Write the equation of the hyperbola centered at the origin with focus (74, 0) and asymptote y=-7/5x
The equation of the hyperbola is =x^2/a^2-y^2/b^2=1
Answers
The equation of the given hyperbola is; x²/25 - y²/49 = 1
What is the equation of the hyperbola?
We are given;
Focus = (74, 0)
Asymptote; y = -⁷/₅x
Centered at origin
We are given that the general form of equation of a hyperbola is;
x²/a² - y²/b² = 1
Now, we know that the equations of the asymptotes are;
y = ±(b/a)x
Thus, comparing the above with our asymptote of y = -7/5x gives us;
a = 5 and b = 7
Thus, the equation of the given hyperbola is;
x²/5² - y²/7² = 1
⇒ The equation of the given hyperbola is;
x²/25 - y²/49 = 1
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Answer:
The answer is 5 and 7
Step-by-step explanation:
Related Questions
Kenya has a population of 3,013,341 people. The area of the country is 580,367 km^2. What is the population density? (Make sure you round to the nearest whole number. ) *
Answers
Required population density is 5.19 people per square kilometer.
Population density is the number of people living in a certain area. It is calculated by dividing the population of a country by its area.
The population density of Kenya is: 3,013,341/580,367 ≈ 5.19 people per square kilometer.Rounding to the nearest whole number, the population density is 5 people per square kilometer. This is a very low population density compared to other countries around the world
. A low population density can be an indicator of underdevelopment, especially in rural areas, and can pose challenges to the provision of public services like healthcare, education, and infrastructure in general.In big answer, the population density of Kenya is approximately 5 people per square kilometer, rounded to the nearest whole number.
This is a very low population density compared to other countries and can pose challenges to the provision of public services like healthcare, education, and infrastructure.
So,
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Violet rents a bike in a city she is visiting. She pays an initial fee of $2.50 plus $3.75 per hour she rents the bike. Which equation can be used to find y, the total cost of renting a bike, if x represents the number of hours Violet rents the bike?
Answers
Answer: y = 3.75x + 2.50
Step-by-step explanation:
The equation that can be used to find y, the total cost of renting a bike, if x represents the number of hours Violet rents the bike is:
y = 3.75x + 2.50
Explanation:
Violet pays an initial fee of $2.50, which is a fixed cost that does not depend on the number of hours she rents the bike. Additionally, she pays $3.75 per hour she rents the bike, which is a variable cost that depends on the number of hours. Therefore, the total cost of renting a bike (y) can be expressed as the sum of the fixed cost ($2.50) and the variable cost ($3.75x), which gives the equation:
HELPPP ME I WILL MARK GOOD
Answers
Answer:
surface area≈126.65
Step-by-step explanation:
A=2AB+(a+b+c)h
AB=s(s﹣a)(s﹣b)(s﹣c)
s=a+b+c
2
Solving forA
A=ah+bh+ch+1
2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=5·7+5·7+5·7+1
2·﹣54+2·(5·5)2+2·(5·5)2﹣54+2·(5·5)2﹣54≈126.65064
1. Each of the six cards shows a shape.
N
3
X
5
4
z
a. Which pair of cards shows a shape and its image after a rotation?
b. Which pair of cards shows a shape and its image after a reflection?
Answers
Answer:
a). Cards (1) and (4)
b). Cards (3) and (5)
Step-by-step explanation:
(a). From the cards attached,
If card (1) is rotated by an angle of 180° counterclockwise, we get the image given in card (4).
Therefore, card (4) will be the image of card (1) after a rotation.
(b). If we reflect card (3) across a horizontal line (or x- axis) image card (4) is obtained.
Therefore, card (3) and card (5) is the pair of cards.
. If 18 defective glass bricks include 10 that have cracks but no discoloration, 5 that have discoloration but no cracks, and 3 that have cracks and discoloration, what is the probability that among 6 of the bricks (chosen at random for further checks) 3 will have cracks but no discoloration, 1 will have discoloration but no cracks, and 2 will have cracks and discoloration
Answers
There are 18 defective glass bricks: 10 with cracks but no discoloration, 5 with discoloration but no cracks, and 3 with cracks and discoloration.
We want to choose 6 bricks at random and check them further, with the goal of selecting 3 with cracks but no discoloration, 1 with discoloration but no cracks, and 2 with cracks and discoloration. We'll use the formula for hypergeometric probability to find the probability of this event.
