I need to find the constant variation y=-2/3x

The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

for such more question on derivative

https://brainly.com/question/23819325

#SPJ8

The measures of the two complementary angles are 44° and 132°.

Given that the difference between the measures of two complementary angles of any given triangle is 88°, it means that one angle is 88° smaller than the other. To find the measures of the two angles, divide the sum of the difference by 2. That is given as, (88°/2) = 44°. One angle is given as  44°, and the other angle is equal to the sum of the two angles in a triangle, which is 180°, minus the first angle, which is 44°, which is equal to 136°.

Learn more on Complementary Angles:

https://brainly.com/question/20728641

#SPJ4

You don't give much information but I will give you the definition of "density".

In all simpleness, the definition of density is the compactness of a substance.

Density can be found with the formula; p = m/v

p = density

m = mass

v = volume

Best of Luck!

Answer:

sorryyyyyy dont knowwwwwwww

since vectors v1 and v2 are parallel, the system xv1 + yv2 = v3 will have infinitely many solutions regardless of the specific values of v1, v2, and v3.

Geometrically, this is due to the fact that v1 and v2 span the same direction in space, so any combination of x and y will still lie on the same line or in the same direction.

Since vectors v1 and v2 are parallel, they lie on the same line or are scalar multiples of each other. Let's analyze the possible cases geometrically:

1. **Vectors v1 and v2 are collinear (lie on the same line):**

  In this case, any combination of x and y that satisfy the equation \(xv1 + yv2 = v3\) will lie on the same line as v1 and v2. This means there are infinitely many solutions for x and y.

2. **Vectors v1 and v2 are scalar multiples of each other:**

  If v1 and v2 are scalar multiples of each other, then they represent the same direction in space. In this case, any combination of x and y that satisfy the equation will give a vector that lies on this line (spanned by v1 and v2), which is also the direction of v3. Hence, again there are infinitely many solutions.

3. **Vectors v1 and v2 are not collinear but have different directions:**

  This scenario is not possible because you stated that v1 and v2 are parallel. If they have different directions, they would not be parallel.

To know more about vectors:

https://brainly.com/question/24905148

#SPJ3

Answer:

E. C. D

Step-by-step explanation:

Thoae are the corrwct ones, hope ir helpa :)

Answer:

Step-by-step explanation:

Zeros are solutions, are answers. So x = -1 and x = 5

What would've been the previous step to find that answer?

x + 1 = 0 would be where you'd get x = -1 from.

x - 5 = 0 would be where you'd get x = 5 from.

So the factors of this quadratic must've been:

(x + 1) and (x - 5)

Multiply these together.

(x + 1)(x - 5)

x^2 - 4x - 5

Since they were asking for an equation we ought to throw an = 0 on the end there, so you get

x^2 - 4x - 5 = 0

I like to think of this as a "working backwards" problem. Usually we get an equation, factor and solve it. This time we did all of that exactly in reverse order.

Answer:

6/4 or 1 2/4

Step-by-step explanation:

One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

To know more about Angles.

https://brainly.com/question/28293784

#SPJ11

The transformation of f(x) to g(x) is f(x) is shifted down by 4 units to g(x) and shifted right by 5 units

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

Where, we can see that

f(x) = |x|

g(x) = |x + 5| - 3

So, we have

vertical difference = 0 - 3 = -3

horizontal difference = 5 - 0 = 5

This means that the transformation of f(x) to g(x) is f(x) is shifted down by 4 units to g(x) and shifted right by 5 units

Read more about transformation at

brainly.com/question/27224272

#SPJ1

If an equilateral triangle has a perimeter of 24 feet. the area of the circle is approximately 50.27 square feet.

Since the perimeter of the equilateral triangle is 24 feet, each side has a length of 8 feet (since all three sides are equal).

The diameter of the circle is equal to the length of one side of the equilateral triangle, which is 8 feet. Therefore, the radius of the circle is half the diameter, which is 4 feet.

