Given cosθ=-4/5 and 90°<θ<180° , find the exact value of each expression. tan θ/2

The measure of the arc AC which substends the angle ABC at the circumference of the circle is equal to 130°

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circle's circumference.

Given that the angle ABC = 65°

arc AC = 2(65)°

arc AC = 2 × 65°

arc AC = 130°

Therefore, the measure of the arc AC which substends the angle ABC at the circumference of the circle is equal to 130°°

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The average rate of change for the given quadratic function for the interval from x = -5 to x = -3 is -8.

The correct answer to the given question is option B.

The given quadratic function is shown below:f(x) = x² + 3x - 10

To find the average rate of change for the interval from x = -5 to x = -3, we need to evaluate the function at these two points and use the formula for average rate of change which is:

(f(x2) - f(x1)) / (x2 - x1)

Substitute the values of x1, x2 and f(x) in the above formula:

f(x1) = f(-5) = (-5)² + 3(-5) - 10 = 0f(x2) = f(-3) = (-3)² + 3(-3) - 10 = -16(x2 - x1) = (-3) - (-5) = 2

Substituting these values in the formula, we get:

(f(x2) - f(x1)) / (x2 - x1) = (-16 - 0) / 2 = -8

Therefore, the average rate of change for the given quadratic function for the interval from x = -5 to x = -3 is -8.

The correct answer to the given question is option B.

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The converse is "If x² = 81, then x = 9." which is true hence, these statements can be combined as: x = 9 if and only if   x² = 81.

A conditional statement is of the form "if p, then q." The statement p is called the hypothesis or premise, while the statement q is known as the conclusion.

For the given conditional statement "if x = 9, the x²  = 81," the converse is: "If x²  = 81, then x = 9."

This is an example of a true biconditional statement.

This means that the original conditional statement and its converse are both true. Therefore, they can be combined to form a biconditional statement.

Let's combine the statements:

If x = 9, then x² = 81. If x² = 81, then x = 9.

These statements can be combined as: x = 9 if and only if x² = 81.

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The reason to prove that ∠q ≅ ∠s include the following: C) Subtraction property of equality.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

In Mathematics and Geometry, the subtraction property of equality states that the two sides of an equation would still remain equal even when the same number has been subtracted from both sides of an equality.

Based on the information provided above, we can logically deduce the following equation:

m∠q + m∠r - m∠r = m∠s + m∠r - m∠r

m∠q = m∠s

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Complete Question:

Lines x and y intersect to make two pairs of vertical angles, q, s and r, t. Fill in the blank space in the given proof to prove ∠q ≅ ∠s.

A) Transitive property B) Addition property of equality C) Subtraction property of equality D) Substitution property

A) Write a linear equation expressing the population of the town, P, as a function of t, the number of years since 1996.

The population of a small town in central Florida has shown a linear decline in the years 1996-2005.

In 1996 the population was 49800 people. In 2005 it was 43500 people.

In order to write a linear equation expressing the population of the town,

P, as a function of t, the number of years since 1996,

let's use the point-slope formula which is y - y₁ = m(x - x₁),

where (x₁, y₁) are the coordinates of a point and m is the slope of the line.

Using the point (1996, 49800) and (2005, 43500) we can find the slope of the line.

m = (y₂ - y₁) / (x₂ - x₁)m = (43500 - 49800) / (2005 - 1996)m = -6300 / 9m = -700

Now that we know the slope of the line and have a point on the line,

we can write the linear equation expressing the population of the town,

P, as a function of t, the number of years since 1996.P - 49800 = -700(t - 1996)P - 49800 = -700t + 1397200P = -700t + 1437000

B) If the town is still experiencing a linear decline, what will the population be in 2010 ?To find the population in 2010,

we can use the linear equation we found in part A and substitute t = 2010 - 1996 = 14.P = -700t + 1437000P = -700(14) + 1437000P = -9800 + 1437000P = 1427200

Therefore, if the town is still experiencing a linear decline, the population will be 1427200 in 2010.

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The 34 m of wire that is needed to support the two wires is the overall length.

Given, a tower that is 35 m tall and is to have to support two wires. Both the wires will be attached to the top of the tower and it will be attached to the ground 12 m from the base of each wire. Wires in the show 5 m to complete each attachment. We need to find how much wire is needed to make support the two wires.

