inverse function of k(x)=1/4x-7

C = -3, and the final expression for f(x) is:

f(x) = 2sinx + 9cosx - 3

To discover f(x) whilst f'(x) = 2cosx - 9sinx and f(0)=6, we need to integrate f'(x) with recognize to x to obtain f(x), whilst also considering the regular of integration.

∫f'(x) dx = ∫(2cosx - 9sinx) dx

the use of the integration rules for cosine and sine, we get:

f(x) = 2sinx + 9cosx + C

Wherein C is the constant of integration.

To discover the value of C, we use the given initial circumstance f(0) = 6:

f(0) = 2sin(0) + 9cos(0) + C = 9 + C = 6

Therefore, C = -3, and the final expression for f(x) is:

f(x) = 2sinx + 9cosx - 3

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The given information describes a parallelogram GRPC with point B between C and P, forming triangle GCB. The lengths of the sides of triangle GCB are as follows: GC = 375 ft, CB = 325 ft, and GB = 425 ft.

Point E is outside the parallelogram, and segments BE and PE form triangle BPE. The length of BP is given as 225 ft. To find the length of EP, we can use the triangle proportionality theorem. According to this theorem, if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

In this case, since BP is parallel to GR, we can set up the following proportion:
BP / BE = GR / GE

Substituting the given lengths, we have:
225 / BE = 375 / GE

Solving for GE, we find:
GE = (375 * BE) / 225

Now, to find the length of EP, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In triangle BPE, the sum of BP and BE is greater than EP. Therefore:
BP + BE > EP
225 + BE > EP

Finally, to find the length of EP, subtract BE from both sides of the inequality:
225 > EP - BE
225 + BE > EP

In conclusion, the length of EP is greater than 225 ft, but we cannot determine the exact length without knowing the value of BE. This is the main answer.

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I got radius= 54

arc/2pi r = degrees/360

then fill in what you know: 24pi/2pi r = 80/360

Now cross multiply and you get: 8640pi = 160pi r

Now divide both sides by 160pi and you get: 54= r

Answer: ion know i'm guessing 4

Step-by-step explanation: because it shows 8 at the top, so since it's full and it's 4,000 then that'll basically make 8 the 4000, so since 4 is half of 8 then we prolly have our answer right there

Answer: It would be 20

Step-by-step explanation: The formula for height would be h= v/pi r squared, just plug in the numbers

\(\pink{\sf Third \: side \: of \: the \: triangle = 45}\)

As, the given triangle is a right angled triangle,

Hence, We can use the Pythagoras' Theorem,

\(\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}\)

Here,

In given triangle,

Now, by Pythagoras' theorem,

\(\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}\)

\( \sf : \implies (51)^{2} = (24)^{2} + P^{2}\)

\( \sf : \implies 51 \times 51 = 24 \times 24 + P^{2} \)

\( \sf : \implies 2601 = 576 + P^{2}\)

\( \sf : \implies P^{2} = 2601 - 576\)

\( \sf : \implies P^{2} = 2025\)

By squaring both sides :

\( \sf \sqrt{P^{2}} = \sqrt{2025}\)

\( \sf : \implies P^{2} = \sqrt{2025}\)

\( \sf : \implies P^{2} = \sqrt{(45)^{2}}\)

\( \sf : \implies P^{2} = 45 \)

\(\pink{\sf \therefore \: Third \: side \: of \: the \: triangle \: is \: 45}\)

━━━━━━━━━━━━━━━━━━━━━

the first statement is false, and the 2nd statement is true.

the sign > indicates it is greater than the next value and the sign < indicates it is less than the next value.

In mathematics the above signs are used to compare two mathematical expressions.

7<5 cannot be possible as positive 7 is always greater than positive 5

in the next positive 3 is greater than positive 1 so it is true.

hence, 7<5 is false and 3>1 is true.

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Answer:

2 divided by 2 is one

Step-by-step explanation:

you divide 2 by 2 and you get one

just divide it and it's good

Answer:

A helpful picture is included ^^

Step-by-step explanation:

part b: 12

part c: 16

Answer:

The point on the y-axis is (0,-3) and the point on the x-axis is (6,0)

Step-by-step explanation:

Start by plotting -3 on the y-axis

Then move up 1 and over 2 from there

Step-by-step explanation:

set x as right graph

tan x degree =22/34

x degree =arc tan 22/34

32.91 degree

√22^2+34^2

√1640

40.50miles

so it's current position is 32.91 degree north by west 40.50 miles

Therefore, the average value of f(x) = -x^2 - x^2 - 2 over the interval [0, 2] is -16/3.