The formula for hypergeometric probability is:P(X = k) = (C(n1,k) × C(n2,n-k)) / C(N,n),where:P(X = k) is the probability of selecting k objects with the desired characteristicsn1 is the number of objects in the population with the desired characteristicsn2 is the number of objects in the population without the desired characteristics
N is the total number of objects in the populationn is the sample size
The probability of selecting 3 bricks with cracks but no discoloration from the 10 available is:P(3 cracks) = (C(10,3) × C(8,3)) / C(18,6)≈ 0.2597The probability of selecting 1 brick with discoloration but no cracks from the 5 available is:P(1 discoloration) = (C(5,1) × C(13,5)) / C(18,6)≈ 0.4073
The probability of selecting 2 bricks with cracks and discoloration from the 3 available is:P(2 cracks and discoloration) = (C(3,2) × C(15,4)) / C(18,6)≈ 0.0840
The probability of selecting 3 with cracks but no discoloration, 1 with discoloration but no cracks, and 2 with cracks and discoloration is the product of these probabilities:P(3,1,2) = P(3 cracks) × P(1 discoloration) × P(2 cracks and discoloration)≈ 0.0110
Summary: If 18 defective glass bricks include 10 that have cracks but no discoloration, 5 that have discoloration but no cracks, and 3 that have cracks and discoloration, the probability of selecting 3 bricks with cracks but no discoloration, 1 brick with discoloration but no cracks, and 2 bricks with cracks and discoloration is approximately 0.0110.
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Which point represents the origin? number line from minus 5 to 5 with point M at minus 4, J at minus1, W at 0, and K at 2. Question 1 options: Point W Point J Point M Point K
Answers
The point that represent the origin in the number line is Point W
What is a number line?A number line is a horizontal representation of numbers in parts with equal intervals
The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values at right
number line on -5 to 5 will have the origin at the center and te center here is zero which is similar to p
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Use the compound interest formulas A=P1+
r
nnt and A=Pert to solve the problem given. Round answers to the nearest cent.
Find the accumulated value of an investment of $25,000 for 3 years at an interest rate of 7% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.
Answers
The accumulated value of an investment if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously is $30731.4 $ , $30785.98 $30823.14 , 30841.95
What is Interest ?Interest is the amount received by a person as a result of investing certain amount of money for a certain period of time.
It is given that
Principal = $ 25000
Time = 3 years
Interest Rate = 7 %
The amount is given by
\(\rm A = P( 1+ \dfrac{r}{n}) ^{nt}\)
Compounded semiannually
n = 2
Compounded Quarterly
n = 4
Compounded Monthly
n =12
Compounded Continuously
P = P₀ \(\rm e ^{rt}\)
Therefore the accumulated value for
compounded Semiannually is
\(\rm A = 25000( 1+ \dfrac{7}{200}) ^{2*3}\)
A = $30731.4
Compounded Quarterly
\(\rm A = 25000( 1+ \dfrac{7}{400}) ^{4*3}\)
A = $30785.98
Compounded Monthly
\(\rm A = 25000( 1+ \dfrac{7}{1200}) ^{12*3}\)
A = $30823.14
Compounded Continuously
\(\rm P = 25000 e ^{ 7 * 3 }\)
P = $30841.95
Therefore the accumulated value of an investment if the money is
a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously is
$30731.4 $ , $30785.98 $30823.14 , 30841.95
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To solve a system of equations, you can replace a ____________with an equal value or expression.
NO LINKS
Answers
Answer:
Variable
Step-by-step explanation:
If you can substitute a unknown variable with another expression that is equal, you can then solve for another variable, and with that equal expression, solve for the first variable.
PLEASE HELP!! URGENT!
Answers
I think is B but I am not 100% sure goodluck if I am wrong I am sorry :(
For positive acute angles a an b, it is known that cos A =4/5 and sinB = 8/17. Find the exact value of sun (A-B) in simplest form
Answers
The exact value of sin (A-B) in simplest form for positive acute angle A and B is found to be 221/1445.
We can use the trigonometric identity sin(A - B) = sinAcosB - cosAsinB to find the exact value of sin(A - B) for positive acute angles.
