Answer: x=3
Step-by-step explanation:
A curve is represented by x = 3sec θ, y = 3tan θ where 0 < θ < /2.
Which of the following is the y intercept of the tangent to the curve at (2√3, √3)?
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
3. Is the triangle a right triangle? Explain.
1.9
2.7
3.23
we have: [tex](3,23)^{2} \neq (1,9)^{2} +(2,7)^{2}[/tex]
so the triangle isn't a right triangle
ok done. Thank to me :>
How much money, in dollars, is available on his card after he takes 0
rides?
Answer:
However much he had on his card in the first place.
Step-by-step explanation:
Say he had $500 on his card. He took 0 rides ( no rides ) so he doesn't lose any money. Leaving him with his starting amount, $500.
Find the inverse of f(x) = 1/2x + 3
easy one for you folks. show work.
who ate more?
Answer:
regan ate more than maggie
How do I draw perpendicular line
Answer:
Follow these steps and you will find how to make a perpendicular line.
Step-by-step explanation:
Open the compass to a radius less than half the segment.
Draw two arcs intersecting the line on both sides of the point.
Draw two arcs using the intersection points as the centers. ...
Construct a line between this point and the original point.
Hope this helped :) -ish
165% of what number is 28
Answer:
i belive it is 46.2
Step-by-step explanation:
NEED HELP ASAP…………..
Answer:
It is the second answer.
Step-by-step explanation:
i will make you brainliest
Answer:
The time in Auckland, New Zealand in the 12+ time zone: 21:00
The time in Athens, Greece in the +2 time zone: 22:00
The time in Trinidad in the -4 time zone: 05:00
The time and date in Chicago in the -6 time zone: 02:00 2016-10-19
The time and date Bangkok in the +7 time zone: 11:00 2016-10-20
The time and date in Greenwich: 06:00 2016-10-29
The time and date in Abu Dhabi in the +4 time zone: 30:00 2016-10-30
The time and date in a country in the +12 time zone: Uzbekistan 23:00 2016-11-02
The time and date in a country in the -12 time zone: Brazil 23:00 2016-11-01
The time and date in Honolulu located in the -10 time zone: 01:00 2016-11-02
When the time in Sri Lanka is 09:30 on 2017-05-02, find the time and date in Los Angeles located in the -8 time zone in the USA. 01:30 on 2017-05-02
(These are the answers i calculate i am not sure if they are fully correct)
The Culver City Carnival had a face-painting booth. There were 8 times as many kids as adults who had their faces painted. Pick the diagram that models the ratio in the story. If 56 kids had their faces painted, how many people had their faces painted altogether?
HELP ASAP PLEASEEE What is the equation of the line in the form y=mx+b
Answer:
y=x
Step-by-step explanation:
y=mx+b
m is the slope
b is the y-intercept
Since the y-intercept is at the 0 axis, the y-intercept will be zero
So now the equation is looks like this:
y=mx (Since y=mx+0 doesn't make a difference)
Now find the slope
Which is 1
Thus y=x
Hope this helps!
If x is not equal to zero, what is the value of [tex]\frac{4(3x)^2}{(2x)^2}[/tex]
Answer:
[tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = 9 ,\ x \neq 0[/tex]
General Formulas and Concepts:
Pre-Algebra
Evaluations
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Distributive Property
Terms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \frac{4(3x)^2}{(2x)^2}[/tex]
Step 2: Simplify:
Rewrite [Exponential Distributive Property]: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{4(3^2x^2)}{2^2x^2}[/tex][Order of Operations] Evaluate exponents: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{4(9x^2)}{4x^2}[/tex][Order of Operations] Multiply: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{36x^2}{4x^2}[/tex]Simplify: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = \frac{36}{4} ,\ x \neq 0[/tex][Order of Operations] Divide: [tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = 9 ,\ x \neq 0[/tex][tex]\\ \sf\longmapsto \dfrac{4(3x)^2}{(2x)^2}[/tex]
[tex]\\ \sf\longmapsto\dfrac{ 4(9x^2)}{4x^2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{36x^2}{4x^2}[/tex]
Take x^2 common and cancel.[tex]\\ \sf\longmapsto \dfrac{x^2}{x^2}\left(\dfrac{36}{4}\right)[/tex]
[tex]\\ \sf\longmapsto \dfrac{36}{4}[/tex]
[tex]\\ \sf\longmapsto 9[/tex]
An ant can travel at a constant speed of 980 inches every 5 minutes. At this rate, how far can the ant travel in 7 minutes? *
1 point
4x+2y=7 y=-2x+3.5 how many solutions does this problem have? No solution, one solution, or infinite solutions
Answer: many solutions
Step-by-step explanation:
plesae urgent hurryy for brainlist !!!!!!!!!!!
PLS help me 20 points in total
Answer:
-3.5 is the answer
I mean, I think this is referring to positive and negatives which if it is, it would be -3.5 .
A class has $140 for tickets to a science museum. The teacher writes $140÷10=14. Alma says that tickets are $14 each. Mohamed says that $14 students are going on the trip. Who is correct?
Alma was definitely correct to say that the tickets are $14 each.
The total amount in dollars the class have for tickets to the science museum
is $140.
The teacher writes as follows:
140 ÷ 10 = 14Alma says the tickets are $14 each.
Mohammed says that 14 students are going for the trip
The teacher divided 140 by 10. This means the number of student in the class is 10 not 14 as Mohammed enunciated.
The teacher divided the total amount available for the ticket($140) by the number of student in the class(10). Then the quotient ($14) is the amount in dollars which each student will pay for the ticket to the science museum.
