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
What are the total amount of choices possible if an individual is to create a 4 digit password using the digits 0 through 9 inclusive, but not using the digit 0 as the first character of the password? a. 39 b. 900 c. 399 d. 9000 Please select the best answer from the choices provided. A B C D.
We want to see how many different 4-digit passwords we can create by using digits from 0 to 9, such that the first character can't be 0.
We will see that the correct option is D: 9,000
The total number of different combinations is given by the product between the number of options for each selection.
Here we have 4 selections.
First character.Second character.Third character.Fourth character.Now let's find the number of options for each of these:
First character: 9 options {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}Second character: 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}Third character: 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}Fourth character: 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}The total number of different combinations is just the product of these 4 numbers:
C = 9*10*10*10 = 9,000
So we can conclude that the correct option is D.
If you want to learn more about combinations, you can read:
https://brainly.com/question/2280026
Answer:
✅ D. 9000just took the test
Margie says the set of numbers, 0. 1, -1, -21 4 , 3, are in order from least to greatest. What is her error? She did not use the correct common denominator. The 3 is in the wrong place. She treated all the numbers as positive. The â€"1 should be the first number on the list.
Answer:
3 is in the wrong place
Step-by-step explanation:
:)
One of the errors made by Margie by saying the set of numbers 0, 1, -1, -21, 4, 3 is that the -21 should be the first number on the list.
The given set of numbers is:
0, 1, -1, -21, 4, 3.
Margie says that the set of numbers above is in order from least to greatest
Kindly note that:
The negative number with the highest magnitude is the lowest
The positive number with the highest magnitude is the highest
Arranging this number by carefully following the note above, the set of numbers above from the least to greatest is:
-21, -1, 0, 1, 3, 4
It is obvious that Margie made a mistake in arranging the numbers, and one of the mistake is that the -21 should be the first number on the list since it is the most negative
Learn more here: https://brainly.com/question/25874786
enter a formula using k to connect the two variables. y is proportional to 1/x
[tex]y \propto \dfrac 1x\\\\\implies y = \dfrac kx[/tex]
Identify the domain and range of the following relation. {(3,-2), (5,2), (7,6), (9,10), (11,14)}
Abigail must move a bucket of tomatoes from her garden to her kitchen, as represented on the grid below.
y
Kitchen
L(5, 1)
-1 0
2
Garden
-(-3, 4)
Answer:
Step-by-step explanation:
9.43
41)533
What is 533 divided by 41 using Partial Quotients?
Answer:
13
Step-by-step explanation:
533÷41=13 just use a calculator
You can retry this question below
The sum of two numbers is 71. The difference of the two numbers is 41. What are the two numbers.
Let x be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 71."
Write an equation that expresses the information in the sentence "The difference of the two
numbers is 41."
Solve the system you have written above.
The larger number, x is
The smaller number, y is
Calculator
Answer:
x = 56
y = 15
Step-by-step explanation:
"The sum of two numbers is 71."
x + y = 71
"The difference of the two numbers is 41."
x - y = 41
Solve the system:
From the first eq.
x = 71 - y
Replacing this value in the second eq.
(71-y) - y = 41
71 - 2y = 41
71 - 41 = 2y
30 = 2y
y = 30/2
y = 15
From the second eq.
x - y = 41
x - 15 = 41
x = 41 + 15
x = 56
Check:
from the first eq.
x + y = 71
56 + 15 = 71
Describe the end behavior of the function.
f(x)=3(1/5)^x-2
Answer:
The leading coefficient test requires a polynomial.
Not a polynomial
Step-by-step explanation:
Answer:
x → -∞, f(x) → ∞
x → ∞, f(x) → -2
Step-by-step explanation:
f(x) is an exponential function with a base less than 1. It represents decay, so will approach infinity as x approaches negative infinity. It will approach a horizontal asymptote for large positive x.
The -2 added to the exponential term moves the asymptote from y=0 to y=-2.
x → -∞, f(x) → ∞
x → ∞, f(x) → -2
14÷966 I need help doing this pls help
Answer:
0.01
Step-by-step explanation:
i hope this help only that u need to do next time is to divide 966 with a number that is close to the sum
What is the equation of the line that passes through the point (2,-2) and has a slope of -1/2?
