Part A: dx/dy at y=4 equals 1/3. The correct option is (c) 1/3.
Part B: The value of dx/dy at y=2 is 1/5. the answer is (c) 1/5.
C. f'(x) = (1/2) * sqrt(x)^-1.
Part A:
We know that y=f(x) and x=f^-1(y) are mutually inverse functions, which means that f(f^-1(y))=y and f^-1(f(x))=x. Using implicit differentiation, we can find the derivative of x with respect to y as follows:
d/dy [f^-1(y)] = d/dx [f^-1(y)] * d/dy [x]
1 = (1/ (dx/dy)) * d/dy [x]
(dx/dy) = d/dy [x]
Now, we are given that f(1)=4 and dy/dx = -3 at x=1. Using the chain rule, we can find the derivative of y with respect to x as follows:
dy/dx = (dy/dt) * (dt/dx)
-3 = (dy/dt) * (1/ (dx/dt))
(dx/dt) = -1/3
We want to find dx/dy at y=4. Since y=f(x), we can find x by solving for x in terms of y:
y = f(x)
4 = f(x)
x = f^-1(4)
Using the inverse function property, we know that f(f^-1(y))=y, so we can substitute x=f^-1(4) into f(x) to get:
f(f^-1(4)) = 4
f(x) = 4
Now, we can find dy/dx at x=4 using the given derivative dy/dx = -3 at x=1 and differentiating implicitly:
dy/dx = (dy/dt) * (dt/dx)
dy/dx = (-3) * (dx/dt)
We know that dx/dt = -1/3 from earlier, so:
dy/dx = (-3) * (-1/3) = 1
Finally, we can find dx/dy at y=4 using the formula we derived earlier:
(dx/dy) = d/dy [x]
(dx/dy) = 1/ (d/dx [f^-1(y)])
We can find d/dx [f^-1(y)] using the fact that f(f^-1(y))=y:
f(f^-1(y)) = y
f(x) = y
x = f^-1(y)
So, d/dx [f^-1(y)] = 1/ (dy/dx). Plugging in dy/dx = 1 and y=4, we get:
(dx/dy) = 1/1 = 1
Therefore, the answer is (c) 1/3.
Part B:
Let y=f(x) and x=h(y) be mutually inverse functions. We know that f '(2)=5, which means that the derivative of f(x) with respect to x evaluated at x=2 is 5. Using the chain rule, we can find the derivative of x with respect to y as follows:
dx/dy = (dx/dt) * (dt/dy)
We know that x=h(y), so:
dx/dy = (dx/dt) * (dt/dy) = h'(y)
To find h'(2), we can use the fact that y=f(x) and x=h(y) are mutually inverse functions, so:
y = f(h(y))
2 = f(h(2))
Differentiating implicitly with respect to y, we get:
dy/dx * dx/dy = f'(h(2)) * h'(2)
dx/dy = h'(2) = (dy/dx) / f'(h(2))
We know that f'(h(2))=5 from the given information, and we can find dy/dx at x=h(2) using the fact that y=f(x) and x=h(y) are mutually inverse functions, so:
y = f(x)
2 = f(h(y))
2 = f(h(x))
dy/dx = 1 / (dx/dy)
Plugging in f'(h(2))=5, dy/dx=1/(dx/dy), and y=2, we get:
dx/dy = h'(2) = (dy/dx) / f'(h(2)) = (1/(dx/dy)) / 5 = (1/5)
Therefore, the answer is (c) 1/5.
Part C:
We are given that f(x)= for x>0. Differentiating with respect to x using the power rule, we get:
f'(x) = (1/2) * x^(-1/2)
Therefore, f'(x) = (1/2) * sqrt(x)^-1.
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If index of refraction 1 is 1. 5, index of refraction 2 is 2. 0, and the angle of incidence is 45 degrees, what is the angle of refraction?.
The angle of refraction is 32 degrees. The result is obtained by using the formula from the Snell's Law.
