sec 5A = cosec 7A, prove that A = 7.5°​

This differential equation is separable.

To solve, we can first rewrite the equation as:

y dy = 8x dx

Next, we integrate both sides with respect to their respective variables:

∫y dy = ∫8x dx

(1/2)y^2 = 4x^2 + C

where C is the constant of integration.

Finally, we solve for y:

y = ±sqrt(8x^2 + 2C)

Therefore, the general solution of the differential equation is:

y = ±sqrt(8x^2 + 2C)

In calculus, the constant of integration is an arbitrary constant that appears when finding the indefinite integral (antiderivative) of a function. When taking the derivative of a function, any constant terms drop out, but when integrating a function, there is no way to know whether a constant term was present in the original function, so it is added as the constant of integration.

For example, suppose we want to find the indefinite integral of the function f(x) = x. We can do this by applying the power rule of integration, which states that the integral of x^n with respect to x is (x^(n+1))/(n+1) plus the constant of integration C:

∫x dx = (x^2)/2 + C

The constant of integration C is added to the antiderivative because when we differentiate (x^2)/2, the constant term 1/2 disappears, leaving us with just x.

Visit here to learn more about differential equation brainly.com/question/14620493
#SPJ11

Option B is correct. 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet. This can be obtained by using the formula of density.

Given that there are 22 goldfishes,

mass of tank = 22 goldfishes

volume of tank = 56 cubic feet

                      = 22/56

                      = 0.39 goldfish per cubic feet

Hence 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet.

Learn more about density:

brainly.com/question/14762317

#SPJ1

Answer: 0.39 goldfish

Step-by-step explanation:

Answer: The powers of i have a repetitive cyclic nature.

When we raise the imagenry unit i to increasing powers, we get a pattern which repeats itself.

Observe the following table of powers of i.

Power of i i1 i2 i3 i4 i5 i6 i7 i8 i9

Simplified i -1 -i 1 i -1 -i 1 i

As you see above, the pattern repeats itself and is four members long.

Therefore, ix+8 ix+4 will equalx.

When asked to determine the value of i to a power higher than 4, we can use this information in order to find our position in the cycle.

So, instead of using the actual power, we can take the remainder of the power divided by 4.

Two reasons when a person is entitled too access the Unemployed Insurance Fund are:

The unemployed insurance fund (UIF) is described as a short-term relief given to workers who are unable to work or when they become unemployed due to several reasons. In addition, the fund (UIF), can also be accessed by dependents of a deceased contributor.

Therefore, two reasons when a person is entitled too access the Unemployed Insurance Fund are:

Learn more about unemployed insurance fund (UIF) on:

https://brainly.com/question/26670092

Answer:

1/7

Step-by-step explanation:

negative reciprocal

Answer:

e2 = 112 + 92 − 2(11)(9)cos(140°)

Answer:

A

Step-by-step explanation:

2020 Edge

Answer:

\(m=0\)

General Formulas and Concepts:

Pre-Alg

Alg I

Step-by-step explanation:

Step 1: Define

Point (-6, -7)

Point (5, -7)

Step 2: Find slope m

This means that our line is a horizontal line.

Answer:

0/11

Step-by-step explanation:

You want to do y2-y1/x2-x1=m

So you would -7-(-7)/5-(-6)

Which equals 0/11

Hope this helps!

Since slope of line passing through two points (x

1

,y

1

) and (x

2

,y

2

) is m=

x

2

−x

1

y

2

−y

1

We now find the slope of the line passing through the points (7,5) and (−9,5) as shown below:

m=

−9−7

5−5

=

−16

0

=0

Therefore, the slope of the line is 0.

Now use the slope and either of the two points to find the y-intercept.

y=mx+b

5=(0)(7)+b

b=5

Write the equation in slope intercept form as:

y=mx+b

y=(0)x+5

y=5

Hence, the equation of the line is y=5.

Answer:

a = 3

Step-by-step explanation:

Since the line passes through the origin, we can find its equation using the two given points.

The slope of the line is:

m = (3 - 9) / (40 - a - 2a - 50) = -6 / (10 - 3a)

Using the point (2a+50, 9), we can find the y-intercept (b) of the line:

9 = m(2a+50) + b

b = 9 - m(2a+50)

b = 9 + (6/(3a-10))(2a+50)

So the equation of the line is:

y = (-6 / (3a-10))x + (9 + (6/(3a-10))(2a+50))

Since the line passes through the origin, the y-intercept (b) must be zero. Therefore:

0 = 9 + (6/(3a-10))(2a+50)

6(2a+50) = -9(3a-10)

12a + 300 = -27a + 90

39a = 210

a = 210/39

a = 3

Answer:

(0,4) and (2,0) for the first one the second one is (0,-6) and (12,0)

Step-by-step explanation:

Given:

Where, g = 4

To simplify the expression, substitute g for 4 and evaluate.