The area of a circle is given by the formula:

A = πr^2

where A is the area and r is the radius.

Plugging in the value of the radius, we get:

A = π(4 feet)^2

A = 16π square feet

A ≈ 50.27 square feet (rounded to two decimal places)

Therefore, the area of the circle is approximately 50.27 square feet.

Learn more about area here:https://brainly.com/question/25292087

#SPJ1

Answer: 4

Step-by-step explanation:

1 third of 30 is 10 and 2/5s of 10 is 4

In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,

∠A = ∠L, ∠D =∠M , ∠C = ∠N , and

AB = LB , CD = NM ,  DA = ML.

Quadrilateral ABCD rotates 180 degrees around point B,

New quadrilateral formed named LBMN

The corresponding angle after rotation of 180 degrees around B is equals to,

B remain at same position.

A rotates and point L take the position of A.

D rotates and point M take the position of D.

C rotates and point N take the position of C.

Corresponding angle to A is angle L.

Corresponding angle to D is angle M.

Corresponding angle to C is angle N.

Similarly corresponding segments are of ABCD and LBNM are

Line segment AB corresponds to line segment LB.

Line segment CD corresponds to line segment NM

Line segment DA corresponds to line segment ML.

Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.

Learn more about quadrilateral here

brainly.com/question/27888037

#SPJ1

The distance between the two points is

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

Distance between two points is the length of the line segment that connects the two points in a plane.

The distance between two points is expressed as;

d = √ (X-x )² + (Y-y)²

X = -2

x = x

Y = 3

y = y

Therefore the distance between the two points is

d = √( -2-x)² + (3 -y)²

or it can also be written in this form

d = √ x-(-2)² + (y-3)²

d = √ x+2)² + (y-3)²

therefore the model of the distance between the two points can be

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

learn more about distance between two points from

https://brainly.com/question/7243416

#SPJ1

Answer:

1. Its constant speed is 550 miles per hour.

2. Time taken to fly from Albuquerque to Phoenix is \(\frac{3}{5}\) hours (36 minutes).

Step-by-step explanation:

Speed = \(\frac{distance}{time}\)

a. Its speed from Pittsburgh to Saint Louis can be calculated by;

speed = \(\frac{550}{1}\)

           = 550 miles/hour

b. Its speed from Saint Louis to Albuquerque can be determined by;

42 minutes = \(\frac{42}{60}\) hours

                   = \(\frac{7}{10}\) hours

so that time taken = 1\(\frac{7}{10}\) hours

speed = \(\frac{935}{1\frac{7}{10} }\)

          = \(\frac{9350}{17}\)

          = 550 miles/hour

c. From Albuquerque to Phoenix, let the time be represented by t. We have;

speed = \(\frac{330}{t}\)

since the speed is constant, then'

550 = \(\frac{330}{t}\)

⇒ t = \(\frac{330}{550}\)

      = \(\frac{3}{5}\)

Thus, time taken to fly from Albuquerque to Phoenix is \(\frac{3}{5}\) hours (36 minutes).

Answer:

96

y-step explanation:

volume of 1cm cubes = 1 x 1 x 1 = 1 cm^3

so it will take 96 cubes to fill the prism

Answer:

Where is the image?

Step-by-step explanation:

There must be an image, right?

The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

Answer:

Step-by-step explanation:

The three true statements about circle Q are:

1. The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth.

2. The area of the shaded sector is 4 units 2.

3. The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the circumference of the circle.

The True statements are:

The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8.

The area of the shaded sector depends on the length of the radius.

The area of the shaded sector depends on the area of the circle.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.  

First, The measure of the central angle is 45°.  

So, ratio of the central angle to the entire circle

= 45/360

= 9/72

= 1/8

Now, area of shaded sector

A = πr² = π(6²) = 36π

or, 1/8(36π)

= 36π/8

= 18π/4

= 9π/2

= 4.5π square units.  