Distance of ground from the tower = 12 lengths of wire used for attachment of wire = 5 mWire required to attach the wire to the top of the tower and to ground = 5 + 12 = 17 m

Wire required for both the wires = 2 × 17 = 34 m length of the tower = 35 therefore, the total length of wire required to make the support of the two wires is 34 m.

What we are given?

We are given the height of the tower and are asked to find the total length of wire required to make support the two wires.

What is the formula?

Wire required to attach the wire to the top of the tower and to ground = 5 + 12 = 17 mWire required for both the wires = 2 × 17 = 34 m

What is the solution?

The total length of wire required to make support the two wires is 34 m.

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Answer:

Step-by-step explanation:

f(x) = (−5x2−7x)e^4x

Using the product rule:

f'(x) = (−5x2−7x)* 4e^4x + e^4x*(-10x - 7)

      =  e^4x(4(−5x2−7x) - 10x - 7)

      =  e^4x(-20x^2 - 28x - 10x - 7)

      = e^4x(-20x^2 - 38x - 7)

i. Connected bipartite graph with 6 labelled vertices and 6 edges is shown below:

Here, V1 = {a, c, e} and V2 = {b, d, f}.The corresponding relation rho⊂V1×V2 corresponding with the edges is as follows:

rho = {(a, b), (a, d), (c, b), (c, f), (e, d), (e, f)}.

  a -- 1 -- b

 /              \

f - 2            5 - d

 \              /

  c -- 3 -- e

ii. Let A be a set of six elements and σ an equivalence relation on A such that the resulting partition is {{a,c,d},{b,e},{f}}. The directed graph corresponding with σ on A is shown below:

a --> c --> d

↑     ↑

|     |

b --> e

↑

|

f

iii. A directed graph with 5 vertices and 10 edges representing a relation rho that is reflexive and antisymmetric, but not symmetric or transitive is shown below:

Here, the relation rho is reflexive and antisymmetric but not transitive. This is identified from the graph as follows:

Reflexive: There are self-loops on each vertex.

Antisymmetric: No two vertices have arrows going in both directions.

Transitive: There are no chains of three vertices connected by directed edges.

1 -> 2

↑    ↑

|    |

3 -> 4

↑    ↑

|    |

5 -> 5

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The equation 2sinθ - √2 = 0 can be solved for θ by finding the inverse of the sine function and using trigonometric identities. The solutions are θ = π/4 and θ = 5π/4.

To solve the equation 2sinθ - √2 = 0, we can isolate the sine term by moving the constant √2 to the other side of the equation:

2sinθ = √2

Next, we divide both sides of the equation by 2 to isolate sinθ:

sinθ = √2/2

This indicates that θ is an angle whose sine value is equal to √2/2. We can determine the values of θ by referring to the unit circle or using trigonometric values of common angles.

The sine value √2/2 corresponds to two angles: π/4 and 5π/4. These angles satisfy the equation sinθ = √2/2, and they fall within the interval 0 ≤ θ < 2π.

Therefore, the solutions to the equation 2sinθ - √2 = 0 are θ = π/4 and θ = 5π/4.

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The coefficient for the interval -T ≤ x ≤ 0 in the function g(x) is 1. However, the coefficient for the interval 0 ≤ x ≤ 2π depends on the specific form of the function f(x). Without additional information about f(x), we cannot determine its coefficient for that interval.

To solve for the coefficients in the function g(x), we need to consider the conditions given:

g(x) = { 1, -1, -T ≤ x ≤ 0

{ 1, f(x + 2π) = g(x)

We have two pieces to the function g(x), one for the interval -T ≤ x ≤ 0 and another for the interval 0 ≤ x ≤ 2π.

For the interval -T ≤ x ≤ 0, we are given that g(x) = 1, so the coefficient for this interval is 1.

For the interval 0 ≤ x ≤ 2π, we are given that f(x + 2π) = g(x). This means that the function g(x) is equal to the function f(x) shifted by 2π. Since f(x) is not specified, we cannot determine the coefficient for this interval without additional information about f(x).

The coefficient for the interval -T ≤ x ≤ 0 is 1, but the coefficient for the interval 0 ≤ x ≤ 2π depends on the specific form of the function f(x).

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The project's discounted payback period is approximately 4.5 years.

The discounted payback period is a measure of the time it takes for a company to recover its initial investment in a new project, considering the time value of money.

