Answers
Answer:
[tex]\frac{dy}{dx}[/tex] = 3 cos² y ⇒ B
Step-by-step explanation:
∵ 3x - tan(y) = 4
∵ The differentiation of tan(y) with respect to x is sec² y · dy/dx
∵ The differentiation of 3x with respect to x is 3
∵ the differentiation to 4 with respect to x is 0
∴ d/dx [3x - tan(y) = 4] is 3 - sec² y · dy/dx = 0
∵ 3 - sec²(y) · dy/dx = 0
→ Subtract 3 from both sides
∴ - sec² y · dy/dx = -3
→ Divide both sides by -1
∴ sec² y · dy/dx = 3
→ Divide both sides by sec²(x)
∴ [tex]\frac{dy}{dx}=\frac{3}{sec^{2}y}[/tex]
→ Remember [tex]\frac{1}{secy}[/tex] = cos y
∵ [tex]\frac{1}{sec^{2}y}[/tex] = cos² y
∴ [tex]\frac{3}{sec^{2}y}[/tex] = 3 cos² y
∴ [tex]\frac{dy}{dx}[/tex] = 3 cos² y
dy/dx of 3x – tan y = 4 in terms of y is;
dy/dx = 3cos²y
We are given;
3x - tan y = 4
Let's differentiate in terms of y to get;
3 - sec²y(dy/dx) = 0
This is because the derivative of tan y in terms of y is sec²y(dy/dx).
Thus, using addition property of equality, we have;
3 = sec²y(dy/dx)
Now, in trigonometric ratios;
sec y = 1/cos y
Thus;
sec²y = 1/cos²y
Therefore;
3 = (1/cos²y) (dy/dx)
Thus;
dy/dx = 3cos²y
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Related Questions
1 A brand of cereal is usually sold in 750 g packs. During a special promotion an
extra 15% is added to each box. What will the new weight be?
Answers
Answer:
multiply it by.15
Step-by-step explanation:
Answer: 862.50 g
Step-by-step explanation:
Find what 15% of 750 is then add the obtained value to 750 to find the new weight.
15% * 750 = 112.5
750 + 112.5 = 862.50
The formula for the volume of the sphere = 4(pi) 13. Which of the following is the closest approximation to the volume when r, the
radius, is 11 inches?
Answers
Answer:
5572.5 or 5573 inches
Step-by-step explanation:
First of all, the formula is 4/3(pi)r^3
So 4/3(3.14)11^3
So then 5572.5 or 5573 inches
Set up a proportion for the problem.
11 is what percent of 33 ?
Answers
Answer:
its 3 percent
Step-by-step explanation:
what is the answer to 2/3 - 4/6
Answers
Answer:
0
Step-by-step explanation:
2/3*2/2=4/6. 4/6-4/6=0
Kelly is paid 12.50 per hour she worked for 14hours she gave her mom 1/5 how much money does Kelly have left
Answers
Answer:
10
Step-by-step explanation:
Since Kelly earns 12.50 dollars per hour, and she works 14 hours, you can multiply 12.50 by 14.
1. 12.50*14=175
Kelly gives 1/5 of her money away, so she should be left with 4/5.
2. 4/5*12.50=10
So the answer is 10.
Julie has a part time job after school she gets paid at a constant rate of dollars per hour.Julie works 12$ per month . Use this rate to find many hours it takes for Julie to earn $228
Answers
Find the unit rate from the graph :
Answers
Answer:
1 gift per person
Step-by-step explanation:
The graph here is linear, and it crosses right through values such as (1,1) (2,2) etc. That shows that per person, each one will get 1 gift.
the answer are...
a. -2
b. -1/2
c. 1/2
d. 2
Answers
Answer:
C. 1/2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (0, 4)
Point (-8, 0)
Step 2: Find slope m
Substitute: [tex]m=\frac{0-4}{-8-0}[/tex]Subtract: [tex]m=\frac{-4}{-8}[/tex]Simplify: [tex]m=\frac{1}{2}[/tex]Last year Mr Peterson had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year but he needs to buy more fencing to go around this years garden. How many more meters of fencing is needed for this years garden than last years?
