the triangular plate is fixed at its base, and its apex a is given a horizontal displacement of 5 mm. suppose that a = 600 mm .

Answer:

Im a little confused on what your asking but for 0.4 as a decimal is 0.4,for a fraction 0.4 is 2/5 and for a percent 0.4 is 40%

Step-by-step explanation:

I hope this helps!!

third picture shows cube root of 64=4

Answer:

6/7n÷3

Basically i couldnt input the fraction. So its 6 over7, N next to the fraction, and then divide it by 3

Answer:

y = -x - 2

Step-by-step explanation:

y-3=-1(x+5)

Expand.

y - 3 = -1x - 5

Add 3 on both parts.

y - 3 + 3 = -1x - 5 + 3

y = -1x - 2

Answer:

3

Step-by-step explanation:

Answer:

7 + x + x= 7

Step-by-step explanation:

(7+8) + -8 = 7

Answer:

Price with tax - $31.8

Tax cost - $1.8

The cyclist's total displacement is 18.8 km to the east.

To solve this problem, we can use the formula:

distance = speed × time

Given that the cyclist rides 6.4 km east for 17.4 minutes, we can calculate the speed as follows:

speed = distance / time

     = 6.4 km / 17.4 minutes

Let's calculate the speed:

speed = 6.4 km / 17.4 minutes

     ≈ 0.36782 km/min

Since the cyclist is moving east, the velocity is positive. Therefore, the speed is 0.36782 km/min.

Next, the cyclist turns and heads west for 4.2 km in 5.1 minutes. The speed in this case is:

speed = distance / time

     = 4.2 km / 5.1 minutes

     ≈ 0.82353 km/min

Since the cyclist is moving west, the velocity is negative. Therefore, the speed is -0.82353 km/min.

Finally, the cyclist rides east for 16.6 km, which takes 37.9 minutes. The speed can be calculated as:

speed = distance / time

     = 16.6 km / 37.9 minutes

     ≈ 0.43799 km/min

Since the cyclist is moving east, the velocity is positive. Therefore, the speed is 0.43799 km/min.

Now that we have the speeds for each segment, we can determine the total displacement. Since east is the positive direction, we consider the distance traveled east as positive and the distance traveled west as negative.

Total displacement = distance east - distance west

The distance east is 6.4 km + 16.6 km = 23 km

The distance west is 4.2 km

Total displacement = 23 km - 4.2 km

                = 18.8 km

Therefore, the cyclist's total displacement is 18.8 km to the east.

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The moment of inertia about the z-axis of a solid ball bounded by the sphere r = a with variable density proportional to the radius is:

I = (3/5) k a^5.

To find the moment of inertia about the z-axis of a solid ball bounded by the sphere r = a with variable density, we can use the formula:

I = ∫∫∫ r^2 ρ(r) sin^2θ dV

Where r is the distance from the z-axis, ρ(r) is the density at that distance, θ is the angle between the radius vector and the z-axis, and dV is the differential volume element.

Since the ball is symmetric about the z-axis, we can simplify this integral by only considering the volume element in the x-y plane. We can express this volume element as:

dV = r sinθ dr dθ dz

where r ranges from 0 to a, θ ranges from 0 to π, and z ranges from -√(a^2 - r^2) to √(a^2 - r^2).

Thus, the moment of inertia about the z-axis becomes:

I = ∫∫∫ r^2 ρ(r) sin^3θ dr dθ dz

We can further simplify this by assuming that the density is proportional to the radius. That is, ρ(r) = k r, where k is a constant. Therefore, the moment of inertia becomes:

I = k ∫∫∫ r^4 sin^3θ dr dθ dz

Integrating with respect to r first, we get:

I = k ∫∫ (1/5) a^5 sin^3θ dθ dz

Integrating with respect to θ next, we get:

I = (2/15) k a^5 ∫ sin^3θ dθ

Using the half-angle formula for sin^3θ, we get:

I = (2/15) k a^5 [(3/4)θ - (1/4)sinθcosθ] from 0 to π

Simplifying this expression, we get:

I = (2/15) k a^5 [(3/4)π]

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On solving the provided question, we can say that Area of square = SxS=846 and perimeter of square = 4xS= 846/4=S= 211.5=Side.