The formula for the discounted payback period is as follows:

Discounted Payback Period = (A + B) / C

Where:

A is the last period with a negative cumulative cash flow

B is the absolute value of the cumulative discounted cash flow at the end of period A

C is the discounted cash flow in the period after A

The formula for discounted cash flow (DCF) is as follows:

DCF = FV / (1 + r)^n

Where:

FV is the future value of the investment

n is the number of years

r is the discount rate

Initial cost of the project, P = $14,000

Cash flow for Year 1, CF1 = $6,000

Cash flow for Year 2, CF2 = $6,000

Cash flow for Year 3, CF3 = $10,000

Discount rate, r = 18%

Discount factor for Year 1, DF1 = 1 / (1 + r)^1 = 0.8475

Discount factor for Year 2, DF2 = 1 / (1 + r)^2 = 0.7185

Discount factor for Year 3, DF3 = 1 / (1 + r)^3 = 0.6096

Discounted cash flow for Year 1, DCF1 = CF1 x DF1 = $6,000 x 0.8475 = $5,085

Discounted cash flow for Year 2, DCF2 = CF2 x DF2 = $6,000 x 0.7185 = $4,311

Discounted cash flow for Year 3, DCF3 = CF3 x DF3 = $10,000 x 0.6096 = $6,096

Cumulative discounted cash flow at the end of Year 3, CF3 = $5,085 + $4,311 + $6,096 = $15,492

Since the cumulative discounted cash flow at the end of Year 3 is positive, we need to find the discounted payback period between Year 2 and Year 3.

DCFA = -$9,396 (CF1 + CF2)

DF3 = 0.6096

DCF3 = CF3 x DF3 = $6,096 x 0.6096 = $3,713

Payback Period = A + B/C = 2 + $9,396 / $3,713 = 4.53 years ≈ 4.5 years

Therefore, The discounted payback period for the project is roughly 4.5 years.

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Marcus will receive approximately $21,874.84 when he redeems the CD at the end of 16 years.

To calculate the amount Marcus will receive when he redeems the CD, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the initial principal (in this case, $12,000)

r = the annual interest rate (4.0% expressed as a decimal, so 0.04)

n = the number of times interest is compounded per year (monthly compounding, so n = 12)

t = the number of years (16 years)

Plugging in the values into the formula:

A = 12000(1 + 0.04/12)^(12*16)

A ≈ $21,874.84

Therefore, Marcus will receive approximately $21,874.84 when he redeems the CD at the end of 16 years.

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a. The independent quantity in this scenario is the number of weeks Selena has been collecting aluminum cans.

b. The dependent quantity is the total weight of aluminum cans Selena has collected.

c. The function that represents the relationship between the number of weeks and the total weight of aluminum cans collected can be written as:

Total weight = 100 + 25 * (number of weeks)

d. The rate of change in this context is the increase in the total weight of aluminum cans collected per week.

d. Since Selena plans to collect an additional 25 pounds each week, the rate of change is constant and equal to 25 pounds per week. Selena starts with an initial weight of 100 pounds of aluminum cans. For each subsequent week, she collects an additional 25 pounds, resulting in a linear relationship between the number of weeks and the total weight of aluminum cans.

The function is linear because the rate of change, which represents the slope of the line, is constant. This means that for every additional week, the total weight increases by 25 pounds. The function allows us to calculate the total weight of aluminum cans based on the number of weeks, providing a straightforward and predictable pattern of accumulation.

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L((7,8)) = (-9,23).  To find the value of L((7,8)), we can use the linearity property of the linear operator L.

Since L is a linear operator, we can express any vector in R² as a linear combination of the basis vectors (1,0) and (0,1).

We have L((1,2)) = (-2,3) and L((1,-1)) = (5,2). Therefore, we can express (7,8) as (7,8) = 7(1,2) + 1(1,-1).

Using the linearity property, we can distribute the linear operator L over the linear combination:

L((7,8)) = L(7(1,2) + 1(1,-1))

= 7L((1,2)) + L((1,-1))

= 7(-2,3) + (5,2)

= (-14,21) + (5,2)

= (-9,23)

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Answer:

35

Step-by-step explanation:

substitute n = 6 into h(n) for number of squares

h(6) = 6² - 1 = 36 - 1 = 35

Step-by-step explanation:

[tex]18^{10}\approx3.57*10^{12}[/tex]

Answer:

3.57

Step-by-step explanation:

3.570467 a bit longer if needed

If 480lb is $1920,then how much does it cost for 1lb.The cost for 1 pound is $4.

