[tex]{ \green{ \boxed{ \purple{ \sf{(1 - {x}^{2}) \frac{ {d}^{2}y }{d {x}^{2} } - x \frac{dy}{dx} = 0}}}}}[/tex]
Step-by-step explanation:
Given,
[tex]{ \blue{ \sf{y = { \sin}^{ - 1}x}}}[/tex]
differentiate with respect to x
[tex]{ \purple{ \sf{ \frac{dy}{dx} = \frac{1}{ \sqrt{1 - {x}^{2} } } }}}[/tex]
[tex]{ \purple{ \sf{ \sqrt{1 - {x}^{2} } \frac{dy}{dx} = 1}}} \: { \to} \: { \tt{ {eq}^{n} (1)}}[/tex]
This is in the form of uv method
uv = uv' + vu' = 0
[tex]{ \tt{ \sqrt{1 - {x}^{2} } = u}}[/tex]
[tex]{ \tt{ \frac{dy}{dx} = v}}[/tex]
u' = differentiation of u
v' = differentiation of v
Apply uv method to Eqⁿ (1) then,
[tex]{ \purple{ \sf{ \sqrt{1 - {x}^{2} } = \frac{ {d}^{2} y}{d {x}^{2} } + \frac{dy}{dx} \frac{1}{ \cancel2 \sqrt{1 - {x}^{2} } } (0 { \cancel{- 2}}x) = 0}}}[/tex]
Multiply by [tex]{ \red{ \sf{ \sqrt{1 - {x}^{2}}}}} [/tex] then,
[tex]{ \boxed{ \purple{ \sf{(1 - {x}^{2}) \frac{ {d}^{2}y }{d {x}^{2} } - x \frac{dy}{dx} = 0}}}}[/tex]
Which of the following graphs shows the solution to the system of equations?
Y=5x-1
Y=x+3
Answer: (1,4)
Step-by-step explanation:
The system of equations:
y=5x-1 (1)
y=x+3 (2)
Hence,
5x-1=x+3
5x-1-x=x+3-x
4x-1=3
4x-1+1=3+1
4x=4
Divide both parts of the equation by 4:
x=1
Substitute the value of x=1 into equation (2):
y=1+3
y=4
Thus, (1,4)
△MPQ: M(–4, 3), P(–5, 8), Q(–1, 6) Translation: along –4, –4 Reflection: in y = x
△MPQ: M(-4,3), P(-5,8), Q(-1,6). Translation: along (-4,-4) Reflection: in y=x is M''(-1,-8), P''(4,-9), Q''(2,-5).
Here we need to find translation along (-4,-4) and reflection in y=x.
First we will find translation,
⇒ (x,y)→ (x-4,y-4)
M(-4,3 )→ M'(-8,-1) ,
P(-5,8) → P'(-9,4)
Q(-1,6) → Q'(-5,2)
now we will do reflection,
⇒(x,y) → (y,x)
M'(-8,-1) → M''(-1.-8)
P'(-9,4) → P''(4,-9)
Q'(-5,2) → Q''(2.-5).
Therefore translation along (-4,-4) and reflection in y=x is M''(-1,-8), P''(4,-9), Q''(2,-5).
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Write an equation for the function graphed above.
y=
The equation of the graph is (d) y =sec(x)
How to determine the equation of the function?The graph represents the given parameter
From the graph, we have the following points that can be used in our computation:
(0, 1), (6, 1) and (-6, 1)
This means that
When x = 0, 6 and -6 π radians
The value of y is 1
Solving further, we test these input values in each of the functions in the options
We have
y = sec(0) = 1
y = sec(6) = 1
y = sec(-6) = 1
See that the above values correspond to (0, 1), (6, 1) and (-6, 1)
Hence, the equation is (d) y =sec(x)
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the amount of lemonade at the beginning of the party was 45 quart. At the end of the party there was 8 quarts left. What was his percentage of change in the amount of quarts?
His percentage of change in the amount of quarts is 82.22%.
