frac{B}{s^2} + \frac{Cs^5 + D}{1 - 720s^5} \][/tex]
Multiplying both sides by [tex]\( s^2(1 - 720s^5) \)[/tex], we get:
[tex]\[ 1 = As(1 - 720s^5) + Bs(1 - 720s^5) + (Cs^5 + D)s^2 \]\[ 1 = As - 720As^6 + Bs - 720Bs^6 + Cs^7 + Ds^2 \][/tex]
Equating coefficients:
For [tex]\( s^6 \):[/tex]
-720A - 720B = 0
A + B = 0
A = -B
For [tex]\( s^7 \):[/tex]
C = 0
For [tex]\( s^2 \):[/tex]
D = 1
Substituting back:
A = -B
D = 1
C = 0
So, the partial fraction decomposition is:
[tex]\[ \frac{1}{s^2(1 - 720s^5)} = \frac{-B}{s} + \frac{1}{s^2} + \frac{D}{1 - 720s^5} \][/tex]
Now, we can find the values of [tex]\( A \), \( B \), and \( D \):[/tex]
A = -B
D = 1
Now, we can use Theorem 7.2.1 to find the inverse Laplace transform:
[tex]\[ \mathcal{L}^{-1}\left( \frac{1}{s^2(1 - 720s^5)} \right) = -B \mathcal{L}^{-1}\left( \frac{1}{s} \right) + \mathcal{L}^{-1}\left( \frac{1}{s^2} \right) + D \mathcal{L}^{-1}\left( \frac{1}{1 - 720s^5} \right) \][/tex]
[tex]\[ = -B + t + D \mathcal{L}^{-1}\left( e^{720t} \right) \][/tex]
[tex]\[ = -B + t + De^{720t} \][/tex]
Since [tex]\( B = \frac{1}{720} \), \( D = 1 \)[/tex], the inverse Laplace transform is:
[tex]\[ \mathcal{L}^{-1}\left( \frac{1}{s^2(1 - 720s^5)} \right) = -\frac{1}{720}t + t + e^{720t} \][/tex]
[tex]\[ = \left( 1 - \frac{1}{720} \right)t + e^{720t} \][/tex]
Complete Question:
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of [tex]\( \frac{1}{s^2 - 720s^7} \).[/tex]
The variable z is directly proportional to x and inversely proportional to y. When x is 12 and y is 18 z has the value 2 what is the value of z when x = 19 and y = 22
Andrei has a job in the circus walking on stilts. Andrei is 11/10 meters tall. The foot supports of his stilts are 23/10 meters high.
How high is the top of Andrei's head when he is walking on his stilts?
x = 2, y = -1
14
2. x = 0, y = 2.5
1.665
3. x = -1, y = -3
0.44
4. x = 0.5, y =
9.17
5. x = , y =
-1
6. x = √2, y = √2
-11.25
Answer:
b
Step-by-step explanation:
please factor this problem x^2+7x-8
If the APR of a savings account is 3.6% and interest is compounded monthly, what is the approximate APY of the account?
Answer:
3.66% ( approx )
Step-by-step explanation:
Since, the formula of annual percentage yield is,
[tex]APY = (1+\frac{r}{n})^n-1[/tex]
Where,
r = stated annual interest rate,
n = number of compounding periods,
Here, r = 3.6% = 0.036,
n = 12 ( ∵ 1 year = 12 months )
Hence, the annual percentage yield is,
[tex]APY=(1+\frac{0.036}{12})^{12}-1=1.03659 - 1 = 0.036599\approx 0.0366 = 3.66\%[/tex]
Convert 64.32° into degrees, minutes, and seconds.
A rocket is launched straight up from the ground, with an initial velocity of 224 feet per second. The equation for the height of the rocket at time t is given by:
h=-16t^2+224t
(Use quadratic equation)
A.) Find the time when the rocket reaches 720 feet.
B.) Find the time when the rocket completes its trajectory and hits the ground.
A.) The rocket reaches 720 feet in 5 seconds and 9 seconds.
B.) The rocket completes its trajectory and hits the ground in 14 seconds
Further explanationA quadratic equation has the following general form:
[tex]ax^2 + bx + c = 0[/tex]
The formula to solve this equation is :
[tex]\large {\boxed {x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} } }[/tex]
Let's try to solve the problem now.
Question A:Given :
[tex]h = -16 t^2 + 224t[/tex]
The rocket reaches 720 feet → h = 720 feet
[tex]720 = -16 t^2 + 224t[/tex]
[tex]16 t^2 - 224t + 720 = 0[/tex]
[tex]16 (t^2 - 14t + 45 = 0)[/tex]
[tex]t^2 - 14t + 45 = 0[/tex]
[tex]t^2 - 9t - 5t + 45 = 0[/tex]
[tex]t(t - 9) - 5(t - 9) = 0[/tex]
[tex](t - 5)(t - 9) = 0[/tex]
[tex]t = 5 ~ or ~ t = 9[/tex]
The rocket reaches 720 feet in 5 seconds and 9 seconds.
