Answers
Differentiate x and y with respect to t :
[tex]x = e^{\sec(2t)} \implies \dfrac{dx}{dt} = e^{\sec(2t)} \dfrac{d(\sec(2t))}{dx} = 2\sec(2t)\tan(2t) e^{\sec(2t)}[/tex]
[tex]y = e^{\tan(2t)} \implies \dfrac{dy}{dt} = e^{\tan(2t)} \dfrac{d(\tan(2t))}{dx} = 2\sec^2(2t) e^{\tan(2t)}[/tex]
By the chain rule,
[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
Then
[tex]\dfrac{dy}{dx} = \dfrac{2\sec^2(2t) e^{\tan(2t)}}{2\sec(2t)\tan(2t) e^{\sec(2t)}} = \dfrac{\sec(2t) e^{\tan(2t)}}{\tan(2t) e^{\sec(2t)}} =\dfrac{y \sec(2t)}{x\tan(2t)}[/tex]
and we have
[tex]\log(x) = \sec(2t)[/tex]
[tex]\log(y) = \tan(2t)[/tex]
and the claim follows.
Related Questions
Could someone help me to find the answer for this question, pls help
Answers
A price of a motorcycle is Rs 175000. The year rate of deprecation is 4%. Find the price of motorcycle after 3 years
Answers
[tex]FV = PV (1 - \frac{r}{100})^n\\FV = 175000 (1 - \frac{4}{100})^3\\[/tex]
FV = Rs 154828.8
If the measure of angle 1 is (3 x minus 4) degrees and the measure of angle 2 is (4 x + 10) degrees, what is the measure of angle 2 in degrees?
Answers
Answer:
its 58
Step-by-step explanation:
The measure of angle 2 is 58 degrees
How to determine the measure of angle 2?The figure that completes the question is added as an attachment
The given parameters are:
Angle 1 = 3x - 4Angle 2 = 4x + 10Both angles add up to 90 degrees.
So, we have:
3x - 4 + 4x + 10 = 90
Evaluate the like terms
7x = 84
Divide both sides by 7
x =12
Substitute x =12 in Angle 2 = 4x + 10
Angle 2 = 4 * 12 + 10
Evaluate the expression
Angle 2 = 58
Hence, the measure of angle 2 is 58 degrees
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7
Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an
annual simple interest rate of 8%. After 8 years, the interest earned on the account was $5,760. How much money did Mike's
grandmother deposit in the account?
OA. $8,000
OB. $9,500
OC. $10,000
OD. $9,000
Answers
Answer:
we have to use the formula of simple interest, which is
I = P r t
Where I is the interest earned, P is the amount invested, r is the rate of interest and t is the time duration .
In the given question, I = $4840 , r =11% or 0.11, t=11, P is unknown .
Substituting the values in the formula, we will get
4840=0.11*11*P4840=0.11∗11∗P
4840=1.21 P4840=1.21P
P=4000
So she invested $4000
Answer:
Option: D P = 9000
Step-by-step explanation:
I = PRT
5760 = P * 0.08 * 8
5760 = 0.64P
9,000 = P
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
16
Step-by-step explanation:
How to solve 36 yards=inches
Answers
1 yard = 36 inches
in order to change yard into inches you multiply how many yards you need to solve for by 36.
36 yards = 1,296 inches
Answer:
1,296 inches
In each yard is 3 feet, and there are 12 inches in 1 foot.
Multiply the amount of yards by itself to solve.
[tex]36 * 36 = 1,296~in.[/tex]
__________________________________________________________
Questions?Ask in comments box.
Use vertex form to write the equation of the parabola below.
1
35
A.
y=-(x - 1)2 +1
B. y = (x+1)2 + 2
B
y = (x-1)
Dy= (x+1)+1
Answers
Answer:
It's the first option (A)
Step-by-step explanation:
Since it's heading towards negative Ys so in ax²+bx+c, a is negative and only option that a is negative in it, is option A.