We have:

ANSWER:

37

Answer:

100 square meters

Step-by-step explanation:

\( {x}^{2} + 6x + 8x = 240\)

\( {x}^{2} + 14x = 240\)

\( {x}^{2} + 14x - 240 = 0\)

\((x - 10)(x + 24) = 0\)

\(x = 10\)

x = -24 will not work (it is extraneous).

\( {x}^{2} = 100\)

So the area of the square region is 100 square meters.

Answer:

attached above is the answer

Answer:

- 28     8

- 28    -6  

Step-by-step explanation          

143g

If 10% is 130g and 1% is 13g, that means you have to add both grams 130g + 13g to get the answer.

Step-by-step explanation:

Just add them together   10% + 1% = 11%

                                          130 + 13 = 143 g

Therefore, the answer is option B. 7.84.

To calculate the computed value of F, we need to use the formula:

F = Mean Square Treatment / Mean Square Error

From the ANOVA table, we can see that the Treatment and Error sum of squares are 1116 and 1068, respectively.

The degrees of freedom for Treatment is dfTreatment = 3-1= 2 and the degrees of freedom for Error is dfError = (3 x 6) - 3 = 15.

Using these values, we can compute the Mean Square Treatment as:

Mean Square Treatment = Sum of Squares Treatment / dfTreatment = 1116 / 2 = 558

And the Mean Square Error as:

Mean Square Error = Sum of Squares Error / dfError = 1068 / 15 = 71.2

Thus, the computed value of F is:

F = Mean Square Treatment / Mean Square Error = 558 / 71.2 = 7.84

Therefore, the answer is option B. 7.84.

Learn more about Mean Square Treatment.

brainly.com/question/14860886

#SPJ11

The set of strings that are in both languages, which is {bba, bbab}.

The intersection of the languages specified by (L₁;L₂;) and L₃ is the set of strings that are in both languages.

The language (L₁;L₂;) is formed by concatenating a string from L₁ with a string from L₂. Since L₁ only contains the string "bb", every string in (L₁;L₂;) starts with "bb" and is followed by a string from L₂. Thus, (L₁;L₂;) contains the strings "bba" and "bbab".

The language L₃ contains all strings of length 3 or less over the alphabet {a,b}. Thus, L₃ contains the strings "a", "b", "aa", "ab", "ba", "bb", "aaa", "aab", "aba", "abb", "baa", "bab", "bba", and "bbb".

The intersection of (L₁;L₂;) and L₃ is the set of strings that are in both languages, which is {bba, bbab}.

Learn more about strings

brainly.com/question/4087119

#SPJ11

The area over which the signal is transmitted are: a.\(\pi\) b. \(25\pi\) c. CB transmits 25 times more signal to walkie talkie.

When two quantities of the same units are compared, the ratio shows how much of one quantity is included in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, while part to part ratio is the other.

The area of the circle is given by the formula:

\(A = \pi r^2\)

For the walkie-talkie the signal is received up until 1 mile. Substitute the value of r = 1.

\(A _1= \pi (1)^2\\\\A_1 =\pi\)

For the CB radio the signal is received up until 5 miles. Substitute the value of r = 5.

\(A_2 = \pi (5)^2\\\\A_2= 25 \pi\)

a. The area over which a walkie-talkie can transmit its signal is \(\pi\) miles.

b. The area over which a CB radio signal can transmit its signal is \(25\pi\) miles.

c. The ratio of the transmitted signals are:

\(\frac{CB}{WT} = \frac{25\pi}{\pi} \\\\CB = 25 (WT)\)

Hence, the CB signal transmits 25 times more than the signal transmitted by the walkie-talkie.

Learn more about ratio here:

https://brainly.com/question/13419413

#SPJ1

The distance the cyclist traveled into the country, given that he rides into the country at an average speed of 10 miles per hour is 15 miles

Let the total distance traveled into the country be y.

Now, we shall determine the riding time. Details below:

Riding time = Distance / speed

Riding time = y / 10

Next, we shall obtain the walking time of the cyclist. This is shown below:

Walking time = Distance / speed

Riding time = y / 3

Finally, we shall obtain the total distance traveled. This is illustrated below:

Total time = riding time + walking time

6.5 = y/10 + y/3

6.5 = (3y + 10y) / 30

6.5 = 13y / 30

Cross multiply

13y = 6.5 × 30

13y = 195

Divide both sides by 13

y = 195 / 13

y = 15 miles

Thus, the total distance traveled by the cyclist into the country is 15 miles.

Learn more about distance travelled:

https://brainly.com/question/18265275

#SPJ1

Answer:

12/18

Hope this helps!

The first four terms of the sequence are: -3, 16, -22, 54.

Given the following:

a₁ = -3  

aₙ = -2aₙ₋₁ + 10

where

a₁ is the first term of the sequence

aₙ is the n-th term of the sequence.

