Find dy/dx by implicit differentiation. 4 sin(x) + cos(y) = sin(x) cos(y) Step 1 We begin with the left side. Remembering that y is a function of x, we have [4 sin(x) + cos(y)] = - Dy'. dx

Answer:

First, if we have a function defined as:

\(G(x) = \int\limits^x_0 {f(t)} \, dt\)

then:

G'(x) = f(x)

\(F(x) = \int\limits^x_0 {cos(t)^2} \, dt\)

then:

F' = dF/dt = cos(t)^2

F'(1) = cos(1)^2 = 0.2919

If we round it up to the third digit after the decimal point we get:

F'(1) = 0.292

The correct option is the second one.

Answer:

Magnitude: 23.4 kph

Direction: 50.2° below horizontal.

Step-by-step explanation:

15² + 18² = s²

s² = 549

s = 23.4

Θ = tan^-1 18/15

Θ = 50.2°

The velocity vector is the sum of the two vectors which is a vector that starts at the boat and goes until the lower tip of the vertical arrow.

Its magnitude is 23.4 kph, and its direction is 50.2° below horizontal.

Answer:  boats vector is 23.45 kph, 50.2° south of east

Step-by-step explanation:

A  vector has both direction and magnitude.

The vector for the boat is the shortest route from the boat to that end point which is a diagonal.

In order to find magnitude you use pythagorean

c²=a²+b²

m=15²+18²

m=√549

magnitude=23.45 kph

direction you would use tan∅

tan∅=opp/adj=18/15

∅= \(tan^{-1} \frac{18}{15}\)

∅=50.2

So the boats vector is 23.45 kph, 50.2° south of east

The given limit can be expressed as the definite integral: lim (n→∞) n ∑(i=1 to n) i⁶/n⁷ = ∫[1/n, 1] x⁶ dx

To express the given limit as a definite integral, we need to determine the appropriate function f(x) and the integration limits b and 1.

Let's start by rewriting the given limit:

lim (n→∞) (1/n) ∑(i=1 to n) \(i^6/n^7\)

Notice that the term i⁶/n⁷ can be written as (i/n)⁶/n.

Therefore, we can rewrite the above limit as:

lim (n→∞) (1/n) ∑(i=1 to n) (i/n)⁶/n

This can be further rearranged as:

lim (n→∞) (1/n^7) ∑(i=1 to n) (i/n)⁶

Now, let's define the function f(x) = x⁶, and rewrite the limit using the integral notation:

lim (n→∞) (1/n^7) ∑(i=1 to n) (i/n)⁶ = ∫[a,b] f(x) dx

To determine the integration limits a and b, we need to consider the range of values that x can take. In this case, x = i/n, and as i varies from 1 to n, x varies from 1/n to 1. Therefore, we have a = 1/n and b = 1.

Hence, the given limit can be expressed as the definite integral:

lim (n→∞) n ∑(i=1 to n) i⁶/n⁷ = ∫[1/n, 1] x⁶ dx

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Answer:

the answer is d just to the exam

The required population after 2 years is 337.75 quail.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

here,
An initial population of 295 quail increases at an annual rate of 7%. ,
the exponential growth of the population can be shown as,
y = 295[1 + 0.07]ˣ

Where x is the number of years and y is the population of that year.

Now put x = 2
y = 295[1.07]²
y = 337.75

Thus, the required population after 2 years is 337.75 quail.

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0.4

The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.

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1. -33.963333

2. 28

but i'm not sure

All of the following are measures of central tendency except the range.

The range is a measure of dispersion, representing the difference between the largest and smallest values in a dataset. It provides information about the spread or variability of the data but does not provide information about the central tendency.

On the other hand, measures of central tendency are statistical measures that aim to summarize the center or typical value of a dataset. They include the mode, median, and mean.

The mode represents the most frequently occurring value(s) in the dataset.

The median is the middle value when the data is arranged in ascending or descending order. It divides the dataset into two equal halves.