To find the cost of 1 pound, we can set up a proportion using the given information:

480 lb is $1920

Let's set up the proportion:

480 lb / $1920 = 1 lb / x

Cross-multiplying, we get:

480 lb * x = $1920 * 1 lb

Simplifying, we have:

480x = $1920

To find the value of x, we divide both sides of the equation by 480:

x = $1920 / 480

Calculating the division, we find:

x = $4

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The compound statement "Being human is sufficient for not having antlers" symbolically is represented as "p -> ~q".

The compound statement "Being human is sufficient for not having antlers" can be represented in symbolic form as:

p -> ~q

Here, the symbol "->" represents implication or "if...then" statement. The statement "p -> ~q" can be read as "If p is true (You are human), then ~q is true (You do not have antlers)."

The compound statement "Being human is sufficient for not having antlers" can be represented symbolically as "p -> ~q". In this representation, p represents the statement "You are human," and q represents the statement "You have antlers."

The symbol "->" denotes implication or a conditional statement. When we say "p -> ~q," it means that if p (You are human) is true, then ~q (You do not have antlers) must also be true. In other words, being human is a sufficient condition for not having antlers.

This compound statement implies that all humans do not have antlers. If someone is human (p is true), then it guarantees that they do not possess antlers (~q is true). However, it does not exclude the possibility of non-human beings lacking antlers or humans having antlers due to other reasons. It simply establishes a relationship between being human and not having antlers based on the given statement.

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The length of the hypotenuse is 15.

To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, the lengths of the two sides are given as 12 and 9. Let's denote the hypotenuse as 'c', and the other two sides as 'a' and 'b'.

According to the Pythagorean theorem:

c^2 = a^2 + b^2

Substituting the given values:

c^2 = 12^2 + 9^2

c^2 = 144 + 81

c^2 = 225

To find the length of the hypotenuse, we take the square root of both sides:

c = √225

c = 15

Therefore, the length of the hypotenuse is 15.

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There is no pair of nonzero integers such that both the sum and the difference of their squares are perfect squares.

Let's assume that there exist a pair of nonzero integers (m, n) such that the sum and the difference of their squares are also perfect squares. We can write the equations as:

m^2 + n^2 = p^2

m^2 - n^2 = q^2

Adding these equations, we get:

2m^2 = p^2 + q^2

Since p and q are integers, the right-hand side is even. This implies that m must be even, so we can write m = 2k for some integer k. Substituting this into the equation, we have:

p^2 + q^2 = 8k^2

For k = 1, we have p^2 + q^2 = 8, which has no solution in integers. Therefore, k must be greater than 1.

Now, let's assume that k is odd. In this case, both p and q must be odd (since p^2 + q^2 is even), which implies p^2 ≡ q^2 ≡ 1 (mod 4). However, this leads to the contradiction that 8k^2 ≡ 2 (mod 4). Hence, k must be even, say k = 2l for some integer l. Substituting this into the equation p^2 + q^2 = 8k^2, we have:

(p/2)^2 + (q/2)^2 = 2l^2

Thus, we have obtained another pair of integers (p/2, q/2) such that both the sum and the difference of their squares are perfect squares. This process can be continued, leading to an infinite descent, which is not possible. Therefore, we arrive at a contradiction.

Hence, there is no pair of nonzero integers such that both the sum and the difference of their squares are perfect squares.

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Therefore, the value of the integral ∫S z²dz, where S is the line segment from 0 to -1+2i sin(22)dz, is 14 sin(22) / 3.

a. To evaluate the integral ∫S z²dz, where S is the line segment from 0 to -1+2i sin(22)dz:

We need to parameterize the line segment S. Let's parameterize it by t from 0 to 1:

z = -1 + 2i sin(22) * t

dz = 2i sin(22)dt

Now we can rewrite the integral using the parameterization:

∫S z²dz = ∫[tex]0^1[/tex] (-1 + 2i sin(22) * t)² * 2i sin(22) dt

Expanding and simplifying the integrand:

∫[tex]0^1[/tex] (-1 + 4i sin(22) * t - 4 sin²(22) * t²) * 2i sin(22) dt

∫[tex]0^1[/tex] (-2i sin(22) + 8i² sin(22) * t - 8 sin²(22) * t²) dt

Since i² = -1:

