Answer:
0
Step-by-step explanation:
-4 - -4 = 0
6-4 = 2
0/2 = 0
Answer:
change in y change in x
The change in x
is equal to the difference in x-coordinates (also called run), and the change in y
is equal to the difference in y-coordinates
m=y2−y1x2−x1
Substitute in the values of x
and y
into the equation to find the slope.
m=−4−(4)−3−(6)
m=8/9
Use Trigonometric substitution to eliminate the roots 1.1. 164+2 + 1 Use Trigonometric substitution to eliminate the roots 1.1. V64+2 + 1 1.2. V4z2 – 49
To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.
1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:
V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49
We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:
V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)
Here is a more detailed explanation of the substitution:
In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.
When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3
In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.
When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)
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please help ill mark brilliant
Answer:
2Step-by-step explanation:
Look at the picture.
In 9 minutes, Keiko can type 45 words.
What is her rate in words per minute?
For a right triangle ABC, you are told that cos A = x and sin A = y. Which option below gives an expression that is
equivalent to tan A?
OX
Equivalent to tan A =\(\frac{y}{x}\)
What is meant by the right triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. The perpendicular and the triangle's base are the sides that make up the right angle. The third side is the longest of the three sides, known as the hypotenuse.A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilize specific terminology.A right triangle is a triangle in which one of the angles is at a right angle or two of the sides are perpendicular, or more formally, an orthogonal triangle, formerly known as a rectangled triangle.Equivalent to tan A:
A right triangle ABC so that m∠C = 90°
The lengths are:
Side a is opposite ∠A,
Side b is opposite ∠B,
Side c (the hypotenuse) is opposite ∠C
Because cos A = x, therefore
\(x =\frac{b}{c}\) => \(b = cx\) (1)
Because sin A = y, therefore
\(y =\frac{a}{c}\) => \(a = cy\) (2)
By definition,
tan A = a/b
\(=\frac{cy}{cx}\)
\(=\frac{y}{x}\)
Equivalent to tan A =\(\frac{y}{x}\)
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What is the Y and x intercept of 9X-6Y= 72
Answer: The y-intercept is -12
The x-intercept is 8
Step-by-step explanation: Factor out 3
Divide all by 3 to simplify.
9x - 6y = 72 is equivalent to
3x - 2y = 24
At this point, you can substitute 0 for x and solve for y
3(0) -2y = 24. -2y/-2 = 24/-2
y = -12
And substitute 0 for y and solve for x.
3x -2(0) = 24. 3x/3 = 24/3
x = 8
OR Change to slope intercept form:
y = mx + b. b is the y intercept.
-2y = -3x + 24. Solve for y.
Divide all by-2
y = 3x/2 - 12.
The y-intercept is -12
To find the x-intercept, substitute 0 for y and solve for x.
0 = 3x/2 -12 Add 12 to both sides.
12 = 3x/2. Multiply both sides by 2/3
8 = x
The x-intercept is 8
If f(x) = 2x - 9, which of the following are correct? Select all that apply. f(-1) = -11 f(2) = 5 f(3) = -3 f(0) = -9 f(-3) = 15
f(-1) = -11 and f(3) = -3 . these functions are true .
What does a math function mean?
A relationship between a group of inputs and one output each is referred to as a function. A function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. f(x), where x is the input, is a common way to refer to a function.In mathematics, a function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable).given function f(x) = 2x - 9
f(-1) = -11 ⇒ x = -1 put in function
f( -1 ) = 2 * -1 - 9 ⇒ - 11
f(2) = 5 ⇒ x = 2 put in function
f( 2 ) = 2 * 5 - 9 = 1
f(3) = -3 ⇒ x = 3 put in function
f ( 3 ) = 2 * 3 - 9 = -3
f(-3) = 15 ⇒ x = -3 put in function
f( -3) = 2 * -3 - 9 = - 15
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1. Consider the following LPP
maximize
subject to
z=−x
1
+2x
2
x
1
+x
2
+x
3
=2
x
1
−x
2
+x
4
=1
x
1
,x
2
,x
3
,x
4
≥0
(a) Check that x
0
=(1,1,0,1)
T
is a feasible solution but not a basic feasible solution. Starting from x
0
, find a basic feasible solution. (b) Let x
0
′
=(0,0,2,1)
T
. Show that x
0
′
is a basic feasible solution. (c) Check if x
0
′
is an optimal solution. If not, find a better basic feasible solution.