The mean is the arithmetic average of all the values in the dataset. It is calculated by summing all the values and dividing by the total number of values.

Therefore, option C, range, is not a measure of central tendency as it focuses on the spread or dispersion of the data rather than summarizing the central or typical value.

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Answer:

×= 51

7

Step-by-step explanation:

Divide both sides of the equation by –0.182

Answer:

4 minutes

Step-by-step explanation:

A standard showerhead uses 2.5 gallons a minute, or 25 gallons for 10 minutes, therefore 10/2.5 = 4.

Answer:5566

Step-by-step explanation:

Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.

Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.

To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.

However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.

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Given:

Here a cylinder is given with radius is 2 unit and height is 6 unit.

Required:

Find the base and volume.

Explanation:

The base of cylinder is circle and the area of circle is

Now we have to find the volume of cylinder

now put the value of

so now volume of cylinder is

Final answer:

The base of cylinder is circle and the value of base is 12.56 square unit

Exact volume of cylinder is 24pi cubic unit and approximate volume of cylinder is 75.398 cubic unit

Step-by-step explanation:

(i hope this helps)

speed=distance/time taken

The value of the composite function is found as 68/5.

The function is given as;

g(x) = 32/(x+3)

Write the function as 'y'

y = 32/(x+3)

Replace the value of x with y.

x = 32/(y+3)

Solve for y.

x(y + 3) = 32

xy = 32 - 3x

y = (32 - 3x)/x

Thus, g⁻¹ (x) = (32 - 3x)/x is the inverse of the function.

Now, find the value composite function;  (g⁻¹ o g) (5).

(g⁻¹ o g) (5) =  (32 - 3x)/x . 32/(x+3)

Put x = 5

(g⁻¹ o g) (5) =  (32 - 15)/5 . 32/(5+3)

(g⁻¹ o g) (5) = 17×4/5

(g⁻¹ o g) (5) = 68/5

Thus, the value of the composite function is found as 68/5.

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Answer:

8 5/9

Step-by-step explanation:

9 goes into 77 8 whole times and then 5 is a leftover from 8. and 9 will stay the same so it will be 8 5/9

Answer:

\(8\frac{5}{9}\)

Step-by-step explanation:

I hope this helps!

Answer:

\(34.5575191895\)

Step-by-step explanation:

\(2\pi r(180/360)\\2\pi *11*1/2\\=11\pi\)

The arc length of the semicircle is half the circumference i.e., 11π.

The circumference is the perimeter of a circle.

Formula of Circumference = 2πr.

= Arc length of a semicircle  

= half of the circle's circumference

= 2πr/2

= πr

=11r

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Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

The mathematics curriculum involves examining numbers, the equation the environment we live in, structures, and both actual and hypothetical locations. A function is a variable representation of the relationship between the quantities of intake and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, when combined, provide unique outputs for each input.

Here,

Given :

mass of a population of duckweed is 500g

=>  function m(t)= 500x³^t/45

So,

=> t = 45 hours

Since it is given that the mass of the population of the duckweed triples every 45 hours

it is clear that the time taken for the duckweed to grow a mass triple the original size will be 45 hours .

Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

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The domain of the given function h(x) = 1 - 3x is {-2, 1, -2, -5}.

The domain of a set of ordered pairs includes all possible x values of a function, and the range includes all possible y values of a set of ordered pairs.

The function is given in the question as:

h(x) = 1 - 3x    ....(i)

Here domain= {1, 0, 1, 2}

The range includes all possible y values of a set of ordered pairs.

Substitute the values of the domain i.e. x = 1, 0, 1, 2 in the equation (i),

h(x) = 1 - 3(1)

h(x) = 1 - 3

h(x) = -2

h(x) = 1 - 3(0)

h(x) = 1

h(x) = 1 - 3(1)

h(x) = 1 - 3

h(x) = -2

h(x) = 1 - 3(2)

h(x) = 1 - 6

h(x) = -5

Therefore, the domain of the given function is {-2, 1, -2, -5}.

