When graphed, the two linear equations intersect at the point 4x−2y=−2
12x−3y=9

Answer:

Step-by-step explanation:

[tex]-x+y\leq -1\\x-y\geq 1\\x+2y\geq 4[/tex]

dark blue is the required region.

(a) C(p) is not defined since we can't divide by 0.

(b) The domain of C(p) as given by the equation is (-∞, 100) ∪ (100, ∞)

(c) The domain of C(p) in the context of the application is [0, 100)

(d) The percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100

Here we have given that Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by

C(p) = 8100p / (100 − p)

And we need to find the following.

(a) In general ma the we know that dividing by zero is not possible one.

Therefore, C(p) is undefined when we try to divide it by 0.

(b) The domain of C(p) is the function is not defined at p =100 the domain would be written as,

=> D = (-∞, 100) ∪ (100, ∞)

(c) The domain of C(p) in the context of the application  is calculated as,

=> D = [0, 100)

Therefore, the percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100.

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The value of the equation h(x) = -5x-4 is - 19 when h = (3).

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

The three primary forms of linear equations are point-slope, standard, and slope-intercept.

So, the equation we have is:

h(x) = -5x-4

Now, solve the equation when h = (3)

h(x) = -5x-4

h(3) = -5(3) -4

h(3) = -15 - 4

h(3) = - 19

Therefore, the value of the equation h(x) = -5x-4 is - 19 when h = (3).

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Answer:

x=3

Step-by-step explanation:

step one: first, you want to make it so that the variable x is only on one side. to do this, you use inverse operations. this means adding 7x to both sides.

-2x+7x=5x    -7x+7x cancels itself out

the equation is now 5x+13=28

step two: next, you want to isolate the variable x. to do this you are going to use inverse operations yet again, this time subtracting 13 from both sides.

13-13=0       28-13=15

the equation is now 5x=15

step three: lastly, you want get x by itself without the 5 in front of it. using inverse operations for the last time, you are going to divide both sides by 5 because 5x means "5 times x" and division is the opposite of multiplication.

5x/5=x     15/5=3

the answer is now x=3

x= 3.

[tex]-2x + 13 = -7x + 28[/tex]

[tex]-2x + 13 +7x= -7x + 28+7x\\ \\13+5x=28[/tex]

[tex]-13+13+5x=28-13\\ \\5x=15[/tex]

[tex]\frac{5x}{5}=\frac{15}{5} \\ \\x=\frac{15}{5}\\ \\x=3[/tex]

If the result is correct, when we substitute the value of x in the original equation, it should return the same value on both sides of the equal (=) symbol. Let's test it!

[tex]-2(3 ) + 13 = -7(3) + 28\\ \\-6+13=-21+28\\ \\7=7[/tex]

That's correct! Therefore, the correct answer is x=3.

a. [tex]\frac{dy}{dx} \ at \ x=0 \ is \ c.[/tex]

b.  [tex]\frac{dy}{dx} \at x=-L \ is \ 3aL^2+2bL+c.[/tex]

a. The derivative of a cubic function

[tex]y=ax^3+bx^2+cx+d[/tex]  is  [tex]y'=3ax^2+2bx+c[/tex].

Plugging in x=0, we get y'=c. Thus, [tex]\frac{dy}{dx}[/tex] at x=0 is c.

b. Plugging in x=-L, we get [tex]y'=3a(-L)^2+2b(-L)+c[/tex].

Thus, [tex]\frac{dy}{dx}[/tex] at [tex]x=-L \ is\ 3a(-L)^2+2b(-L)+c.[/tex]

A derivative is a financial instrument that derives its value from an underlying asset. It is a contract between two or more parties that specifies conditions (such as the date, price, and quantity of the underlying asset) under which payments, or payoffs, are to be made between the parties. Derivatives can be used for a variety of purposes, such as hedging risk or speculating on the future price of an asset.