Answers
Complete Question:
Last year Mr. Petersen’s rectangular garden had a width of 5 meters and an area of 20 square meters. This year he wants to make the garden three times as long and two times as wide.
Last year, Mr. Petersen had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year, but he needs to buy more fencing to go around this year’s garden.
How many more meters of fencing is needed for this year’s garden than last year’s?
Answer:
26 meters of fencing needed
Step-by-step explanation:
Given
Last Year:
[tex]Width = 5m[/tex]
[tex]Area = 20m^2[/tex]
This Year:
[tex]Length = 3\ times\ longer[/tex]
[tex]Width = 2\ times\ wider[/tex]
Required
Determine how many more meters is needed
Represent last year's length of Fence with L and last year's width with W
First, we need to calculate L
[tex]Area = L * W[/tex]
Where
[tex]Area = 20m^2[/tex]
[tex]W = 5m[/tex]
[tex]20m^2 = L * 5m[/tex]
Divide both sides by 5m
[tex]\frac{20m^2}{5m} = \frac{L * 5m}{5m}[/tex]
[tex]\frac{20m^2}{5m} = L[/tex]
[tex]L = \frac{20m^2}{5m}[/tex]
[tex]L = 4m[/tex]
So, we have that:
For Last Year
[tex]Length = 4m[/tex] and [tex]Width = 5m[/tex]
For this year:
[tex]Length = 3\ times\ longer[/tex]
[tex]Length = 3 * 4m[/tex]
[tex]Length = 12m[/tex]
[tex]Width = 2\ times\ wider[/tex]
[tex]Width = 2 * 5m[/tex]
[tex]Width = 10m[/tex]
So, for this year, we have:
[tex]Length = 12m[/tex] and [tex]Width = 10m[/tex]
Next, we calculate perimeter of fencing in both years.
[tex]Perimeter = 2 * (Length + Width)[/tex]
Last Year:
[tex]Perimeter = 2 * (4m + 5m)[/tex]
[tex]Perimeter = 2 * 9m[/tex]
[tex]Perimeter = 18m[/tex]
This Year:
[tex]Perimeter = 2 * (12m + 10m)[/tex]
[tex]Perimeter = 2 * 22m[/tex]
[tex]Perimeter = 44m[/tex]
To get the meters of fencing needed this year, we simply calculate the difference in the calculated perimeters.
[tex]Difference = 44m - 18m[/tex]
[tex]Difference = 26m[/tex]
Hence, there are 26 meters of fencing needed
In how many ways can you arrange the books A, B, C, and D on a bookshelf if books A and C must remain neighboring?
Answers
Choose the fraction that has not been reduced to simplest form.
[tex]\frac{1}{16} \frac{21}{34} \frac{3}{57} \frac{11}{17}\\[/tex]
Answers
Answer:
3/57
Step-by-step explanation:
3/57 because 3/3*19=1/19
Refrigerators in a random sample of 55 refrigerators, the mean repair cost was $150.00 and the standard deviation was $15.50. Construct a 90% confidence interval for the population mean repair cost. Interpret the results.
Answers
Answer:
146.5619<x<153.4381
Step-by-step explanation:
The formula for calculating the confidence interval is expressed as:
CI = xbar±(z*s/√n)
xbar is the mean = 150
s is the standard deviation = 15.50
n is the sample size = 55
z is the z score at 90% CI = 1.645
Substitute and get CI
CI = 150±(1.645*15.50/√55)
CI = 150±(1.645*15.50/7.4162)
CI = 150±(1.645*2.09)
CI = 150±(3.4381)
CI = (150-3.4381, 150+3.4381)
CI = (146.5619, 153.4381)
CI = 146.5619<x<153.4381
Hence a 90% confidence interval for the population mean repair cost 146.5619<x<153.4381
The minimum cost is approximately $147 while the maximum cost of the refrigerator is $153
Jay needs to paint one side of his house. He knows 1 can of paint covers and area of 24 square feet. What is the least amount of paint Jay will need to paint the side of his house?
