Given f(x)=x2−2x+3, and a point a in the domain of f. We wish to compute f′(a) using the definition
f′(a)=limh→0 f(a+h)−f(a)/h. Notice this is an indeterminate of the form 0/0 (a) Simplify f(a+h)−f(a)/h= FORMATTING: The answer must be a polynomial in a and h in its simplest form. (b) Compute f′(a)=limh→0 f(a+h)−f(a)/h

To find the altitude of the spherical segment, we need to use the formula for the total surface area of a spherical segment, which is given by:
A = 2πR(r + h), where R is the radius of the spherical surface, r is the radius of the base, and h is the height of the segment.

We are given that the total surface area of the spherical segment is 7 times greater than the surface area of the sphere inscribed in it, which means that:
7(4πR^2) = 2πR(r + h)
Simplifying this equation gives us:
14R = r + h

We are also given that the radius of the spherical surface is equal to R, which means that r = R. Substituting this into the equation gives us:
14R = R + h
Solving for h, we get:
h = 14R - R
h = 13R
Therefore, the altitude of the spherical segment is 13R.

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Fοr the inequality the sοlutiοn set is x > -2.

In Algebra, an inequality is a mathematical statement that uses the inequality symbοl tο illustrate the relatiοnship between twο expressiοns. An inequality symbοl has nοn-equal expressiοns οn bοth sides. It indicates that the phrase οn the left shοuld be bigger οr smaller than the expressiοn οn the right, οr vice versa.

Tο sοlve the inequality, we can fοllοw these steps -

Subtract 3/2 frοm bοth sides -

-x/2 < 5/2 - 3/2

-x/2 < 2/2

-x/2 < 1

Multiply bοth sides by -2 (and flip the inequality since we're multiplying by a negative number) -

x > -2

The graph is drawn fοr the sοlutiοn.

The circle οn the left endpοint is nοt filled because the inequality is strict (i.e., nοt less than οr equal tο).

The arrοw οn the right endpοint is filled because the sοlutiοn set includes all values greater than -2.

Therefοre, the sοlutiοn set is all real numbers greater than -2, which can be represented οn a number line as a ray starting at -2 and mοving tοwards pοsitive infinity.

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The minimum amount of money Camille could have is 0 dollars if she doesn't buy anything, and the maximum amount of money she could have is 166 dollars if she buys the maximum quantity of each item.

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

We are given that;

The prices of different items at a garage sale: pants, shirts, shorts, and belts.  

Camille can buy up to 5 shirts.

Now,

If Camille buys 5 shirts, she would spend 5 * 6 = 30 dollars on shirts. Since she can buy up to 5 shirts, she may spend less than 30 dollars if she buys fewer shirts.

She can buy up to 10 pants, which would cost her 10 * 8 = 80 dollars.

She can buy up to 5 shorts, which would cost her 5 * 4 = 20 dollars.

She can buy up to 12 belts, which would cost her 12 * 3 = 36 dollars.

30 + 80 + 20 + 36 = 166 dollars

Therefore, by the  maxima and minima the answer will be 166 dollars if she buys the maximum quantity of each item.

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The answer of set U by listing its elements is {-3, -2, -1}

To rewrite the set U by listing its elements, we need to identify the integers that fall within the given range of -3<=z<=-1.

The appropriate set notation for listing the elements of a set is {element1, element2, element3, ...}.

So, the integers that fall within the given range are -3, -2, and -1.

Therefore, we can rewrite the set U as:

U = {-3, -2, -1}

This is the answer in the appropriate set notation, listing the elements of the set U.

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The equation with a solution of -7 is x^2 = 49

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

The list of options and x = -7

To check which equation has a solution of x = -7, we can simply substitute -7 for x in each equation and see which one is true.

Hence, the equation x^2 = 49 has x = -7 as a solution.

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For the given square, m∠OKL=45° and m∠MOL=90°.

A square is a regular quadrilateral in Euclidean mathematics because it has four equal sides and four equal angles (right angles, 90-degree angles). It can also be explained as a rectangle with two adjacent sides that are of identical length. It is the only regular polygon whose diagonals are all the same length and whose internal, central, and exterior angles are all equal (90°).

