To eliminate the parameter t in the equations x=t^2 and y=2+10t, solve [tex]t = \sqrt(x)[/tex] and substitute into the second equation to get [tex]y = 2 + 10\sqrt(x)[/tex]. This results in the cartesian equation [tex]y = 2 + 10\sqrt(x).[/tex]
To eliminate the parameter t and find the cartesian equation, follow these steps:
Start with the given parametric equations: x=t^2 and y=2+10t
Solve the first equation for t:
[tex]t = \sqrt(x)[/tex]
Substitute this expression for t into the second equation:
[tex]y = 2 + 10(\sqrt(x))[/tex]
Thus, the cartesian equation is [tex]y = 2 + 10 \sqrt(x).[/tex]
Triple my number add six and subtract twice my number my number plus three
Convert 64.32° into degrees, minutes, and seconds.
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.
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
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.
Sidney made $26 more than seven times Casey's weekly salary. If x represents Casey's weekly salary, write an expression for sidney's weekly salary
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.
How many inches are in a foot?
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]
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.
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:
Quadrilateral ABCD is similar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet, 40 feet, and 30 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 12 feet long, how long is the 4th side on quadrilateral ABCD?
Final answer:
The length of the fourth side on quadrilateral ABCD is 120 feet.
Explanation:
Given that quadrilateral ABCD is similar to quadrilateral EFGH, we can use the property of similar figures to find the length of the fourth side on quadrilateral ABCD.
If the two shortest sides of quadrilateral EFGH are 6 feet and 12 feet long, we can set up a proportion using the corresponding sides of the two quadrilaterals.
Let x be the length of the fourth side on quadrilateral ABCD.
Using the property of similar figures, we have:
(60/6) = (x/12)
Cross multiplying, we get:
6x = 720
Dividing both sides by 6, we find:
x = 120
Therefore, the length of the fourth side on quadrilateral ABCD is 120 feet.
What is equivalent to the expression "the quotient of five and seven"?
A bag of fruit contains 3 apples and 2 oranges and 1 banana and 4 pears.Gerald will randomly selected two pieces of fruit one at a time from the bag and not put is back. What is the probability that the first piece of fruit Gerald selects will be a banana and the second piece of fruit will be a pear??
Final answer:
The probability that Gerald will first select a banana and then a pear from the bag without replacement is 2/45.
Explanation:
To determine the probability that Gerald selects a banana first and then a pear without replacement, we have to consider the total number of possible outcomes for each draw and the favorable outcomes for the event.
For the first draw, the total number of fruits is 10 (3 apples + 2 oranges + 1 banana + 4 pears). The favorable outcome of drawing a banana is 1 since there's only one banana.
The probability of drawing a banana on the first draw is therefore 1/10. After drawing the banana, there are 9 fruits left in the bag with 4 pears among them.
The probability of then drawing a pear is 4/9. To find the total probability of both events happening in sequence (a banana first and then a pear), multiply the two probabilities:
P(banana first and pear second) = P(banana first) × P(pear second)
= (1/10) × (4/9)
= 4/90
= 2/45.
The simplification process shows that the probability Gerald will first select a banana and then a pear is 2/45.
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.
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?
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?
hey can you just please help me solve these two problems
1- according to the bipartisan policy center (BPC), 57.5% of all eligible voted in the 20112 presidential elections. while there are over 350 million Americans, the BPC estimates that only 219 million are eligible to vote. how many eligible voters in 2012 election?
2-sarah's sandwich shop sells a specialty sandwich for $4.95 that contains a quarter of a pound of turkey. if sarah buys 12 pounds of turkey meat but eats a tenth of a pound on the way to her sandwich shop, what is the maximum number of sandwiches she can make?
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
0.2(x + 1) + 0.5x = –0.3(x – 4)
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]
Please I'm stuck in this problem
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?
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?
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
Learn moremethod for solving a quadratic equation : https://brainly.com/question/10278062solution(s) to the equation : https://brainly.com/question/4372455best way to solve quadratic equation : https://brainly.com/question/9438071Answer detailsGrade: College
Subject: Mathematics
Chapter: Quadratic Equation
Keywords: Quadratic , Equation , Formula , Rocket , Maximum , Minimum , Time , Trajectory , Ground
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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please factor this problem x^2+7x-8
The principal $3000 is accumulated with 3% interest, compounded semiannually for 6 years.
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:
Find the rectangular coordinates of the point with the polar coordinates. ordered pair negative 5 comma 5 pi divided by 3