Therefore, Alma was definitely correct.
learn more about algebra here: https://brainly.com/question/11455464?referrer=searchResults
Find the slope of the line that passes through (-10, -52) and (56, -37).
Jay decides to take out a $12,000 student loan during his first year in college. If he is charged 4.5% interest that is compounded annually, how much will the total loan amount equal in four years when he graduates?
Answer:
2,160.00
Step-by-step explanation:
okay so first we have to find 4.5% of 12,000
which is 540, then multiply 540 by the four years and
540 x 4 = 2,160.00
The total loan amount would be equal to $14,310 in four years when Jay graduates.
Given the following data:
Principal = $12,000Interest rate = 4.5%Time = 4 yearsTo determine how much (future value) the total loan amount would equal in four years when he graduates:
Mathematically, compound interest is given by the formula:
[tex]A = P(1 + r)^{t}[/tex]
Where;
A is the future value.P is the principal or amount borrowed.r is annual interest rate.t is the number of years for the compound interest.Substituting the given parameters into the formula, we have;
[tex]A = 12000(1 + 0.045)^{4}\\\\A=12000(1.045)^{4}\\\\A=12000(1.1925)[/tex]
Future value, A = $14,310
Read more: https://brainly.com/question/16992474
Х
Probability with permutations and combinations
file
Nia is 1 of 24 students in a class. Every month, Nia's teacher randomly selects 4 students from their class to act
as class president, vice president, secretary, and treasurer. No one student can hold two positions.
Do
In a given month, what is the probability that Nia is chosen as president?
Choose 1 answer:
BRE
TA
1
24 P4
As
A
1
MY
TATU
Co
©
23 P 3
24 P4
SAT
MY
D
(24 P.). (24 P3)
24 P4
Pro
2 of 4 .OOO
Using permutations and the probability concept, it is found that there is a 0.0417 = 4.17% probability that Nia is chosen as president.
A probability is the number of desired outcomes divided by the number of total outcomes.As there are different roles, the order in which the students are chosen is important, hence, the permutation formula is used to solve this question.Permutation formula:
The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Desired outcomes:
Nia's president.For the other roles, 3 students from a set of 23, hence:[tex]D = P_{23,3} = \frac{23!}{20!} = 10626[/tex]
Total outcomes:
4 students from a set of 24, hence:
[tex]T = P_{24,4} = \frac{24!}{20!} = 255024[/tex]
Then:
[tex]p = \frac{D}{T} = \frac{10626}{255024} = 0.0417[/tex]
0.0417 = 4.17% probability that Nia is chosen as president.
To learn more about probabilities, you can take a look at https://brainly.com/question/24437717
Answer:The answer is 23 P 3/ 24 P 4
Step-by-step explanation:
Help Me On These 3 Please
Answer:
see explanation
Step-by-step explanation:
(1)
Using the sine ratio in the right triangle
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{4}{6}[/tex] , then
x = [tex]sin^{-1}[/tex] ([tex]\frac{4}{6}[/tex] ) ≈ 41.8° ( to the nearest tenth )
(2)
Using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{29}{14}[/tex] , then
x = [tex]tan^{-1}[/tex] ([tex]\frac{29}{14}[/tex] ) ≈ 64.2° ( to the nearest tenth )
(3)
Using the cosine ratio in the right triangle
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{25}{40}[/tex] , then
x = [tex]cos^{-1}[/tex] ([tex]\frac{25}{40}[/tex] ) ≈ 51.3° ( to the nearest tenth )
What is the answer?
To this question
Answer:
y = 3.2
Step-by-step explanation:
8/y = 10/4
10y = 32
y = 32 / 10
y = 3.2
simplify 4 (5x+3)-4x
Answer:
16x + 12
Step-by-step explanation:
20x + 12 - 4x
20x - 4x = 16x
16x + 12
Answer: 15x + 12
Step-by-step explanation:
(4 x 5x). (4 x 3). (20x - 4x). 15x + 12 is your answer.
Domain and Range of a linear function
Answer:
domain is the lenght of the road (in miles)
range is the number of days
Step-by-step explanation:
domain is the input because there building the road that is the input because the number of days is the output (range) because that is what happens from working on the roads (the input) what come out is the days they worked on the road
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
2y - 2 = -14
You are running a fuel economy study. One of the cars you find is blue. It can travel 44 1/2miles on 1 and 1/4 gallons of gasoline. Another car is red. It can travel 27 1/5 miles on 4/5 gallon of gasoline. What is the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline?
Answer:
Blue carStep-by-step explanation:
Find the miles per gallon rate of each car
Blue car:
44 1/2 ÷ 1 1/4 = 89/2 ÷ 5/4 = 89/2 × 4/5 = 356 / 10 = 35.6 miles per gallonRed car:
27 1/5 ÷ 4/5 = 136/5 × 5/4 = 136/4 = 34 miles per gallonAccording the rates, the blue car could travel the greater distance
The corner store sells pairs at a rate of $2.50 for per pair if Fiona has $15 how many pairs can if you fiona buy?
Answer: Fiona can buy six pairs.
15/2.5 = 6
Answer:
Fiona can buy 6 pairs
Step-by-step explanation:
2.50x 6
Can anyone help me please?
Answer:
ñññ
Step-by-step explanation:
This is due tonight please tell me the answer If correct will get brainlest thing
Answer:
5⁵ is your answer bro mark me brainlist
Can someone help me with this?
Answer:
Step-by-step explanation:
[tex]\frac{\sqrt{36x^3y^4}}{2x^{2/3}y^{-4}}=\frac{6x^{3/2}y^2}{2x^{2/3}y^{-4}}=3x^{5/6}y^6[/tex]
a=3, b=5/6, c=6
3*(5/6)*6= 15