Which graph represents the parametric equations x = t^2 + 2t and y = –t, where –4 ≤ t ≤ 1?
Answers
Answer:
We have:
x = t^2 + 2*t
y = -t
where:
–4 ≤ t ≤ 1
Isolating t in the "y" equation, we get:
t = -y
Now we can use the limits of t, to find similar limits for y.
When t = -4
-4 = -y
4 = y
when t = 1
1 = -y
-1 = y
Then the limits for y are:
-1 < y < 4
Now, knowing that t = -y
we can replace that in the "x" equation:
x = t^2 + 2*t
x = (-y)^2 + 2*(-y)
x = y^2 - 2*y
Then the graph of the parametric equation is the one defined by:
x = y^2 - 2*y
in the range
-1 < y < 4
The graph of this can be seen below, where the two black dots are the points where the graph should start/end.
The graph that represents the parametric equations is a parabola with an axis of symmetry is parallel to the x-axis.
An approach to determine the possible graph consists in eliminating [tex]t[/tex] and simplify the resulting expression of the form [tex]f(x)[/tex]:
[tex]x = t^{2}+2\cdot t[/tex] (1)
[tex]y = -t[/tex] (2)
By (2):
[tex]t = -y[/tex]
(2) in (1):
[tex]x = (-y)^{2} + 2\cdot (-y)[/tex]
[tex]x = y^{2}-2\cdot y[/tex]
In a nutshell, the graph that represents the parametric equations is a parabola with an axis of symmetry is parallel to the x-axis.
To learn more on parametric equations, we kindly invite to check this verified question: https://brainly.com/question/9056657
Related Questions
If the cylinder above is similar to a second cylinder that has a radius of 10mm, what is the height of the second cylinder
Answers
Answer:
The height of the second cylinder is 30mm
Step-by-step explanation:
Given
Cylinder 1:
[tex]R = 15mm[/tex]
[tex]H = 45mm[/tex]
Cylinder 2
[tex]r = 10mm[/tex]
See attachment
Required
Determine h, the height of the small one
To do this, we make use of the following equivalent ratios;
[tex]R : H = r : h[/tex]
This gives:
[tex]15 : 45 = 10 : h[/tex]
Express as fraction
[tex]\frac{15 }{ 45 }= \frac{10 }{ h}[/tex]
Simplify
[tex]\frac{1 }{ 3}= \frac{10 }{ h}[/tex]
Cross multiply
[tex]h *1 = 3 * 10[/tex]
[tex]h = 30[/tex]
Adam wants to compare the fractions and He wants to order them from least to greatest and rewrite them so they all have the same denominator. Explain how Adam can rewrite the fractions.
Answers
Answer:
[tex]\frac{1}{6},\ \frac{3}{12},\ \frac{1}{3}[/tex]
Step-by-step explanation:
Given
The fractions are:
[tex]\frac{3}{12},\ \frac{1}{6},\ \frac{1}{3}[/tex]
Required
How the fractions can be rewritten
The fractions can be rewritten by taking the LCM of the denominators.
The [tex]LCM[/tex] of [tex]12; 6\ and\ 3[/tex] is [tex]12[/tex]
So, we have:
[tex]\frac{3}{12},\ \frac{2*1}{12},\ \frac{4*1}{12}[/tex]
Simplify the numerators
[tex]\frac{3}{12},\ \frac{2}{12},\ \frac{4}{12}[/tex]
Now, the fractions can be ordered based on the numerators
[tex]\frac{2}{12},\ \frac{3}{12},\ \frac{4}{12}[/tex]
Return to original form
[tex]\frac{1}{6},\ \frac{3}{12},\ \frac{1}{3}[/tex]
If you borrow $4,000 for five years at an interest rate of 4.5%, how much will you pay back in total?If you borrow $4,000 for five years at an interest rate of 4.5%, how much will you pay back in total?
Answers
Answer:
you will pay back $4,984 in total and you will owe 984 in interest alone just in case you need that too.
Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system.
x > 3 y < 2x - 5 answers: (-3, -1) (1, 11) (4, -1) (5, 6)
Answers
Given:
The system of inequalities:
[tex]x>3[/tex]
[tex]y<2x-5[/tex]
To find:
The point that represents a solution to the system by using the graph.
Solution:
We have,
[tex]x>3[/tex]
[tex]y<2x-5[/tex]
The related equations of these inequalities are:
[tex]x=3[/tex]
[tex]y=2x-5[/tex]
The line [tex]x=3[/tex] is a vertical line that intersect the x-axis at 3.