A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.

Area of square = SxS=846

Perimeter of square = 4xS= 846/4=S= 211.5=Side.

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The correct question is -

A parking lot is shaped like a trapezoid as shown. If the area of the parking lot is 846 square meters, what is the perimeter? (Hint: The formula for the area of a trapezoid is (A=h2(b1+b2)

The limit as x approaches 1 of (4x - 5)^3 is 27.

To evaluate this limit, we substitute the value 1 into the expression (4x - 5)^3.

This gives us (4(1) - 5)^3, which simplifies to (-1)^3. The cube of -1 is -1. Therefore, the limit of (4x - 5)^3 as x approaches 1 is 27.

In summary, the limit as x approaches 1 of (4x - 5)^3 is 27.

This means that as x gets arbitrarily close to 1, the value of the expression (4x - 5)^3 approaches 27.

This result holds true because when we substitute x = 1 into the expression, we obtain (-1)^3, which equals 1 cubed, or simply 1.

Thus, the value of the limit is 27.

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Sean approximately 5.07 hours to bike a total distance of 71 miles.

Sean is biking at a steady rate of 14 miles per hour, and his goal is to cover a total distance of 71 miles. To determine the time it will take him to complete the entire distance, we can use the formula: time = distance / rate.

Using this formula, we can calculate Sean's biking time. Dividing the total distance of 71 miles by the rate of 14 miles per hour gives us:

Time = 71 miles / 14 miles per hour

Simplifying the equation, we find:

Time = 5.07 hours

Therefore, it will take Sean approximately 5.07 hours to bike a total distance of 71 miles.

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A stadium brought in an average revenue of $11,000 per night for a professional sports tournament. Total receipts for the period of time the tournament took place was $132,000. This means the tournament took place throughout is 12 days

How to find the number of members ?

When the teachers joined the members of the chess club for a tournament, the number of members that Alan counted was 31 people which means that the number of members in the chess club would be this number, less the number of teachers.

A stadium brought in an average revenue of $11,000 per night for a professional sports tournament.

Total receipts for the period of time the tournament took place was $132,000.

This means the tournament took place throughout how many days?

since total divide by per night is equal to number of days

now 132000/11000= 12

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Answer:

Step-by-step explanation:

Remark

2 angles are complementary means that 2 angles add up to 90°. That is the guiding princeple behind the problem.

Givens

Let the smallest angle = x

Let the largest angle = 4x + 30

Equation

4x + 30° + x = 90°                   Combine like terms on the left

Solution

5x + 30 = 90                            Subtract 30 from both sides.

5x + 30 - 30 = 90 - 30             Combine

5x = 60                                     Divide both sides by 5

5x/5 = 60/5

x = 12

Answer

Solving for C(t), we get:C(t) = 0.05 kg/LAt steady state, the concentration of salt in the tank is 0.05 kg/L or 50 g/L. Note that the units are converted from kg/L to g/L for convenience.

In order to solve the problem, we can start by finding out how much salt is entering the tank every minute. This can be done by multiplying the concentration of the solution by the rate at which it is entering the tank:

0.05 kg/L x 8 L/min = 0.4 kg/min

So, for every minute that the solution is entering the tank, 0.4 kg of salt is being added to the original 100 kg. The total amount of salt in the tank at any given time can be represented by the equation:

S(t) = 100 + 0.4t, where S(t) is the amount of salt in kg at time t in minutes.We can also find the total amount of liquid in the tank at any given time using the rate at which the solution is entering and leaving the tank:

V(t) = 1000 + 8t.

Next, we can find the concentration of salt in the tank at any given time by dividing the amount of salt by the amount of liquid:C(t) = S(t)/V(t) = (100 + 0.4t)/(1000 + 8t)Finally, we can find the concentration of salt in the tank when it reaches a steady state, which occurs when the amount of salt entering the tank equals the amount leaving the tank. At steady state, the rate of salt entering the tank is 0.4 kg/min and the rate of salt leaving the tank is:C(t) x 8 L/min.

