Final answer:
The problem requires finding an equation for y in terms of x given a differential equation and an initial condition. Solving for y, we get:[tex]\[ y = \arcsin(-\cos(x)) \][/tex]
This is the equation for y in terms of x.
Explanation:
To solve this ordinary differential equation (ODE), we can separate variables and then integrate both sides. Given:
[tex]\[\frac{dy}{dx} = \frac{\sin(x)}{\cos(y)}\][/tex]
We separate variables by multiplying both sides by \(dx\) and dividing by Cos(y) to isolate y terms:
[tex]\[\cos(y) \, dy = \sin(x) \, dx\][/tex]
Now, we integrate both sides. For the left side, we integrate with respect to y, and for the right side, we integrate with respect to x:
[tex]\[\int \cos(y) \, dy = \int \sin(x) \, dx\][/tex]
Integrating each side gives us:
[tex]\[ \sin(y) = -\cos(x) + C\][/tex]
Where C is the constant of integration.
Given the initial condition [tex]\(y(0) = \frac{3\pi}{2}\)[/tex], we can plug this into the equation to find [tex]\(C\):[/tex]
[tex]\[ \sin\left(\frac{3\pi}{2}\right) = -\cos(0) + C \][/tex]
[tex]\[ -1 = -1 + C \][/tex]
[tex]\[ C = 0 \][/tex]
So the equation becomes:
[tex]\[ \sin(y) = -\cos(x) \][/tex]
Therefore, solving for y, we get:
[tex]\[ y = \arcsin(-\cos(x)) \][/tex]
This is the equation for y in terms of x.
Help me on this please
Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols.
2x+7y=4
-4x-3y=14
how would i go about this? please help!!,
Use this function below to help find F(2)?
Rudy collects baseball cards, and he currently has 300 cards. Starting tomorrow, he will purchase 1 pack of 15 baseball cards every day, and every pack he purchases will contain 1 card of a member of his brother???s favorite team. Every time Rudy purchases a pack of cards, he will immediately trade the card of the member of his brother???s favorite team to his brother for 3 cards of members of a different team. Which of these recursive formulas produces the sequence that represents the number of baseball cards that Rudy will have at the end of each day, starting today?
A contractor purchases 7 dozen pairs of padded work gloves for $94.92. He incorrectly calculates the unit price as $13.56 per pair for the expense report. What is the correct unit price? What is the error?
The correct unit price for the work gloves is $1.13 per pair, and the error in the reported unit price is $12.43 per pair, as the contractor incorrectly reported it as $13.56 per pair.
The question is asking to calculate the correct unit price for the padded work gloves purchased by the contractor and to identify the error in the calculation provided in the expense report.
Firstly, let's determine the total number of pairs of gloves. Since 1 dozen represents 12 items, 7 dozen pairs of gloves will be [tex]7 \times 12 = 84[/tex] pairs of gloves.
Now, to find the correct unit price, we divide the total cost by the total number of pairs:
Unit Price = Total Cost / Total Number of Pairs
Unit Price = $94.92 / 84 pairs
Unit Price = $1.13 per pair
The incorrect unit price was calculated as $13.56 per pair. Therefore, the error in the calculation is:
Error = Incorrect Unit Price - Correct Unit Price
Error = $13.56 - $1.13
Error = $12.43 per pair
The contractor overestimated the unit price by $12.43 per pair.
If you flip three fair coins, what is the probability that you'll get all three tails?
Let H be the event that head occurs and let T be the event that tail.
Then the complete Sample Space,S for the experiment given in the question is:
S={ HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
As we can see the total number of elements in the sample space is 8. Let us represent this by the letter N.
Therefore, N=8
Now, the event of interest to us is TTT and it's occurrence is once. Let represent this by the letter E.
Therefore, E=1
Thus, the probability of the event E occurring is given as:
[tex] P(E)=\frac{E}{N}=\frac{1}{8} [/tex]
[tex] \frac{1}{8} [/tex] is the required answer. This can be represented in percentage too as:
[tex] \frac{1}{8}\times 100=12.5 [/tex]%
PLEASE HELP ASSAAAAPPPPP
Algebra 2 help please? And explanation too. Thanks!
5. Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
2 log 4 – log 3 + 2 log x – 4 = 0
(1 point)
12.3308
43.3013
86.6025
1,875,
Find the surface area of this square pyramid. The base has area 1764 cm^2 and perimeter 168 cm.
4116 cm^2
4704 cm^2
31,038 cm^2
2940 cm^2
While standing on a roof, you drop a hamner. The function y=16-64t^2 represents the height y (in feet) of the hammer t seconds after it is dropped. After how many seconds does the hammer land on the ground?