(a) To check if x₀ = (1, 1, 0, 1)ᵀ is a feasible solution, we substitute its values into the constraints: x₁ + x₂ + x₃ = 2; 1 + 1 + 0 = 2 (satisfied).
x₁ - x₂ + x₄ = 1; 1 - 1 + 1 = 1 (satisfied). Since x₀ satisfies all the constraints, it is a feasible solution. However, to determine if it is a basic feasible solution, we need to check if it satisfies the non-negativity condition and if it has exactly two non-zero variables. In this case, x₀ has three non-zero variables (x₁, x₂, and x₄), so it is not a basic feasible solution. To find a basic feasible solution starting from x₀, we need to identify two non-zero variables and set the remaining variables to zero. We can choose x₁ and x₂ as the non-zero variables: x₁ + x₂ + x₃ = 2; 1 + 1 + 0 = 2; x₁ - x₂ + x₄ = 1; 1 - 1 + 1 = 1. Setting x₃ and x₄ to zero, we get a basic feasible solution: (x₁, x₂, x₃, x₄) = (1, 1, 0, 0). (b) To show that x₀' = (0, 0, 2, 1)ᵀ is a basic feasible solution, we substitute its values into the constraints: x₁ + x₂ + x₃ = 2; 0 + 0 + 2 = 2 (satisfied). x₁ - x₂ + x₄ = 1; 0 - 0 + 1 = 1 (satisfied).
Since x₀' satisfies all the constraints and has exactly two non-zero variables (x₃ and x₄), it is a basic feasible solution. (c) To check if x₀' is an optimal solution, we need to compare its objective function value with other feasible solutions. However, since the objective function is not provided, we cannot determine if x₀' is optimal without additional information. To find a better basic feasible solution, we can perform the simplex method or explore other points in the feasible region that may yield a higher objective function value.
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one method of conducting a survey involves selecting a sampling of a representative group of people. true false
It is true that one method of conducting a survey involves selecting a sampling of a representative group of people. This is called survey sampling.
Survey sampling is defined as a statistical method that involves selecting and surveying individuals from a particular group of people. The population that is chosen to survey could be based on a range of attributes. The target audience could be a general group like the United States' population or a more specific group, like young adults, voters in California, or male pet owners from New England.
Survey sampling involves three steps, which are:
sample selection: what group of people to include in one's sample,data collection: collecting data from the sample's answers, andestimation: the estimation about the general population using statistical calculations.Learn more about survey at https://brainly.com/question/19637329.
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Solve the equation. (Give an exact answer. Do not round.) 5x/2−6=2x−7/ Enter a fraction, Integer, or exact decimal. Do not approximate.
The solution to the equation (5x/2) - 6 = (2x - 7) is x = -2 as per the concept of solving equations.
To solve the equation (5x/2) - 6 = (2x - 7), we will first simplify the equation by clearing the fractions.
Multiply every term in the equation by the common denominator of 2, which is (2/1):
2[(5x/2) - 6] = 2(2x - 7)
This simplifies to:
5x - 12 = 4x - 14
Next, we will isolate the variable x by moving all the terms containing x to one side of the equation and the constant terms to the other side.
Subtract 4x from both sides:
5x - 4x - 12 = 4x - 4x - 14
Simplifying further:
x - 12 = -14
Now, we will isolate x by moving the constant term to the other side of the equation.
Add 12 to both sides:
x - 12 + 12 = -14 + 12
This simplifies to:
x = -2
Therefore, the solution to the equation (5x/2) - 6 = (2x - 7) is x = -2.
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of the last 16 people at a carnival booth, 6 won a prize. what is the experimental probability that the next person at the booth will win a prize?
Answer:
Step-by-step explanation:
big cheeze
Answer: 3/8
The given information is as follows: Out of the last 16 people, 6 people won a prize. We need to calculate the experimental probability of the next person winning the prize. To calculate experimental probability, we use the formula of experimental probability is given as: Experimental probability = Number of favorable outcomes / Total number of outcomes.
The given information tells us that out of the last 16 people, 6 people won a prize. It means that the number of favorable outcomes is 6. So, the experimental probability of winning a prize = Number of favorable outcomes / Total number of outcomes. Total number of outcomes is 16.