To find the average value of a function f(x) over an interval [a, b], we need to evaluate the definite integral of the function over that interval and divide it by the width of the interval (b - a).

In this case, we have f(x) = -x^2 - x^2 - 2, and we want to find the average value over the interval [0, 2].

First, let's calculate the definite integral of f(x) over the interval [0, 2]:

∫[-x^2 - x^2 - 2]dx from 0 to 2

To integrate f(x), we can break it down into three separate integrals:

∫-x^2 dx from 0 to 2 + ∫-x^2 dx from 0 to 2 + ∫-2 dx from 0 to 2

Evaluating each integral:

[-(x^3 / 3)] from 0 to 2 + [-(x^3 / 3)] from 0 to 2 + [-2x] from 0 to 2

Substituting the limits:

[-(2^3 / 3) - (0^3 / 3)] + [-(2^3 / 3) - (0^3 / 3)] + [-2(2) - (-2(0))]

Simplifying the expression:

[-8/3] + [-8/3] + [-4]

Combining the terms:

-8/3 - 8/3 - 4 = -8 - 8/3 = -32/3

Next, we divide the integral result by the width of the interval (2 - 0 = 2):

(-32/3) / 2 = -16/3

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Answer:

That should equal 725.3125.

Answer:

Step-by-step explanation:

(7x^2-5x+3)

+(2x^2+4x-6)=9x^2-x-3

Answer: To divide 9x³ - 18x² - x + 2 by 3x + 1 using long division, we can follow the following steps:

Step 1: Divide the first term of the dividend 9x³ by the first term of the divisor 3x. The result is 3x².

Step 2: Multiply the divisor 3x + 1 by 3x². The result is 9x³ + 3x².

Step 3: Subtract 9x³ + 3x² from 9x³ - 18x² - x + 2. The result is -18x² - 4x + 2.

Step 4: Repeat the division and multiplication process by dividing the first term of the new dividend, -18x², by the first term of the divisor, 3x. The result is -6x.

Step 5: Multiply the divisor 3x + 1 by -6x. The result is -18x + 6.

Step 6: Subtract -18x + 6 from -18x² - 4x + 2. The result is -4x² + 10.

Step 7: Repeat the division and multiplication process by dividing the first term of the new dividend, -4x², by the first term of the divisor, 3x. The result is -4/3 x.

Step 8: Multiply the divisor 3x + 1 by -4/3 x. The result is -4/3 x + 4/3.

Step 9: Subtract -4/3 x + 4/3 from -4x² + 10. The result is 10 - 4/3.

Thus, the final answer is:

(9x³ - 18x² - x + 2) / (3x + 1) = 3x² - 6x - 4/3 x + 4/3 + 10

Step-by-step explanation:

The whole number(s) are 3 and -2.  A whole number doesn't have fractions or places after the decimal.  

The natural number(s) is 3.  Think of a natural number as those used for counting, like "1, 2, 3, 4..."

The integer(s) are 3 and -2.  An integer includes positive or negative whole numbers, and 0.

The rational number(s) are 3, -2, and 1/4.  A rational number can be written as a fraction.

And irrational number, the square root of 5, cannot be written as a fraction.  It is the opposite of a rational number.  

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Using diagram whole numbers, natural numbers, integers, and rational or irrational numbers, which category does -2, 3, 1/4, and square root of 5

which is a whole number, natural number, integer, or rational or irrational number: -2, 3,  1/4, and square root of 5

Answer:

1.1666... recurring

Step-by-step explanation:

Answer:

1/2 + 2/3 = 7/6

Step-by-step explanation:

Answer:

y = 4/5x + 32/5

Step-by-step explanation:

(-3,4) and (2, 8)

Slope:

m=(y2-y1)/(x2-x1)

m=(8-4)/(2+3)

m= 4/5

Slope-intercept:

y - y1 = m(x - x1)

y - 4 = 4/5(x + 3)

y - 4 = 4/5x + 12/5

y = 4/5x + 32/5

A graph shows the relationship between two or more variables

To graph an equation with slope of -2/5 plot (2, -4) on the plane and then move;

2 steps down and 5 steps right to plot the next point at (7, -6)

Reason:

To graph an equation with a slope -2/5 that passes through the point (2, -4), the steps are;

Plot the point (2, -4) on the graph

Move two steps down vertically to the point (2, -4 - 2) = (2, -6)

Then move five steps to the right to point (2 + 5, -6) = (7, -6)

The point (7, -6) is another point on the graph

Join the two points (2, -6), and (7, -6), with a straight line and extend it to complete the graph

Therefore;

To graph an equation with slope of -2/5 plot (2, -4) on the plane and then move 2 steps down and 5 steps right to plot the next point at (7, -6)

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The length of t, to the nearest tenth of an inch, is approximately 85.6 inches.