What is Snell's Law?The Snell's Law is a formula to describe the relationship between the angles of incidence and refraction when a light passes through two medias. It can be expressed as
n₁ / n₂ = sin θ₂ / sin θ₁
Where
n₁ = refractive index of medium 1n₂ = refractive index of medium 2 θ₁ = incident angleθ₂ = refracted angleWe have:
Index of refraction 1, n₁ = 1.5.Index of refraction 2, n₂ = 2.0.Angle of incident, θ₁ = 45°.Find the angle of refraction!
Using the formula of Snell's Law, we'll get the refracted angle.
n₁ / n₂ = sin θ₂ / sin θ₁
1.5 / 2.0 = sin θ₂ / sin 45°
3 / 4 = sin θ₂ / (½√2)
sin θ₂ = 3(½√2)/4
sin θ₂ = 3/8 √2
sin θ₂ = 0.53
θ₂ = arc sin 0.53
θ₂ = 32°
Hence, the refracted angle is 32 degrees.
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NEED HELP ASAP PLEASE AND THANK YOU
The midpoint of AB is M (3,-1). If the coordinates of A are (8,4), what are the coordinates of B?
The coordinates of B is (-2, -6)
How to find the coordinates of BThe formula to determine the midpoint of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.
The formula is of the form
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
From the formula the coordinates of B is solved knowing that midpoint is
M (3,-1) and A is (8,4) and say B (x₁, y₁)
3 = (8 + x₁)/2
6 = 8 + x₁
x₁ = -2
-1 = (4 + y₁)/2
-2 = 4 + y₁
y₁ = -6
hence B is (-2, -6)
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the sum of the angle measures of a quadrilateral is 360 find the measure of the missing angle (please help)
The equation for the volume of a cylinder is
V = r²h. The positive value of r, in terms of h
π
and V, is
V
Υπη
1) r=
2)
r=√√√Vah
3) r=2Vлh
V
4) r= 2π
R's positive value is [tex]\sqrt{\frac{v}{\pi h} }[/tex] V =r²h in terms of h is the formula used to calculate the volume of a cylinder.
what is volume ?The object's capacity is another name for it. The basic formula for volume is length, width, and height, as opposed to the basic formula for the area of a rectangular shape, which is length, breadth, and height. No matter how you refer to the various dimensions, the calculation remains the same. For instance, you can use "depth" instead of "height." The capacity of an object is expressed in terms of volume. A cup's capacity is said to be 100 ml, for instance, if it can hold 100 ml of water in its brim. The quantity of space a three-dimensional item takes up can also be referred to as volume.
given
Cylinder(volume )'s is equal to = [tex]\pi r^{2}h[/tex]
where r = radius, h = height, and v = volume of the cylinder
⇒ [tex]r^{2} = \frac{v}{\pi h}[/tex]
⇒ ±r = [tex]\sqrt{\frac{v}{\pi h} }[/tex]
The problem states that only the positive value of r is necessary.
So, r = [tex]\sqrt{\frac{v}{\pi h} }[/tex]
R's positive value is [tex]\sqrt{\frac{v}{\pi h} }[/tex] V =r²h in terms of h is the formula used to calculate the volume of a cylinder.
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How many rules are there in algebra?
Answer: There is only 5 rules in algebra.
Step-by-step explanation:
How do you find the hypotenuse of an isosceles right triangle when given the area?
The formula for finding the hypotenuse of an isosceles right triangle when given the area is A = (1/2)bh, where A is the area, b is the base, and h is the height.
To calculate the hypotenuse, first solve for h, which is h = 2A/b. Then, use Pythagorean theorem to solve for the hypotenuse c, which is c = sqrt((b^2)+(2A/b)^2). To illustrate the formula, consider a triangle with an area of 20 and a base of 10. First, solve for h, which is h = 2(20)/(10) = 4. Then, solve for c, which is c = sqrt((10^2)+(4^2)) = sqrt(196) = 14. Therefore, the hypotenuse of the isosceles right triangle with an area of 20 and a base of 10 is 14.