In mathematics, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal sections. An angle bisector is a beam that divides an angle into two identical segments of the same length.

Angle bisector points are equally spaced from both angle lines.

Any angle, including acute, obtuse, and right angles, can have an angle bisector traced to it.

In the given square,

The diagonals NL and KM are angle bisectors of ∠K, ∠L, ∠M and ∠N.

Therefore, ∠OKL= 90/2

                  ∠OKL=45°

We know that, in a square, diagonals are equal and bisect each other at right angles.

Therefore, ∠MOL=90°

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The value of (f - g) (3) is 32.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given are two functions, f and g.

f(x) = 3x² and g(x) = x - 8

Subtraction of two functions is defined as,

(f - g) (x) = f(x) - g(x)

             = 3x² - (x - 8)

             = 3x² - x + 8

To find (f - g)(3), substitute 3 in place of x.

(f - g)(3) = 3(3)² - 3 + 8

             = 27 - 3 + 8

             = 32

Hence the value of the subtraction of functions is 32.

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Answer: See the Picture.

Step-by-step explanation:

Please follow this account

Answer:

x = 16

AB = 25

BC = 15

AC = 20

Step-by-step explanation:

I have marked the vertices to explain

There are three right triangles that can be seen in the picture

Δ ABC with legs BC and AC and hypotenuse AB

ΔACD with legs AD and CD and hypotenuse AC

ΔBCD with legs CD and BD and hypotenuse BC

We will using the Pythagorean formula in all three triangles:
hypotenuse² = sum of squares of legs

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

(1) Let's first find missing side BC

In right triangle ΔBCD ,
BC² = CD² + BD²

We have CD = 12, BD = 9
BC² = 12² + 9²
= 144 + 81

= 225

BC = √225 = 15

--------------------------------------------------------------------------------------------------
(2) Now let's focus on ΔABC

AB is the hypotenuse
AC and BC are the legs

AB² = AC² + BC²

or

AC² = AB² - BC²

Since AB = AD + BD = x + 9 and BC = 15

AC² = (x + 9)² - 15²

(x + 9)² = x² + 2 · 9 · x + 9² = x² + 18x + 81

15² = 225

AC² =  x² + 18x + 81 -225

AC² =  x² + 18x - 144                  (1)

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

(3) Now let's turn our attention to ΔACD with legs AD and CD  and hypotenuse AC

AC² = AD² + CD²

With AD = x and CD = 12,

AC² = x² + 12²

AC² = x² + 144                               (2)

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

Equations (1) and (2) have the same left side, AC²
So the expressions on the right side must be equal

Therefore:

x² + 18x - 144     =  x² + 144

x² terms cancel out from left and right sides giving

18x - 144 =  144

Add 144 on both sides:
18x - 144 + 144 = 144 + 144

18x = 288

x = 288/18 = 16

Plugging this into equation (2) AC² = x² + 144 gives
AC² = 16² + 144

AC² = 256 + 144

AC² = 400

AC = √400

or

AC = 20

Since AB is the third unknown side and AB = x + 9 we get
AB = 16 + 9 = 25

It is unlikely that the projected rebounds in 15 shots will actually happen.

Total shots fired equals 10.

To find that there were 15 shots total.

Consider S to be the likelihood that your team will rebound and miss a shot.

P(S) = Number of rebounds / Total Number of outcomes

P(S) = 7/15

P(S) = 0.46

Consequently, it is unlikely that the projected rebounds in 15 shots will actually happen.

Thus, it is unlikely that the projected rebounds in 15 shots will actually happen.

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The complete question is-

During a basketball game, you record the number of rebounds from missed shots for each team.  How many rebounds should your team expect to have in 15 missed shots?

Picture for question is attached.

You need to buy 1 stamp that costs 12 cents, 3 stamps that cost 4 cents each, and 8 stamps that cost 1 cent each, to have a total of 40 stamps and spend exactly $1.