To determine the length of t in triangle TUV, we can use the law of sines.

The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

In this case, we have:

- u = 380 inches (the length of side u)

- m∠V = 151° (the measure of angle V)

- m∠T = 25° (the measure of angle T)

We need to find the length of side t.

Using the law of sines, we can set up the equation;

sin(25°) / t = sin(151°) / 380

To solve for t, we can cross multiply and then divide by sin(25°):

t = (380 x sin(25°)) / sin(151°)

t ≈ 85.6 inches

Therefore, the length of t, to the nearest tenth of an inch, is approximately 85.6 inches.

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Answer:

y(25) = 150

Step-by-step explanation:

Substitute t = 25 into y(t) , that is

y(25) = - 14(25) + 500 = - 350 + 500 = 150

A function assigns the value of each element of one set to the other specific element of another set. The value of the function y(25) is 150.

A function assigns the value of each element of one set to the other specific element of another set.

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

Given that the function y(t) is represented as y(t) = -14t + 500. Now, the value of y(25) will be,

y(t) = -14t + 500

y(25) = -14(25) + 500

y(25) = -350 + 500

        = 150

Hence, the value of the function y(25) is 150.

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Answer:

Ray DC and Ray DE

Step-by-step explanation:

check the attached file

Answer:

You can buy 10 mangoes for $4.

Step-by-step explanation:

40/16 = x/4

16x = 160

x = 10

Answer:

  C. The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.

Step-by-step explanation:

You want to know the transformations needed to form g(x) = 1/2(x+4)^2 -3 from f(x) = x^2.

The transformations ...

  f(x) ⇒ g(x) = c·f(x -h) +k

represent vertical expansion by a factor of 'c', right shift by 'h' units, and an upward shift of 'k' units.

Here, we have c=1/2, h=-4, k=-3. These mean the function f(x) has been vertically compressed to 1/2 its original height, and shifted left 4 and down 3.

The vertical compression will cause the graph to appear to be wider for any given distance above the vertex.

I am not sure if your question is saying f(x) is x² or if it is 2x so I am giving you two answers.

If f(x) is x² the answer for f(g(x))= (x-6)²

If f(x) is 2x the answer for f(g(x))=2x-12

How did I get these answers? For fog, it basically means f(g(x)) so you just plug in what g(x) equals for the variable x in f(x)

W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.

To show that W=Rn, we need to show that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W.

Let v be any vector in Rn. Since the n non-zero orthogonal vectors span W, we can write v as a linear combination of them:

v = c1v1 + c2v2 + ... + cnvn

where c1, c2, ..., cn are scalars, and v1, v2, ..., vn are the n non-zero orthogonal vectors that span W.

To show that v is in W, we need to show that v is orthogonal to all vectors in W except itself. Since the n non-zero orthogonal vectors are linearly independent, any linear combination of them that is orthogonal to v must be the zero vector.

Therefore, if w is any vector in W that is not equal to v, we have:

=  = c1 + c2 + ... + cn = 0

since v is orthogonal to all the non-zero orthogonal vectors. This means that v is orthogonal to all vectors in W except itself.

Therefore, since v is in W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.

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The ordered pair that is the best exact solution is (0.9, 1)

Substitution of variable is the act of replacing variable with exact values. for example for an equation of y = x² +2

The value of y for the values of x = 1,2,3,4 will be

y = 1² +2 = 3

y = 2² + 2 = 6

y = 3² + 2 = 11

y = 4² +2 = 18

Similarly l, for the equation y = -4x+3

when x is 0.9

y = -4(0.9) +3

y = -3.6 +3 = -0.6

when x = 1.0

y = -4(1) +3

= -4+3 = -1

For the equation y = 3x-1

when x is 0.9

y = 3(0.9) -1

y = 2.7 -1

y = 1.7

when x is 1

y = 3(1) -1

= 3-1 = 2

Therefore the best value of x that gives the appropriate answer is ( 0.9,1)