We can apply the aₙ formula repeatedly by substituting for the value of n.

n = 1, 2, 3 and 4 (since we are to find first four terms)

Given:

a₁ = -3

a₂ = -2a₁ + 10

   = -2(-3) + 10

   = 6 + 10

   = 16

a₃ = -2a₂ + 10

   = -2(16) + 10

   = -32 + 10

   = -22

a₄ = -2a₃ + 10

   = -2(-22) + 10

   = 44 + 10

   = 54

Therefore, the first four terms of the sequence are:

a₁ = -3

a₂ = 16

a₃ = -22

a₄ = 54

Learn more about sequence here:

https://brainly.com/question/7882626

#SPJ1

Answer:

ITS B

Step-by-step explanation:

Step-by-step explanation:

m ~ 6.9

6.9! = 4122.7

4122.7 average 4125

n ~ 8.9

8.9! = 289867.7

289867.7 average 281600

The function f(d(x))=9/5|x^100|+32 shows the composition (d(x).

The function d(x) calculates how many degrees a container of water at temperature x is away from boiling water. It accepts a value of x in degrees centigrade. The formula f(d) converts a value in degrees Celsius, d, into a value in degrees Fahrenheit, d(x). As a result, when we do f(d(x)), we are integrating d(x) into f. (d).

The domain of f(d(x)) is now the range of d(x). This means that the function f(d(x)) displays the number of degrees Fahrenheit that a water container is away from the boiling point of water at a temperature x in degrees Celsius.

Learn more about function here

https://brainly.com/question/6561461

#SPJ4

Answer:

I don't think so

Step-by-step explanation:

but I'll try

The initial speed of a ball thrown horizontally from the roof of a building at a height of 54 m and hitting the ground at a height of 32 m from the bottom is equal to 9.64 m/sec.

A ball throws horizontally from the roof of a building. This is where we have to take horizontal movement into account.

Height of building = 54 m

Height of ground from base = 32 m Calculates the initial speed of the ball.

Since the ball is thrown horizontally, its initial velocity has no vertical component. When released, the ball is subject to gravity and accelerates downward until it hits the bottom. To determine how long the ball stayed in the air before hitting the ground, use the following formula,

d = 1/2×g×t²

where g --> acceleration due to gravity

t --> time

d --> the distance covered by ball before hitting the ground, g= 9.81 m/s².

So, 54 m = (1/2) × 9,81 m/s² × t²

=> t² = 54/4.90

=> t² = 540/49

=> t² = 11.02 sec²

=> t = 3.31963 ~ 3.32 sec

So the ball will stay in the air for about 3.32 seconds. Let v₀ₓ be the horizontal component of the initial velocity. According to the information of the problem, the ball landed 32 m from the bottom of the building. Let's make the initial position x₀ = 0. Then, the final horizontal displacement of a ball will be equals to 32 metres. Using the distance velocity relation, x = x₀ + v₀ₓt and substituting all known values in it,

=> 32 m = 0 + v₀ₓ × 3.32 sec

=> v₀ₓ = 32/3.32

=> v₀ₓ = 9.6385 ≈ 9.64 m/sec

Hence, required value is 9.64 m/sec.

To learn more about initial speed, visit :

https://brainly.com/question/30854534

#SPJ4

Complete question:

A ball is thrown horizontally from the roof of a building 54 m high and hits the ground 32 m from the base. What was the initial speed of the ball?

Given:

Simplife:

The given simplifies equation is:

After the compare the both inequality:

a=2

b=2

c=2

d=6

e=1

f=9

Number of measurements that must be made so that the diameter can be estimated with an uncertainty of only 0.5 mm is 16

To estimate the diameter with an uncertainty of 0.5 mm, we need to reduce the uncertainty to that level. Let's call the number of measurements we need to make "N". We can use the formula for the standard deviation of the mean

σ_mean = σ / sqrt(N)

where σ is the standard deviation of the individual measurements. In this case, the uncertainty of each measurement is given as 1.4 mm, which we can assume is the standard deviation.

To reduce the uncertainty to 0.5 mm, we need

0.5 = 1.4 / sqrt(N)

Solving for N, we get

N = (1.4 / 0.5)^2 = 15.68

≈ 16

Learn more about standard deviation here

brainly.com/question/23907081

#SPJ4

Answer:

Step-by-step explanation:

you hav to times it

The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled. This model helps to identify the mathematical correlations between variables and provides a foundation for developing a more detailed and accurate mathematical model.

The modeling process begins with the framing of a mathematical model that shows the relationships between the various parts of the problem being modeled. This model is often based on data analysis and utilizes statistical techniques to establish correlations between the different variables in the problem. Ultimately, the goal of the modeling process is to create a predictive tool that can be used to make informed decisions about the problem at hand.

Process models involve graphically representing processes or functions that capture, manage, store, and distribute information between the system and its environment and physical objects. One type of process model is the flowchart (DFD). A data flow is a diagram that shows the movement of data between external sources and processes and the data stored in the system. While several different tools have been developed for modeling, we focus only on data streams as they are effective tools for modeling. While not all organizations use all analytical methods, including these methods such as data flow, they have a significant impact on the development process.

Learn more about correlations:

brainly.com/question/28898177

#SPJ11

Answer:

it was long 4cm because 4/100 meters is like 4cm/100cm. 1 meter is 100cm so thats why