Initial amount of lemonade = 45 quart
End amount of lemonade = 8 quart
Change in amount = 45 - 8
= 36
Percent = [tex]\frac{change in value}{initial value}*100[/tex]
= [tex]\frac{37}{45}*100[/tex]
= 0.8222 * 100
= 82.22%
Hence, his percentage of change is 82.22%.
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Colinda has just purchased her first home for $125,000. She put down a 20 percent down payment of $25,000 and took out a 6 percent mortgage for the rest. Her mortgage payment is $599.55 per month. How much of her first monthly mortgage payment is amortization?
The amount of her first monthly mortgage payment is amortization is: $99.55.
How to find the mortgage payment?First step is to find the down payment:
Down payment = $125,000 -$25,000
Down payment = $100,000
Second is to find the remaining mortgage
Mortgage = $100,000 × 6%
Mortgage = $6,000
Third step is to find the mortgage payment per month
Mortgage = $6,000 /12 months
Mortgage = $500
Now let find the amortize mortgage payment
amortize mortgage payment = $599.55 -$500
amortize mortgage payment =$99.55
Therefore the amortize payment is $99.55.
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Fill in the blanks to create a true statement. If ST =QR, then QR=ST by ________,of_______
If ST = QR, then QR = ST by the symmetric property of congruence.
What is symmetric property?The symmetric property states that -
For all real numbers [x] and [y] , if x = y , then y = x .
Given is if ST =QR, then QR=ST.
If ST = QR, then QR = ST by the symmetric property of congruence. If ST = QR, then we can say that ST is congruent to QR.
Therefore, if ST = QR, then QR = ST by the symmetric property of congruence.
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Anyone mind helping me out? Photo is in picture!
Answer:
The 3rd answer.
Step-by-step explanation:
2(pi)10 is the equation.
I dont understand…please help
Answer:we need a better picture
Step-by-step explanation:I cant since my eyes are bad
Use four unit multipliers to convert 40 square inches to square meters?
The convertion 40 square inches to square meters is 0.0258064 square meters.
You can convert a square inch measurement to a square metre measurement by multiplying the square inch measurement by 0.00064516. (the conversion factor). Here is the equation:
Square inch value divided by square metre value is 0.00064516.
Consider converting 40 square inches to square metres. Using the above conversion formula, you will obtain:
= 40 sq in * ( 2.54 cm / 1 in)² * (1 m/100cm)²
= 40 × 0.00064516
= 0.0258064 square meter.
Hence, convert 40 square inches to square meters is 0.0258064 square meters.
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Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: (-3,1) (-7,-2)
Line 2: (2,-1), (8, 4)
The slope of line 1 is
.
The slope of line 2 is
.
Answer:
Answer:
We use the formula:
y2 - y1 / x2 - x1
-2 - 1 / -7 - (-3) ---> this gives us -3 / -4 or simply 3/4. So our slope for line 1 is 3/4.
Now using the formula, (y - y1) = m (x - x1) we find the line.
(y - 1) = 3/4 (x - (-3)) ---> (y - 1) = 3/4x + 9/4.
Now we add one to each side to get y = 3/4x + 13/4.
Now for line 2, we use the same process and formulas.
Find the slope of line 2.
4 - (-1) / 8 - 2 gives us 5/6. Our slope for line 2 is 5/6.
(y - (-1)) = 5/6 (x - 2).
(y + 1) = 5/6x - 5/3 ---> now subtract one from both sides to get...
y = 5/6x - 8/3.
Since the two lines do not have the same slope or the negative reciprocal of one slope being the other, the two lines through the given points are neither parallel nor are they perpendicular
Help me solve this please
From trigonometric ratio, we used the tangent of the angle to determine that the flagpole is leaning by an angle of 47.12°
Trigonometric RatioThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
In the question, we can assume the point of view and the flagpole makes a right angle triangle.
Flagpole = opposite = 14ftDistance to flag pole = adjacent = 13ftangle = ?Since we have the opposite and adjacent, we can find the acute angle by using the tangent of the angle
tanθ = opposite / adjacent
tan θ = 14 / 13
θ = tan⁻¹(14/13)
θ = 47.12°
The flagpole is leaning with an acute angle of 47.12 degrees
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)
The time taken for the rocket to reach its maximum height is; 2.25 seconds.