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I am trying to find the second, fourth, and eleventh terms of the sequence for A(n)=-9+(n-1)(3)
By evaluating the formula for the sequence, we will get the terms:
A(2) = -6A(4) = 0A(11) = 21How to find the terms in the sequence?Here we want to find the second, fourth, and eleventh terms in the sequence:
A(n) = -9 + (n - 1)*3
n defines the "number" of the term in the sequence.
So to get the second term, we need to use n = 2, we will get.
A(2) = -9 + (2 - 1)*3
A(2) = -9 + 3 = -6
The fourth term is what we get if we evaluate in n = 4, then:
A(4) = -9 + (4 - 1)*3
A(4) = -9 + 9 = 0
And the eleventh term is what we get when we use n = 11, we will get:
A(11) = -9 + (11 - 1)*3
A(11) = -9 + 30 = 21
These are the 3 terms of the sequence that we wanted to find.
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What is horizontal line test inverse?
The horizontal line test is a method used to determine if a given function is one-to-one, which means that for every unique x-value, there is a unique y-value. A function that is one-to-one can be inverted, meaning that it has an inverse function.
The inverse function of a one-to-one function is a function that undoes the original function.
The horizontal line test is used to determine if a given function is one-to-one by drawing a horizontal line through the graph of the function and seeing if the line intersects the graph at most once.
If the function is one-to-one, it has an inverse function and it can be found by switching the x and y values and solving for y.
For example, if the original function is f(x) = 2x + 1, its inverse function is f^-1(x) = (x-1)/2. This inverse function undoes the original function and it can be used to solve equations, find derivatives, and study geometric transformations.
It's important to note that the horizontal line test is only a sufficient condition, meaning that a function that passes the horizontal line test is one-to-one, but not all one-to-one function pass the horizontal line test.
In conclusion, the horizontal line test is a method used to determine if a given function is one-to-one, which is important because one-to-one functions can be inverted.
The inverse function undoes the original function, and it can be found by switching the x and y values and solving for y. The test is simple and easy to apply, but only a sufficient condition.
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Which of the following is the correct solution for the equation 5t 3 3t 5?A. -1B. -2C. 1D. 2
The solution for the equation 5t - 3 = 3t - 5 is when value of t is equal to -1.
Therefore the answer is A. -1.
To find the solution, you can start by isolating the variable t on one side of the equation by adding 3 to both sides and subtracting 3t from both sides:
5t - 3 + 3 = 3t - 5 + 3
5t = 3t - 2
Then subtract 3t from both sides:
5t - 3t = 3t -2 - 3t
2t = -2
Finally, divide both sides by 2 to solve for t:
t = -2/2
t = -1
So, the value of t that satisfies the equation 5t - 3 = 3t - 5 is -1.
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Power of a power quotient rule
The quotient rule essentially asserts that we may divide two powers by subtracting the exponents as long as the base is the same. This is a quick way to simplify exponents.
What is power?The quotient rule essentially asserts that we may divide two powers by subtracting the exponents as long as the base is the same. This is a quick way to simplify exponents. A power series is an infinite series in mathematics in which a represents the coefficient of the nth term and c is a constant. Power series may be found in mathematical analysis as Taylor series of indefinitely differentiable functions. The power of a number indicates how many times the number may be multiplied. Exponents and Indices are other names for powers. For example, 8^2 might be labeled "8 to the power 2" or "8 to the second power", or simply "8 squared".
Here,
The quotient rule essentially asserts that as long as the base is the same, we may divide two powers by subtracting the exponents. This is a shortcut for simplifying exponents.
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please helppppp need this by tonighttt
Pleaseee
Answer:
A. The domain should be all reals.
B. The range is y≤1 if the function is |x-2|+1.
C. It's a function.
If you get this wrong then my bad
Choose the function that represents the data in the table. Y = 3x + 2 y = 3x2 + 2 y = y = 3x + 2.