A function is a mathematical relation between two sets of numbers that assigns each element in one set to exactly one element in the other set. For example, the function f(x) = 2x+3 assigns each real number x to the real number 2x+3

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percentage rate increase by 206%

What is exponential growth?

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases with time.

Consider a population of mice that increases exponentially every year by a factor of two, starting with 2 in the first year and increasing to 4 in the second, 8 in the third, 16 in the fourth, and so on. The population is rising by a factor of 2 per year in this example. If mice gave birth to four pups instead, you would then have 4, 16, 64, and 256.

Linear growth, which is additive, and geometric growth can be contrasted with exponential growth, which is multiplicative (which is raised to a power).

This equation represents exponential growth because the base is greater than 1, the function represents growth and  Whenever the base is less than 1, the function represents decay.

The base 1.06 is greater than 1, hence The equation represents exponential growth.

The formula for exponential growth:

[tex]y=a(1+r)^{x}[/tex]

where,

f(x) = exponential growth function

a = initial amount

r = growth rate

x = number of time intervals

In this case, [tex]r=1.06+1 = 2.06[/tex]

which represents percentage rate increase by 206%

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Answer:196

Step-by-step explanation:

Verified that during the first 3 seconds of fall the instantaneous velocity equals the average velocity, the time is 1.5 seconds

The height of an object t seconds after it is dropped from a height of 300 meters is

s(t) = -4.9t^2 + 300

The average velocity of object during first 3 seconds

= s(3) - s(0) / 3 - 0

s(3) = -4.9 × (3)^2 + 300

= -44.1 + 300

= 255.9 meters

s(0) = -4.9(0)^2 + 300

s(0) = 300

The average velocity = (255.9 - 300) / 3 - 0

= -44.1 / 3

= -14.7 meter per second

To find  instantaneous velocity differentiate the function

= -9.8t

The instantaneous velocity = The average velocity

-9.8t = -14.7

t = -14.7/-9.8

t = 1.5 seconds

Therefore, time is 1.5 seconds

I have answered the question in general, as the given question is incomplete

The complete question is :

The height of an object t seconds after it is dropped from a height of 300 meters is s(t) = -4.9t^2 + 300.

(b) Use the Mean Value Theorem to verify that at some time during the first 3 seconds of fall, the instantaneous velocity equals the average velocity. Find that time.

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Answer: [tex](x-3)^2+(y+4)^2=64[/tex]

Step-by-step explanation:

The equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]. h and k are the points of the center corresponding with x and y respectively. r is radius. All we have to do is plug the values in.

[tex](x-3)^2+(y-(-4))^2=8^2[/tex]

With our values plugged in, we can now simplify.

[tex](x-3)^2+(y+4)^2=64[/tex]

Therefore, our final equation is [tex](x-3)^2+(y+4)^2=64[/tex].

Answer:

non-violence and kindness with animals

Step-by-step explanation:

The volume of each brick is 0.75m³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object. It is measured in cubic units.

A brick has a cuboidal shape. This means the volume of a cuboid is given as:

V = l×b×h

This means volume = area × height

The volume of the whole wall is calculated as:

15× 6× 20 = 18000m³

Since there are 24000 bricks needed for the wall. The volume of each brick is therefore calculated as:

V =18000/24000

= 0.75m³

Therefore the volume of each brick is 0.75m³

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The amount of paint needed is 196.35 [tex]cm^{2}[/tex].

We know that,

                 [tex]V = \frac{2}{3}\pi r^{3}[/tex]

Remember that we have a hemisphere here, So

                 [tex]dV = \frac{2}{3} (3\pi r^{2} )dr[/tex]

Now the amount of paint needed is [tex]dV = 2\pi r^{2} dr[/tex].