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (2, - 2 ) into the partial equation
- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1
y = - [tex]\frac{1}{2}[/tex] x - 1 ← equation of line
Answer:
y=-1/2x-1
Step-by-step explanation:
y-y1=m(x-x1)
y-(-2)=-1/2(x-2)
y+2=-1/2(x-2)
y=-1/2x+2/2-2
y=-1/2x+1-2
y=-1/2x-1
12x(8x-20)÷4(2x-5) please solve it
Answer: 48[tex]x^{3}[/tex]-240[tex]x^{2}[/tex]+300x
hopes this helps
A plant grows at a constant rate. The table shows the heights of the plant for different numbers of days of growth. Which of the following pairs of days and heights could also be included in the table? Select all that apply.
Mean and median of 1024 divided by 16 and of these numbers 34,48,52,61,76,76,61,84,61,39,83,61,79,81,56,88
Answer:
8
Step-by-step explanation:
88888888888888888888888888888888888
I need help and I can’t find any sadly. Help!!
Answer: 1 is given, 2 is combine like terms, 3 is addition property of equality
Step-by-step explanation:
Nolan was given a box of assorted chocolates for his birthday. Each night, Nolan treated himself to 3 chocolates. After 8 nights, there were 6 chocolates remaining in the box.
Step-by-step explanation:
i am trying to solve it but how
many chocolate were there in a box
Roger is paid $50 to sell videos of a play to an audience after the play is performed.
He also receives $2 for each video he sells. The equation E=50+2v
E=50+2v
models the amount of money Roger earns selling v videos. The play's audience consists of 230 people.
What is the practical range of the equation?
Question options:
The set of all even integers greater than or equal to 50 and less than or equal to 510
The set of all integers greater than or equal to 50 and less than or equal to 510
The set of all real numbers greater than 0 and less than 230
The set of all real numbers greater than 50
The set of all even integers greater than or equal to 50 and less than or equal to 510
In other words, [tex]0 \le E \le 510[/tex] where E is an even integer.
===========================================================
Explanation:
The domain is the set of allowed inputs, while the range is the set of allowed outputs. For now, let's focus on the domain.
In this case, the domain is the set of integers between 0 and 230. We're dealing with the set {0,1,2,..., 229, 230} to represent the possible number of people who bought the video.
Let's plug in the smallest item from the domain (v = 0).
E = 50+2v
E = 50+2*0
E = 50+0
E = 50
This matches with the fact Roger gets paid $50 even if he didn't sell anything. This is the flat up front fee he got.
Now let's plug in the largest value for v (230).
E = 50+2v
E = 50+2*230
E = 50+460
E = 510
This tells us that $510 is the most Roger can get from the audience of 230 people. This is assuming that each person buys only one copy.
So we can see that the range of E values spans from $0 to $510.
Furthermore, notice that 2 can be factored from 50+2v to get 2(25+v). This shows that the expression 50+2v is always even. Therefore, we must clarify that we're dealing with the set of even numbers between 0 and 510
In symbolic form, we'd say [tex]0\le E \le 510[/tex] where E is an even integer.
In roster form, the range of possible E values is {0, 2, 4, ..., 506, 508, 510}.
Answer: the answer is A
Solve the inequality: 4(2x-11) is less than equal to -12 + 2(x-4) No "files" please and also need an explanation
[tex]4(2x-11) \leq -12 +2(x-4)\\\\\implies 8x - 44 \leq -12 + 2x -8\\\\\implies 8x -44 \leq 2x -20\\\\\implies 4x - 22 \leq x - 10~~~~~~~~~~~~~~~~~~~;[\text{Dividing both sides by 2}]\\\\\implies 4x -22 +22 \leq x -10 +22~~~~~~;[\text{Adding 22 to both sides}]\\\\\implies 4x \leq x+12\\\\\implies 4x -x \leq x+12-x~~~~~~~~~~~~~~~~;[\text{Subtracting x from both sides}]\\\\\implies 3x \leq 12\\\\\implies x \leq 4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\text{Dividing both sides by 3}][/tex]
[tex]\text{Interval solution,} ~(-\infty, 4][/tex]
Mark earns $165 every 12 hours. At this
rate, how much does he earn in 9 hours?
Answer:
123.75
Step-by-step explanation:
165/12= 13.75
$13.75 and hour
13.75x9=123.75
Answer:
$123.75
Step-by-step explanation:
165 / 12 = 13.75
13.75 x 9 = 123.75
I need help ! This paper is due tmr
Can someone help me please?? It’s due on thursday ❤️ (rotate picture if u can)
Answer: The two companies never charge the same amount to rent a bicycle for the same number of hours.
Gabriella earns $17 an hour and gets a 15%
raise. With her raise, how much will she earn after working 40 hours?