Question B:The rocket hits the ground → h = 0 feet
[tex]0 = -16 t^2 + 224t[/tex]
[tex]16 (t^2 - 14t ) = 0[/tex]
[tex]t^2 - 14t = 0[/tex]
[tex]t( t - 14 ) = 0[/tex]
[tex]t = 0 ~ or ~ t = 14[/tex]
The rocket completes its trajectory and hits the ground in 14 seconds
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Subject: Mathematics
Chapter: Quadratic Equation
Keywords: Quadratic , Equation , Formula , Rocket , Maximum , Minimum , Time , Trajectory , Ground
The area of a rectangle wall of a barn is 216 ft.² it's length is 6 feet longer than twice it's width. find the length and width of the wall of the barn
What is equivalent to the expression "the quotient of five and seven"?
There is a line through the origin that divides the region bounded by the parabola
y=4x−3x^2 and the x-axis into two regions with equal area. What is the slope of that line?
What standard deviation below the mean of normal young adults equals osteoporosis?
How do you find a vector that is orthogonal to 5i + 12j ?
To find a vector orthogonal to 5i + 12j, we can use the property that orthogonal vectors have a dot product of 0. By setting up equations and solving them accordingly, you can find a vector that is perpendicular to 5i + 12j.
Orthogonal vectors: To find a vector orthogonal to 5i + 12j, we need to find a vector with a dot product of 0 with 5i + 12j. Since the dot product of orthogonal vectors is zero, we can set up equations and solve them to find a vector that is perpendicular to 5i + 12j.
The sun’s rays are striking the ground at a 55° angle, and the length of the shadow of a tree is 56 feet. How tall is the tree?
select one:
a. 80.0 feet
b. 45.9 feet ( Incorrect)
c. 34.2 feet (incorrect)
d. 32.1 feet
Solve cos x +sqr root of 2 = -cos x for x over the interval 0,2pi
0.2(x + 1) + 0.5x = –0.3(x – 4)
Which value is a discontinuity of x^2+7x+1/x^2+2x-15? x=-1 x=-2 x=-5 x=-4
The value of x=-5 is a discontinuity of the function x^2+7x+1 / x^2+2x-15 since it makes the denominator of this function equal to zero.
Explanation:The subject of this question is the discontinuity of a rational function. In Mathematics, a function f(x) = (p(x))/(q(x)), where p(x) and q(x) are polynomials, is said to be discontinuous at a particular value of x if and only if q(x) = 0 at that value. From the equation in the question; x^2+7x+1/x^2+2x-15, we can determine its discontinuity by finding the values of x that would make the denominator equal to zero. This is done by solving the polynomial equation x^2+2x-15 = 0 for x. The solutions to this equation represent the values at which the function is discontinuous.
By applying the quadratic formula, (-b ± sqrt(b^2 -4ac))/(2a), where a = 1, b = 2, and c = -15, we get that x = -5, and 3. However, the values given in the question are x=-1, x=-2, x=-5, and x=-4. From these options, only x=-5 makes the denominator zero, thus, x = -5 is a point of discontinuity in the function x^2+7x+1 / x^2+2x-15.
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A spinner is divided into 10 equal sections numbered 1 through 10. If the arrow is spun once, what is the probability it will land on a number less than 3?
The probability with the condition of the spinner landing on a number less than 3 is 0.2
What is a conditional probability?A conditional probability is a probability of an event occuring with a condition that another event had previously occurred. The event in the question is spinning the spinner once while the condition is that the number landed on is less than 3.
The spinner has 10 equal sections numbered 1 through 10.
The conditional probability of landing on a number less than 3 is the same as the probability of landing on either 1 or 2.
There are two sections out of ten that corresponds to numbers less than 3. The probability of landing on a number less than 3 is therefore;
P(Landing on a number less than 3) = P(Landing on 1) + P(Landing on 2)
P((Landing on 1) = 1/10
P(Landing on 2) = 1/10
P(Landing on 1) + P(Landing on 2) = (1/10) + (1/10) = 2/10
(1/10) + (1/10) = 2/10 = 0.2
The probability of landing on a number less than 3 is 0.2
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Write the equation of the line that is parallel to the line 7−4x=7y 7 − 4x = 7 y through the point (2,0).
To find the equation of a line parallel to the given line, we can use the slope of the given line and the point-slope form of a line. The equation of the line parallel to 7−4x=7y and passing through the point (2,0) is y = (7/4)x - (7/2).
Explanation:To find the equation of a line parallel to the given line, we need to find the slope of the given line first. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Rearranging the given equation, we have y = (7/4)x - 1. Dividing the coefficient of x by the coefficient of y, we find that the slope of the given line is 7/4. Since the line we're looking for is parallel to this line, it will also have a slope of 7/4. Now, we can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point on the line. Substituting in the values (2, 0) and slope (7/4), we can solve for y to find the equation of the line.
Using the point-slope form, we have y - 0 = (7/4)(x - 2). Simplifying, we get y = (7/4)x - (7/2), which is the equation of the line parallel to the given line and passing through the point (2, 0).