Here,

                [tex]dr = 0.05 cm[/tex]

and

                 [tex]r = 25cm[/tex]              [Because [tex]d = 50cm[/tex]]

Hence

              [tex]dV = 2\pi (25)^{2} (0.05)[/tex]

              [tex]dV = \frac{125\pi }{2}[/tex]

              [tex]dV =[/tex] 196.35 [tex]cm^{2}[/tex].

Therefore The amount of paint needed is 196.35 [tex]cm^{2}[/tex].

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The measures of the lengths of the sides and angles of the triangles found using the law of cosines and the law of sines are presented as follows;

Question 1

∠A = 47.35°

∠B = 78.65°

c = 3.3

Question  2

∠B = 78.24°

∠C = 29.76°

a = 67.03

Question 3

∠A = 45.77°

∠B = 86.417°

∠C = 47.813°

Question 4

∠A = 36.15°

∠B = 60.48°

∠C = 93.37°

Question 5

a = 258.98

b = 327.41

∠C = 53°

Question 6

a = 34.11

b = 73.987

∠C = 53°

The law of cosines is a relationship between two sides (b and c) and the included angle, (∠A) and the third side (a) of the triangle.

Mathematically; a² = b² + c² - 2·b·c·cos(A)

Question 1

The dimensions of the triangle ΔABC are;

a = 3.0, b = 4.0, ∠C = 54°

The law of cosines indicates that we get;

c² = b² + a² - 2·b·a·cos(∠C)

Therefore;

c² = 3.0² + 4.0² - 2 × 3.0 × 4.0 × cos(54°) ≈ 10.893

The law of sines indicates that we get;

sin(54°)/3.3 = sin(∠A)/3.0

Question 2

b = 69, c = 35, ∠A = 72°

a² = 69² + 35² - 2 × 69 × 35 × cos(72°) ≈ 4493.45

The law of sines indicates that we get;

sin(72°)/67.03 = sin(∠B)/69

∠B = arcsine(69 × sin(72°)/67.03) ≈ 78·24°

∠C = 180° - 72° - 78.24° ≈ 29.76°

Question 3

a = 28, b = 39, c = 29

a² = b² + c² - 2·b·c·cos(A)

cos(A) = (a² - (b² + c²)) ÷ (2·b·c)

Therefore; cos(A) = (28² - (39² + 29²)) ÷ (-2 × 39 × 29) ≈ 0.6976

sin(45.77)/28 = sin(B)/39

sin(B) = 39 × sin(45.77)/28 ≈ 0.998

Question 4

a = 13, b = 17, c = 22

cos(A) = (13² - (17² + 22²)) ÷ (-2 × 17 × 22) ≈ 0.807

sin(36.15)°/13 = sin(∠B)/17

sin(∠B) = 17 × sin(36.15)°/13

Question 5

The parameters of the triangle are; ∠A = 50°, ∠B = 77°, c = 270

Please find attached the sketch of the triangle in the correct option created with MS Word

a/sin(50°) = 270/sin(53°)

a = sin(50°) × 270/sin(53°) ≈ 258.98

b = sin(77°) × 270/sin(53°) ≈ 329.41

Question 6

The parameters of the triangle are;

∠A = 27°, ∠B = 100°, c = 60

Please find attached the drawing of the correct triangle

∠C = 180° - 27° - 100° = 53°

∠C = 53°

60/sin(53°) = a/sin(27°)

a = sin(27°) × 60/sin(53°) ≈ 34.11

b = sin(100°) × 60/sin(53°) ≈ 73.987

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A)

A manufacturer of banana chips would like to know whether its bag-filling machine works correctly at the 414-gram setting.

So, Null hypothesis: [tex]H_{0}[/tex] : μ < 414

It is believed that the machine is underfilling the bags.

So, Alternate hypothesis: [tex]H_{1}[/tex] : μ < 414

Given,

n= 8

Population standard deviation (б) = 18

x= 407

We will use the t-test since n > 8 and we are given the population standard deviation.

t=x-μ / (б/[tex]\sqrt{n-1}[/tex])

t= [tex]\frac{407-414}{\frac{18}{\sqrt{7} } }[/tex]

t= -1.028

Use the t table to find p value

p-value = 12.706

Level of significance α = 0.025

p-value>α

It is a two-tailed test.

