Given f(x)= 15/2x+7
a. Find f′(x) using the definition of the derivative
b. Find f′(x) using the formula from chapter 3

There are several statements that are true when it comes to a smooth function in a neighborhood around a point and the forward and backward finite differences.

The true statements are:

1) The forward finite difference is the difference between the function value at a point and the function value at the next point.

2) The backward finite difference is the difference between the function value at a point and the function value at the previous point.

3) The forward and backward finite differences can be used to approximate the derivative of a function at a point.

4) The forward and backward finite differences are both equal to the slope of the tangent line to the function at the point.

5) The forward and backward finite differences are both equal to the derivative of the function at the point.

Therefore, the true statements are "The forward finite difference is the difference between the function value at a point and the function value at the next point.", "The backward finite difference is the difference between the function value at a point and the function value at the previous point.",

"The forward and backward finite differences can be used to approximate the derivative of a function at a point.", "The forward and backward finite differences are both equal to the slope of the tangent line to the function at the point.", and "The forward and backward finite differences are both equal to the derivative of the function at the point."

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Answer:

7  13/24 miles

Step-by-step explanation:

First reduce 11/6 into 1 5/6

Then add them all together to get 7  13/24

Answer:

The total would be 6 7/8 miles.

Step-by-step explanation:

Hope this helps :)

Equation of the line perpendicular to y=3/4(x-2) and passes through (2,0) is y = 4/3(2-x).

let say our given line is L1 and the line perpendicular to L1 is L2. We are provided equation of line L1 is y=3/4(x-2).

slope of line L1 is M1 = 3/4

Let say the slope of line L2 is M2, we know, when two line are perpendicular, the products of their slopes is equal to -1.

M1 x M2 = -1

3/4 x M2 = -1

M2 = -4/3.

The line L2 passes through (2,0) and has slope -4/3.

We can apply the point slope form of the line to find the equation,

(y-0)/(x-2) = -4/3

y = 4/3(2-x)

So, the equation of the line L2 is y = 4/3(2-x).

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Answer:

3,468?

Step-by-step explanation:

I think the prompt is a little confusing, but I went with the logic of literally using the numbers and combining them.

9514 1404 393

Answer:

  B  y-3 = 6(x-8)

Step-by-step explanation:

For point (h, k) and slope m, the point-slope form equation is ...

  y -k = m(x -h)

Your point is (8, 3) and your slope is 6, so the equation is ...

  y -3 = 6(x -8) . . . . . . . . matches choice B

The value of the length x in a given triangle by using the trigonometry formula would be 9.6 units.

Given that,

A triangle UVW is shown in the image with sides and angles,

vw = 6.4

uv = x

And, ∠wuv = 42°

Used the trigonometry formula which states that,

\(\text{ sin x} = \dfrac{\text{ Opposite}}{\text{ Hypotenuse}}\)

Here, we have;

An angle ∠wuv = 42°.

So, we get;

\(\text{ sin 42} = \dfrac{\text{ vw}}{\text{ uv}}\)

Substitute given values,

\(\text{ sin 42} = \dfrac{\text{ 6.4}}{\text{ x}}\)

Since, sin (42°) = 0.67

Hence,

\(0.67 = \dfrac{6.4}{x}\)

Multiply by x on both sides,

\(0.67 \times x = 6.4\)

Divide both sides by 0.67, we get;

\(x = \dfrac{6.4}{0.67}\)

\(x = 9.55\)

Round to the nearest tenth,

\(x = 9.6\)

So, the value of x is 9.6 units.

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The minimum value of the given function is 3 at x=-5.

By locating the vertex of the parabola that the function defines, we may determine the lowest or maximum value of G(x).

The x-coordinate of the vertex may be determined by using the formula x = -b/(2a), where a and b are the coefficients of the quadratic components in the function.

In this case, a = 3 and b = 30, so:

x = -b/(2a) = -30/(2*3) = -5

Now we can find the y-coordinate of the vertex by plugging in x = -5 into the function:

\(G(-5) = 3(-5)^2 + 30(-5) + 78 \\= 3(25) - 150 + 78 \\= 3(25) - 72 \\= 3(25 - 24) \\= 3(1) \\= 3\)

Therefore, the minimum value of G(x) is 3 and there is no maximum value.