A. $680
B. $702
C. $782
D. $796
c: 782 dollars
.15 times 17 is 2.55
17+2.55= 19.55
19.55 times 40=782
Find the slope of the line from the points and the graph.
15. (2,4) and (5, 13)
16. (4,5) and (9,-3)
Answer:
15. m=3 16. m=-8/5 or -1.6
Step-by-step explanation:
The formula for slope is m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
so for #15
[tex]\frac{13-4}{5-2}[/tex]=[tex]\frac{9}{3}[/tex]=3
and for #16
[tex]\frac{-3-5}{9-4}[/tex]=[tex]\frac{-8}{5}[/tex]=-1.6
Which choice is similar to the figure shown?
Answer:
The parallelogram whose sides are 5 and 20 is similar
Step-by-step explanation:
The parallelogram whose sides are 5 and 20 is similar to the given parallelogram whose sides are 2 and 8 because the figures are the same shade and corresponding sides are proportional.
[tex]\frac{2}{5} = \frac{8}{20}[/tex] [tex]\frac{2}{4} \neq \frac{8}{18}[/tex]
[tex]\frac{2}{5} =\frac{2}{5}[/tex] [tex]\frac{2}{4} \neq \frac{8}{4}[/tex]
Victoria kicked a soccer ball laying on the ground. It was in the air for 5 seconds before it hit the ground. While the soccer ball was in the air, it reached a height of approximately 15 feet. Assuming that the soccer ball height (in feet) is a function of time (in seconds), what is the domain in the context of this problem?
Answer:
the Domain would be represented by Time in this problem, since time can only be positive, the domain would start at zero seconds and end at 5 seconds when the soccer ball hits the ground.
Step-by-step explanation:
"The square root of two times a number subtract five is equal to ten."
I think this is √2n-5 = 10.
Barbara has some dimes and quarters. If she has 16 coins worth a total of $2.50, how many of each type of coin does she have?
Answer:
10 dimes and 6 quarters.
Step-by-step explanation:
2.50-25-25=2.00-10 dimes = 1.00-4 0.25=0
so
10 dimes and 6 quarters.
Answer:
10 Dimes and 6 Quarters.
Step-by-step explanation:
Important info:
16 Coins
Total = $2.50
Note:
Dimes = 0.10 Cents
Quarters = 0.25 Cents
Question to answer:
How many of each type of coin does she have?
Solution:
10 Dimes = $1.00
6 Quarters = $1.50
$1.00+$1.50 = $2.50
Therefore 10 Dimes and 6 Quarters = $2.50 and = 16 Coin.
Chef Ira has 613 pies he wants to sell at his restaurant. Each slice is 16 pie and costs $1.50. Chef Ira sells all the remaining slices of pie.
How much money will he earn?
A. $9.00
B. $9.50
C. $38.00
D. $57.00
I need helppp help meeeeeeee
1) [tex]\frac{11-13}{4-7}= \frac{2}{3}[/tex]
2) [tex]\frac{-2-7}{-10-(-7)}=\frac{-9}{-3} =3[/tex]
3) [tex]\frac{9-3}{-11-(-14)} =\frac{6}{3}=2[/tex]
4) [tex]\frac{8-4}{11-(-9)} =\frac{4}{20}= \frac{1}{5}[/tex]
ok done. Thank to me :>
15.
Write a direct variation equation if x = 7 and y = 42.
16.
Use the equation in example 15 to find x if y = 66.
Answer:
15. y = 6x
16. x = 11
Step-by-step explanation:
15. A direct variation equation is of the form ...
y = kx
Solving for k, we find ...
k = y/x = 42/7 = 6
The equation is y = 6x.
__
16. Filling in the given values, we have ...
66 = 6x
11 = x . . . . . . . divide by 6
Can someone plz help me? I really don’t get this
Answer:
D.
Step-by-step explanation:
The question is asking which expressions are the same. To find the answer, or rather confirm it, you should simplify each expression.
A. 8+(3*y) and (8+3)*y
8+3y and 11y
This cannot be the answer, when simplified they are not equal
B. (7-3)*y and 7-(3*y)
4y and 7-3y
This cannot be the answer, when simplified they are not equal
C. (6/y)+13 and 13+(y/6)
13+6/y and y/6+13
This cannot be the answer, when simplified they are not equal
D. 7+(y*5) and 7+(5*y)
7+5y and 7+5y
This is the answer, when simplified they are equal
I hoped this helped and made it easier to understand! :)