The reasoning is as follows:

If you were to buy only 1 cent stamps, you would need to purchase 100 of them to spend $1, which would exceed the required 40 stamps. On the other hand, if you were to buy only 12 cent stamps, you would only be able to purchase 8 stamps, which would fall short of the required 40 stamps. Therefore, a combination of all three types of stamps is necessary.

Starting with the most expensive stamp, one 12 cent stamp leaves you with 88 cents. Then, 3 stamps of 4 cents each will cost you 12 cents, leaving you with 76 cents. Finally, 8 stamps of 1 cent each will cost you 8 cents, which adds up to $1 and gives you a total of 40 stamps.

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Therefore , the solution of the given problem of unitary method comes out to be Browns books are less expensive than Noble books at $5.50 each.

Take the lengths of this minute subsection and split the sum by two to complete a task using a unitary variable technique. The unit technique, in a nutshell, removes a wanted item both from the specific sets and color subsets. For instance, 40 pencils will cost Rs/kg ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality. There are unanswered questions and changes (mathematics, algebra).

Here,

We must ascertain the price per book for each retailer in order to evaluate the costs of Browns and Noble books.

Two of Brown's books cost $11, so each volume costs $5.50 (11/2 = 5.50).

Five novels from Barnes & Noble cost $31, making each book $6.20 (31/5 = 6.20).

Browns books are less expensive than Noble books, which cost $6.20 per volume, at $5.50 each.

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Answer:

  x = 1 or 5

Step-by-step explanation:

You want the value(s) of x that make 3x^2-x+1 and 2x^2+5x-4 have the same value.

Equating their values, we have ...

  3x² -x +1 = 2x² +5x -4

  x² -6x +5 = 0 . . . . . . . . . subtract (2x²+5x-4)

  (x -5)(x -1) = 0 . . . . . . . factor

  x = 1 or x = 5 . . . . . . values of x that make the factors zero

The two trinomials will have the same value for x=1 and for x=5.

__

Additional comment

The attached graph shows the points where the trinomials have the same value.

The length of the rectangular box will be 2.03 cm. Then the correct option is C.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,

V = L x W x H

The volume of a rectangular box is 109.86 cubic centimeters. The prism's breadth is 13.2 cm. The prism stands 4.1 cm tall.

The length of the rectangular prism is given as,

109.86 = L x 13.2 x 4.1

109.86 = 54.12L

L = 109.86 / 54.12

L = 2.03 cm

The length of the rectangular box will be 2.03 cm. Then the correct option is C.

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The values of a and b that will result in an inconsistent system are a = 12/5 and b = 20x - 5y.

To find two numbers a and b such that the system of linear equations is inconsistent, we need to make sure that the two equations have the same slope but different y-intercepts. This will result in the two equations being parallel to each other and never intersecting, making the system inconsistent.

The first equation is: ax - 3y = 2. We can rearrange this equation to solve for y and find the slope:

3y = ax - 2
y = (a/3)x - (2/3)

The slope of this equation is a/3.

The second equation is: -4x + 5y = b. We can rearrange this equation to solve for y and find the slope:

5y = 4x + b
y = (4/5)x + (b/5)

The slope of this equation is 4/5.

For the system to be inconsistent, the slopes need to be equal. So we can set a/3 = 4/5 and solve for a:

a/3 = 4/5
a = 12/5

Now we need to find a value for b that will result in a different y-intercept. We can do this by plugging in the value of a into one of the equations and choosing a different value for the y-intercept:

y = (12/5)(1/3)x - (2/3)
y = 4x - (2/3)

If we choose a different value for the y-intercept, such as -1, we can solve for b:

y = 4x - 1
5y = 20x - 5
b = 20x - 5y

So the values of a and b that will result in an inconsistent system are a = 12/5 and b = 20x - 5y.

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When the wet-bulb reading is 66°F, the relative humidity is 100%.

Based on the given information, the dry-bulb temperature and wet-bulb temperature are the same, which means the air is fully saturated with water vapor, and the relative humidity is 100%.