From the given information, we know that cosA = 4/5 and sinB = 8/17. Using identities, sin²A + cos²A = 1 and sin²B + cos²B = 1:
sinA = √(1 - cos²A)
= √(1 - (4/5)²)
= 3/5
cosB = √(1 - sin²B)
= √(1 - (8/17)²)
= 15/17
Now, we can substitute these values into the identity:
sin(A - B) = sinAcosB - cosAsinB
sin(A - B) = (3/5)(15/17) - (4/5)(8/17)
sin(A - B) = 9/17 - 32/85
sin(A - B) = (765 - 544)/1445
sin(A - B) = 221/1445
Therefore, the exact value of sin(A - B) in simplest form is 221/1445.
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which factor would most likely distort the relationship between the indepedent and dependent variables
Answers
There are various factors that can distort the relationship between the independent and dependent variables. Nonetheless, the factor that most likely distorts the relationship between the two is the presence of a confounding variable.
What is a confounding variable
A confounding variable is an extraneous variable in a statistical model that affects the outcome of the dependent variable, providing an alternative explanation for the relationship between the dependent and independent variables. Confounding variables may generate false correlation results that lead to incorrect conclusions. Confounding variables can be controlled in a study through the experimental design to avoid invalid results. Thus, if you want to get a precise relationship between the independent and dependent variables, you need to ensure that all confounding variables are controlled.An example of confounding variables
A group of researchers is investigating the relationship between stress and depression. In their study, they discovered a positive correlation between stress and depression. They concluded that stress is the cause of depression. However, they failed to consider other confounding variables, such as lifestyle habits, genetics, etc., which might cause depression. Therefore, the conclusion they made is incorrect as it may be due to a confounding variable. It is essential to control all possible confounding variables in a research study to get precise results.Conclusively, confounding variables are the most likely factors that can distort the relationship between the independent and dependent variables.
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what is not a method that can be used to solve a system of equations
Answers
Rate of change is not a method that can be used to solve a system of equations.
EquationsWhen solving a system of equations, it is important to use a valid method to find the solution. A system of equations is a set of two or more equations with multiple variables that must be solved simultaneously. There are different methods to solve a system of equations, but some methods are more effective than others.
Elimination (Linear Equations) is a method of solving a system of equations by adding or subtracting the equations to eliminate one of the variables. This allows the remaining variable to be solved easily. Substitution is another method where one variable is solved for in one equation and then substituted into another equation to solve for the other variable. Graphing involves plotting the equations on a graph and finding the intersection point(s) of the two lines. This is the solution(s) to the system of equations.
Rate of change, on the other hand, is not a method of solving a system of equations. It refers to the ratio of the change in one variable to the change in another variable. It is a concept used in calculus and differential equations, but it is not a valid method to find solutions to systems of equations. Therefore, when solving a system of equations, it is important to use a valid method to ensure accurate results.
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Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14
Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
Create a graph of the polynomial function you created in Question 4.
Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.
Answers
Answer:
Tell a Small question i cant read it tho
Step-by-step explanation:
Answer:
i am doing the same thing lol basically the farthest i got was
Step-by-step explanation:
1. They both cannot be correct because a three-degree polynomial can only have 3 maxium terms.
2. i chose g(x) = (x + 2)(x − 1)(x − 2)
3. the graph is the first one shown
Please Help ASAP
The table gives the value of Bianca's saving account at the end of each of the first four years. Which best describes the terms of this investment?
Answers
The term that best describes the investment is $1,250 invested at 4% compounded interest. The Option A is correct.
What is $1,250 invested at 4% compounded interest?We will use compound interest: A = P(1 + r/n)^(nt) formula to get the annual total investment. In this case, P = $1,250, r = 0.04, n = 1 and t = 1.
Plugging the values, we get:
A = 1250(1 + 0.04/1)^(1*1)
A = 1250(1.04)
A = $1,300
Therefore, term that best describes the investment is $1,250 invested at 4% compounded interest.
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Leading coefficient of F(x)=-4x^2-9x^5+7x^3+4x^4
Answers
Answer:
-9
Step-by-step explanation:
To solve this problem, you first need to put this problem in degree descending order.
monoidalTo do this, you first put the mononoimal with the highest exponent (The one with the most value).