Answers
Answer:
he will need 4 cans to make it 100 %compleate
f(x) = -x -5, solve for x when f(x) = -6
Answers
Answer:
x = 1
Step-by-step explanation:
Hhhhhheellllppppppp asap
Answers
Answer:
A
Step-by-step explanation:
Answer:
i think A is the answer
Step-by-step explanation:
5.5 is worth more than 5.05 is this is not what ur asking plz clarify :)
A company that makes hair-care products had 7,000 people try a new shampoo. Of the 7,000 people, 56 had a
mild allergic reaction. What percent of the people had a mild allergic reaction?
Answers
Answer:
0.8
Step-by-step explanation:
i believe it would be 56/7000 and you multiply your answer 0.008 by 100 so 0.8 had a mild reaction
Answer:
0.8%
Step-by-step explanation:
Think of it as a fraction: 56/7,000. To get a percent you want to simplify the denominator to 100. Then what you do to the denominator, you must do to the numerator, so simplify 56 by the number you simplified 7,000 to get to 100. Then you will have your answer of 0.8%.
Suppose you want to save in order to purchase a new boat. Take the APR to be 6.0%.
You want to have $15,000 toward the purchase of a boat in three years. How much do you need to deposit each month? (Round your answer to the nearest cent.)
Answers
Answer:
Amount deposit each month = $365.26
Step-by-step explanation:
Given:
Amount deposit = $15,000
Rate = 6% = 6% / 12 = 0.005
Number of time = 3 x 12 = 36
Find:
Amount deposit each month
Computation:
Amount deposit each month = [(15,000) x 0.005]/[(1.005){(1.005)³⁶-1}]
Amount deposit each month = $365.26
The amount needed to be deposited each month is;
P ≈ $393.23
We are given;
APR = 6% = 0.06
Total accumulated amount; A = $15000
number of years; n = 3 years
To calculate the amount needed to be deposited each month, we will use the formula;
A = [P(1 + APR/12)¹²ⁿ - 1)] ÷ (APR/12)
Plugging in the relevant values gives;
15000 = [P(1 + (0.06/12))⁽¹²*³⁾ - 1] ÷ (0.06/12)
Rearrange to get;
[P(1 + (0.06/12))³⁶ - 1] = 15000 × 0.06/12
⇒ [P(1 + 0.005)³⁶ - 1] = 75
⇒ P(0.19073) = 75
⇒ P = 75/0.19073
⇒ P ≈ $393.23
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ME NEEDS SOME MORE HELP FOR QUESTION 2
also whoever answers this question first I will mark them the brainliest :3
Answers
Answer:
C is answer I think 0, because
Answer:
C.
Step-by-step explanation:
100%sure
Because -5 in front will equal a positive because you have a positive 0 in back therefore it will be C brainliest please!
an 8-ounce cup of gourmet coffee costs 4.50. if the unit price remains the same, how much would 3 quarts of coffee costs ?
Answers
Answer:
$54
Step-by-step explanation:
3 quarts is 96 ounce
96/8 = 12
12*4.50= 54
I need help someone ?
Answers
Answer:
1) y=4x+5, 2) y=-2x+2, 3)y= 4/3x+4
Step-by-step explanation:
1) y=4x+5
2) y=-2x+c
-4= -2(3)+c
-4=-6+c
+6 +6
2=c
y=-2x+2
3) 4-0/0--3
4/3= gradient
y= 4/3x+c
4= 4/3(0)+c
4=0+c
4=c
y= 4/3x+4
Graph the line with slope -6 and y-intercept 3.
Answers
Answer:
See Attachment.
Genera Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define variables
Slope m = -6
y-intercept b = 3
Step 2: Write linear equation
Substitute into general form.
Slope-Intercept Form: y = -6x + 3
Step 3: Graph
Answer:
*See Below*
Step-by-step explanation:
It was hard to find this answer. Sorry if the graph glitches.