The maximum height reached by the toy rocket as evaluated from the given parameters is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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Find the value of x. Round to the dearest hundredth .
Step-by-step explanation:
the Hypotenuse (the inclined length of the staircase) of the right-angled triangle is the radius of an imaginary circle with the center at the vertex with the 64°.
then
11 = cos(64) × r
r = 11/cos(64) = 25.09289236...
and
x = sin(64) × r = sin(64) × 11/cos(64) = 11 × tan(64) =
= 22.55334226... ≈ 22.55
Write an equation of the line that passes through the given point
and is (a) parallel and (b) perpendicular to the given line.
(6,2)
Answer:
B FS
Step-by-step explanation:
Write a word problem that could be represented with 2 divided by 6 =2/6
Answer:
0.33=0.33
Step-by-step explanation:
it is answer 0.33=0.33
PLEASE HELP! WILL GIVE BRAINLIEST IF RIGHT!
Answer:
last dagre would be 3
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
The degree of a polynomial will be no less than one more than the number of turning points of its graph.
From inspection of the given graph, there are 3 turning points.
Therefore, the least degree is 4.
Didn't mean to post question
You're question should be deleted soon probably 10-15 minutes.
↑ My opinion not answer by a admin/moderator.
If the 100th term of an arithmetic sequence is 287, and its common difference is 3, then
its first term a1 = ________
its second term a2 = ________
its third term a3 = _______
Hint: Use an =a1 + (n-1) d
Answer:
-10
-7
-4
Step-by-step explanation:
287 = [tex]a_{1[/tex] + (n-1)3
287 = [tex]a_{1}[/tex]+ (100-1)3
287 = [tex]a_{1}[/tex] + 99(3)
287 = [tex]a_{1}[/tex] + 297 Subtract 297 from both sides
-10 = [tex]a_{1}[/tex]
If the first term is -10 The second term is 3 greater -7 and the third terms is 3 greater than that. -4
What is the value of the expression when a = 2 and b = 3 ? 4a + b - 2 Question 1 options: 7 9 12
Answer:
9
Step-by-step explanation:
4 * 2 + 3 - 2 =
= 8 + 1 =
= 9
how to find p-value for hypothesis test
The following are needed to find p-value for hypothesis test:
Determine the proper test statistic.Calculate the test statistic using the relevant sample properties.Specify the sampling distribution characteristics of the test statistic.To determine the p value, place your test statistic in the sampling distribution.What is the p value?The p value is a number calculated from a statistical test that describes the likelihood of finding a specific set of observations if the null hypothesis is true. P values are used in hypothesis testing to help determine whether the null hypothesis should be rejected.
Given the probability distribution of the statistic, p-values are calculated as the difference between the observed value and a chosen reference value, with a greater difference between the two values corresponding to a lower p-value.
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This is the way to find the p value that is required in a hypothesis test:
Choose the appropriate test statistic.Utilize the pertinent characteristics of your sample to calculate the test statistic.Indicate the features of the sample distribution for the test statistic.To determine the p value, place your test statistic in the sample distribution.What is the P value?The likelihood of receiving outcomes from a statistical hypothesis test that are at least as extreme as the actual results, assuming the null hypothesis is true, is known as the p-value in statistics.
The p-value provides the minimal level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by stronger evidence when the p-value is lower.
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A mixture of paint calls for 1/3 cups of red paint and 3/4 cups of yellow paint. How many cups of red paint would be needed for every 1 cup of yellow paint?
The cups of red paints for 1 yellow cup is 4/9 cups
How to determine the cups of red paints?From the question, we have the following parameters that can be used in our computation:
Red paint = 1/3 cups
Yellow paint = 3/4 cups
When these parameters are represented as ratio, we have the following expression
Ratio = Red : Yellow
This is then represented as
Red : Yellow = 1/3 : 3/4
When the number of yellow cups is 1, we have
Red = 1/3/3/4
Express as products
Red = 1/3 * 4/3
Evaluate
Red = 4/9
Hence, the red cups is 4/9 cups
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On October 23, 2011, one South African rand was worth 0.12 U.S. dollars.