Additionally, the parabola is moved 1 unit towards positive Xs, so —(x—1)²
and it's one unit up so —(x—1)²+1
A rectangle is such that its breadth is 2m less than its length. Find the length of the rectangle if the perimeter is 8mP
Answers
[tex]\huge\mathbb\purple {✒✨ ANSWER ✨⚘}[/tex]
A rectangle is such that its breadth is 2m less than its length. Find the length of the rectangle if the perimeter is 8mP
[tex]ANSWER & SOLUTION[/tex]
Let breadth = XTHEN length=X+2Perimeter = 2(X + 2 +. X)Thus 2(2X + 2) = 84X + 4 = 84X = 4Divide both sides by the same factor
[tex]4 \times = 4 \\ \frac{4 \times }{4} = \frac{4}{4} [/tex]
Cancel terms that are in both the numerator and denominator
Divide the numbers
[tex] x = \frac{4}{4 } [/tex][tex]\large\mathtt\green {x = 1 }[/tex]#BRAINLY EVERYDAYPLEASE HELP ME WITH THIS!!!!
Answers
Answer:
D: (x,y) → (x +1, y - 8)
Step-by-step explanation:
The red shape, KHIJ, is similar to the blue shape, KHIJ.
Looking at the shapes from the points K, Blue K is forward on the x-axis by 1, Hence x + 1.
Lokkin at the same points, but on y-axis this time. Red K is up 2 and Blue K is down 6. 2 + 6 = 8. Since the blue shape is down, make the 8 into -8. Now you have y -8.
What is 20 2/4+12 3/4?
Answers
Answer:
33 1/4 or 33.25
Step-by-step explanation:
K'Drien has a recipe that needs 3/4 tablespoon of butter for every 2
cups of milk. If K'Drien increases the recipe such that he uses 6
cups of milk, how many
tablespoons of butter will he need?
Answers
Answer:
6/4. Simplified, is 1 2/4
Step-by-step explanation:
A total of $8000 is invested: part at 6% and the remainder at 10 %. How much is invested at each rate if the annual interest is $750?
Answers
Answer: $400 was invested
Step-by-step explanation: Based on the scenario in the question, our calculation goes thus:0.11x + 0.06(8000 - x) = 5000.11x + 480 - 0.06x = 5000.11x - 0.06x = 500 - 4800.05x = 20x = 20/0.05x = 400
$400 was invested at 11% Also, 8000 - 400 = 7600 invested at 6%
BRAINLIEST would make my day :D
Which equation can be simplified to find the inverse of y = 2x2?
StartFraction 1 Over y EndFraction = 2 x squared
y = one-half x squared
–y = 2x2
x = 2y2
Answers
The correct answer would be: x = 2y^2
Answer:
its D
Step-by-step explanation:
Please help me thank you!
Answers
Answer:
46.7%
Step-by-step explanation:
The fraction of youths preferring printedbooks
= 21/(21+24)
= 21/45
= 21 *100 / 45
= 46.67%
Loojk ate the rectangle a) A square has the same area as the rectangle above what is the side length of this square
Answers
Answer: The length of one side of the square is 10 sq cm.
Step-by-step explanation: Area of the rectangle = 4 x 25 = 100 sq cm.
Area of a square = s x s, where s is the length of the side of the square.
So, s x s = 100
Or, s^2 = 100
And, s = sqrt(100) = 10
Answer asap and only if yk 100% its correct
Answers
the answer is 3 and thats cause if you were to multiply 12x75 you get 900, and if 1 gallon of paint covers 400 square feet then you will need 3 gallons to get to 900. so there for the answer is 3
There are 700 students at Bowman High School. The students come from Wylie Middle School, Parker Middle School, and Richardson Middle School. Of the 28 students in Mr. Henry's gym class, 4 are from Richardson Middle School.