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Answer:

Step-by-step explanation:

3x^2+kx+12=0

k= -3x-12/x

Answer:

k = 12  

Step-by-step explanation:

3(x² + kx + 2²) = 3(x² + ____x + 4) = 3(x² + 4x + 4) = 3x² + 12x + 12 ⇒ k = 12

Answer:x=35/2 or 17.5

Step-by-step explanation:

x + .2x = 21

1.2x = 21

1.2x/1.2 = 21/1.2

x = 17.5

answer a i just did it

Step-by-step explanation:

The dimensions of the window that minimize the perimeter are h = 1.40625w and T = 1.5w.

Given that the window is in the shape of a rectangle of height h surmounted by a triangle having a height T that is 1.5 times the width w of the rectangle.

Let the width of the rectangle be ‘w’.We have to find the height of the rectangle ‘h’ and the width of the rectangle ‘w’ that minimize the perimeter of the window.

Using the given diagram, the height of the rectangle is h and the base of the triangle is 1.5w, therefore the height of the triangle is 1.5w/2 = 0.75w.

Area of the rectangle = hw and area of the triangle = 0.5 (1.5w) × 0.75w = 0.5625w²

The total area A is given by A = hw + 0.5625w² = w(h+0.5625w) …….(1)

Let the perimeter of the window be P. Then P = 2l + 2w + T …….(2)

Substitute T = 1.5w in (2) to get, P = 2l + 4.5w + 2h …….(3)

Solve (1) for h to get, h = (A/w) – 0.5625w …….(4)

Substitute (4) into (3) to get, P = 2l + 4.5w + 2((A/w) – 0.5625w) …….(5)

Differentiating (5) w.r.t ‘w’ and equating to zero to get the minimum value,

∂P/∂w = 4.5 – 2A/w² + 0.5625 = 0 ⇒ 2A/w² = 4.5 – 0.5625 = 3.9375 ⇒ A/w² = 1.96875

From (1), A = w(h+0.5625w)

Substitute A/w² = 1.96875 in the above equation to get,

1.96875w² = w(h+0.5625w) ⇒ h = 1.96875w – 0.5625w = 1.40625w

Therefore the dimensions of the window that minimize the perimeter are h = 1.40625w and T = 1.5w.

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Answer: The paint mixer should mix 2.75 gallons of 30% gloss paint and 1 gallon of 15% gloss paint to make 3.75 gallons of paint that is 20% gloss.

To calculate the number of gallons of each paint that the mixer should mix, we need to use the formula: C1V1 + C2V2 = C3V3, where C1 and V1 are the concentration and volume of the first paint, C2 and V2 are the concentration and volume of the second paint, and C3 and V3 are the concentration and volume of the mixture. Using this formula and the given information, we can set up the equation:0.30V1 + 0.15V2 = 0.20(3.75)Simplifying the equation, we get:V1 + V2 = 3.75And, rearranging it, we get:V2 = 3.75 - V1.Substituting this in the first equation, we get:0.30V1 + 0.15(3.75 - V1) = 0.20(3.75).Simplifying and solving for V1, we get:V1 = 2.75.

Therefore, the mixer should mix 2.75 gallons of 30% gloss paint and 1 gallon of 15% gloss paint to make 3.75 gallons of paint that is 20% gloss.

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Answer:

285°

Step-by-step explanation:

90 + 180 = 270

270 + 15 = 285

Answer:

285°

Step-by-step explanation:

Lets solve your problem :)

90° + 180° = 270°

270° + 15° = 285°

Mark my answer brainliest to tell you the 4 algebra calulators :)

Answer:

t^2+4

Step-by-step explanation:

The perimeter of the table can be given by the equation 2l+2w, and we know the length is 2t-3, meaning 2(2t-3)+2w=2t^2+4t+2, as we know 2t^2+4t+2 is the perimeter. Simplifying we get:

4t-6+2w=2t^2+4t+2

4t+2w=2t^2+4t+8

2w=2t^2+8

w=t^2+4

This means that the table's width is t^2+4

A jug holds 10 pints of milk. If each child gets one cup of milk, it can serve 20 children. To determine how many children can be served with the 10 pints of milk, we need to convert pints to cups and divide the total amount of milk by the amount each child will receive.

