Socrates was alive from 469 to 399 B.C.E , Plato from 427 to 347 B.C.E ,Aristotle from 384 to 322 B.C.E. What years were they all alive simultaneously

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

Learn more about trigonometric identity :

https://brainly.com/question/3785172

#SPJ1

Answer:

Step-by-step explanation:

A

Notice that we can draw a triangle in the square , and that the length of the square's diagonal is the same as the length of the triangle's hypotenuse. The triangle is a right triangle therefore it satisfies the Phytagorean Theorem. To calculate for it's hypotenuse , we will use:

where c is the hypotenuse, and a, b are the other legs of the triangle.

Since the hypotenuse of the triangle is 42.43 cm. Therefore, the square's diagonal is also 42.43 cm

Answer:

The square's diagonal is 42.43 cm

The value of length of side AB is,

⇒ AB = 5 units

We have to given that;

The figure is shown a trapezoid.

Hence, By using Pythagoras theorem we get;

⇒ AB² = 4² + (5.25 - 2.25)²

⇒ AB² = 16 + 3²

⇒ AB² = 16 + 9

⇒ AB² = 25

⇒ AB = √25

⇒ AB = 5 units

Therefore, The value of length of AB is,

⇒ AB = 5 units

Learn more about the Pythagoras theorem visit:

https://brainly.com/question/343682

#SPJ1

Answer:

answer is 0.025

Step-by-step explanation:

answer is 0.025

The rational function f(x) = (x² + 1)/(x² + 2x + 2) has no vertical asymptotes and no holes.

We have,

A rational function is a function that can be expressed as the ratio of two polynomials.

It can have vertical asymptotes and/or holes in its graph, depending on the behavior of the denominator polynomial.

To construct a rational function with no vertical asymptotes and no holes, we need to ensure that the denominator polynomial does not have any real roots.

This means that the denominator polynomial should either have no roots or only complex roots.

One way to achieve this is to use a quadratic polynomial in the denominator that has no real roots.

For example, consider the function:

f(x) = (x² + 1)/(x² + 2x + 2)

The denominator polynomial x² + 2x + 2 has no real roots because its discriminant, 2² - 4(1)(2) = -4, is negative.

This means that the function f(x) has no vertical asymptotes.

To check if the function has any holes, we need to simplify the function by canceling out any common factors between the numerator and denominator.

However, since the numerator x² + 1 has no common factors with the denominator, there are no terms to cancel out.

Therefore, the function f(x) has no holes either.

Thus,

The rational function f(x) = (x² + 1)/(x² + 2x + 2) has no vertical asymptotes and no holes.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

We can Identify the Valid Equivalance values if the option c) 29,30,31 student clears the exam.

The values that the system or component being tested need to be able to accept are known as valid partitions. The "Valid Equivalence Partition" is the name given to this partition. The values that the component or system under test should reject are known as invalid partitions. The "Invalid Equivalence Partition" is the name of this partition.

For the purpose of the student passing the exam, the values of marks that they can obtain that are equal to or higher than the minimum required marks to pass the exam, which is 24 marks, are regarded real equivalency values. In this case, 29, 30, 31, and all mark values higher than 31 are valid equivalence values.

The appropriate selections are (c), 29, 30, and 31.

To learn more about Valid Equivalance: https://brainly.com/question/12545173

#SPJ4

Answer:

1•7

Step-by-step explanation:

Answer Accorfing ti te pasaje we no get:

The value of c does not affect the covariance of Y and Z.

The covariance of Y and Z can be calculated as Cov(Y, Z) = E[YZ] - E[Y]E[Z]. Since X is Bernoulli with parameter p and E[X] = p, we have E[Z] = pE[Y]. Hence,

Cov(Y, Z) = E[YZ] - E[Y]E[Z]

= E[YXY] - pE[Y]^2

= pE[Y^2 X] - pE[Y]^2

= p(E[Y^2]E[X] + Var[Y]p) - pE[Y]^2

= p(1 * p + 1 * p^2) - p^2

= p - p^2

It can be seen that the value of c does not affect the covariance of Y and Z.

learn more about covariance: https://brainly.com/question/21287720

#SPJ1

Answer:

96 square feet

Step-by-step explanation:

Area= length x width

So for the rug it would be 12x8

12x8=96

Answer:

  B  35,501

Step-by-step explanation:

The least integer that will round up to 36,000 is 35,500.

The greatest integer that will round down to 36,000 is 36,499.

The only listed integer between those numbers is ...

  35,501

Answer:

20. bcg

21. 124

Step-by-step explanation:

Both the gongs will strike together at 3 pm.

Given,

Two gongs strike at intervals 90 and 60 minutes respectively.

Use LCM to find at what time they will strike together

Using prime factorization:

LCM of (60,90)=\(2^2*3^2*5=4*9*5=180\)

They will strike together after 180 minutes i.e. 3 hours

Hence, if they start simultaneously at 12 noon then they will strike together again at 3 pm

To learn more about LCM refer here

https://brainly.in/question/332006

#SPJ9

30 + 110 + 30 + 110 = 280

360-280 = 80

2y = 80

y = 40 degrees

If y is 40. Then the angle next to 30 is also y due to vertically opposite angles.

30 + 40 = 70

The line with 2 arrows is parallel to the line with x degrees. So, I use co-interior angles adds to 180.

In that c shaped, we got the bottom angle to be 70 & the top to be 110 because co-interior angles =180

Forget the c shape exists, and move onto the triangle that's visible. The top angle is 110 as found.

Angles in triangle add to 180.

180 - 110 - 30 = 40.