Which algebraic expression represents this phrase? the product of 86 and the depth of the river
An algebraic expression is a mathematical phrase that contains numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide).
We have to form the algebraic expression for the phrase
" The product of 86 and the depth of the river"
Let the depth of the river be 'd'
Therefore, the algebraic expression = Product of '86' and 'd'
= [tex] 86 \times d [/tex]
= 86d.
Therefore, the algebraic expression for the given phrase is "86d".
The vertices of quadrilateral abcd are a(1, a - 3), b(10, a), c(9, a + 3) and d(0, a).prove that the quadrilateral is a rectangle.find the midpoints of the diagonals.the midpoint of ac is (5,1)the midpoint of bd is (5,1)find the lengths of the diagonals.
Answer with explanation:
The Vertices of quadrilateral A B CD, are A(1, a - 3), B(10, a), C(9, a + 3) and D(0, a).
Mid point of AC= (5,1)
Mid point of B D= (5,1)
Mid point formula of two points having coordinates , (a,b) and (c,d) is , if (x,y), then
[tex]x=\frac{a+b}{2},y=\frac{c+d}{2}[/tex]
[tex]So,\rightarrow \frac{a-3+a+3}{2}=1\\\\\rightarrow \frac{2a}{2}=1\\\\\rightarrow a=1[/tex]
So, the coordinates of vertices of quadrilateral A B CD, are A(1, -2), B(10, 1), C(9, 4) and D(0, 1).
Distance formula of two points having coordinates, (a,b) and (c,d) is,
[tex]=\sqrt{(a-c)^2+(b-d)^2}[/tex]
[tex]AB=\sqrt{(10-1)^2+(1+2)^2}=\sqrt{81+9}=\sqrt{90}=3\sqrt{10}\\\\BC=\sqrt{(10-9)^2+(1-4)^2}\\\\=\sqrt{1+9}\\\\=\sqrt{10}\\\\CD=\sqrt{(9-0)^2+(3-0)^2}=\sqrt{90}=3\sqrt{10}\\\\DA=\sqrt{(1-0)^2+(1+2)^2}=\sqrt{10}\\\\AC=\sqrt{(9-1)^2+(4+2)^2}=\sqrt{64+36}\\\\AC=\sqrt{100}\\\\AC=10\\\\BD=\sqrt{(10-0)^2+(1-1)^2}\\\\BD=10[/tex]
Opposite sides AB and CD are equal to 3√10 unit and , BC and AD are equal to √10 unit.
Also,length of Diagonals , AC=B D=10 unit.
∴ The Quadrilateral, AB CD is a Rectangle.
The diameter of a sphere is 8 centimeters. What is the volume of the sphere? Use 3.14 for pi. Enter your answer, as a decimal, in the box. Round only your final answer to the nearest tenth. cm³
WILL GIVE MEDAL AND FAN! your anniversary is usually when you are given _____ by a company
A. an award
B. a job review and possible increase in pay
C. an evaluation
D. a promotion
Answer: Option 'B' is correct.
Step-by-step explanation:
Your anniversary is usually when you are given a job review and possible increase in pay.
As in a job, job review is given at the time of anniversary, then on the basis of their performance there may be increase in pay.
So, Meaning of anniversary in a official way is when work performance of an individual is discussed and if there is good record , there is an increment.
Hence, Option 'B' is correct.
Emma likes to knit hats and mittens for friends and family. Last fall, she knitted 4 hats and 3 pairs of mittens, which took a total of 46 hours. This fall, she knitted 2 hats and 1 pair of mittens, which took a total of 18 hours. If each hat and each pair of mittens takes the same amount of time to knit, how long does it take Emma to knit a hat and a pair of mittens?
Final answer:
Emma takes 4 hours to knit a hat and 10 hours to knit a pair of mittens, which was determined by solving two linear equations based on the time she spent knitting during two different falls.
Explanation:
Emma likes to knit hats and mittens, and we need to find out how long it takes her to knit a hat and a pair of mittens individually. Given that last fall she knitted 4 hats and 3 pairs of mittens in 46 hours, and this fall she knitted 2 hats and 1 pair of mittens in 18 hours, we can set up two equations to solve for the time it takes to knit each item.
Let's define H as the number of hours it takes to knit one hat and M as the number of hours it takes to knit one pair of mittens. The equations based on the given information are:
4H + 3M = 46 (Last fall's knitting)
2H + 1M = 18 (This fall's knitting)
To solve these equations, multiply the second equation by 2 to align the hats:
2(2H + 1M) = 2(18)
4H + 2M = 36
Now subtract this equation from the first equation to find M:
4H + 3M - (4H + 2M) = 46 - 36
M = 10
Substituting M back into the second original equation:
2H + 1(10) = 18
2H = 8
H = 4
Emma takes 4 hours to knit a hat and 10 hours to knit a pair of mittens.