Therefore, we can set up the equation:0.4 = C(t) x 8Solving for C(t), we get:

C(t) = 0.05 kg/LAt steady state, the concentration of salt in the tank is 0.05 kg/L or 50 g/L.

Note that the units are converted from kg/L to g/L for convenience.

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The lengths of the diagonals are approximately 10.6 cm and 31.8 cm.

To solve this problem, we can use the formula for the area of a rhombus, which is A = (d₁ x d₂)/2, where A is the area, and d₁ and d₂ are the lengths of the diagonals.

We are given that the area of the rhombus is 168 square centimeters, so we can substitute this value into the formula:

=> 168 = (d₁ x d₂)/2.

We are also given that one diagonal is three times as long as the other, so we can express the length of one diagonal in terms of the other: d₁ = 3d₂.

Substituting this expression for d₁ into the formula for the area, we get:

168 = (3d₂xd₂)/2 336 = 3d₂²2 d₂² = 112 d₂ = √(112) = 10.6 (to the nearest tenth of a centimeter)

Using the expression for d₁ in terms of d₂, we can find the length of the other diagonal:

d₁ = 3d₂ = 3(10.6) = 31.8 (to the nearest tenth of a centimeter)

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H.S value of the following operations is (-30000-45000J) + j(85000-15000)

The given operations are as follows:

(A) We are given (A) 20∠−50∘1000∠60∘ = 50∠110∘

On solving, we getL.H.S = 20 ∠ −50∘1000 ∠ 60∘

= 50∠110∘,

Hence proved.

(B) We are given (B) 5×10−6 ∠ 100∘0.008 ∠ 50∘ = 1600/−50∘

On solving, we getR.

H.S = 1600/−50∘,

Hence proved.

(C) We are given (C) 2+J26+J6 = 3

On solving, we get L. H.S = 2+J26+J6 = 3,

Hence proved. (D) We are given (D) 4+J1010∠30∘ = 116On solving, we get

L.H.S=4+J1010∠30∘ =  116,

Hence proved.

(E) We are given (E) 5000∠−50∘20,000+J10,500

On solving, we get L.H.S = 5000∠−50∘20,000+J10,500

= (-5 + j10) × 103,

Hence proved.

(F) We are given (F) (5+J5)(4∠−10∘)(50∠20∘)(20∠−30∘)

On solving, we getL. H.S = (5+J5)(4∠−10∘)(50∠20∘)(20∠−30∘)

= (-30000-45000J) + j(85000-15000)

Hence proved.

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Answer:

28

The first 5 are

2+3+5+7+11

A scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.

Therefore, a scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.

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The given board measures include 30 pieces of 4x4x12' lumber, 144 pieces of 2x8x16' lumber, and 19 pieces of 2x6x6' lumber.

In the first measure, there are 30 pieces of lumber, each measuring 4 inches by 4 inches by 12 feet. This implies that each piece has a width and depth of 4 inches and a length of 12 feet.

In the second measure, there are 144 pieces of lumber, each measuring 2 inches by 8 inches by 16 feet. Each piece has a width of 2 inches, a depth of 8 inches, and a length of 16 feet.

Finally, the third measure consists of 19 pieces of lumber, each measuring 2 inches by 6 inches by 6 feet. This means that each piece has a width of 2 inches, a depth of 6 inches, and a length of 6 feet.

These board measures provide information about the quantities and dimensions of the lumber pieces, enabling accurate planning and estimation for construction or woodworking projects.

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Answer:

\( {(4x - 1)}^{2} = 11 \\ 4x - 1 = \sqrt{11} \: \: \: \: 4x - 1 = - \sqrt{11} \\4 x = \sqrt{11} + 1 \: \: \: \: 4x = - \sqrt{11} + 1 \\ x = \frac{ \sqrt{11} }{4} + \frac{1}{4} \: \: \: \: \: \: x = - \frac{ \sqrt{11} }{4} + \frac{1}{4} \)

Answer:

Step-by-step explanation:

I got 12 so not sure.