Based on this information, what is the best prediction for the number of students at Bowman High School that come from Richardson Middle School?
Answers
The best prediction for the number of students at Bowman High School that come from Richardson Middle School is; 175
How to find proportions?We are given;
Total number of students = 700
Number of students in Mr. Henry's gym class = 28
Number of students in Mr. Henry's gym from Richardson Middle School = 4
Thus, to find the best prediction for the number of students at Bowman High School that come from Richardson Middle School is simply;
Number of students = 700/4
Number of students = 175
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A pronghorn running up a steep cliff to escape its predator covered 45 miles in 1 hour and 45 minutes.
Answers
Answer:
25 . 71 mph
Step-by-step explanation:
45 miles in 1.75 hr
45 miles / 1.75 hr = 25.71 mph
Stephanie
invests $6,688 in a savings
account with a fixed annual interest rate of
2% compounded 6 times per year. What
will the account balance be after 5 years?
Answers
Answer:
$7,390.15
Step-by-step explanation:
A = $7,390.15
A = P + I where
P (principal) = $6,688.00
I (interest) = $702.15
First, convert R as a percent to r as a decimal
r = R/100
r = 2/100
r = 0.02 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 6,688.00(1 + 0.02/6)^(6)(5)
A = 6,688.00(1 + 0.0033333333333333)^(30)
A = $7,390.15
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $6,688.00 at a rate of 2% per year compounded 6 times per year over 5 years is $7,390.15.
6. A gas tank holds 450 gal. when it is filled to the height of 12 ft. How many
gallons will it hold when it is filled to 5 ft.?
Answers
Answer:
[tex]\huge\boxed{\sf 187.5\ gal.}[/tex]
Step-by-step explanation:
Given that:
For,
12 ft. height, gas tank can hold 450 gal.
Using unitary method:
12 ft = 450 gal.
Divide 12 to both sides
1 ft = 450/12 gal.
1 ft = 37.5 gal.
Multiply 5 to both sides
5 ft. = 37.5 × 5 gal.
5 ft. = 187.5 gal.
So, the height of 5 ft. holds 187.5 gal.
[tex]\rule[225]{225}{2}[/tex]
Answer:
187.5 gal
Step-by-step explanation:
A=lw
450=12(w)
450/12=37.5ft
A=lw
A=37.5(5)
A=187.5 gal
Hope that helps
According to these three facts, which statements are true?
Circle W has center (−3, 0) and radius 8.
Circle V is a translation of circle W, 2 units down.
Circle V is a dilation of circle W with a scale factor of 2.
Select each correct answer.
The radius of circle V is 16.
The center of circle V is (−5, 0).
Circle V and circle W have the same center.
Circle V and circle W are similar.
Answers
a.
Circle W centre is (-3,0) - (0,-2)* = (-3,-2)
*note that the centre of the circle W is going down by 2 units this only affects the y axis hence the substraction
A dilation of a factor of 2 does not change the centre of the circle rather the radius ( the size of the circle decreases and hence the radius)
So now the radius becomes 8 UNITS/2 = 4UNITS
From the statements given,neither is correct
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
Big bro I can barley read the image but here we go.
Angle B = 51
Angle E = 65?
So to solve if we know angle e is 65 and the angles are identical to eachother then we can say
4y - 3 = 65
4y = 62
y = 15.5
HELP ME OUT PLS!!!!!!!!!!!!!!!!
Answers
Answer:
D) -9
Step-by-step explanation:
2(x - 3) + 1 = 3x + 4
-> 2x - 6 + 1 = 3x + 4
-> 2x - 5 = 3x + 4
-> 2x - 3x = 4 + 5
-> -x = 9
-> x = - 9
The population of a village has increased this year by 8 percent.This year it's population is 10,800.How much was it's population last year?