Final answer:
The equation of the line parallel to 7 - 4x = 7y through the point (2, 0) is y = (-4/7)x + 8/7.
Explanation:
To find the equation of a line parallel to the line 7 - 4x = 7y, we need to find the slope of the given line. First, rearrange the equation in the form y = mx + b, where m is the slope. So, 7y = 7 - 4x becomes y = (-4/7)x + 1. The slope of this line is -4/7. Since the line we want is parallel, it will have the same slope.
Next, we have the point (2, 0) through which the line passes. To find the equation, we'll use the point-slope form: y - y1 = m(x - x1). Substituting the given values, we have y - 0 = (-4/7)(x - 2). Simplifying, we get y = (-4/7)x + 8/7.
Therefore, the equation of the line parallel to 7 - 4x = 7y through the point (2, 0) is y = (-4/7)x + 8/7.
The function for the cost of materials to make a shirt is f(x) = five sixths x + 5, where x is the number of shirts. The function for the selling price of those shirts is g(f(x)), where g(x) = 5x + 6. Find the selling price of 18 shirts
There was 2/3 of a pan of a lasagna in the refrigerator. Bill and his friends ate half of what was left. Write a number sentence and draw a model to represent the problem. How much of the pan did they eat?
What is the general form of the equation for the given circle centered at O(0, 0)? x2 + y2 + 41 = 0 x2 + y2 − 41 = 0 x2 + y2 + x + y − 41 = 0 x2 + y2 + x − y − 41 = 0
The general form of the equation for the given circle centered at O(0, 0) is:
[tex]x^2+y^2-41=0[/tex]
Step-by-step explanation:We know that the standard form of circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where the circle is centered at (h,k) and the radius of circle is: r units
1)
[tex]x^2+y^2+41=0[/tex]
i.e. we have:
[tex]x^2+y^2=-41[/tex]
which is not possible.
( Since, the sum of the square of two numbers has to be greater than or equal to 0)
Hence, option: 1 is incorrect.
2)
[tex]x^2+y^2-41=0[/tex]
It could also be written as:
[tex]x^2+y^2=41[/tex]
which is also represented by:
[tex](x-0)^2+(y-0)^2=(\sqrt{41})^2[/tex]
This means that the circle is centered at (0,0).
3)
[tex]x^2+y^2+x+y-41=0[/tex]
It could be written in standard form by:
[tex](x+\dfrac{1}{2})^2+(y+\dfrac{1}{2})^2=(\sqrt{\dfrac{83}{2}})^2[/tex]
Hence, the circle is centered at [tex](-\dfrac{1}{2},-\dfrac{1}{2})[/tex]
Hence, option: 3 is incorrect.
4)
[tex]x^2+y^2+x-y=41[/tex]
In standard form it could be written by:
[tex](x+\dfrac{1}{2})^2+(y-\dfrac{1}{2})^2=(\sqrt{\dfrac{83}{2})^2[/tex]
Hence, the circle is centered at:
[tex](\dfrac{-1}{2},\dfrac{1}{2})[/tex]
Which of the following statements is not true?
An angle bisector can be a median of a triangle.
A perpendicular bisector can be an altitude of a triangle.
A median can be an altitude of a triangle.
All of the statements are true.
Department w had 2,400 units, one-third completed at the beginning of the period; 16,000 units were transferred to department x from department w during the period; and 1,800 units were one-half completed at the end of the period. assume the completion ratios apply to direct materials and conversion costs. what is the equivalent units of production used to compute unit conversion cost on the cost of production report for department w? assume the company uses fifo.
The equivalent units of production for calculating conversion costs in Department W using FIFO are 16,900 units. This consists of 16,000 units transferred out and 900 equivalent units for the 1,800 units at half completion stage.
Explanation:To calculate the equivalent units of production for unit conversion cost in Department W, using the FIFO method, we need to account only for the work done in the current period. Department W had 2,400 units at the beginning that were one-third completed, which means 800 units (2,400 units * 1/3) were already processed in the previous period. Therefore, these do not count for the current period. During the period, 16,000 units were transferred out. We also need to consider the 1,800 units at the end at one-half completion, which contributes 900 equivalent units (1,800 units * 1/2) for the current period.
To determine the number of equivalent units for conversion costs, we perform the following calculation:
Equivalent units for units transferred to Department X: 16,000 units (these are complete with respect to Department W's work).Equivalent units for ending work-in-process: 1,800 units * 1/2 = 900 units.Total equivalent units of production for conversion costs: 16,000 units + 900 units = 16,900 units.
A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second.
Write an equation to model the height h in feet of the ball t seconds after it has been punted.
The football is caught at 5.5 feet above the ground. How long was the football in the air?
When patey pontoons issued 6% bonds on january 1, 2016, with a face amount of $600,000, the market yield for bonds of similar risk and maturity was 7%. the bonds mature december 31, 2019 (4 years). interest is paid semiannually on june 30 and december 31?
A map is scaled so that 3 cm on the map is equal to 21 actual miles. if two cities on the map are 5 cm apart, what proportion would you use to solve the problem?