This is done below:
\(F(x)=-4x^2-9x^5+7x^3+4x^4\\\\\) - This is the original problem just rewritten
\(F(x)=-9x^5-4x^2+7x^3+4x^4\) - You move the -9x first because it has the highest exponent of 5
\(F(x)=-9x^5+4x^4-4x^2+7x^3\)exponent - We put the 4x next because the expinet of 4 is higher than both 2 and 3
\(F(x)=-9x^5+4x^4+7x^3-4x^2\)because - Next, we put the 7x before the -4x because it has a higher exponent
After doing this, we can see that the leading monomial is \(-9x^5\). The leading coefficient is the number in front of the variable or, in this case, -9.
Yesterday, Alonso walked 6 miles in 2 hours. Assume he continued at that pace. Complete the table in the interactive, and graph the relationship.
Answers
Answer: y = 3x is your answer in Edg
Step-by-step explanation:
Answer:
The answer is y=3x i just got it right
Step-by-step explanation:
sorry if i'm to late :)
What are the 3 linear functions?.
Answers
Answer:
point-slope form, standard form, and slope-intercept form
Step-by-step explanation:
The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.
Here is an image with each form
Question 3*
What are the zeros of the function f(x) = x2 – 5x – 6?
(1) -2 and 3
(3) 1 and 46
(2) 2 and -3
(4) -1 and 6
pls help lol
Answers
I’ll mark as brainliest
Answer:
option 4
Step-by-step explanation:
Given
f(x) = x² - 5x - 6
To find the zeros let f(x) = 0 , that is
x² - 5x - 6 = 0
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)
The factors are - 6 and+ 1, since
- 6 × 1 = - 6 and - 6 + 1 = - 5 , then
(x - 6)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x - 6 = 0 ⇒ x = 6
Write this expression using exponents
34
Answers
Answer: 17²
Step-by-step explanation:
Let n be the largest integer for which 14n has exactly 100 digits. Counting from right to left, find the 68th digit of n
Answers
Counting from right to left, find the 68th digit of n is 10.
An integer, is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.
The largest integer with exactly 100 digits is the integer that consists of 100 copies of the digit 9.
This integer is equal to 10100 = 10
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7. The ratio of basketball players to baseball players at Cypress High School is 4 to 3. If Coach Nelson has 20 basketball players, how many players does he have for basketball and baseball combined?
A. 15
A. 15
B. 140
B. , 140,
C. 35
C. 35
D. none of these
D. none of these
Answers
\( \huge{ \blue{ \frac{4}{3} = \frac{20}{n} }}\)
\( \bold{ = \frac{3 \times 20}{4n} }\)
\( = \frac{60}{4} \)
\( \huge{ \bold{ \gray{ \boxed{ = \boxed{15}}}}}\)
Step 2: Add the number of basketball players and the number of baseball players\( \huge{ \orange{20 + 15}}\)
\( \huge{ \bold{ \red{ \boxed{ = \boxed{35}}}}}\)
Answer:\( \huge{ \bold{ \green{ \boxed{ \boxed{ \underline{c. \: 35}}}}}}\)
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Explain how you know that segment DE is not parallel to segment BC.
Answers
Answer:
a person who fortells an event is called
a rectangle room has an area of 400 square feet. the length is 7 feet less than twice the width. find the dimensions of the room.
Answers
Economic growth typically results in rising standards of living and prosperity. However, it also invites negative externalities such as environmental degradation due to over- exploiting of natural resources. As such, the world is confronted with the dilemma of growth versus environmental sustainability. Developing a model explaining the disparity of economic development concentrating on drivers such as tourism sustainability, technological innovation and the quality of leadership would be important not only to facilitate future economic growth in developing countries, but also to the environmental and sociocultural sustainability which ultimately lead to global sustainable development. The present research objective is to develop and test framework of sustainable development by considering the elements of tourism, technological innovation, and national leadership. This further would facilitate growth, environmental and socio-cultural sustainability. Understanding the integration of these dimensions would enable the building of a Sustainable Development Framework (SDF) that would provide better insight in promoting the SDGS agenda. Ultimately, growth and environmental sustainability can be achieved which will benefit the society, the economy, and nations and of course for future sustainable policy recommendation. Based on the issue above, you are required to propose relevant econometric approaches with the aims to test sustainable development by considering the elements of tourism, technological innovation, and national leadership. Question 1 [10 marks] [CLO2] Based on the scenario above, a. Propose an appropriate model specification based on the scenario above. [4 marks] used in the [4 marks] [2 marks] b. Justify the selection of the dependent and independent variables model. c. Justify the selection of the sample period.