The function that represents the data in the table is 3x²+2. The correct answer is B.
The quadratic function is shown in the data table.
We must ascertain the function's equation.
The quadratic equation's generic form is
Let's replace the general form with the three coordinates (1,5, (2,14), and (3,29).
We therefore have;
a+b+c =5——— (1)
4a+2b+c= 14——— (2)
9a+3b+C =29------(3)
When (2) is subtracted from (1), we have;
9= 3a+b(4)
Subtracting (3) from (2) gives us;
15= 5a +b(5)
Subtracting (5) from (4) gives us;
6= 2a
3= a
As a result, the value of an is 3. When we replace this value in equation (4), we obtain;
3(3)+b= 9
b= 0
When a = 3 and b = 0 are substituted in equation (1), we obtain;
a+b+c =5
3+0+c=5
c=2
As a result, c has a value of 2.
As a result, when we substitute a = 3, b = 0, and c = 2 in the quadratic equation's general form y =ax²+bx+c, we obtain;
3x²+2
Consequently, the function that symbolizes the information in the table is 3x²+2
As a result, Option B is the right response.
Your question is incomplete but maybe your full question attached below
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A high chool courtyard ha a idewalk laid out a hown. Sidewalk A,B, and C are horizontal, with idewalk D connecting the other three. Decribe the relationhip of thee idewalk
If the sidewalk A , B ,C are horizontal to each other and D is connecting them, then we can say that the the sidewalk D is perpendicular to them .
We say that two lines are perpendicular if they form the angle of 90 degree between them. Thus , we can say that the sidewalk D are having a perpendicular relationship whit the other 3 sidewalks.
Horizontal means something which has a parallel relationship with the horizon . The opposite of horizontal is vertical which is also known as the portrait mode. A horizontal line is any line normal to a vertical line. Horizontal lines do not cross each other similarly the vertical lines do not cross each other.
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Question 3 1Points Hector paid $2.70 for a package of cheddar cheese slices. There are 18 slices in the package. What is the unit price of the cheddar cheese?
the unit price of the cheddar cheese is $0.15.
What is division?Division is the process of splitting a number or an amount into equal parts.
here, we have,
Hector paid $2.70 for a package of cheddar cheese slices.
There are 18 slices in the package.
i.e. the unit price of the cheddar cheese = $2.70/18
=$0.15
hence, the unit price of the cheddar cheese is $0.15.
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For each systems of equations below, choose the best method for solving
and solve. Show your work.
y=-x-6
x+3y=-18
The equation which gives solutions, x=0 and y=-6.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y=-x-6............................(1)
x+3y=-18.........................(2)
now, solving both equation we get
x+3y=-18
x + 3(-x-6) = -18
x - 3x - 18 = -18
-2x = 0
x= 0
and, y= -0 -6 = -6
Hence, the solution is x=0 and y=-6.
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The temperature was 30 degrees this morning but is dropping 4 degrees per hour.
The slope of the line will be
In 5 hours the temperature will be at
The graph of this line will
y = temp and x = hours
Type the equation WITH NO SPACES
(positive or negative)
degrees (type the number)
(increase or decrease)
I don’t know how to do this (geometry)
Answer: The value of x = 7
Step-by-step explanation:
In the figure consider the parallelogram is a ABCD parallelogram
A parallelogram is a two-dimensional shape.
It has four sides, in which two pairs of sides are parallel.
Also, the parallel sides are equal in length.
If the length of the parallel sides is not equal in measurement, then the shape is not a parallelogram.
Similarly, the opposite interior angles of a parallelogram should always be equal. Otherwise, it is not a parallelogram.