Since, we use the circle's radius to determine area, the shaded sector's area is dependent on the circle's radius.

Given that the sector is a portion of the circle, its size is also influenced by the size of the circle.

and, The ratio of the shaded sector's area to the circle's area wouldn't be the same as the ratio of the arc's length to the circle's area.

Learn more about Circumference here:

https://brainly.com/question/28757341

#SPJ5

By using scale and prοpοrtiοn, the dimensiοns οf the actual painting are 144 inches² by 216 inches².

Scale refers tο the relatiοnship between the dimensiοns οf a scaled οbject and the cοrrespοnding dimensiοns οf the οriginal οbject. If an οbject is scaled dοwn tο half its οriginal size, then the dimensiοns οf the scaled οbject will be half οf the dimensiοns οf the οriginal οbject.

Prοpοrtiοn, οn the οther hand, refers tο the relatiοnship between twο οr mοre quantities that have the same ratiο. In οther wοrds, if twο quantities are in prοpοrtiοn, then their ratiο is cοnstant.

Tο find the dimensiοns οf the actual painting, we need tο "undο" the 6:1 scale.

If the scaled painting is 6 times smaller than the actual painting, then the actual painting is 6 times larger than the scaled painting.

Sο we can find the actual dimensiοns by multiplying the scaled dimensiοns by 6:

Actual width = 24 inches x 6 = 144 inches

Actual height = 36 inches x 6 = 216 inches

Therefοre, the dimensiοns οf the actual painting are 144 inches² by 216 inches².

To know more about scale and proportion visit:

brainly.com/question/21882232

#SPJ1

Answer:

Step-by-step explanation:

!od

7x=96

The equation that represents the balance of the loan, y, if he borrows the money for x years is presented as follows;

\(y = 5000\cdot e^{0.089\cdot t}\)

A continuous compounding interest involves finding the accrued interest and repeat reinvestment of the interest in which the number of periods is infinite.

The formula for the amount of a compound interest loan compound continuously is expressed as follows;

\(A(t) = P_0\cdot e^{r\cdot t}\)

Where;

P₀ = The principal amount = The amount loaned

r = The interest rate

t = The duration of the loan

The amount of loan Landis is taking, P₀ = $5,000

The interest rate compounded continuously, r = 8.9%

Where, y = The balance of the loan, and x = The number of years the loan is borrowed, we get;

P₀ = $5,000

r = 8.9% = 0.089

y = A(t)

x = t

Therefore; \(y = 5000\times e^{0.089 \times t}\)

Learn more about continuous compounding interest here:

https://brainly.com/question/12377617

#SPJ1

Answer:

Slope = 0.25

Step-by-step explanation:

m= -3 / -12 = -1 / -4 = 0.25

distance between x's = 12

distance between y's = 3

hope this helped thank you!

12x+10+4y

= 2(6x+5+2y)

=D

Answer:

11.11% probability that it will rain on the day of Marie's wedding, given the weatherman forecasts rain

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

\(P(B|A) = \frac{P(B)*P(A|B)}{P(A)}\)

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Forecast of rain.

Event B: Raining.

In recent years, it has rained only 5 days each year.

A year has 365 days. So

\(P(B) = \frac{5}{365} = 0.0137\)

When it actually rains, the weatherman correctly forecasts rain 90% of the time.

This means that \(P(A|B) = 0.9\)

Probability of forecast of rain:

90% of 0.0137(forecast and rains)

10% of 1 - 0.0137 = 0.9863(forecast, but does not rain)

\(P(A) = 0.0137*0.9 + 0.9863*0.1 = 0.11096\)

What is the probability that it will rain on the day of Marie's wedding, given the weatherman forecasts rain

\(P(B|A) = \frac{0.0137*0.9}{0.11096} = 0.1111\)

11.11% probability that it will rain on the day of Marie's wedding, given the weatherman forecasts rain

Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.