Therefore, Experimental probability = 6 / 16. Let's simplify this fraction. We can divide the numerator and denominator by 2.6/16 = 3/8Therefore, the experimental probability of the next person winning a prize is 3/8.
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help me yo!
A bag held 2 orange marbles, 3 black marbles, and 5 pink marbles. I drew a pink marble and did not replace it. What is the probability of drawing a pink marble next?
A) 2/5
B) 4/9
C) 1/2
D) 5/9
A bag held 3 white marbles, 1 orange marble, and 2 green marbles. Anna drew a white marble and did not replace it. What is the probability of drawing a green marble next?
A.) 1/6
B.) 1/5
C.) 1/3
D.) 2/5
A locker combination has three nonzero digits, and digits cannot be repeated. If the first digit is 3, what is the probability that the next digit is odd?
A.) 4/9
B.) 1/5
C.) 1/2
D.) 5/9
My locker combination has three digits. None of the digits are zero. What is the probability that the first digit of my locker combination is less than 4?
A.) 3/10
B.) 1/3
C.) 2/5
D.) 4/9
Answer:
1 is B 2 is D
Step-by-step explanation:
5+3+2=10
but since you took a pink one out its now 9 you also need to subtract 1 from the 5 since you didn't replace it
so your chances of getting a pink one are 4/9
26. This week 6 different students paid $2.00 each in fines to the school librarian. The librarian also received a $60.00 donation from a local business. She spent $37.50 to buy books and supplies. Write an expression that shows the amount of money the librarian has at the end of the week. DO NOT SOLVE. YOU SHOULD NOT HAVE AN EQUAL SIGN.
Answer:
2x + 60 - 37.50
x = 6
Need help with these 3
Answer:
Step-by-step explanation:
Corresponding angles: When two parallel lines are intersected by a transversal, the acute angles on the same side are congruent & the obtuse angles on the same side of the transversal are congruent and they are called corresponding angles.
Co-interior angles: The interior angles on the same side of the transversal are called co -interior angles and they are supplementary.
a) c + 123 = 180 {linear pair}
c = 180 - 123
c = 57
a = 123 {Corresponding angles}
b = a {Vertically opposite angles are congruent}
b = 123
b) f + 82 = 180 {Linear pair}
f = 180 - 82
f = 98
d = f {Corresponding angles}
d = 98
e = d {Vertically opposite angles}
e = 98
c) h = 75 {Corresponding angles}
g = h {Vertically opposite anges}
g = 75
12y=360 solve for y
Answer:
30
Step-by-step explanation:
divide both sides by 12 to find y
12y / 12 = y
360 / 12 = 30
therefore y = 30
What is the equation of this line?
A. y=1/2x-3
B. y=-1/2x-3
C. y=-2x-3
D. y=2x-3
What transformation maps rectangle QRST to rectangle Q’R’S’T’?
The figure in the question shows QRST and Q'R'S'T', having the positions
of the lettering flipped over a line parallel to side RS.
The transformation that maps rectangle QRST to rectangle Q'R'S'T' is; reflection.Reasons:
From the attached figure, likely to be that of the question we have that, a reflection of the sides RS and QT, across a line parallel to the side RS and equidistant to the side RS on rectangle QRST and R'S' on rectangle Q'R'S'T', maps the RS to R'S', QT to Q'T', QR to Q'R', and TS to T'S'.
Therefore;
The transformation that maps rectangle QRST to rectangle Q'R'S'T' is a reflection.Learn more here:
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The likely question options are;
Reflection
Translation
Rotation
Stretch
The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If p is the price of the item, then three equivalent forms for the profit are
Standard form: - 2 p^2 + 24p - 54
Factored form: -2(p - 3)(y-9)
Vertex form: -2(p-6)^2 + 18.
Which form is most useful for finding a. The prices that give a profit of zero dollars?
b. The profit when the price is zero?
c. The price that gives the maximum profit?
Answer:
Step-by-step explanation:
If the profit of a company made by the company is in the form a quadratic expressions but in the different forms as given in the question.
a). The prices that give a profit of zero dollars.
Expression that is most useful,
Factored form: -2(p - 3)(p - 9) = 0
p = 3, 9
b). The profit when the price is zero .
Standard form:
Profit = -2p² + 24p - 54 = 0
-p² + 12p - 27 = 0
-p² + 3p + 9p - 27 = 0
-p(p - 3) + 9(p -3) = 0
(-p + 9)(p - 3) = 0
p = 3, 9
c). The price that gives the maximum profit.