1. Convert 10 pints to cups:
Since there are 2 cups in a pint, we can multiply 10 pints by 2 to get the total number of cups.
10 pints x 2 cups/pint = 20 cups of milk.
2. Divide the total cups of milk by the amount each child will receive:
Since each child gets one cup of milk, we can divide the total cups of milk by 1 to find the number of children that can be served.
20 cups ÷ 1 cup/child = 20 children.
Therefore, the jug of milk can serve 20 children if each child receives one cup of milk.

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Answer:

√7

Step-by-step explanation:

\(\displaystyle \frac{7}{\sqrt{7}}=\frac{7}{\sqrt{7}}*\frac{\sqrt{7}}{\sqrt{7}}=\frac{7\sqrt{7}}{7}=\sqrt{7}\)

The correct pair of constraints that needs to be added to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units is: P24 - P25 <= 80; P25-P24 <= 80. Therefore, the correct option is 5.

Here, the given information is Pij = the production of product i in period j. We need to find the pair of constraints that will specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Thus, let the production of product 2 in period 4 and in period 5 be represented as P24 and P25 respectively.

Therefore, we can write the following inequalities:

P24 - P25 <= 80

This is because the production of product 2 in period 5 can be at most 80 units less than that of period 4. This inequality represents the difference being less than or equal to 80 units.

P25-P24 <= 80

This is because the production of product 2 in period 5 can be at most 80 units more than that of period 4. This inequality represents the difference being less than or equal to 80 units.

Therefore, we need to add the pair of constraints P24 - P25 <= 80 and P25-P24 <= 80 to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Hence, option 5 is the correct answer.

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Answer:

Negative infinity.

Step-by-step explanation:

It behaves as it behaves the leading term. The leading term you can simply extract for being \(-x^3\) which goes to negative infinity.

Rigorously, you do all the multiplication, then collect \(x^3\) and in what's left you end up with -1 and a number of terms that go to zero.

Fast and loose, positive infinity, means "very big". Let's say 100. Now cubed, that's -1M. Now, even if you are adding a bunch of positive numbers - and some of these aren't - no way you can catch up that -1M lead your cubic term gives the polynomial

Answer:

10

Step-by-step explanation:

→ Find the difference in x coordinates

8 - 2= 6

→ Find the difference in y coordinates

-1 - 7 = -8

→ Use Pythagoras

√6² + (-8)² = 10

Question 16:

\(\alpha\) and \(\beta\) are the roots of the equation.

That means \((x-\alpha )(x-\beta ) = 2x^{2} -6x+5 = 0\\\)

\((x-\alpha )(x-\beta ) = 2x^{2} -6x+5 = 0\)

          \(2x^{2} -6x+5 = 0\\x^{2} -3x+\frac{5}{2} =0\)

          \((x-\alpha )(x-\beta ) =x^{2} - (\alpha +\beta )x +\alpha \beta\)

So,

\(x^{2} - (\alpha +\beta )x +\alpha \beta = x^{2} -3x+\frac{5}{2}\)

Compare coefficient

\(\alpha +\beta = 3\\\alpha \beta = \frac{5}{2}\)

Consider \(\frac{\beta }{\alpha } + \frac{\alpha }{\beta }\)

\(\frac{\beta }{\alpha } + \frac{\alpha }{\beta } =\frac{ \alpha ^{2} +\beta ^{2}}{\alpha \beta }\)

\(= \frac{(\alpha +\beta )^{2} -2\alpha \beta }{\alpha \beta } \\= \frac{3^{2} -2*\frac{5}{2} }{\frac{5}{2} } \\= 4*\frac{2}{5} \\=\frac{8}{5}\)

Ans: 8/5

Question 19:

\(f(x+2) = 2x^{2} +5x-3\\\)

Substitute x with -1

So,

\(f(1) = 2(-1)^{2} +5(-1)-3\\=2-5-3\\=-6\)

Ans: -6

Answer:

Nope. It isn't.

Step-by-step explanation:

6^2 + 8^2 = 100, and 100 = 10^2. So that means that the thing that you chose is incorrect.

The volume of a cylinder is equal to the area of the base times the height. The area of the base is pi * r^2, where r is the radius. In this case, the radius is 5 meters, so the area of the base is pi * 5^2 = 25pi. The height is 15 meters, so the volume of the cylinder is 25pi * 15 = 375pi cubic meters.

Pi is approximately equal to 3.14, so the volume of the cylinder is approximately equal to 375 * 3.14 = 1177.5 cubic meters.

To the nearest tenth, the volume of the cylinder is 1178 cubic meters.