So, we fail to reject the null hypothesis.

So, its bag-filling machine works correctly at the 414-gram setting.

B)

Let μ be the population mean amount of ozone in the upper atmosphere.

As per the given, we have

[tex]H_{0}[/tex]    : μ = 4.8

[tex]H_{1}[/tex] : μ ≠ 4.8

Sample size: n= 26

Sample mean = 4.6

Standard deviation = 1.2

Since population standard deviation is now given, so we use a t-test.

t= [tex]\frac{4.6-4.8}{\frac{1.2}{\sqrt{25} } }[/tex]

t= -0.2/0.24

t= -0.833

It is a two-tailed test.

We are accepting the null hypothesis.

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Answer:

75

Step-by-step explanation:

I hour and 15 minutes in minutes is 75 minutes

1 hour = 60 minutes

you add 15 and you get

60+15=75

The answer would be 75 Minutes.

1 Hour = 60 Minutes

[tex]60 + 15 = 75[/tex] Minutes.

In order for m n to be even, m must be even or n must be an even number.

Let's understood what is integers.

In mathematics, a collection of both positive and negative integers is referred to as an integer. Like whole numbers, integers do not contain a fractional portion. The definition of an integer is that a number that can be either positive, negative, or zero but is not a fraction. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. Examples of integers include 1, 2, 5, 8, -9, and -12. "Z" stands for an integer.

Proof by contraposition:

Suppose that the statement m“ is even or is even n” is not true. Consequently, m and n should both be odd. Let's check to determine if the sum of two odd numbers is even or odd: Let m and n be equal to 2a+1 and 2b+1 respectively, then their product is:

(2a+1) (2b+1) = 4ab+2a+2b+1 =2(2ab+a+b) +1

This shows that the expression 2(2ab+a+b) +1 is of the form 2n+1, thus the product is odd. If the product of odd numbers is odd, then m n is not true to be even. Therefore, in order for m n to be even, m must be even, or n must be an even number.

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Answer: 8 Nights

Step-by-step explanation:

Cost of a plane ticket to Florida(c) = $1000

cost at the hotel per night (n)

Amount left with Karla after spending on the flight ticket =

$3000-$1000= $2000

To find out how many nights she can stay we should divide the remaining amount she has with (n) = $2000/$250 = 8

Hence Karla can stay for 8 nights

Answer:

x = 15°

Step-by-step explanation:

⭐the exterior angle of a triangle is equal to the sum of the angles that is opposite of said exterior angle

Thus, to solve for x, we have to make an equation in regards of the exterior angle.

132° = x° + 117°

∴ 15 = x° . . . .  subtract 117 from LHS and RHS

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(1, 5); (4, 7) - corresponding, (3, 5) - Alternate Interior, (2, 7); (1, 8) - Exterior

(3, 6) are Consecutive Interior Angles.

Any line that crosses two straight lines at different locations is known as a transversal.

Corresponding Angles:

When two parallel lines cross the third one, the angles that are in the same relative position at each junction are referred to as corresponding angles to one another

Alternate Interior Angles:

The alternative interior angles are those that are on the inner side of the parallel lines but on the opposing sides of the transversal.

Alternate Exterior Angles:

Alternate external angles are positioned on the opposing sides of the transversal and are always outside the two lines where the transversal intersects.

Consecutive Interior Angles:

The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles.

Here we have

Two parallel lines intersected and formed the angles, ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.