AB = 3x+5
CD = 5x-9
where AB || CD and AD || BC
Also, AB = CD and AD = BC
then 3x+5 = 5x-9
when simplify the equation,
5x = 3x+5+9
5x = 3x+14
then
5x-3x = 14
2x = 14
x = 14÷2
x = 7
then the value of x = 7
when substituting value of x in equations
AB = 3x+5 = 21+5 = 26
CD = 5x-9 = 35-9 = 26
AB = CD
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find the maximum value of y= -8x^2 + 80x -196
Answer:
(5,4)
Step-by-step explanation:
first, if you have a calculator you can put the equation into y = and just find the maximum point there
to find the x value of the maximum point you do -B/2A
-80/2(8) = 5 so the x value would be 5
then to find y just plug in 5 for x and you should get 4
Answer:
Maximum value of
[tex]f(x) = - 8x^2 + 80x - 196[/tex]
is
[tex]\boxed{f(x) = 4}[/tex]
Step-by-step explanation:
The maximum or minimum value of a function f(x) occurs when the first derivative equals zero
The first derivative of
[tex]f(x) = - 8x^2 + 80x - 196[/tex]
[tex]f'(x) = \dfrac{d}{dx}\left(-8x^2+80x-196\right)[/tex]
[tex]=-\dfrac{d}{dx}\left(8x^2\right)+\dfrac{d}{dx}\left(80x\right)-\dfrac{d}{dx}\left(196\right)[/tex]
[tex]\dfrac{d}{dx}\left(8x^2\right) = 16x\\\\=- \dfrac{d}{dx}\left(8x^2\right) = -16x\\\\\\\dfrac{d}{dx}\left(80x\right)=80\\\\\dfrac{d}{dx}\left(196\right)=0[/tex]
[tex]\dfrac{d}{dx}\left(-8x^2+80x-196\right) \\\\\\ =-16x + 80 + 0\\\\= -16x + 80\\\\[/tex]
Set this expression equal to 0 and solve for x to find the x value which maximizes or minimizes the function
[tex]-16x + 80 = 0\\\\\implies -16x = -80\\\\x = -80/-16\\\\x = 5\\\\[/tex]
Plug this value of x into the original function to get the maximum or minimum value.
[tex]f(5) = -8(5^2) + 80(5) - 196\\\\= -8 (25) +400 -196\\\\= -200 + 400 - 196\\\\= 4\\\\[/tex]
So the maximum value of [tex]\boxed{f(x) = 4}[/tex] ANS
and occurs at [tex]x = 5[/tex]
(Strictly speaking to find if this is a maximum or minimum, we have to find the second derivative and see if it is negative or positive. If negative, it is a maximum, if positive it is a minimum
But since the question does not ask for this, I am skipping it. In case you are interested, the second derivative of f(x) is the derivative of f'(x) which will work out to -16 so it is a maximum)
Metric month 1 month 2 month 3 % customer questions 896 10% 1296 % shipped on time - 10% -796 -5% % shipped incorrectly 2% 4% 496 % discounted 18% 18% 1496 units shipped (thousands) so 85 100 question 2 of 4 how impactful were product discounts on customer questions? not impactful extremely impactful
Customer questions had no impact on changes in discounts or customer behavior, according to those two variables.
Explain the term customer inquiries?A non-binding request for a quote or sales information from a customer to a business. The request may mention particular goods or services, terms, and, if required, delivery deadlines.
A discount that is based on a percentage is the most typical type of discount. Small discounts (5–10% off) and bigger discounts (15–25%) are used by online retailers to entice customers to make a purchase. To get rid of outdated and excess inventory, it's also common to see brands offer discounts of 50% or more.For the stated question-
Customer queries and discounts have a relationship.Customer questions increased by 2 to 10% even when the discounts remained at 18%.Customer questions still increased at their typical rate of 2 percent to 12 percent when discounts were reduced to 14 percent.Since, customer inquiries did not alter in response to changes in discount, we can conclude that discounts had no influence on them.
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The correct question is attached.
I don’t understand someone please help 20 points!