A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times. What is the experimental probability of the arrow stopping over Section 3? Section 1: 18 Section 2: 30 Section 3 :32
Answer: [tex]\dfrac{2}{5}[/tex]
Step-by-step explanation:
From the given table, The number of times arrow stops over Section 3 = 32
The total number of times spinner spins = 80
Now, the experimental probability of the arrow stopping over Section 3 is given by :-
[tex]P(S-3)=\frac{32}{80}\\\\\Rightarrow P(S-3)=\dfrac{2}{5}[/tex]
Hence, the experimental probability of the arrow stopping over Section 3 is [tex]\dfrac{2}{5}[/tex]
I need help to answer this please thank you ?
choose the most appropriate strategy and then use it to solve the quadratic equation.
7. (x-8)^2=121
8. 2a^2=8a-6
9. x^2+12x+36=4
10. x^2-x+30=0
osha requires a ladder to meet the ground at 75 degree angle in order to function as safely as possible. of you need the ladder to reach a ledge 20 feet up a vertical wall, how long does the ladder need to be?
Just want to know if this is right...
You are shopping for T-shirts. Clothing Warehouse sells 3 T-shirts for $52. The Scene sells 2 T-shirts for $83. New Threads sells 4 T-shirts for $127. Which store has the best deal?
Jose wants to rewrite 24+9 using the greatest common factor and the distributive property. Which expression should he write?
Answer:
3(8+3)
Step-by-step explanation:
A reader of a book wants to estimate the mean word length in the book they are currently reading. they randomly select 19 pages from the book and count the length of 5 words they randomly selected on each of those pages. the table shows the results from the survey. using the sample results estimate the mean word length of any word in the book.
a.5.22 letters
b.5.49 letters
c.5.77 letters
d.5.92 letters
Answer:
B-5.49
Step-by-step explanation:
A manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions of this part are shown below.
Which estimate is closest to the volume in cubic millimeters of the part?
(1 point)
• 306
• 768
• 1,008
• 2,016
Someone help me plz .....
Which statement is logically equivalent to the following conditional statement?
If it is a rectangle, then it does not have three sides.
Answers
If it is not a rectangle, then it has three sides.
If it has three sides, then it is not a rectangle.
If it does not have three sides, then it is a rectangle.
If it is not a rectangle, then it does not have three sides.,
Angela spent $30.00 at a resturaunt. if she leaves a 15% tip, how much wll her total bill be
Final answer:
Angela's total restaurant bill, after adding a 15% tip to her $30.00 original charge, will be $34.50.
Explanation:
To find out how much Angela's total bill will be after leaving a 15% tip at a restaurant, you first need to calculate the tip amount and then add it to the original bill. You calculate the tip by converting the percentage to a decimal and then multiplying by the cost of the meal. In this case, 15% of $30.00 is found by multiplying $30.00 by 0.15 which gives you $4.50. After calculating the tip amount, add it to the original bill to get the total amount Angela will pay.
Tip: $30.00 * 0.15 = $4.50.
Total bill: $30.00 + $4.50 = $34.50.
Therefore, Angela's total bill, including the 15% tip, will be $34.50.
1.The ordered pair ( 1, 2 ) lies in which quadrant?
Quadrant I
Quadrant IV
Quadrant II
Quadrant III
2.Find the difference. 86 - ( -17 )
69
-69
103
-103
3.Simplify the expression 14 · 2 ÷ 7.
-4
-1
0
4
4.Write a variable expression for the word phrase, "five less than a number m".
M + 5
5 - m
M - 5
5 ÷ m
5.Identity the expression as a numerical expression or a variable expression. 50x
Numerical expression
Variable expression
6. the set of whole numbers and their opposites are known as ________.
Absolute Values
Positive numbers
Integers
Negative numbers
7.Use <, >, or = to complete the statement. -55 ____ -56
Evaluate 4( 6 ) + 7(5 - 3).
118
80
10
38
Find the -5 + (-6).
-11
-1
1
11
Abcd is a parallelogram find the measure of a if b is (7x+13)degrees and d d is (8x-8)degrees brainly
f(x) = (x − 3)(x + 3)[x − (2 − i)][x − (2 + i)] The function has real roots and imaginary roots.
Answer:
The function has
2 real roots and
2 imaginary roots.