Answers
Answer:
SOLUTION:-
Let,last year population be x.We have last year population+Increased population=10,800[tex]x + 8\% \: of \: x = 10800[/tex]
[tex]\displaystyle{x + \frac{8x}{100} = 10800 }[/tex]
[tex]\displaystyle{ \frac{100x + 8x}{100} = 10800}[/tex]
[tex]\displaystyle{ \frac{108x}{100} = 10800}[/tex]
[tex]108x = 10800 \times 100[/tex]
[tex]108x = 1080000[/tex]
[tex]x = \displaystyle{ \frac{1080000}{108} }[/tex]
[tex]x = 10000[/tex]
Therefore,required last year population=10000
Answer:
The Correct Answer is 10,000.
Step-by-step explanation:
Becuase The Question itself is providing us that this year it increased by 8%. Then the said that the total population for this year is 10,800. So, that tells us that the 8% equal 800. 10,000+800=10,800.
10,800-800=10,000
The correct answer is 10,000.
Hope this helps you!!
Don't forget to Mark me Brainleast if my answer is correct!!
║Thanks for joining Brainly community!!║please answer the question in the picture below
Answers
Answer:
E
Step-by-step explanation:
5 is to ST as ST is to (5+7)
5/ST = ST/12 (ST)^2 = 60 ST = sqrt (60) = 2 sqrt 15
What is your 95% credible interval for the number of people who will be alive in the year 3000 CE (including digital people)? Explain your reasoning by giving a roughly one-sentence justification for each important step of your reasoning.
A 95% credible interval means that you believe there is a 95% chance that thetrue value will fall within your interval. If I were 95% confident that the number of books in a library was between 100 and 500, then my 95% credible interval would be 100-500.
Answers
Answer:
Because there are many different ways to teach introductory astronomy, we have made the text as flexible as we could. Math examples are shown in separate sections throughout, so that you can leave out the math or require it as you deem best. Each section of a chapter treats a different aspect of the topic being covered; a number of sections could be omitted in shorter overview courses and can be included where you need more depth. And, as we have already discussed, you can customize the book in a variety of ways that have never been possible in traditional textbooks.
Step-by-step explanation:
This book is written to help students understand the big picture rather than get lost in random factoids to memorize. The language is accessible and inviting. Helpful diagrams and summary tables review and encapsulate the ideas being covered. Each chapter contains interactive group activities you can assign to help students work in teams and pool their knowledge.
Luke works in the shipping department of a toy company
Answers
Answer:
Could you send the question properly so I can Help you with the answer
Step-by-step explanation:
Thanks
Answer:
I don't understand the question.
A canoe travels 5 miles downstream at rate r, and then 5 miles back upstream at
70% of its downstream rate. Write and simplify a rational expression for the total
time of the trip.
Answers
Answer:
See below
Step-by-step explanation:
distance / rate = time
d/r + d/(.7r) = total time
5 /r + 5 /(.7r) = time
35/7r + 50/7r = time
85/7r = time
Mira buys a telescope that costs $180. She has to pay 4% sales tax. how much will she pay in all
Answers
Mira would pay $187.2
What is the formula for tax rate?"Tax rate = (Tax amount / Price before tax) × 100% "
What is the formula for tax amount?"Tax amount = Final price - Price before tax"
For given question,
Mira buys a telescope that costs $180.
⇒ Price before tax = $180
sales tax = 4%
Let 'm' be the tax amount.
Using the formula of tax rate,
⇒ Tax rate = (Tax amount ÷ Price before tax) × 100%
⇒ 4% = ([tex]\frac{m}{180}[/tex]) × 100%
⇒ 0.04 × 180 = m
⇒ m = 7.2
Using the formula for the tax amount,
⇒ Tax amount = Final price - Price before tax
⇒ Final price = Tax amount + Price before tax
⇒ Final price = 7.2 + 180
⇒ Final price = $187.2
Therefore, Mira would pay $187.2
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Find the area of this trapezoid. Be sure to include the correct unit in your answer.
Answers
Answer:
the answer is in the picture