Vertex form: -2(p - 6)² + 18
Vertex of the given expression → (6, 18)
Maximum profit will be at p = 6.
Therefore, profit = -2(6 - 6)² + 18 = 18
Question 4 Which one is correct about omitted variable bias? Check all that apply. (Two correct answer.) If the omitted variable and included variable are correlated, there is a bias. If the omitted variable is relevant, there is a bias. Random assignment of included variables cuts the relationship between the omitted variable and included variable and bring the bias to zero. If the omitted variable and included variable are correlated AND the omitted variable is relevant, there is a bias.
The correct statements about omitted variable bias are:
1. If the omitted variable and included variable are correlated, there is a bias.
2. If the omitted variable is relevant, there is a bias.
Omitted variable bias refers to the bias introduced in an econometric model when a relevant variable is left out of the analysis. The bias occurs when the omitted variable is correlated with both the dependent variable and the included variables in the model.
If the omitted variable and included variable are correlated, there is a bias because the included variable may capture some of the effects of the omitted variable. In this case, the estimated coefficient of the included variable will be biased, as it will include the influence of the omitted variable.
Similarly, if the omitted variable is relevant, there is a bias because it has a direct impact on the dependent variable. By excluding the relevant variable, the model fails to account for its influence, leading to biased estimates of the coefficients of the included variables.
Random assignment of included variables does not eliminate omitted variable bias. While random assignment may help control for confounding factors and reduce bias in certain experimental designs, it does not address the issue of omitting a relevant variable from the analysis. Omitted variable bias can still exist even with random assignment of included variables.
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Solve the system by eliminating one of the variables by addition or subtraction
2x-y=4
3x+y=6
Answer:
(2,0)
Step-by-step explanation:
2x-y=4 equation 1
3x+y=6 equation 2
5x=10 eliminate y by adding equations
x=2
solve for y
2x-y=4
2(2)-y=4
4-y=4
-y=0
y=0
check answer:
3x+y=6
3(2)+0=6
6=6
to calculate the average of the numeric values in a list, the first step is to get the total of values in the list.
True, to calculate the average of numeric values in the list, the first step is to get the total of values in the list.
Steps to calculate the Average:
Let’s assume there are 4 numbers having values of 2,8,22,48 respectively.
To find the average we first have to take the total of all values.
2+8+22+48=80.
Our next step will be to divide this total by the number we have in our question i.e., 4.
so, our average will be 80/4= 20.
So, 20 will be our average.
So yes, it is true that to calculate the average of numeric values in the list, the first step is to get the total of all values in the list.
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find mBc
A) 62°
B) 65°
C) 67°
D) 70°
E) 72°
put 62 it does have instructions right
Una guitarra electroacústica cuesta 1700 y un bajo eléctrico 7520. Si Carlos compro los dos instrumentos y pago $7922, si le descontaron el 15% en el bajo eléctrico ¿Qué porcentaje le descontaron de la guitarra electroacústica?
Answer:
irrelevant answr
Step-by-step explanation:
In one baseball season, Peter hit twice the difference of the number of home runs Alice hit and 6. Altogether, they hit 18 home runs. How many home runs did each player hit that season.
Answer:
Peter hit 12 home runs and alice hit 6 home runs
Step-by-step explanation:
this is right because if Peter hit 6 and then he hit twice the amount that would bring his total to 12 due to 6 x 2 = 12 and if together they hit 18 home runs that would mean you want to subtract the total from Peter's and that would be explained as 18-12=6 and the 6 left over would leave you with alice number of home runs. Hope this helps :)
1.Discuss the population scenario of Dhaka City.? (3 point)
2.How do you want to restructure the population of Dhaka City to mitigate the present traffic jam situation?
The population scenario of Dhaka City is characterized by rapid urbanization, high population density, and significant population growth.
1. The population scenario of Dhaka City is characterized by rapid urbanization, high population density, and significant population growth. These factors have led to numerous challenges, including increased traffic congestion, inadequate infrastructure, and strain on public services. The city's population is growing at a rapid pace, resulting in overcrowding, housing shortages, and environmental concerns.
