Answer:
The equation of the line is [tex](x(t),y(t))=(1-4t,2+6t)[/tex] and the equation of the circle is [tex]F(t)= (3cos(t)+4,3sin(t)+1)[/tex].
Step-by-step explanation:
(a) Given: The given points are [tex](1,2)[/tex] and [tex](-3,8)[/tex].
To find: The parametric equation of line containing points [tex](1,2)[/tex] and [tex](-3,8)[/tex].
We know that the parametric equation of line containing [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is given by [tex](x(t),y(t))=(x_{1}+(x_{2}-x_{1})t,y_{1}+(y_{2}-y_{1})t)[/tex] where [tex]t[/tex]∈[tex][0,1][/tex].
Now, [tex]x(t)=1+(-3-1)t[/tex]
i.e, [tex]x(t)=1-4t[/tex]
And, [tex]y(t)=2+(8-2)t[/tex]
i.e, [tex]y(t)=2+6t[/tex]
Hence, the required parametric equation of the line is [tex](x(t),y(t))=(1-4t,2+6t)[/tex].
(b) Given: The radius of circle is 3 and centre is [tex](4,1)[/tex].
To find: The parametric equation of circle with radius 3 and centre [tex](4,1)[/tex].
We know that parametric equation of circle with radius [tex]r[/tex] and centre [tex](h,k)[/tex] is given by [tex]F(t)= (x(t),y(t))[/tex] where [tex]x(t)=rcos(t)+h[/tex] and [tex]y(t)=rsin(t)+k[/tex].
Now, [tex]x(t)=3cos(t)+4[/tex]
[tex]y(t)=3sin(t)+1[/tex]
So, the parametric equation of circle having radius 3 and centre [tex](h,k)[/tex] is [tex]F(t)= (3cos(t)+4,3sin(t)+1)[/tex].
Hence, the required equation of the circle is [tex]F(t)= (3cos(t)+4,3sin(t)+1)[/tex].
F(x)=x-7
What is the value of x when f(×) =3
Answer:
3= x - 7 (write out the equation and think of what number with 7 subtracted would be equal to 3)
3= 10-7 (10-7 is equal to three, so that's what x has to be)
x=10
Step-by-step explanation:
find the angle which y= equals to root 3 x -4 makes with yaxis
9514 1404 393
Answer:
30°
Step-by-step explanation:
The angle a line makes with the x-axis is arctan(slope). Here, that is ...
angle with x-axis = arctan(√3) = 60°
So, the angle made with the y-axis is the complement of this:
angle with y-axis = 90° -60° = 30°
Could y’all pls help out brainlest correct answer only
Answer:
The third option with the decimal on top as a fraction
Answer:
C
Step-by-step explanation:
Think of the proportional relationship as algebra.
k*number of MovieTickets = Cost, where k is the constant of proportionality.
To find k, you can substitute values in the table and solve for k.
In this example:
k*5 = $28.75
k = $28.75/5
This answer is C.
In a batch of lightbulbs, 30% are tinted, if 45 lightbulbs are tinted, how many lightbulbs are in the batch?
Step-by-step explanation:
30% of lightbulbs = 45 lightbulbs
100% of lightbulbs
= 45 * (100/30) = 150 lightbulbs.
Hence there are 150 lightbulbs in the batch.
I attached the files
Answer: why do you have so many files
Step-by-step explanation: plz tell me lol
Jeremy can tow 1/3 of a mile in 1/4 of an hour. What is the unit rate?
Answer:
1 1/3 - miles per hour.
Step-by-step explanation:
(1/3) / (1/4) =
(1/3) x (4/1) =
4/3 = 1 1/3
SelectTWO ordered pairs that satisfy the function y=−4x−1.
A
(−4,−1)
B
(−1,3)
C
(2,−9)
D
(5,19)
Compare these data sets. The equation of the trend line is listed below each data set.
2 tables. For table 1, column 1 is labeled H R and column 2 is labeled W. The regression equation is y = 0.39 x + 20.23. For table 2, column 1 is labeled R and column 2 is labeled W. The regression equation is y = 0.15 x minus 23.2.
Which statements are true about these data sets? Check all that apply.
Both sets have negative correlation.
Both sets have positive correlation.
There is no correlation between the sets.
The Runs set has a greater rate of change than the Home Runs set.
The Home Runs set has a greater rate of change than the Runs set.
Answer:
b and e
Step-by-step explanation:
Answer:
2 and 5 or B and E
Step-by-step explanation:
on edge
Hello! :)
Please help me solve this + explain your answer :)
I will indeed give you Brainlst <3
Answer:
C. 350 - acres of pumpkins
Step-by-step explanation:
The Uncle owns 510 acres, and wants 190 more acres of pumpkin than squash totaling at 510.
When looking at the possible answers D is automatically wrong since the Uncle only owns 510 acres. When I added A and C I got 510 as an answer;
160 + 350 = 510
So he wants 190 more pumpkin acres than squash so 160 represents the squash and 350 represents the pumpkin.
160 + 190 = 350
--------------------------------------------------------------------------
Another way to find the answer is by taking 510 and subtracting 190 then dividing by two;
510 - 190 = 320
320 / 2 = 160
160 + 190 = 350
Then 160 would be squash and 350 would be pumpkin.
I hope this helps!
need help with this
Answer:
1 ½% of x = 15
3/2 × x = 15
x = 15/1.5
x = 10
So
1½ 15
— = —
100 10
Round 4.24 to the nearest tenth.
