Applying derivative concepts, the y-intercept of the line tangent to the curve at (2√3, √3) is: [tex]y = \sqrt{3}[/tex]
The equation of the line is:
[tex]y - y_1 = m(x - x_1)[/tex]
In which:
There is a point [tex](x_1, y_1)[/tex].The slope is [tex]m = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]In this problem, point [tex](2\sqrt{3}, \sqrt{3})[/tex], hence [tex]x_1 = 2\sqrt{3}, y_1 = \sqrt{3}[/tex]
To find the value of [tex]\theta[/tex], we have that:
[tex]3\tan{\theta} = \sqrt{3}[/tex]
[tex]\tan{\theta} = \frac{\sqrt{3}}{3}[/tex]
[tex]\theta = \frac{\pi}{6}[/tex]
Then, for the slope:
[tex]\frac{dy}{d\theta} = 3\sec^{2}{\theta}[/tex]
[tex]\frac{dx}{d\theta} = 3\sec{\theta}\tan{\theta}[/tex]
Considering [tex]\theta = \frac{\pi}{6}[/tex]:
[tex]\frac{dy}{d\theta} = 3\left(\frac{2}{\sqrt{3}}\right)^2 = 2[/tex]
[tex]\frac{dx}{d\theta} = 3\left(\frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{3}\right) = 2[/tex]
[tex]m = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} = 1[/tex]
Then, the equation of the line is:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - \sqrt{3} = x - 2\sqrt{3}[/tex]
[tex]y = x - \sqrt{3}[/tex]
The y-intercept is the value of y when x = 0, hence:
[tex]y = \sqrt{3}[/tex]
A similar problem is given at https://brainly.com/question/22426360
Which of the following function rules represents the graph shown?
o f() = Xhy3
of(x) = 3 - X
Of(x) = -3х
Answer:
f(x) = 3 - x.......!!!!
I think so this is the. answer.....!!!
Rihanna used this number line to solve this problem. Which problem could she have been solving
Answer:
what kind kind of prob
Step-by-step explanation:
dp you have a Story
Answer:
there is no picture to explain your qustion and im confused
Step-by-step explanation:
Find the
17th
term of the arithmetic sequence whose common difference is d=5 and whose first term is a1 = 1.
The [tex]17th[/tex] term of the arithmetic sequence is [tex]81[/tex]
An arithmetic sequence is a sequence of numbers produced by adding a fixed number, called the common difference, to a term in the sequence to get the next term of the sequence.
The formula for calculating the [tex]nth[/tex] term of a sequence is
[tex]a_n=a_1+(n-1)d[/tex]
where
[tex]a_n=\text{the nth term}\\a_1=\text{the first term}\\d=\text{the common difference}[/tex]
from the question
[tex]n=17\\d=5\\a_1=1[/tex]
from this information, we can calculate the [tex]17th[/tex] term of the sequence thus
[tex]a_n=a_1+(n-1)d\\a_{17}=1+(17-1)\times5\\=81[/tex]
so, [tex]a_n=81[/tex]
Learn more about arithmetic sequences here: https://brainly.com/question/16130064
Which function is represented by the graph? f(x) = â’|x â’ 3| 4 f(x) = â’|x 3| 4 f(x) = â’|x â’ 4| 3 f(x) = â’|x 4| 3.
Functions are used to represent graphs, and vice versa.
The function represented by the graph is [tex]f(x) =- |x + 4| + 3[/tex]
The graph (see attachment) is an absolute value graph.
An absolute value graph is represented as:
[tex]f(x) =a |x - h| + k[/tex]
Where
[tex]Vertex = (h,k)[/tex]
The vertex is the minimum or the maximum point on the graph.
So, we have:
[tex]Vertex = (-4,3)[/tex]
The function becomes
[tex]f(x) =a |x + 4| + 3[/tex]
The function also passes through the point (-1,0).
So, we have:
[tex]0 =a |-1 + 4| + 3[/tex]
[tex]0 =a |3| + 3[/tex]
Remove the absolute bracket
[tex]0 =3a + 3[/tex]
Subtract 3 from both sides
[tex]3a =- 3[/tex]
Divide both sides by 3
[tex]a =- 1[/tex]
Substitute -1 for (a) in [tex]f(x) =a |x + 4| + 3[/tex]
[tex]f(x) =- |x + 4| + 3[/tex]
Hence, the function represented by the graph is [tex]f(x) =- |x + 4| + 3[/tex]
Read more about absolute value graphs at:
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Jenna walks 12 miles in 5 days. Alex walks 15 miles in 6 days. Who walks more miles per day? Show your work to prove your answer.
Answer:
Alex walked more
Step-by-step explanation:
Jenna: 12/5= 2.4
alex: 15/6=2.5
What is the slope of the following line?
Answer:
1/2
Step-by-step explanation:
becase 1(0,0) 2(2,1) = 1/2
The first modern humans appeared on Earth about 200,000 years ago. Would it be possible to measure that number in terms of feet on the football field? Explain your answer.
Which inequality represents this sentence?