2. To mitigate the present traffic jam situation in Dhaka City, a restructuring of the population can be pursued through various strategies. One approach is to promote decentralization by developing satellite towns or encouraging businesses and industries to establish themselves in other regions. This would help reduce the concentration of population and economic activities in the city center. Additionally, improving public transportation systems, including expanding the metro rail network, introducing dedicated bus lanes, and enhancing cycling and pedestrian infrastructure, can provide viable alternatives to private vehicles. Encouraging telecommuting and flexible work arrangements can also help reduce the number of daily commuters. Moreover, urban planning should focus on creating mixed-use neighborhoods with residential, commercial, and recreational spaces to minimize the need for long-distance travel.
By implementing these measures, the population of Dhaka City can be restructured in a way that reduces the strain on transportation systems, alleviates traffic congestion, and creates a more sustainable and livable urban environment.
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Which statement best describes the end behavior of the following function?
F(x) = 3x³+4x³ - x +11
The statement which best describes the end behavior of the function given is option C. The graph of the function starts low and ends high.
What is End Behavior of a Function?End behavior of a function is the statement which describes the behavior of the graph of the function towards the end of the X axis.
Given function is,
F(x) = 3x⁵ + 4x³ - x + 11
We have to find the behavior of the function as x value approaches to infinity or negative infinity.
The end behavior of a polynomial is same as the end behavior of the monomial which is the leading term.
Here the leading term is 3x⁵.
As x approaches infinity, 3x⁵ also approaches infinity.
As x approaches negative infinity, 3x⁵ approaches negative infinity, since the power is negative.
So the function starts at low and end at high.
Hence the correct statement is C. The graph of the function starts low and ends high.
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Your question misses something. The complete question is given below.
Which statement best describes the end behavior of the following function?
F(x)= 3x^5 + 4x^3 - x + 11
A. The graph of the function starts low and ends low.
B. The graph of the function starts high and ends low.
C. The graph of the function starts low and ends high.
D. The graph of the function starts high and ends high.
Ronald is trying to reconstruct his spending pattern from May. He knows that he had $315 in his account on May 1, but after that, his receipts and balance statements are all scrambled. Here are Ronald’s records: Date Transaction Type Amount ($) 5/25 Purchase 66 5/18 Purchase 90 5/30 Purchase 188 5/24 Deposit 151 5/22 Purchase 152 5/8 Deposit 104 5/3 Purchase 175 5/6 Purchase 82 Assuming that this is a complete, if scrambled, record of Ronald’s May spending and that any overdraft fees incurred do not affect the running total, how many times did Ronald overdraw his account in May? a. Ronald never overdrew his account. b. Ronald only overdrew his account once. c. Ronald overdrew his account twice. d. Ronald overdrew his account more than twice. Please select the best answer from the choices provided A B C D
Answer: C. Ronaldo overviewed his account twice.
Step-by-step explanation:
Just took a test on edge.
After Batman brought the Joker to justice, the crime rate in Arkham City decreased by 12\%12%12, percent. Previously, the crime rate was ccc incidents per 100010001000 people.
0.88 is the new crime rate in Arkham City.
What is crime rate?The number of offenses reported to law enforcement authorities per 100,000 people in a population is referred to as the crime rate. By dividing the total number of reported offenses by the population, the crime rate is determined.
Given,
The crime rate in Arkham City decreased by 12% when Batman managed to capture the Joker.
In the past, there were c occurrences of crime per 1000 persons.
How can one create an expression that models the issue?
A drop in the percent of crime is subtracted from the prior crime rate, which was defined as incidences per 1000 persons.
c the number of recent crimes per 1,000 individuals;
New crime rate = previous crime rate - decrease in crime %.
New crime rate = c - 12%c
New crime rate = c - 0.12c
New crime rate = 0.88c
Hence, the new crime rate is 0.88c.
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The complete question is:
"After batman brought the joker to justice , the crime rate in arkham city decreased by 12%. Previously the crime rate was c incidents per 1000 people. Which of the following expressions could represent the crime rate in Arkham City after Batman brought the Joker to justice?
a. 22/25 c
b. 0.12c
c. -0.12
d. 0.88c
e. c/1.12"
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.
x = t⁵ + 1, y = t⁶ + t; t = ?1
The equation of tangent to a curve corresponding to the given value of the parameter x = t⁵ + 1, y = t⁶ + t; t = 1 is y = 7x/5 - 4/5
What is the equation of tangent to a curve?The equation of tangent to a curve is the equation of the line that touches the curve at one point.