Thus, x = 40 degrees

There's a short cut I realise now because we can have alternate angles are equal; creating a z shape to find what x is equal to & that turns out to be the same value as y. ( due to vertically opposite angles)

Hope this helps!

Answer: C.

Step-by-step explanation:

Total number of plants in Robert's garden = 8 + 4 + 16 + 22

= 50

Number of tomato plants in Robert's garden = 8

Ratio of total number of plants to the number of tomato plants = 50 : 8

Simplify

50 : 8 = 25:4

From Triangle 1,

∠X=43°

From Triangle 2,

∠y=106°

Hence,

Are the figures similar? YES

∠X=43°

∠Y=106°

The probabilities that have been calculated here are:

The probability that he is a smoker = 0.08 + 0.16

= 0.24

The given probability that has been calculated is 0.24.

The probability that he does not have lung disease = 0.16 + 0.73

= 0.89

The probability that he has lung disease given that he is a smoker

= 0.08 / 0.08 + 0.16

= 0.08 / 0.24

= 0.333

The probability here is calculated to be 0.333

The probability that he has lung cancer given that he does not smoke

= 0.03 / 0.03 + 0.73

= 0.03 / 0.76

= 0.0395

The given probability here is 0.0395

Read more on probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

The surface area is \(325.4m^2\)

The lateral surface area is: \(292.4m^2\)

Step-by-step explanation:

Given

\(L = 3m\) -- Length

\(H =17.2m\) --- Height

\(W = 5.5m\) --- Width

See attachment for prism

Solving (a): The surface area

This is calculated as:

\(S.A = 2 * (LW + WH + LH)\)

This gives:

\(S.A = 2 * (3*17.2 + 17.2 * 5.5 + 3 * 5.5)\)

\(S.A = 2 * (51.6 + 94.6 + 16.5)\)

\(S.A = 2 * 162.7\)

\(S.A = 325.4m^2\)

Solving (b): The lateral surface area

This is calculated as:

\(L = 2 * (L + W) * H\)

So, we have:

\(L = 2 * (3 +5.5) * 17.2\)

\(L = 2 * 8.5 * 17.2\)

\(L = 292.4m^2\)

Answer:

See explanations below

Step-by-step explanation:

What the step for answer

Given the nth terms of as sequence expressed as

Sins a ≥ 3, we can find the third term of the sequence

an  = 2an-1 + an-2 - 2an-3

If a1 = 6 and a2 = 0 and a0 = 3

a3 = 2a2 + a1 - 2a0

a3 = 2(0) + 6 - 2(3)

a3 = 0 + 6 - 6

a3  = 0

If n = 4

a4 = 2a3 + a2 - 2a1

a4 = 2(0) + 0 - 2(6)

a4 = 0 + 0 - 12

a4  = -12

Answer:

3rd quadrant

Step-by-step explanation:

Given:

Point (-2, -9)

Computation:

In 1st quadrant (+ , +)

In 2nd quadrant (- , +)

In 3rd quadrant (- , -)

In 4th quadrant (+ , -)

So given point (-2, -9) is in 3rd quadrant.

Using properties of square,

a. Equation for total area = 2x² - 16x + 64

b. Area will be minimum for the value of x = 0

c. Minimum area will be 64cm².

With four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. The equal sides and 90° internal angles of each square form serve as indicators of its identity.

Total length of wire = 32cm.

Now side of one square is given as x.

Perimeter of big square will be = 4x.

Now perimeter of small square = 32- 4x.

Side of small square = (32-4x)/4

= 4(8-x)/4

= 8-x

Area of big square = x × x

= x².

Area of small square = (8-x) ².

Now Total area, A(x) = x² + (8-x) ²

= x² + 64 + x² - 16x

= 2x² - 16x + 64

The side length that will minimize the area will be, x = 0.

Minimum area of the total figure will be = 64cm²

To know more about square, visit:

https://brainly.com/question/28776767

#SPJ1

Answer:

48000cm

Step-by-step explanation:

5:15000

But, 1cm will be 3000

16cm will be 16*3000 =48000cm

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x=0

Step-by-step explanation:

Answer:

one solution (x=0)

Step-by-step explanation:

First, let's simplify the equation to 3x=-2x (we subtract 5 from both sides). Now we can add 2x to both sides to get 5x=0. There is only one solution to this (x=0).

Answer:

Therefore the lenght of line segment is :√13

Step-by-step explanation:

Refer to the attachment for your answer.

Answer:

1/6

Step-by-step explanation:

4/4 - 1/4 = 3/4. (1 = 4/4)

3/4 - 1/4 = 2/4 = 1/2

1/2 - 1/3. (Common denominator is 6)

3/6 - 2/6 = 1/6

The value of g(h(10)) is 2√2. the correct option is A.

Given that the functions are g(x)=√x-4 and h(x)=2x-8.

A function is defined as the relationship between a set of inputs where each input has an output.

Firstly, we will find the value of h(10) by substituting x=10 in the function h(x)=2x-8.

h(10)=2(10)-8

h(10)=20-8

h(10)=12

Now, we will find g(h(10)) where h(10)=12.

By substituting h(10)=12 in g(h(10)), we get

g(h(10))=g(12).

Further, we will find g(12) by substituting x=12 in the function g(x)=√x-4, we get

g(12)=√(12-4)

g(12)=√8

g(12)=2√2

Hence, the value of function g(h(10)) when g(x)=√x-4 and h(x)=2x-8 is 2√2.

Learn more about the function from here brainly.com/question/24160317.

#SPJ9

Answer:

i think that it is 83.94 ft of i am correct