A number is at least 65
On < 65
On > 65
On > 65
On < 65
Answer:
n ≥ 65Step-by-step explanation:
A number is at least 65. It means the number n can be 65 or greater.
Its translation is:
n ≥ 65The answer options don't have this included.
Let the number be n
At least 65 means the number is equal to 65 or greater than 65.Hence here we use greater than equal to sign.Inequality:-
[tex]\\ \sf{:}\Rrightarrow n\geqslant 65[/tex]
Dress:$35.99 tax:6.75%
Answer:
38.14 but if rounded up it becomes 38.15
I don’t understand someone please give me answer
What is 0.2 rounded to the nearest whole number?
Answer:
0
Step-by-step explanation:
since 2 isnt up to 5, it cannot equate to 1
HELP IVE BEEN STUCK ON THE SAME QUESTION NOBODY WILL HELP ME I CANT CALM DOWN HELP ME
Hello! :p
[tex]\sqrt{-8}[/tex] = [tex]2i\sqrt{2}[/tex]
[tex]\sqrt{-36}[/tex] = [tex]6i[/tex]
[tex]\sqrt{-5}[/tex] = [tex]i\sqrt{5}[/tex]
I hope you do well on your assignment! I also hope this helps! :)
Please help me solve #9, and please 10
Answer:
#9. y = -250x
#10. y = -2500, x = 100
Step-by-step explanation:
y = mx +b
y: y-value
m: slope
x: x-value
b: y-intercept
since your answer for #8 is -250, the slope would be -250 or m would be -250
y = -250x+b
now to solve for b, we take one of the points and plug it in, any works, but we'll use (1,-250)
plug in the points
-250 = -250(1)+b
solve for b
b = 0
thus the equation is y = -250x + 0 or y = -250x
#10 plug in x values and y values into equation to get answer
x = 10 -> y = -250(10) = -2500
y = -25,000 -> -25,000 = -250x
x = -25,000/-250
x = 100
What did Diocletian do to change the way the Roman Empire was ruled?How would we add -3 + (-9) on the number line?
GEOMETRY QUESTION NEED HELP ASAP 20 POINTS
Answer:
24 units
Step-by-step explanation:
I dont know if im right but hope this helps!
9/4 divided 5/8
I don’t know help me
Answer:
9/4 divided 5/8 = 3.6 (Ans)
Answer
9/4 ÷ 5/8 = 3.6
i hope it will help you
Convert each of the ingredient amounts below from ounces to fractions
Example: 8.2 = 8 2/10 *
2 points
Puppy Chow Trail Mix
• Trail Mix:
• 1 (12.65 ounce) can salted peanuts
• 1 (10.5 ounce) package miniature marshmallows
• 1 (3.2 ounce) package sunflower seeds
• 1(1.69 ounce) package candy-coated milk chocolate pieces (such as M&M's(R))
• 1 (1.5 ounce) box raisins
Your answer
Answer:
12.65 = 12 65/100
= 12 13/20
10.5 = 10 5/10
= 10 1/2
3.2 = 3 2/10
= 3 1/5
1.69 = 1 69/100
1.5 = 1 5/10
= 1 1/2
Step-by-step explanation:
The weight of salted peanuts is expressed in fraction as [tex]12 \frac{13}{20}[/tex] ounce.
Given that, salted peanuts = 12.65 ounce.
How to convert decimals to fractions?Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value.
Now, salted peanuts = 12.65 ounce in fraction is
12.65 = [tex]12 \frac{65}{100}[/tex]
= [tex]12 \frac{13}{20}[/tex] ounce
10.5 ounce package miniature marshmallows
In fraction 10.5 = [tex]10 \frac{5}{10}[/tex]
= [tex]10 \frac{1}{2}[/tex] ounce
3.2 ounce package sunflower seeds
In fraction 3.2 = [tex]3 \frac{2}{10}[/tex]
= [tex]3 \frac{1}{5}[/tex] ounce
1.69 ounce package candy-coated milk chocolate pieces
In fraction [tex]1 \frac{69}{100}[/tex]
1.5 ounce box raisins
In fraction [tex]1 \frac{5}{10}[/tex]
= [tex]1 \frac{1}{2}[/tex]
Therefore, the weight of salted peanuts is expressed in fraction as [tex]12 \frac{13}{20}[/tex] ounce.
To learn more about the conversion of decimal to fraction visit:
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Which graph represents an even function?
Answer:
the first one, it's linier (even)
The first graph is the one that represents an even function. See why below.
What is a even function?An even function is a mathematical function where f(x) = f(-x) for all x in the function's domain. It exhibits symmetry with respect to the y-axis.
The graph of an even function is symmetric with respect to the y-axis. If you fold the graph along the y-axis, the two halves will overlap perfectly.
Understanding even functions is relevant because they possess specific symmetry properties, which can help in analyzing and solving mathematical problems involving symmetry and function transformations.
Learn more about even function at:
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MY HEAD IS HURTING I BEG FOR YOUR HELP. I WILL MARK BRAINLIST!!