To find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.
x = t⁵ + 1, y = t⁶ + t; t = 1, we proceed as follows.
We know that the tangent to the curve is the derivative dy/dx.
Now dy/dx = dy/dt ÷ dx/dt
x = t⁵ + 1
So, differntiating, we have
dx/dt = d(t⁵ + 1)/dt
= dt⁵/dt + d1/dt
= 5t⁴ + 0
= 5t⁴
Also, y = t⁶ + t
differentiating, we have that
dy/dt = d(t⁶ + t)/dt
= dt⁶/dt + dt/dt
= 6t⁵ + 1
= 6t⁵ + 1
Since dy/dx = dy/dt ÷ dx/dt, substituting the values of the variables into the equation, we have that
dy/dx = dy/dt ÷ dx/dt
dy/dx = (6t⁵ + 1) ÷ 5t⁴
At t = 1, we have that
dy/dx = (6t⁵ + 1) ÷ 5t⁴
dy/dx = (6(1)⁵ + 1) ÷ 5(1)⁴
dy/dx = (6(1) + 1) ÷ 5(1)
= (6 + 1) ÷ 5
= 7/5
Now, we know that the equation of the tangent is the equation of a straght line.
So, using the equation of a straight line in slope-point form, we have that
(y - y')/(x - x') = dy/dx
Now, y' = y at t = 1
So,y = t⁶ + t
y = 1⁶ + 1
= 1 + 1
= 2
Also, x' = x at t = 1
So,x = t⁵ + 1
x = 1⁵ + 1
= 1 + 1
= 2
Since
x' = 2y' = 2 anddy/dx = 7/5Substituting the values of the variables into the equation, we have that
(y - y')/(x - x') = dy/dx
(y - 2)/(x - 2) = 7/5
Cross-multiplying,we have that
5(y - 2) = 7(x - 2)
5y - 10 = 7x - 14
5y = 7x - 14 + 10
5y = 7x - 4
y = 7x/5 - 4/5
So, the equation is y = 7x/5 - 4/5
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find the area of the surface generated by revolving the curve about the given axis. (round your answer to two decimal places.) x = 1 6 t3, y = 7t 1, 1 ≤ t ≤ 2, y-axis
Therefore, the approximate area of the surface generated by revolving the given curve about the y-axis is 8847.42 square units, rounded to two decimal places.
To find the area of the surface generated by revolving the curve around the y-axis, we can use the formula for the surface area of revolution:
A=2π∫abx(t)(dydt)2+1dtA=2π∫abx(t)(dtdy)2+1
dt
In this case, the curve is defined by the parametric equations: x(t)=16t3x(t)=16t3 and y(t)=7t−1y(t)=7t−1, where 1≤t≤21≤t≤2.
First, let's find dxdtdtdx and dydtdtdy:
dxdt=48t2dtdx=48t2
dydt=7dtdy=7
Now we can substitute these values into the formula and integrate:
A=2π∫1216t3(48t2)2+1dtA=2π∫1216t3(48t2)2+1
dt
Simplifying further:
A=2π∫1216t32304t4+1dtA=2π∫1216t32304t4+1
dt
To evaluate this integral, numerical methods or specialized software are typically used. Since this is a complex calculation, let's use a numerical integration method such as Simpson's rule to approximate the result.
Approximating the integral using Simpson's rule, we get:
A≈2π(163t42304t4+1)∣12A≈2π(316t42304t4+1
)∣
∣12
A≈2π(163(24)2304(24)+1−163(14)2304(14)+1)A≈2π(316(24)2304(24)+1
−316(14)2304(14)+1
A≈2π(163(16)2304(16)+1−163(1)2304(1)+1)A≈2π(316(16)2304(16)+1
−316(1)2304(1)+1
)
Now we can calculate this expression:
A≈2π(256336865−1632305)A≈2π(325636865
−3162305
Using a calculator, we can find the decimal approximation:
A≈2π(1517.28−108.74)A≈2π(1517.28−108.74)
A≈2π×1408.54A≈2π×1408.54
A≈8847.42A≈8847.42
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Mr. Davis has 30 baseballs and 12 footballs. What is the ratio of all balls
to baseballs?
Answer: 5:2 Ratio
Step-by-step explanation:
Answer:
8:5
Step-by-step explanation:
total no of balls= 30+12=42
ratio of all ball to baseballs= 42:15
simplified it would be= 8:5