The table of values for [tex]y=2x-5[/tex] is:
x y
0 -5
1 -3
Plot (0,-5) and (1,-3) on a coordinate plan and connect them by a straight line.
The boundary lines are dotted lines because the points on the lines are not included in the solution set.
Check the inequalities for (0,0).
First inequality: [tex]0>3[/tex] ( False)
Second inequality: [tex]0<2(0)-5[/tex]
[tex]0<-5[/tex] (False)
Both inequalities are false for (0,0). It means the shaded region of the lines is in the opposite direction of (0,0).
Plot the shaded region and the points (-3, -1), (1, 11), (4, -1), (5, 6) as shown in the below graph.
From the below graph, it is clear that the point (4,-1) is the only point lies in the common shaded region. So, (4,-1) represents a solution to the system.
Therefore, the correct option is C.
Which value is equivalent to √-25
Answers
Mark as brainy ? :
I’ll mark as brainliest.
Answers
Answer:
12 feet
Step-by-step explanation:
48 divided by 4 is 12 and 48 is the total area
Answer:
12 sq. ft.
Step-by-step explanation:
To find the area of a square (or rectangle) you multiply the length by the width.
To find the length of one side, when you have the area and one side, you divide the area by the side you have.
48 divided by 4 equals 12.
Hope this helps :)
URGENTT!!!!!!!
A simple random sample of
150 San Antonio area policemen found that the average time these police officers had worked for the police department was 16
years with a standard deviation of 5 years. Ten years ago the average amount of time policemen stayed on the job was 15 years.
What is the test statistic And P value that the researchers will use for this significance test?
Answers
Solve for y in the two equations below using substitution.
3x – 6y = 9
– 3x + 3y=9
A. y = 1/3
B. y = - 1/3
C. y = -6
D. y = 6
Answers
Answer:
C. y = -6
Step-by-step explanation:
3x – 6y = 9
–3x + 3y = 9
-3y = 18
y = -6
If a + b = 7 and b=3, what is 4a
A. 20b
B. 17a
C. 16
D.20
Answers
The requried simplified value of 4a is 16. Option C is correct.
What is simplification?Simplification is the process of reducing a mathematical expression to its simplest form by combining like terms, using the distributive property, and performing other algebraic operations.
If b=3, then substituting in the first equation, we get:
a + 3 = 7
Solving for a:
a = 4
Now, 4a = 4 x 4 = 16.
Therefore, the answer is C. 16.
Learn more about simplification here:
https://brainly.com/question/12501526
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Three same-sized cubes are attached to the top of a rectangular prism as shown below
If 5 cm, b = 18 cm, and c = 2 cm, what is the surface area of the figure?
ANSWER ASAP!! PLEASE!!
Answers
Answer:
458 cm²
Step-by-step explanation:
5 × 5 × 2 + 5 × 18 × 4 = 50 + 360 = 410
2 × 2 × 4 × 3 = 48
410 + 48 = 458
5 small containers of capacity 16, 72, 12, 24 and 56 Litres are to be used to fill a bigger container. What is the capacity of the bigger container which can be filled by each of the above containers exactly without leaving a remainder when used seperately?
Answers
Answer: 1008
Step-by-step explanation:
Given
5 small containers of capacity 16,72,12,24, and 56 litres is required to fill a big container.
The volume of big container is the LCM of the 5 given containers
[tex]LCM(16,72,12,24,56)=1008[/tex]
Therefore, the capacity of the bigger container is 1008 litres.
graph it please????????????
Answers
What is the product of V3 and 2V30 in simplest radical form?
Answers
Answer:
Step-by-step explanation:
[tex]\sqrt{3[/tex] *2[tex]\sqrt{30[/tex]
2[tex]\sqrt{30*3}[/tex]
2[tex]\sqrt{3*3*2*5}[/tex]
2*3[tex]\sqrt{2*5}[/tex]
6[tex]\sqrt{10}[/tex]
Round your answer to the nearest hundredth.
с
4
А
25°
B
Answers
Answer:
take 25 degree as reference angle
let hypotenuse be x
using cos rule
cos 25=adjacent/hypotenuse
0.90=4/x
0.90x=4
x=4/0.90
x=4.44
Step-by-step explanation:
1. Which graph represents the inequality y < 4?
Answers
Answer:
The third one.