(a) On that date, how many dollars was 199.65 rand worth?
Round your answer to the nearest hundredth of a dollar,
dollars
(6) On that date, how many rand was 29.11 dollars worth?
Round your answer to the nearest hundredth of a rand,
0-
rand
The value of 199.65 rand was worth $24 and $29.11 was worth 243 rand with rounding off.
What is foreign currency exchange?
A global decentralized or over-the-counter market for trading currencies is known as the foreign exchange market. For every currency, exchange rates are set by this market.
Main body:
Given: 1 rand = $0.12
a) According to question ,
199.65 rand = 0.12* 199.65
= 23.948
Now rounding off to nearest hundred , we get
199.65 rand = $24
b) According to question,
$1 = 1/ 0.12
$29.11 = 29.11/ 0.12
=242.5833333
Now rounding off to nearest hundred , we get
$29.11 = 243 rand.
Hence answer are $24 and 243 rand.
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Tanay’s full time job is to work as a sales clerk at clothing store. She’s hired at the rate $9.20/h for a 37.5 h week. In the last week of August she works her regular hours and then works 8 hours on Sunday to do inventory. For working on Sunday she is paid time and half her regular rate. Calculate Tanya’s earnings for the last week of August.
Tanya's earnings for the last week of August is $455.40.
What is the total earnings?Tanya's earnings for the last week of August is the sum of the amount earned for working regular hours and overtime.
Earnings = amount earned working regular hours + amount earned for working overtime
Amount earned working regular hours = number of hours worked x wage rate
Amount earned working regular hours =37.5 x 9.20 = $345
Amount earned for working overtime = wage per hour worked overtime x number of hours worked overtime
Wage rate for overtime = 1.5 x $9.20 = $13.80
Amount earned for working overtime = $13.80 x 8 = $110.40
Total earnings = $110.40 + 345 = $455.40
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Kalia’s parents give her simple interest on any money she saves for college. Which equation and solution represents the total interest, T, earned when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10?
Answer:$110
Step-by-step explanation:
$100x0.01x10
Answer:
44
Step-by-step explanation:
Solve for x
(x + 2) (x + 3) = 0
please help
Answer:
-2,-3
Step-by-step explanation:
only -2 or -3 will make one side equal 0 so the equation will equal 0
with -2
(-2+2)(x+3)=0
0(x+3)=0
0x+0=0
0=0
-2 works
with -3
(x+2)(-3+3)
(x+2)0=0
0x+0=0
0=0
-3 works
A square, two congruent trapezoids, and two congruent semicircles were used to form the figure shown. Which measurement is closest to the area of the figure in square centimeters? 40 cm 37cm² 28 cm² 55 cm²
Answer:
B. 37 cm²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where $s$ is the side length.\\\end{minipage}}[/tex]
Given the side length of the square is 4 cm:
[tex]\begin{aligned}\implies \sf Area\;of\;the\;square&=4^2\\&=\sf 16\;cm^2\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a semicircle}\\\\$A=\dfrac{1}{2}\pi r^2$\\\\where $r$ is the radius. \\\end{minipage}}[/tex]
The radius of a circle is half its diameter.
Given the diameter of the semicircles is 2 cm, then their radius is 1 cm.
[tex]\begin{aligned}\implies \textsf{Area of one semicircle}&= \sf \dfrac{1}{2} \pi (1)^2\\& = \sf \dfrac{1}{2} \pi \; cm^2\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a trapezoid}\\\\$A=\dfrac{1}{2}(a+b)h$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the bases. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given the bases of the trapezoids are 2 cm and 4 cm, and their height is 3 cm:
[tex]\begin{aligned}\implies \textsf{Area of one trapezoid}&= \sf \dfrac{1}{2} (2+4)(3)\\&= \sf \dfrac{1}{2} (6)(3)\\&= \sf (3)(3)\\&=\sf 9\;cm^2\end{aligned}[/tex]
Given the figure is made up of a square, two congruent trapezoids and two congruent semicircles:
[tex]\begin{aligned}\implies\textsf{Area of the figure}&= \sf square+2\;trapezoids+2\; semicircles\\&= \sf 16+2(9)+2\left(\dfrac{1}{2} \pi\right)\\& = \sf 16 + 18 + \pi \\& = \sf 34 + \pi \\& = \sf 37.14159...\; cm^2\end{aligned}[/tex]
Therefore, the measurement that is closest to the area of the figure in square centimeters is 37 cm².