4
4.3
4.2
5
Answer:
4.2
Step-by-step explanation:
Answer:
4.2
Step-by-step explanation:
........................
PLEASE HELP WILL MARK BRAINLIEST AND GIVE 20 POINTS!!!
A right rectangular pyramid is sliced vertically (down) at the red line by a plane not passing through the vertex of the pyramid. What is the shape of the cross-section.
A Trapezoid
B Triangle
C Rectangle
D Cylinder
Answer:
I feel like it might or might not be rectangle because it didn't pass through the vertex so it's almost like it's cutting off the top part of the pyramid.
Answer: Trapezoid
Step-by-step explanation:
I just did the test and got 100
Algebraic Expression
43 times greater than
the sum of 57 and 93
What is the answer to f(1)= ?
Answer:
f(1) = 1
Step-by-step explanation:
To go 1 on the x-axis and check to see where it is on the y-axis. In this case, when x = 1, y = 1.
Therefore, f(1) = 1.
1/4+1/2 divided by 3/8
Answer:
1 7/12
Step-by-step explanation:
The histogram shows a distribution of girls' heights in inches.
Which statement best describes the distribution?
A.
The data is positively skewed because the majority of the data is clustered to the left of the center.
B.
The data is negatively skewed because the majority of the data is clustered to the left of the center.
C.
The data is positively skewed because the majority of the data is clustered to the right of the center.
D.
The data is negatively skewed because the majority of the data is clustered to the right of the center.
Answer:
I believe the answer is B
For weeding the garden Arjun was given $18.29 . Now he has $42.38 . How much money did he have before ?
Answer:
24.09
Step-by-step explanation:
42.38 - 18.29 = 24.09
Triangle ABC ~ Triangle DEF, which of the following is a conclusion that can be drawn?
A. AB/AC=DE/DF
B. AB/DE=CA/DE
C. BC/AB=DE/EF
D. BC/AC=EF/DE
i need help again pls
Answer:
the answer is A
Step-by-step explanation:
Answer:
B. Add two -1 counters to each side
Step-by-step explanation:
If you were to do this problem normally you would subtract 2 from each side so B just makes sense.
Photo attached please help
Answer:
A
Step-by-step explanation:
Multiply:
[tex](\frac{5}{5+\sqrt{10x} } )(\frac{5+\sqrt{10x} }{5+\sqrt{10x} } )[/tex]
Simplify:
[tex]\frac{5(5-\sqrt{10x}) }{(5+\sqrt{10x})(5-\sqrt{10x} ) }[/tex]
Factor:
[tex]\frac{5(5-\sqrt{10x}) }{25-10x}[/tex]
Reduce:
[tex]\frac{5(5-\sqrt{10x}) }{5(5-2x)}[/tex]
Solution:
[tex]\frac{5-\sqrt{10x} }{5-2x}[/tex]
HL
ASA
SSS
AAS
SAD
Not congruent
Answer: 4
Step-by-step explanation:
i think
Solve the given inequality and graph the solution on a number line. -x/2 + 3/2 < 5/2 Answer?
25 POINTS FOR BRAINLIEST
Answer:X>-2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don’t contain the variable.
Is this a positive trend or negative trend or no trend please help
Answer:
negative trend because the values are decreasing
I’ll brainlest pls help me
What is the value of y in this triangle?
Answer:
value of y in triangle is D. 36° okay
You have a square that has a side length of $1$ centimeter. Each minute, $2$ centimeters are added to the side length. After $10$ minutes, what will be the difference between the area of the last square and the area of the initial square in square centimeters (do not include the units in your answer)?
Answer:
Difference in area of the last square and the initial square = 440 cm²
Step-by-step explanation:
Length of the side of a square = 1 cm
Area of the square = (side)² = 1 cm²
Addition of side length every minute = 2 cm
After x minutes length of each side of the square = (1 + 2x) cm
If x = 10 minutes
Length of each side of the square = [1 + 2(10)]
= 21 cm
Area of the square after 10 minutes = (21)²
= 441 cm²
Therefore, difference in area of the last square and area of the initial square
= 441 - 1
= 440 cm²
what is the slope for (4.6) and (8,4
Answer:
This is a vertical line; there is no change in the x coordinate value; and since the slope is defined to be change in y any attempt to corresponding change in x evaluate the slope would result in an attempt ot divide by zero.
Step-by-step explanation:
There your answer hope it helps.
A
8
B
7
D
С
CD = [?]
Sammy has $180 in her savings account and plans to deposit $20 each month.
help me plz
Answer:
For a function f(x) = y.
The independent variable is the one that we chose to input in the function, in this case, is x, and the dependent variable is the variable that changes in response to the independent variable, in this case, is y.
In this problem we have:
"Sammy has $180 in her savings account and plans to deposit $20 each month."
We can define:
y = money in her savings account
x = number of months that have been passed since she started saving.
Originally, she has $180, and she saves $20 per month, so if x months have been passed, the total amount of money in her savings account is:
y = f(x) = $180 + $20*x
Now we want to know if this function is continuous or discrete, to see this we need to look at the possible values of x.
x represents the number of months that have been passed, then the values that x can take are:
x = 0, 1, 2, 3, 4, ...
So x can only take the values of positive integers, this means that the domain of x is discrete, then the function f(x) is a discrete function.
Solve the equation + 6 = 2.
Question 13 options:
A)
No Solution
B)
a = 13
C)
a = 7
D)
a = 61
Question 14 (5 points)
Solve the equation 10 + y√
y
= 14
Question 14 options:
A)
y = 576
B)
y = 4
C)
y = 16
D)
y = 2