∫[tex]0^1[/tex] (2 sin(22) + 8 sin(22) * t + 8 sin²(22) * t²) dt

Integrating term by term:

=2 sin(22)t + 4 sin(22) * t² + 8 sin(22) * t³ / 3 evaluated from 0 to 1

Substituting the limits of integration:

=2 sin(22) + 4 sin(22) + 8 sin(22) / 3 - 0

=2 sin(22) + 4 sin(22) + 8 sin(22) / 3

=14 sin(22) / 3

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A. The solution to the given system of differential equations is x = 2t + 1 and y = -10t^2 + 20t + C, where C is an arbitrary constant.

B. To solve the system of differential equations, we'll use a combination of separation of variables and integration.

Let's start with the first equation, dx/dt - y = -10t. Rearranging the equation, we have dx/dt = y - 10t.

Next, we integrate both sides with respect to t:

∫ dx = ∫ (y - 10t) dt

Integrating, we get x = ∫ y dt - 10∫ t dt.

Using the second equation, 16x - dy/dt = 10, we substitute the value of x from the previous step:

16(2t + 1) - dy/dt = 10.

Simplifying, we have 32t + 16 - dy/dt = 10.

Rearranging, we get dy = 32t + 6 dt.

Integrating both sides, we have:

∫ dy = ∫ (32t + 6) dt.

Integrating, we get y = 16t^2 + 6t + C.

Therefore, the general solution to the system of differential equations is x = 2t + 1 and y = -10t^2 + 20t + C, where C is an arbitrary constant.

Note: It's worth mentioning that the arbitrary constant C is introduced due to the integration process.

To obtain specific solutions, initial conditions or additional constraints need to be provided.

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The  system has: A unique solution when k is not equal to 2 or -1.

We can solve this problem using the determinant of the coefficient matrix of the system. The coefficient matrix is:

[1  k  1]

[1  k  1]

[1  1  k]

The determinant of this matrix is:

det = 1(k^2 - 1) - k(1 - k) + 1(1 - k)

   = k^2 - k - 2

   = (k - 2)(k + 1)

Therefore, the system has:

A unique solution when k is not equal to 2 or -1.

No solution when k is equal to 2 or -1.

More than one solution when det = 0, which occurs when k is equal to 2 or -1.

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The second derivative of y with respect to z (y") is given by (-sin(x)/5)/(4x²), where x is related to z through the equation z = x².

y", we need to differentiate the equation twice with respect to x. Let's start by differentiating both sides of the equation with respect to x:

dy/dx = d/dx(cos(2x^2) - 4y + sin(x))

Using the chain rule, we have:

dy/dx = -4(dy/dx) + cos(x)

Rearranging the equation, we get:

5(dy/dx) = cos(x)

Taking the second derivative of both sides, we have:

d²y/dx² = d/dx(cos(x))/5

The derivative of cos(x) is -sin(x), so we have:

d²y/dx² = -sin(x)/5

However, we want to express y" in terms of z, not x. To do this, we can use the chain rule again:

d²y/dz² = (d²y/dx²)/(dz/dx)²

Since z = x², we have dz/dx = 2x. Substituting this into the equation, we get:

d²y/dz² = (d²y/dx²)/(2x)²

Simplifying, we have: d²y/dz² = (d²y/dx²)/(4x²)

Finally, substituting -sin(x)/5 for d²y/dx², we get: d²y/dz² = (-sin(x)/5)/(4x²)

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The model in Problem 6 is: y = a + b sin(cx)

y is the average temperature in the town, a is the average temperature in the town at the beginning of the year, b is the amplitude of the temperature variation, c is the frequency of the temperature variation, and x is the number of days into the year.

We are given that the average temperature in the town at the beginning of the year is 50 degrees Fahrenheit, and the amplitude of the temperature variation is 10 degrees Fahrenheit. The frequency of the temperature variation is not given, but we can estimate it by looking at the data in Problem 6. The data shows that the average temperature reaches a maximum of 60 degrees Fahrenheit about 100 days into the year, and a minimum of 40 degrees Fahrenheit about 200 days into the year. This suggests that the frequency of the temperature variation is about 1/100 year.