Step-by-step explanation:
i give brainliest if you help me out
Answers
What is the probability that a randomly selected value from the distribution will be less than 2.1 standard deviation from the mean
Answers
Answer:
0.9821
Step-by-step explanation:
Probability that a randomly selected value will be less than 2.1 deviations from the mean ; this means the Zscore = 2.1
Hence, using :
P(Z < 2.1) = 0.9821 (standard normal table
= 0.9821
i need help please
Answers
Answer:
54
Step-by-step explanation:
55+71=126
180-126=54
Solve for x. Round to the nearest tenth, if necessary.
K
X
J
69
400
I
Answers
Answer:
44.4
Step-by-step explanation:
sin(40)= x/69
x=69(sin40)
x= 44.4
What is the solution of y= 4x + 6 when y= 18?
Answers
Answer:
18 = 4(3)+6
12 + 6
Step-by-step explanation:
the answer is 18 = 4(3)+6
because y is 18
Answer:
x=3
Step-by-step explanation:
[tex]18 = 4x + 6[/tex]
subtract 6 on both sides
[tex]12 = 4x[/tex]
divide both sides by 4
[tex]3 = x[/tex]
Fill in the missing monomial (please answer fast a lot of points) 49y^4x^6=(___)^2
Answers
Answer:
[tex](7y^2x^3)^2[/tex]
Step-by-step explanation:
Find the GCF then factor out all the numbers
4x-1/y -3=2 solve for y
Answers
What is the greatest common factor of 5 x 7 ,30 x 4 and 10 x 3
Answers
7/2h-3(5h-1/2)
I ALSO NEED STEP BY STEP INSTRUCTIONS NO WEBSITES OR SCREENSHOTS TYSM
Answers
Answer:
the simplified expression of this is -23/2h + 3/2 or -11 1/2h + 1 1/2.
Step-by-step explanation:
7/2h - 3(5h - 1/2)
3(5h - 1/2)
First, we need to use the distributive property to distribute the expression which requires multiplication or division. We take 3 and multiply it by both values in the parentheses which gives us 15h - 1/2. However, since there is subtraction, we need to do the opposite of that which would be 15h + 1 1/2 or 15h + 3/2. Now we can't forget 7/2h at the beginning of the expression. Here is the remaining expression :
7/2h - 15h + 3/2 or 7/2h - 15h + 3/2
Now, we need to combine like terms which requires values to have the same variable. 7/2h and 15h have the same variable so combine like terms. We do subtraction.
7/2h - 15h
We subtract this and get a result of -23/2 or -11 1/2 but don't forget the variable.
-23/2h
1/2 doesn't have a variable so we no longer can combine like terms. Therefore, it would just be -23/2h + 3/2 or -23/h + 1 1/2.
Simplify:2(2x+4y-y)
Answer is ?
Answers
Answer:
4x+6y
Step-by-step explanation:
distribute and add like terms
Answer:
[tex]4x + 6y[/tex]
Step-by-step explanation:
Collect like terms:
[tex]2(2x + 3y)[/tex]
Distribute 2 through the parentheses:
[tex]4x + 6y[/tex]
Therefore, the answer will be 4x + 6y.
What is the area of quadrilateral
Answers
Answer:
area=1÷2×diagonal(H1+H2)
=1÷2×8(2+2)
=16m2
Answer:
16 m squared,
Step-by-step explanation:
Thre are two triangles. triangle area formula = 1/2 bh
plug in numbers but there's another rectangle so times 2
1/2 8*2 = 8*2=16
if correct, please mark brainliest if you feel like it:)
Find the surface area of the pyramid. The faces of the triangular pyramid are equilateral triangles 34.6 mm 40 mm 40 mm The surface area is?
Answers
Answer:
would you still like me to help you with this problem?
The function f(x) = { x + is used to complete this table. Which statements are true of the given function?
(-1,1) (0,3/2) (1,2) (2,5/2)
Answers
Answer:
i don't know
Step-by-step explanation:
can you explain? thank you
hey! please help i’ll give brainliest
Answers
Answer:
C
Step-by-step explanation:
"grow or develop in a healthy or vigorous way, especially as the result of a particularly favorable environment."
Answer:
C.
hope this helps
have a good day :)
Step-by-step explanation:
The sketch shows two parallel lines cut by a transversal. Which pair of angles are alternate interior angles?
Answers
Answer:
B) Angle 5 and angle 4
Step-by-step explanation:
Given
See attachment for sketch
See comment for options
Required
The alternate interior angles
Interior angles are such that they are located between the given parallel lines.
In the attached sketch, the interior angles are: 3, 4, 5 and 6
Alternate angles are at the opposite sides of the transversal
Hence:
4 and 5 are alternate interior
3 and 5 are also alternate interior