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When the weight moves from x = -8 cm to x = 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

Given: Displacement x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. To find: What is the spring?Explanation:We know that displacement is given by x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0.Comparing this with the standard equation, x

= Acos(ωt+ φ)A

= amplitude

= 8 cmω

= angular frequencyφ

= phase angleWhen the spring is at equilibrium position, the weight attached to the spring does not move. Hence, no force is acting on the weight at the equilibrium position. Therefore, the spring is neither stretched nor compressed at the equilibrium position.Now, the spring is set in motion resulting in a displacement of x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. The maximum displacement of the spring is 8 cm in the positive x direction. When the weight is at x

= 8 cm, the restoring force of the spring is maximum in the negative x direction and it pulls the weight towards the equilibrium position. At the equilibrium position, the weight momentarily stops. When the weight moves from x

= 8 cm to x

= -8 cm, the spring moves from its natural length to its maximum stretched position. At x

= -8 cm, the weight momentarily stops. When the weight moves from x

= -8 cm to x

= 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

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The displacement of the weight attached to the spring is given by the equation x = 8 cos t. The amplitude of the motion is 8 centimeters and the period is 2π seconds.

The equation x = 8 cos t represents the displacement of a weight attached to a spring in simple harmonic motion. In this equation, x is measured in centimeters and t is measured in seconds.

The amplitude of the motion is 8 centimeters, which means that the weight oscillates between x = 8 and x = -8.

The period of the motion can be determined from the equation T = 2π/ω, where ω is the angular frequency. In this case, ω = 1, so the period T is 2π seconds.

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The cylindrical shell is subjected to an internal pressure of 70MPa. The shell's inner radius is 10 cm, and the outer radius is 16 cm. The maximum and minimum hoop stresses in the cylindrical shell are determined below.

For an element of thickness dr at a distance r from the center, the hoop stress is given by equation i:

σθ = pdθ...[i]Where, p is the internal pressure.

The thickness of the shell is drThe circumference of the shell is 2πr.

Therefore, the force acting on the element is given by:F = σθ(2πrdr)....[ii]

Let σmax be the maximum stress in the shell. The stress at radius r = a, which is at the maximum stress, is given by:σmax = pa/b....[iii]

Here a = radius of the shell, and b = thickness of the shell.

According to equation [i], the hoop stress at radius r = a is given by:σmax = pa/b....[iii].

Substitute the given values:σmax = 70 × 10^6 × (16 - 10)/(2 × 10) = 56 × 10^6 Pa.

The minimum hoop stress in the shell occurs at the inner surface of the shell. Let σmin be the minimum stress in the shell.σmin = pi/b....[iv].

According to equation [i], the hoop stress at radius r = b is given by:σmin = pi/b....[iv]Substitute the given values:

σmin = 70 × 10^6 × 10/(2 × 10) = 35 × 10^6 Pa.

Therefore, the maximum hoop stress in the shell is 56 × 10^6 Pa and the minimum hoop stress is 35 × 10^6 Pa.

A thick cylindrical shell with an inner radius of 10 cm and an outer radius of 16 cm is subjected to an internal pressure of 70MPa. Maximum and minimum hoop stresses in the cylindrical shell can be determined using equations and the given data. σθ = pdθ is the formula for hoop stress in the cylindrical shell.

This formula calculates the hoop stress for an element of thickness dr at a distance r from the center.

For the cylindrical shell in question, the force acting on the element is F = σθ(2πrdr).

Let σmax be the maximum stress in the shell. According to equation [iii], the stress at the radius r = a, which is the maximum stress, is σmax = pa/b.σmax is calculated by substituting the given values.

The maximum hoop stress in the shell is 56 × 10^6 Pa according to this equation.

Similarly, σmin = pi/b is the formula for minimum hoop stress in the shell, which occurs at the inner surface of the shell.

The minimum hoop stress is obtained by substituting the given values into equation [iv].

The minimum hoop stress in the shell is 35 × 10^6 Pa.As a result, the maximum and minimum hoop stresses in the cylindrical shell are 56 × 10^6 Pa and 35 × 10^6 Pa, respectively.

Thus, the maximum hoop stress in the shell is 56 × 10^6 Pa and the minimum hoop stress is 35 × 10^6 Pa. These results are obtained using equations and given data.

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Answer:

1/2

Step-by-step explanation:

you're trying to put the variable(y) by itself. it would be divided by 14 on both sides, which 7/14 is 1/2