Relative humidity is the ratio of the amount of moisture in the air compared to the amount of moisture that the air can hold at a particular temperature. The wet-bulb temperature measures the lowest temperature that can be achieved by evaporating water into the air until it is fully saturated, while the dry-bulb temperature measures the actual temperature of the air.

When the wet-bulb and dry-bulb temperatures are the same, it means that the air is fully saturated and cannot hold any more moisture, resulting in a relative humidity of 100%.

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The simplified expression is  [tex]8x^4y^4[/tex].

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.

Here the given expression is

=> [tex](4x^3y^3)(2x.2y)[/tex]

=> [tex]4\times x^3\times y^3\times2x\times2y[/tex]

=> [tex]4\times2\times2\times x^3\times x \times y^3\times y[/tex]

=> 8[tex]\times x^{3+1}\times y^{3+1}[/tex]

=> [tex]8x^4y^4[/tex]

Hence the simplified expression is  [tex]8x^4y^4[/tex].

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Answer:

Trust me I guarantee you it's correct.

Step-by-step explanation:

D. 8x^5y^4

Answer: why do u need help again? this is easy boy

Step-by-step explanation:

Answer:-15

Step-by-step explanation:

To solve for x, start by expanding the expression in the parentheses:

x = 6+((4x-28)1/2)
x = 6 + 2√(4x-28)

Next, subtract 6 from both sides of the equation:

2√(4x-28) = x - 6

Next, square both sides of the equation:

(2√(4x-28))2 = (x - 6)2

Then, solve for x:

(4x-28) = (x - 6)2
4x-28 = x2 - 12x + 36
x2 - 16x + 64 = 0

Solve for x by factoring:

(x-8)(x-8) = 0

x = 8

Therefore, the solution to the equation x = 6+((4x-28)1/2) is x = 8.

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The solutions to the given polynomial equation are x = (1 + √5)/(3) and x = (1 - √5)/(3).

To solve the given polynomial equation using the quadratic formula, we need to first identify the values of a, b, and c. In this case, a = -9, b = 6, and c = 4. The quadratic formula is given by:

x = (-b ± √(b^(2) - 4ac))/(2a)

Plugging in the values of a, b, and c into the formula, we get:

x = (-(6) ± √((6)^(2) - 4(-9)(4)))/(2(-9))

Simplifying the equation, we get:

x = (-6 ± √(36 + 144))/(-18)

x = (-6 ± √180)/(-18)

x = (-6 ± 6√5)/(-18)

x = (1 ± √5)/(3)

Therefore, the solutions to the given polynomial equation are x = (1 + √5)/(3) and x = (1 - √5)/(3).

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Answer:

D

Step-by-step explanation:

1. 286

2. False

3. 84

1. The number of non-negative integer solutions of x1​+x2​+x3​+x4​=10 is 286.

2. The answer to the above question is not the same as the number of non-negative integer solutions of x1​+x2​+x3​≤10. The reason is that the first equation has 4 variables, while the second equation has only 3 variables.

Therefore, the number of solutions will be different.

3. The number of positive integer solutions of x1​+x2​+x3​+x4​=10 is 84.

1. To find the number of non-negative integer solutions of x1​+x2​+x3​+x4​=10, we can use the formula: C(n+k-1, k-1) = C(10+4-1, 4-1) = C(13, 3) = 286

Therefore, there are 286 non-negative integer solutions of x1​+x2​+x3​+x4​=10.

2. The answer to the above question is not the same as the number of non-negative integer solutions of x1​+x2​+x3​≤10 because the first equation has 4 variables, while the second equation has only 3 variables.

Therefore, the number of solutions will be different.

3. To find the number of positive integer solutions of x1​+x2​+x3​+x4​=10, we can use the formula: C(n-1, k-1) = C(10-1, 4-1) = C(9, 3) = 84

Therefore, there are 84 positive integer solutions of x1​+x2​+x3​+x4​=10.

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Answer:

y = -  125/18

Step-by-step explanation:

okay so here what i got when i was doing the equation

5 ( y + 25) = - 13y

5 y + 125 = - 13y

then you subtract 125 from both sides

subtract the numbers

and my solution was y = - 125 / 18 trust me!