Answer: No association
Step-by-step explanation:
There is absolutely no pattern going on. This means that the miles ran per week are not really affecting the standing heartbeat. Therefore, I'd say there is no association.
Please help me with this question.
Answer:
TrueTrueStep-by-step explanation:
Dilation does not affect angles or the direction of lines. The lines of a dilated figure will be parallel to the original, unless they go through the center of dilation.
Line CD does not go through P, so C'D' is distinct and parallel to it (True).
Angles B and B' are congruent. (True)
HELP ME GUYS PLEASE!!! :)
Answer:
(10,-2)
Step-by-step explanation:
You can see that the first equation has already given as x-isolated equation aka x = 10.
With this, you can substitute x = 10 in the second equation 3x+5y = 20 then solve for y.
3(10)+5y=20
30+5y=20
Subtract both sides by 30.
5y=-10
Divide both sides by 5.
y=-2
So from x = 10 and y = -2, we can write as (10,-2) in coordinate form.
Answer:
(10,-2)
Step-by-step explanation:
since they already give u x, u can just sub it into the other equation
3(10)+5y=20
30+5y=20
5y=20-30
5y=-10
y=-2
HELP ME PLS THIS IS GRAPHING MATH ITS DUE VERY SOON PLS HELP BEFORE A BOT EATS MY QUESTION!!!!
Answer:
.
Step-by-step explanation:
.
Answer: I quessed on this with what I learned and we never learned it this way so im not sure if this is correct
It's probably not right
Step-by-step explanation:
Simplifying
13x + 6y = 180
Solving
13x + 6y = 180
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6y' to each side of the equation.
13x + 6y + -6y = 180 + -6y
Combine like terms: 6y + -6y = 0
13x + 0 = 180 + -6y
13x = 180 + -6y
Divide each side by '13'.
x = 13.84615385 + -0.4615384615y
Simplifying
x = 13.84615385 + -0.4615384615y
What would make this conditional a false statement? If you go to the gym for an hour a week, then you will lose at least 10 pounds in a month.
You go to the gym for an hour a week and lose 10 pounds in a month
You go to the gym for an hour a week and lose 17 pounds in a month
You go to the gym for an hour a week and lose 7 pounds in a month
You go to the gym for an hour a week and lose 50 pounds in a month
We must see which thing would make the conditional statement a false statement. We will see that the correct option is:
"You go to the gym for an hour a week and lose 7 pounds in a month"
So we start with the conditional statement:
"If you go to the gym for an hour a week, then you will lose at least 10 pounds in a month"
Remember that the general conditional statement is:
If P, then Q.Where P is the hypothesis and Q is the conclusion.
The conditional statement is false if:
P is true and Q false.
So the given statement is only false if you meet the hypothesis (you go to the gym for an hour a week) but not the conclusion (you lose less than 10 pounds in a month).
With that in mind, the correct option is the third one, the only one where you lose less than 10 pounds in a month.
"You go to the gym for an hour a week and lose 7 pounds in a month"
If you want to learn more about conditional statements, you can read:
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Study and Learn
pasagutan plss..
Could someone help please
Step-by-step explanation:
1. x/3-2=6
x-6=18
x=18+6
x=24
2. x/5+1=5
x+5=25
x=25-5
x=20
Answer:
x = 24 , x = 20
Step-by-step explanation:
(a)
[tex]\frac{x}{3}[/tex] - 2 = 6 ( add 2 to both sides )
[tex]\frac{x}{3}[/tex] = 8 ( multiply both sides by 3 to clear the fraction )
x = 24
(b)
[tex]\frac{x}{5}[/tex] + 1 = 5 ( subtract 1 from both sides )
[tex]\frac{x}{5}[/tex] = 4 ( multiply both sides by 5 to clear the fraction )
x = 20
Which table is y a function of x?
Answer:
The first chart
Step-by-step explanation:
i dont want to fail please anyone with a kind heart help its just thid one question im stuck with :(
Your parents decide to build a rectangular pool in your backyard. They determine that the length of the pool should be 15 feet longer than the width.
*Your parents put in fencing around the walkway for safety. If 110 feet of fencing is used, what are the dimensions of the pool? Show your work.*
Answer:
110
Step-by-step explanation:
there
Use the distributive property to write an equivalent expression.
9(w + 3x)
Triangle J K L is shown. Point M is the midpoint of side K L and point J is the midpoint of side J L. The length of K J is 12.8 meters, the lengths of J N and N L are 3.7 meters, and the lengths of K M and M L are 5.9 meters. Which statements about triangle JKL are true? Select two options. M is the midpoint of line segment KJ. N is the midpoint of line segment JL. MN = One-halfKJ MN = 4.4m MN = ML
Answer:
1 and 3
Step-by-step explanation:
Answer:
B) N is the midpoint of line segment JL.
D) MN = 1/2 KJ
Step-by-step explanation:
edgeeee
Find an equation of the line described. Write the equation in slope-intercept form when possible.
Through (-8, -7), perpendicular to the y-axis
The equation of the line is y=
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Answer:
-7
Step-by-step explanation:
Because the step in puting slope is respectly (x,y)