We can now use the model to calculate the average temperature in the town 150 days into the year.

y = 50 + 10 sin (1/100 * 150)

y = 50 + 10 * sin (1.5)

y = 50 + 10 * 0.259

y = 53.45 degrees Fahrenheit

Therefore, the average temperature in the town 150 days into the year is 53.45 degrees Fahrenheit.

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The show that all points the curve on the tangent surface of are parabolic is intersection of a plane containing the tangent line and a surface perpendicular to the binormal vector.

Let C be a curve defined by a vector function r(t) = , and let P be a point on C. The tangent line to C at P is the line through P with direction vector r'(t0), where t0 is the value of t corresponding to P. Consider the plane through P that is perpendicular to the tangent line. The intersection of this plane with the tangent surface of C at P is a curve, and we want to show that this curve is parabolic. We will use the fact that the cross section of the tangent surface at P by any plane through P perpendicular to the tangent line is the osculating plane to C at P.

In particular, the cross section by the plane defined above is the osculating plane to C at P. This plane contains the tangent line and the normal vector to the plane is the binormal vector B(t0) = T(t0) x N(t0), where T(t0) and N(t0) are the unit tangent and normal vectors to C at P, respectively. Thus, the cross section is parabolic because it is the intersection of a plane containing the tangent line and a surface perpendicular to the binormal vector.

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The direction of the edges is indicated by -1 and 1 in the incidence matrix. If the number is -1, the edge is directed away from the vertex, and if it is 1, the edge is directed towards the vertex. Here is the graph: We have now drawn the graph based on the given incidence and adjacency matrix. The vertices are labeled A to J, and the edges are labeled E1 to E10.

The incidence and adjacency matrix are given as follows:-1 0 0 0 1 0 1 0 1 -11 0 1 -1 0 0 -1 -1 0 0

Here, we have -1 and 1 in the incidence matrix, where -1 indicates that the edge is directed away from the vertex, and 1 means that the edge is directed towards the vertex.

So, we can represent this matrix by drawing vertices and edges. Here are the steps to do it.

Step 1: Assign names to the vertices.

The number of columns in the matrix is 10, so we will assign 10 names to the vertices. We can use the letters of the English alphabet starting from A, so we get:

A, B, C, D, E, F, G, H, I, J

Step 2: Draw vertices and label them using the names. We will draw the vertices and label them using the names assigned in step 1.

Step 3: Draw the edges and label them using E1, E2, E3, and so on. We will draw the edges and label them using E1, E2, E3, and so on.

We can see that there are 10 edges, so we will use the numbers from 1 to 10 to label them. The direction of the edges is indicated by -1 and 1 in the incidence matrix. If the number is -1, the edge is directed away from the vertex, and if it is 1, the edge is directed toward the vertex.

Here is the graph: We have now drawn the graph based on the given incidence and adjacency matrix. The vertices are labeled A to J, and the edges are labeled E1 to E10.

Learn more about edges from this link:

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The equivalent statement for ~q → ~p is p → q.

Two or more expressions with an Equal sign is called as Equation.

To determine the equivalent statement for ~q → ~p, we can use the rule of logical equivalence, which states that:

~(p → q) ≡ p ∧ ~q

Using this rule, we can rewrite ~q → ~p as ~(~p) ∨ (~q), which is equivalent to p ∨ (~q).

Therefore, the equivalent statement for ~q → ~p is p ∨ (~q).

Now, let's translate the original statements p and q into logical statements:

p: n is a multiple of two this can be written as n = 2k, where k is some integer.

q: n is an even number. This can also be written as n = 2m, where m is some integer.

Using the definition of these statements, we can see that p and q are logically equivalent, as they both mean that n can be written as 2 times some integer.

Therefore, we can rewrite p as q, and the equivalent statement for ~q → ~p is p → q.

To learn more on Equation:

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Answer: Rs. 2000

Step-by-step explanation:

Given that: height of room= 5m

volume of room= 2000m³

cost of plastering per metre square= Rs. 4

To find: cost of platering on the floor

Solution:

volume of room = 2000m³

l×b×h = 2000m³

l×b × 5 = 2000m³

l×b = 2000/5

l×b = 400[tex]m^{2}[/tex]

area of floor = 400[tex]m^{2}[/tex]

cost of plastering on the floor= area of floor × cost per m square

                                  = 400[tex]m^{2}[/tex] × 5

  cost of plastering on the floor = Rs. 2000