3x-3=x+3

2x=6

X=3

So 3x3 =9. +3. =12

The equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.

The equation of the hyperbola is the equation which is used to represent the hyperbola in the algebraic equation form, with the value of center point in the coordinate plane and foci.

The standard form of the equation of the hyperbola can be given as,

\(\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=r^2\)

Here (h,k) is the center of the hyperbola, (b) is the transverse axis, and (a) is the conjugate axis.

The foci of the hyperbola is,

\((h,k\pm c)\)

The directrix is,

\(y=k\pm \dfrac{a^2}{c}\)

A hyperbola is given with directrices at x = ±2 and foci at (6, 0) and (−6, 0). Thus, the directrix is,

\(y=k\pm \dfrac{a^2}{c}\\\pm 2=k\pm \dfrac{a^2}{c}\\\dfrac{a^2}{6}=2\\a^2=12\\\)

It is known that,

\(a^2+b^2=c^2\\\)

Put the value of a and c,

\((12)+b^2=6^2\\b^2=36-12\\b^2=24\)

The value of center is (0,0). Thus, the equation of hyperbola is,

\(\dfrac{(y-0)^2}{24^2}-\dfrac{(x-0)^2}{12^2}=1\\\dfrac{y^2}{24^2}-\dfrac{x^2}{12^2}=1\)

Thus, the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.

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The inverse function of the given is \(y^-1\)= \(\frac{x}{2}\)-4 .

What is inverse function?

The domain of the original function becomes the range of the inverse function, and the range of the given function becomes the domain of the inverse function. The inverse function is denoted by the notation f-1 in relation to the original function f. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function. Only when f is both a one-one and an onto function does it have an inverse, indicated by the symbol f-1. Keep in mind that f-1 is NOT f's inverse. The domain value of x is given by combining the function f and the reciprocal function f-1.

Here the given function is,

=> y = 2x+8

Now interchange x and y then

=> x=2y+8

Now simplify the expression with respect to y then,

=> x-8=2y

=> y = \(\frac{x}{2}\)-4

=>\(y^-1\)= \(\frac{x}{2}\)-4

Hence inverse function is \(y^-1\)= \(\frac{x}{2}\)-4 .

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Answer:

6

Step-by-step explanation:

slope is rise/run

to get from -1 to 5 is 6 points

y axis to 1 is 1 point

6/1=6

Step-by-step explanation:

Using the formula for the area of a circle, we have:

Area = πr²

where r is the radius of the circle.

Given that the radius is 10 inches, we can substitute this value into the formula to get:

Area = π(10)²

Area = 100π

Therefore, the area of the circle is 100π square inches. We can leave the answer in terms of π and do not need to round it.

Answer: It looks like you are trying to find the value of the function h(x) = √ (x-3) - 2.

To find the value of this function for a given value of x, you need to substitute the value of x into the function definition and simplify the expression.

For example, if you want to find the value of h(x) for x = 5, you would substitute 5 for x in the function definition and simplify the expression to get:

h(5) = √(5-3) - 2

= √2 - 2

= 1.4 - 2

= -0.6

Therefore, the value of h(x) for x = 5 is -0.6.

You can follow this same process to find the value of h(x) for any other value of x. Just be sure to substitute the correct value of x into the function definition and simplify the expression to find the final result.

Step-by-step explanation:

Answer:

g[f(x)]

Step-by-step explanation:

Given functions:

\(f(x)=x-3\)

\(g(x)=\sqrt{x}-2\)

Composite functions are when the output of one function is used as the input of another.

Therefore, to create √(x-3)-2, substitute the function f(x) in place of the x in function g(x):

\(\begin{aligned}\implies g[f(x)]&=\sqrt{f(x)}-2\\&=\sqrt{x-3}-2\end{aligned}\)