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The transformations to the graph of the quadratic function are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Additionally, when the function is multiplied by |a| > 1, it is said that the function is vertically stretched by a factor of a.

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The time the plane arrives at the London airport from the airport in Manchester, found using the kinematic equation for speed, and the conversion of the units from hours to minutes is 11:40 a.m.

The kinematic equations describe the motion of an object that moves with constant acceleration.

Distance from the London airport to the Manchester airport, D = 200 miles

The average speed of the plane, v = 120 mph

Time the plane leaves Manchester airport = 10 a.m.

The kinematic equation that can be used to find the time of flight is presented as follows;

\(Speed, \, v = \dfrac{Distance, \, D }{Time, \, t}\)

Therefore;

\(t = \dfrac{D}{v}\)

The time of flight is therefore;

\(t = \dfrac{200}{120} = \dfrac{5}{3} = 1\dfrac{2}{3}\)

The time of flight is \(1\frac{2}{3}\) hours or 5/3 hours which in minutes is therefore:

\(t = \dfrac{5}{3} \, hr \times 60 \, min/hr= 100 \, min\)

The time of arrival is 10 a.m. + 1 hour 40 minutes = 11:40 a.m.

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DO u need the percetage or the price?Step-by-step explanation:

a) P(mean length of 16 fish > 14.5 inches) ≈ 0.0668; b) P(mean length of 64 fish > 14.5 inches) ≈ 0.499; c) probabilities not equal due to Central Limit Theorem.

(a) The probability that the mean length of 16 randomly selected fish is more than 14.5 inches can be found using the standard normal distribution and the formula for a z-score. The z-score represents how many standard deviations a value is from the mean, and can be calculated as (14.5 - 14) / (2 / √16). Using a standard normal table or a calculator with a normal distribution function, the z-score can be used to find the probability of a value being above 14.5 inches.

(b) The probability that the mean length of 64 randomly selected fish is more than 14.5 inches can be found using the same method as in (a), with the only difference being the sample size in the calculation of the z-score. The z-score would be (14.5 - 14) / (2 / √64).

(c) The probabilities in (a) and (b) are not equal because the sample size is different. As the sample size increases, the standard deviation of the sample mean (known as the standard error) decreases, making it more likely that the sample mean will be close to the population mean. Therefore, as the sample size increases, the probability of the sample mean being above a certain value decreases.

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We are given that LaTeX: A\:=\:\log_72

A = log 7 ⁡ 2 and LaTeX:

B\:=\:\log_73

B = log 7 ⁡ 3 and LaTeX:

C\:=\:\log_75

C = log 7 ⁡ 5 and need to use the properties of logarithms to write LaTeX:

\log_735  in terms of A and B and C. Let us use the following properties of logarithms which are frequently used for simplification of logarithmic expressions: Product rule:

LaTeX: \log_{b}(mn)=\log_{b}m+\log_{b}n

Quotient rule: LaTeX: \log_{b}\left(\frac{m}{n}\right)=\log_{b}m-\log_{b}n.

Power rule: LaTeX: \log_{b}(m^n)=n\log_{b}(m) Applying these properties, we have,

LaTeX: \begin{aligned}

\log_7 35 &= \log_7 (5\cdot 7) \\ &

= \log_7 5 + \log_7 7 \\ &

= C + 1 \end{aligned}Therefore,

LaTeX: \log_735=C+1.

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On a scale drawing of a basketball court, 1 inch equals 8 feet the actual area of the basketball court if the scale drawing is 11. 75 inches by 6. 25 inches will be 4,700 square feet.

Given:

To solve the given question we will assume the court is rectangular in shape so we will solve by using formula of Area of rectangle

\(\rm Area \;of\;rectangle\;= l\times b\)

Where, l=length

            b=breadth

According to the given question,

    \(\rm Area = 94\; feet \times 50\; feet\\\\ = 4,700 \;square\; feet.\\\)

Therefore, Area of the basketball court will be 4,700 square feet.

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Answer:

-1/2

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

12 squared plus 5 squared=169