Answers
According to the given information, the sample period should be from 2010-2020.
a) Model specification
The model specification based on the scenario above is as follows:
SDF= f(T, TI, NL)
Where: SDF= Sustainable Development Framework
T= Tourism
TI= Technological innovation
NL= National leadership
b) Justification for the selection of the dependent and independent variables model:
Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.
Independent variables:
The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.
The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.
c) Justification for the selection of the sample period:
The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.
Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.
The sample period should be from 2010-2020.
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Can someone help me find the surface area
Answers
Answer:
144 m²
Step-by-step explanation:
top triangle area: (8 x 6) / 2 = 24
bottom triangle area: (8 x 6) / 2 = 24
back rectangle area: 8 x 4 = 32
left rectangle area: 6 x 4 = 24
right rectangle area: 10 x 4 = 40
add all: 144 m²
Answer:
There are 5 surfaces for which you will have to calculate area.
the back is 4 by 8 = 32 mi^2
The bottom is 4 by 6 = 24 mi^2
the tilted ramp 4 by 10 = 40 mi^2
There are 2 side triangles 8 by 6 area of 1 triangle = 8*6/2 = 24 mi^2
area of BOTH triangles = 2 * 24 = 48 mi^2
Total area = 32 + 24 + 40 + 48 = 144 mi^2
Step-by-step explanation:
a batch of one hundred items is inspected by testing four randomly selected items. if one of the four is defective, the batch is rejected. what is the probability that the batch is accepted if it contains five defectives?
Answers
The probability that the batch is accepted if it contains five defectives will be 0.812.
What is probability?The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Here,
P(A)=(1-5/100)*(1-5/99)*(1-5/98)*(1-5/97)
=0.812
If the batch has five defects, there is a 0.812 percent chance that it will be approved.
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determine the equation of line from the graph
Answers
Answer:
y=2x+0
Step-by-step explanation:
This is slope intercept form. The slope is 2 you can tell by the two points on the graph at (0,0) and (1,2). The points move up 2 and over 1. That makes the slope 2/1 but since the bottom half is just a one it can be simplified to 2.
And the +0 just means that its y intercept is 0,0
however it is not required to put +0 at the end
Answer:y=2x+0
Step-by-step explanation:
Three impedances are connected in parallel. Z -2-5j, Zn = 6 --, 23 - 2j. Find the equivalent admittance Y where 1 Y Z 22 23 1 Y- + + Express the admittance in both rectangular and polar forms. 0.23"
Answers
Admittance in rectangular form: Y = (1/-2-5j) + (1/6) + (1/23-2j)
Admittance in polar form: |Y| = √(Re(Y)^2 + Im(Y)^2)
Resulting admittance: Y = |Y| ∠ θ = 0.23 ∠ 16.94°.
When three impedances are connected in parallel, the equivalent admittance Y can be found by summing the reciprocals of the individual impedances. Given the impedances Z1 = -2-5j, Z2 = 6, and Z3 = 23 - 2j, we can calculate the admittance Y as follows:
Y = 1/Z1 + 1/Z2 + 1/Z3
To express the admittance in rectangular form, we convert each impedance to its reciprocal and then add them:
Y = (1/-2-5j) + (1/6) + (1/23-2j)
To express the admittance in polar form, we convert the rectangular form to polar form by finding the magnitude (|Y|) and angle (θ) of Y:
|Y| = √(Re(Y)^2 + Im(Y)^2)
θ = arctan(Im(Y)/Re(Y))
The resulting admittance can be expressed as Y = |Y| ∠ θ = 0.23 ∠ 16.94°.
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Given that a travel a distance of 210km in 3hours calculate the speed in unit form in km/h
Answers
Answer:
70 Km/ h
Step-by-step explanation:
speed = \(\frac{distance }{time}\) = \(\frac{210}{3}\) = 70 Km/h
Jaxon made 12 shots in five minutes during practice, and he consistently shoot the same, how long did it take him to make 5 shots?
Answers
Step-by-step explanation:
12 shots in 5 minutes.
12/5 ratio.
how long for 5 shots ? x minutes
5/x must be the same ratio as 12/5
so,
5/x = 12/5
25/x = 12
25 = 12x
x = 25/12 = 2 1/12 ≈ 2.08 minutes =
= 2 minutes and 5 seconds
(60 seconds per minute divided by 12 = 5)