Ratio of red to yellow marbles is 6 to 5 if there are 33 total marbles in the bag how many red
Answers
Answer:
18 red marbles and 15 yellow marbles.
red: 18 yellow: 15
explanation
33 divided by 6+5 is 3
multiply by both and there’s ur answer!
can i be marked brainliest?
the first term of GP where second term is 2 and sum of infinity is8 it will be
Answers
Answer:
a = 4
Step-by-step explanation: Given that
ar=2 where a is the first term and is the common ratio.
ar=2 ............1
Also give that a/1-r = 8 where a is the first term and r is the common ratio as well.
a/1-r = 8 ......... 2
From equation 1 make r the subject
ar=2
r= 2/a...........3
Put equation 3 into 2
a/1-2/a =8
a÷1-2/a
a = 8(1-2/a)
a= 8/1-16/a
a/1= 8a-16
a^2= 8a-16
Rewriting the above equation
a^2-8a+16=0
This will eventually be
a^2-8a+16=0
(a-4)^2= 0
a =4
Pregnancy length (in days) is a normally distributed random variable with a mean of 266 days and a standard deviation of 16 days. Calculate the z-score for a pregnancy lasting 286 days. Do not round.
Answers
Answer:
it=552
Step-by-step explanation:
with rounding it = 550
The value of z-score for a pregnancy lasting 286 days will be;
⇒ z - score = 1.25
What is Standard deviation?Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
Mean = 266 days
Standard deviation = 16 days
Now,
We know that;
⇒ z - score = (X - μ) / σ
Substitute all the values, we get
⇒ z - score = (286 - 266) / 16
⇒ z - score = 20/16
⇒ z - score = 1.25
Thus, The value of z - score = 1.25
Learn more about the standard deviation visit:
https://brainly.com/question/475676
#SPJ5
helppppp please I will give brainliest
Answers
Answer:
0
Step-by-step explanation:
Y-intercept is where the line touches the y-axis, in this case it was the origin (0,0) so the y-intercept is 0
Which list represents integers ordered from least to greatest?
A 4,-7, -6, 10
B 4, -5, -6, 10
C -7, -6, 4, 10
D-6, 4, 5, 10
OA
B
OC
D
Answers
It’s C
Why:
Because i’m smart duh
Answer:
C,-7,-6,4,10
Step-by-step explanation:
I guessed and that is all I did
Your friend and her parents are visiting colleges. They leave their home in Enid, Oklahoma, and drive to Tulsa, which is 107 mi east and 18 mi south of Enid. From Tulsa, they go to Norman, 83 mi west and 63 mi south of Tulsa. Where is Norman in relation to Enid?
Answers
24 miles east and 81 miles south.
3x = 0.5.x2
o o
O x= -6 or x = 0
O
x= -4 or x = 3
o
x = -2 or x = 1.5
x = 0 or x = 6
Answers
Answer:
the answer is x=0 or x=6, hope this helps
On a television game show, contestants earn 5 points for each correct answer, but lose 2 points for each wrong answer. On last week's show, the winning contestant earned 80 points and answered 30 questions.
Given that x represents the number of questions answered correctly, and y represents the number of questions answered incorrectly, determine which system of equations correctly represents this situation.
A. 5x-2y=30
x+y=80
B. 5x-2y+80
x+y=30
C. 5x+2y=80
x-y=30
D. 5x+2y=30
x+y=80
Answers
Sorry to inform that I can't find the answer to this question.
Socratic can help! This learning app, powered by Google AI, helps you understand your school work at a high school and university level. Ask Socratic a question and the app will find the best online resources for you to learn the concepts.
What is 3/4 divided by 2 1/2
Answers
Answer:
3/10
Step-by-step explanation:
Convert 2 number to improper fraction find a common denominator and KFC, Keep, Change, Flip.
Keep first fraction
Change / into x
And flip the other fraction (2 1/2 or 5/2) to (2/5)
3/4 x 2/5 is 3/10