Answer:
Step-by-step explanation:
y = kx
proportionality constant = k = y/x
A. k = y/x = 7/2 = 3.5 (you can plug in any x,y pair from the table and will get the same answer, 3.5)
B. k = y/x = 12/3 = 4 (you can choose any point on the line)
C. k = y/x = 2.75 (same as the slope of the line)
D. k = y/x = earnings/games = 65/5 = 13
E. k = y/x = 12/3 = 4 (you can plug in any x,y pair from the table and will get the same answer, 4)
Casey was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:
-8, which represents the depth of water in the swimming of pool
+7, which represents the height of the slide at the pool
Part A: What does 0 represent in this situation? (3 points)
Part B: Describe the height the slide in relation to 0 in the situation. (3 points)
Part C: Casey held pole the swimming pool. The bottom of the pole was at a depth of 2 feet. How should Casey mark the level of the bottom of the pole
number line? Explain how you determined this. (4 points)
The pole was at a depth of 2 feet = - 2
What is height and distance ?
height can be defined as the the measurement in vertical direction where as the distance can be defined as the measurement in horizontal direction.
Given :
Casey was at the surface of a swimming pool and recorded the following two measurements,
in feet, on a number line: −8, which represents the depth of water in the swimming pool +7,
which represents the height of the slide at the pool
To Find, What does 0 represent in this situation?
Describe the height of the slide in relation to 0 in the situation
Casey held a pole in the swimming pool. The bottom of the pole was at a depth of 2 feet. How should Casey mark the level of the bottom of the pole on the number line
0 represent in this situation - Top surface of Swimming pool - Surface matching with ground
height of the slide in relation to 0 in the situation = 7 feet
pole was at a depth of 2 feet = - 2
Hence, The pole was at a depth of 2 feet = - 2
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Is it possible to draw a triangle the length of whose sides are 2.5 cm 4.2 cm 8 cm?
Yes, it is possible to draw a triangle the length of whose sides are 2.5 cm 4.2 cm 8 cm.
The possibility to draw a triangle from mentioned three sides can be checked through SSS or side-side-side rule of triangle. It states that sum of any two sides should be greater than third side of the triangle. Assuming 2.5 cm to be side a, 4.2 and 8 cm to be side b and c respectively.
Side a + side b > side c
2.5 + 4.2 > 8
Add the values
6.7 not greater than 8
Side b + side c > side a
4.2 + 8 > 2
Add the values
12.2 > 2.5
side c + side a > side b
8 + 2.5 > 4.2
Add the values
10.5 > 4.2
As we see, that two cases show sum to be greater than third side. Thus, triangle can be drawn.
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Find the radius of the circle with:
Knowing a circle's circumference can be used to calculate its radius, which is given by the formula r = c / (2 * π ). If you know the diameter, D, you may calculate the radius, R, which is equal to D divided by 2.
How do you find the radius of a circle?If you know the area A, then you can calculate the circle's radius using the formula r = (A / π).Knowing the circumference, c, will allow you to calculate the radius, r, which is equal to c / (2 * π).If you know the diameter d of a circle, you can calculate its radius by multiplying it by 2.This eliminates the need for you to select the radius of a circle formula you require.For Example
Circumference c = 26.8in
Area A = 57.156
Diameter = 8.5307
Radius of the circle Radius r = 4.26535.
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It is a 7th grade question btw easy
The value of q, based on the equation given, can be found to be - 1 / 6
How to find q?To find q, you need to collect like terms on the correct side of the equation to be able to solve for q.
When given the equation,
1 / 2 = q + 2 / 3
You collect like terms to be:
q = 1 / 2 - 2 / 3
q = ( 3 - 4 ) / 6
q = - 1 / 6
In conclusion, the value of q is - 1 / 6.