Hope that helped

It will take 11 days to sell 3872 liters of fuel at the same rate as 1760 liters sold in 5 days.

We can use the following proportion to solve the problem:

1760 liters / 5 days = 3872 liters / x days

Where x is the number of days it will take to sell 3872 liters of fuel.

We can use the unitary method to solve this problem.

Let's start by finding out how much fuel is sold in one day. To do this, we need to divide the total amount of fuel sold (1760 liters) by the number of days it was sold for (5 days):

1760 liters ÷ 5 days = 352 liters per day

Now we can use this rate to find out how many days it will take to sell 3872 liters of fuel:

3872 liters ÷ 352 liters per day = 11 days (rounded to the nearest whole number)

Therefore, it will take 11 days to sell 3872 liters of fuel at the same rate as 1760 liters sold in 5 days.

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The given function, f(x)=-3x^(2)+4, has three types of symmetry: 1. Symmetry with respect to the y-axis (even symmetry).
2. Symmetry with respect to the x-axis (odd symmetry). 3. Symmetry with respect to the origin (rotational symmetry)

To check for symmetry with respect to the y-axis, we can substitute (-x) for x in the function and see if it is equal to the original function.

f(-x)=-3(-x)^(2)+4=-3x^(2)+4

Since f(-x)=f(x), the function is symmetric with respect to the y-axis.

To check for symmetry with respect to the x-axis, we can substitute (-y) for y in the function and see if it is equal to the original function.
-3x^(2)+4=-y
y=-3x^(2)-4

Since this is not equal to the original function, the function is not symmetric with respect to the x-axis.

To check for symmetry with respect to the origin, we can substitute (-x) for x and (-y) for y in the function and see if it is equal to the original function.
-3(-x)^(2)+4=-y
y=-3x^(2)-4

Since this is not equal to the original function, the function is not symmetric with respect to the origin.

Therefore, the given function f(x)=-3x^(2)+4 has symmetry with respect to the y-axis, but does not have symmetry with respect to the x-axis or the origin.

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Therefore, the length of the other side of Ross's garden is approximately 13.7 feet.

A rectangle is a four-sided flat shape with four right angles (90-degree angles) between opposite sides. It is a type of quadrilateral, which means it has four sides. In a rectangle, the opposite sides are equal in length and parallel to each other, which makes it different from a square, where all sides are equal in length. The area of a rectangle can be found by multiplying the length by the width, and the perimeter can be found by adding up the lengths of all four sides.

Here,

Let the length of the other side of the garden be x feet.

Using the Pythagorean theorem, we have:

x² + 30² = 33²

Simplifying the equation:

x² = 33² - 30² = 1089 - 900

= 189

Taking the square root of both sides:

x = √189 ≈ 13.7 feet

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The factors which would be considered while constructing a road for a steep slope are the terrain of the area, the estimated daily traffic, minimum and maximum sight distance, and the design speed.

Constructing roads on a steep slope is a challenge for every civil engineer. It is because such slopes which are possibly found in hilly areas have less access to main land from where the resources/ material for construction are to be transported and also need specific calculations to estimate maximum durability of the roads and also prevent accidents which might occur due to steep slopes.

Hence, an engineer has to keep in mind several factors which can help to reduce the accident cases, provide road safety and better connectivity with major areas.  It is essential that roadway engineers design roads that allow drivers to travel at the right speed. Topography determines the terrain, the different gradient and the construction cost. Every roadway should be built with illuminated raised pavement markings for facilitating safe travel during the night.

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The graph of the function y=3x+1 is shown.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

We are given that;

The function is y=3x+1

Now,

When x = 0, y = 3(0) + 1 = 1, so one point on the function is (0, 1).

When x = 1, y = 3(1) + 1 = 4, so another point on the function is (1, 4).

When x = -1, y = 3(-1) + 1 = -2, so a third point on the function is (-1, -2).

Therefore, the graph will be given the attachment

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