Complete (assume $50,000 of overhead to be distributed): (Round your Ratio answers to the nearest hundredth.) Sq. Ft. Ratio Amount of Overhead Allocated Dept. A 20,000 A B Dept. B 80,000 C D
The ratios were calculated using the square footage each department occupied and the overhead expenses split equally between the two departments.
Ratio Amount
Department A 1/5 $10,000
Department B 4/5 $40,000
Ratio;-
Ratios can be represented using fractions, decimals, and percentages because they are fractional numbers.
Similar to proportions, ratios display how much of one value or variable fits within another.
Total overhead = $50,000
Department Square Feet Ratio Amount of Overhead Allocated
Dept. A 20,000 A = 1 B = $10,000 ($50,000 x 1/5)
Dept. B 80,000 C = 4 D = $40,000 ($50,000 x 4/5)
Ratios = 20,000:80,000
= 1:4
Sum of Ratios = 5
As a result, Department A will suffer $10,000 while Department B will receive $40,000 based on the cost driver allocation ratios.
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A student's cost for last semester at her community college was $2900. She spent $290 of that on books. What percent of last semester's college costs was spent on books?
The percentage of last semester's college costs was spent on books is 10 %
What is a percentage?A percentage is a ratio out of 100.
How to find the percent of last semester's college costs was spent on books?Since a student's cost for last semester at her community college was $2900 and she spent $290 of that on books.
The percentage spent on books is given by x = amount spent on books/student cost × 100 %
Given that
Amount spent on books = $ 290 and student cost last semester = $2900Substituting the values of the variables into the equation, we have
percentage spent on books x = amount spent on books/student cost × 100 %
= $290/$2900 × 100 %
= 1/10 × 100 %
= 10%
So, thus we see that the percentage that was spent is 0 %
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A class contributed $19.00 in quarters and dimes to a local shelter. In all there were 100 coins. How many of each kind were there?
Step-by-step explanation:
x = number of dimes
y = number of quarters
x + y = 100
x = 100 - y
0.1x + 0.25y = 19
0.1(100 - y) + 0.25y = 19
10 - 0.1y + 0.25y = 19
10 + 0.15y = 19
0.15y = 9
y = 9/0.15 = 60
x = 100 - y = 100 - 60 = 40
there were 60 quarters and 40 dimes.
A manufacturer has costs C(q) and revenues R(q) for producing a units.
The cost of producing 200 units is 2,958 dollars, and the marginal costs
at that production level is 9.2 dollars per unit. The revenue from
producing 200 units is 6,868 dollars, and the revenue at that production
level is decreasing by 2.7 per unit.
Estimate how many dollars is the profit when producing 204 units.
The profit when producing 204 units is $1,560.6
Cost of producing 200 units = $2958
Cost of producing 1 unit = $2958 / 200
= $ 14.79
Marginal cost of production = $9.2
Total cost per unit = cost of producing unit + Marginal cost
= $(14.79+9.2)
= $23.99
Cost incurred in producing 204 units = $(23.99 * 204)
= $4,893.96
Revenue from producing 200 unit,
R(q) = 6868
For each units, Revenue = R(q) / q
= 6868 / 200
= 34.34 dollars per cent
Revenue per unit is decreasing by $2.7
i.e., Final revenue = $(34.34 - 2.7)
= 31.64 dollars per cent
Final revenue for 204 units
= $(31.61 * 204)
= $ 6454.56
∴ Total profit from 204 units = R(q) - C(q)
= $(6454.56 - 4,893.96)
=$1,560.6
Hence, the profit when producing 204 units is $1,560.6
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