By the given information,

∠1  and ∠ 5 are corresponding angles

∠4 and ∠ 7 are corresponding angles

∠3 and ∠5 are Alternate Interior Angles

∠2, and ∠7 are Alternate Exterior angles

∠1 and ∠ 8 are Alternative Exterior angles

∠3 and ∠ 6 are Consecutive Interior Angles

Therefore,

(1, 5); (4, 7) - corresponding, (3, 5) - Alternate Interior, (2, 7); (1, 8) - Exterior

(3, 6) are Consecutive Interior Angles.

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Answer:

Step-by-step explanation:

3.14 x 3=9.42

The lines that carry the rectangle onto itself are x = 0 and y = 1

The graph that completes the question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The rectangular graph

The coordinates of one end of the graph are

(-3, 3) and (-3, -1)

Next, we calculate the midpoint of these ends

So, we have

Midpoint = 1/2(x₁ + x₂, y₁ + y₂)

Substitute the known values in the above equation, so, we have the following representation

Midpoint = 1/2(-3 + 3, -1 + 3)

Evaluate the like terms

Midpoint = 1/2(0, 2)

So, we have

Midpoint = (0, 1)

So, we have

x = 0 and y = 1

Hence, the reflection lines are x = 0 and y = 1

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By using matrix, it can be calculated that:

[tex]\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]

The term "matrix" refers to any configuration of numbers in the form of rows and columns. a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers.

In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. Solving linear equations is made easier by it. Matrices are incredibly priceless items that are used in a variety of contexts. In addition to mathematical applications, matrices are employed in a wide range of scientific disciplines. Nearly every element of our life uses engineering mathematics.

Here,

[tex]C = \begin{bmatrix} 12 & 16 & -20 \\ 4 & -24 & 28 \end{bmatrix}[/tex]

[tex]\frac{1}{4}C = \begin{bmatrix} 12\times \frac{1}{4} & 16 \times \frac{1}{4} & -20 \times \frac{1}{4} \\ 4 \times \frac{1}{4} & -24 \times \frac{1}{4}& 28 \times \frac{1}{4}\end{bmatrix}\\\\\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]

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The equation of given graph is y = 2x + 6.

What is equation of line?

The formula for a straight line is y = mx + c where c is the height at which the line intersects the y-axis, also known as the y-intercept, and m is the gradient.

Given:

The graph of the line is given.

From graph we have to find the equation of line.

Let the graph passes through the points (0, 6) and (2, 10).

From these two points to find the slope.

Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here, [tex](x_1, y_1) = (0, 6), (x_2, y_2) = (2, 10)[/tex]

⇒ Slope = m = [tex]\frac{10-6}{2-0}= \frac{4}{2} = 2[/tex]

So, the slope is 2.

Now to find the equation of line.

Consider, the point - slope form of the line,

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex]m = 2, (x_1, y_1) = (0, 6)[/tex]

⇒

[tex]y-6=2(x-0)\\y-6=2x\\y=2x+6[/tex]

Hence, the equation of given graph is y = 2x + 6.

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Answer:

[tex]\dfrac{1}{36n^2+6n}[/tex]

Step-by-step explanation:

Given factorial expression:

[tex]\dfrac{(6n-1)!}{(6n+1)!}[/tex]

[tex]\boxed{\begin{minipage}{6cm}\underline{Factorial Rule}\\\\$n!=\:n\cdot \left(n-1\right) \cdot \left(n-2\right) \cdot ... \cdot 3 \cdot 2\cdot 1$\\ \end{minipage}}[/tex]

Apply the factorial rule to the numerator and denominator of the given rational factorial expression:

[tex](6n-1)!=\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1[/tex]

[tex]\left(6n+1\right)!=\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1[/tex]

Therefore:

[tex]\begin{aligned}\implies \dfrac{(6n-1)!}{(6n+1)!}&=\dfrac{\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1}{\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1}\\\\&=\dfrac{1}{(6n+1) \cdot 6n}\\\\&=\dfrac{1}{6n(6n+1)}\\\\&=\dfrac{1}{36n^2+6n}\end{aligned}[/tex]