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Mr Dunn drives 640 m from work at a speed of 4.8m/s mrs. dunn  drives 810 m from work at speed of 5.4m/s they both leave work at the same time how many minutes later is it before the second person gets home
i need the answer to the top
The value of b is 2. Therefore (2, 1) is the midpoint of the line segment with endpoints (-4, 2) and (8, 0)
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
If a point O(x, y) divides line segment AB with endpoints A(x₁, y₁) and B(x₂, y₂) in the ratio of 1:1 (midpoint). The coordinates of O is:
x = (x₁ + x₂)/2
y = (y₁ + y₂)/2
Given that (2, 1) is the midpoint of the line segment (-4, b) and (8, 0). Therefore:
1 = (0 + b)/2
b/2 = 1
b = 2
The value of b is 2.
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I really need help on this!
The constraint to make the statement true is -A< -B: Option C
What is constraint?A Constraint is a situation when an individual is limited or restricted to carry out an activity. It can also be seen as strictness or inhibition in relation to a variable
In most organizations, project managers are faced with constraints when they want to carry out an activity. Most of these constraints are external and out of the project manager's control.
Based on that if A<B, then - A < -B and this makes the constraint true.
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Suppose cot(日) = = 2, where
○
12
5
○ 13
ㅇㅇㅇ
13
晉
where n
ㅠ
ㅇ픔
Answer: sinθ=-12/13
Step-by-step explanation:
[tex]\displaystyle\\Given:\ cot\theta=\frac{5}{12} \ \ \ \ \pi < \theta < \frac{3\pi }{2} \ \ \ \ Find:\ sin\theta\\\\\frac{cos\theta}{sin\theta} =\frac{5}{12}[/tex]
Multiply both parts of the equation by 12sinθ:
[tex]12cos\theta=5sin\theta[/tex]
Squared both parts of the equation:
[tex](12cos\theta)^2=(5sin\theta)^2\\\\144cos^2\theta=25sin^2\theta\ \ \ \ (1)\\[/tex]
[tex]Find\ sin\theta[/tex]
Add 144sin²θ to both parts of the equation (1):
[tex]144cos^2\theta+144sin^2\theta=25sin^2\theta+144sin^2\theta\\\\144(sin^2\theta+cos^2\theta)=169sin^2\theta\\\\144(1)=169sin^2\theta\\\\144=169sin^2\theta\\\\Thus,\ 169sin^2\theta=144[/tex]
Divide both parts of the equation by 169:
[tex]\displaystyle\\sin^2\theta=\frac{144}{169} \\\\sin\theta=б\sqrt{\frac{144}{169} } \\\\sin\theta=б\sqrt{\frac{12^2}{13^2} } \\\\sin\theta=б\sqrt{(\frac{12}{13})^2 } \\\\sin\theta=б\frac{12}{13}[/tex]
[tex]\displaystyle\\As, \ \pi < \theta < \frac{3\pi }{2} \ \ \ \ \Rightarrow\ \ \ \angle\theta\ is \ in\ the\ 3rd\ quadrant\\\\ So \ sin\theta\ takes \ negative \ values\\\\sin\theta=-\frac{12}{13}[/tex]
Write 72/50 as a percentage.
Answer:
144%
Step-by-step explanation:
I hope this helps you
How to calculate CSS pixel ratio?
Calculating the pixel ratio of a website involves measuring the width and height of each element on the page and then dividing the width by the height.
What is ratio?Ratio is a comparison of two numbers or values expressed as a fraction or proportion. Ratios are used to compare different measures, such as costs, efficiency, productivity, or profitability, and to evaluate the relative importance of different elements. Ratios are also used to compare different items to each other, such as the ratio of sales to expenses. Ratios can be used to compare different time periods, and to assess the performance of a company over time.
The result is the pixel ratio, which can be used to determine how much of an element is visible on the page and how much is hidden. To calculate the pixel ratio, you can use a variety of tools, such as online tools, browser extensions, or specialized software. It is also important to note that the pixel ratio will vary depending on the device used to view the website, so it is important to test the website on multiple devices. Once the pixel ratio is calculated, it can be used to optimize the website for different devices.
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