Answer:

--------------------------------

We know that:

Therefore:

Therefore:

==========================================================

The given graph have four zeros at x = -3 , 0 , 2 , 7

==========================================================

f(x) = x³ + x² -6x

The function f(x) is polynomial has degree = 3

so, it has only 3 zeros

==========================================================

g(x) = (x²+x-6)(x²-7x)   ⇒  By factoring

⇒  By factoring

∴ g(x) = x(x-7)(x+3)(x-2)

∴ g(x) has zeros  at x = -3 , 0 , 2 , 7

==========================================================

h(x) = x(x-7)(x+3)(x-2)

h(x) has zeros  at x = -3 , 0 , 2 , 7

==========================================================

m(x) = (x³-4x²-21x)(x-2)

⇒  By factoring

∴ m(x) = x(x-7)(x+3)(x-2)

∴ m(x) has zeros  at x = -3 , 0 , 2 , 7

==========================================================

n(x) = x²-9x+14

The function f(x) is polynomial has degree = 3

so, it has only 3 zeros

==========================================================

p(x) = x(x+2)(x-3)(x+7)

∴ p(x) has zeros  at x = 3 , 0 , -2 , -7

==========================================================

By comparing zeros of the given graph to zeros of the functions

The result will be:

        The functions that have the same zeros as the graph are

                               g(x) , h(x) and m(x)          

Answer:

A.[tex] \frac{7}{6} \sqrt{x} [/tex]

Step-by-step explanation:

Solution Given:

[tex] \sqrt{98{x}^{3} } \div \sqrt{72 {x}^{2} } [/tex]

Bye using indices formula

[tex] \sqrt{x} \div \sqrt{y} = \sqrt{ \frac{x}{y} } [/tex]

we get

[tex] \sqrt{ \frac{98{x}^{3} }{72 {x}^{2} } } [/tex]

[tex] \sqrt{ \frac{49 {x}^{3} }{ 36 {x}^{2} } }[/tex]

[tex] \sqrt{ \frac{{7}^{2} {x}^{3 - 2} }{{6}^{2} } } [/tex]

[tex] \frac{7}{6} \sqrt{x} [/tex]

The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.

Given :

Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,

Let g(x) = f(x) − 5.

g(x) = (x−p)(x−q)(x−r)(x−s)h(x)

The condition f(t) > 5 translates to g(t) > 0.

Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :

the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }

The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.

Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have

f(x)=x(x−1)(x−3)(x−4)+5

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Full question ;

Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?

The stopping distance table and the analysis of the stopping distance are presented as follows;

1. The stopping distance calculator, an online tool, provides the stopping distance at a specified speed as presented in the table on the following sections.

2. Increasing the vehicle speed by 10 mph, increases the required stopping distance exponentially, which reduces the safety of driving

The stopping distance is the distance traveled by a vehicle, which is the sum of the distance traveled during the reaction time and the distance traveled during braking (the braking distance)

The table in the question using a perception–reaction time of 2.5 seconds, and the online stopping distance calculator is completed as follows;

Speed (mph)       [tex]{}[/tex] Speed (m/s)        Stopping Distance (m)

60 mph [tex]{}[/tex]                 26.82 m/s           119.55 m

50 mph  [tex]{}[/tex]                22.35 m/s           92.34 m

40 mph  [tex]{}[/tex]                17.88 m/s            68.05 m

30 mph   [tex]{}[/tex]               13.41 m/s             46.665 m

20 mph [tex]{}[/tex]                 8.94 m/s             28.197 m

10 mph [tex]{}[/tex]                  4.47 m/s             12.642 m

2. The details from the above table indicates that as the speed increases, the stopping distance increases exponentially, such that increasing the speed by 10 mph increases the required stopping distance when the vehicle is moving at an already high speed, thereby reducing safety by increasing the speed by 10 mph.

Learn more about stopping distance here:

https://brainly.com/question/5254029

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