Here are the steps in more detail:

- Find the area of the base: pi * r^2 = pi * 5^2 = 25pi

- Multiply the area of the base by the height: 25pi * 15 = 375pi

- Approximate pi to 3.14: 375pi * 3.14 = 1177.5

- Round to the nearest tenth: 1177.5 rounded to the nearest tenth is 1178

The volume of the cylinder is 1178.6 m³.

We know that,

the volume of a cylinder = π×r²×h

where r is the radius of the base of the cylinder,

and, h is the height of the cylinder.

Now, according to the question,

the radius of the base of the cylinder = 5m,

the height of the cylinder is 15 m

Putting the value of base and height in the above formula for the volume of the cylinder, we get,

the volume of the cylinder = π × r²×h

                                               = 22/7 × 5² × 15

                                               = 1178.6

Hence, the volume of the cylinder is 1178.6 m³.

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The complete question is -

Find the volume of the cylinder. Round your answer to the nearest tenth.

The radius of the cylinder is 5 meters and its height is 15 meters.

The volume of the cylinder is about ? cubic meters.

Answer:

when finding the area of a triangle you need to multiple the base and hight then divide that number by 2

Answer:

It would take 5.9 years to the nearest tenth of a year

Step-by-step explanation:

The formula of the compound continuously interest is A = P\(e^{rt}\) , where

∵ Serenity invested $2,400 in an account

∴ P = 2400

∵ The account paying an interest rate of 3.4%, compounded continuously

∴ r = 3.4% ⇒ divide it by 100 to change it to decimal

∴ r = 3.4 ÷ 100 = 0.034

∵ The value of the account reached to $2,930

∴ A = 2930

→ Substitute these values in the formula above to find t

∵ 2930 = 2400\(e^{0.034t}\)

→ Divide both sides by 2400

∴ \(\frac{293}{240}\) = \(e^{0.034t}\)

→ Insert ㏑ in both sides

∴ ㏑(\(\frac{293}{240}\)) = ㏑(\(e^{0.034t}\))

→ Remember ㏑(\(e^{n}\)) = n

∴ ㏑(\(\frac{293}{240}\)) = 0.034t

→ Divide both sides by 0.034 to find t

∴ 5.868637814 = t

→ Round it to the nearest tenth of a year

∴ t = 5.9 years

∴ It would take 5.9 years to the nearest tenth of a year

The domain of the function is defined as 0 ≤  x ≤ 4.

option A is the correct answer.

A domain of a function refers to "all the values" that can go into a function without resulting in undefined values.

So the domain of a function is the set of x values, while the range of a function is the set of y values.

From the given statement, the range of the function is defined as;

y = vt

where;

y = 60 mph x 4 hr

y = 240 miles

From the given statement, the domain of the function is defined as;

0 ≤  x ≤ 4

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Answer:

BC≈8,38

Step-by-step explanation:

AB=a

BC=c

CA=b

a²+b²=c²

3.3²+7.7²=c²

√70,18=√c²

c≈8,38

Answer:

70 kg

Step-by-step explanation:

\(\frac{5}{8}*\frac{112}{1}kg\\\frac{5}{1}*\frac{14}{1}kg\\5 * 14kg\\70 kg\)

Decreasing 112kg by 3/8 is equal to 70kg.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

To decrease 112kg by 3/8,

we can multiply 112 by 3/8 and then subtract the result from 112:

112 - (112 x 3/8)

First, we simplify 3/8 by finding a common denominator of 8:

= 3/8

= 3/8 x 8/8

= 24/64

So we have:

112 - (112 x 24/64)

To simplify this expression, we can first divide both the numerator and denominator of 24/64 by the greatest common factor, which is 8:

= 24/64

= (24 ÷ 8) / (64 ÷ 8)

= 3/8

Substituting this value, we get:

112 - (112 x 3/8)

Multiplying 112 by 3/8, we get:

= (112 x 3/8)

= (336/8)

= 42

Substituting this value, we get:

= 112 - 42

= 70

Therefore,

Decreasing 112kg by 3/8 is equal to 70kg.

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The dimensions of the closed rectangular box with a square base and volume of 8000 cubic centimeters that can be constructed with the least amount of material are 20 cm.

Let the length and width of the rectangular box with a square base be x.

and the height is y.

The volume, V = 8000 = \(x^{2} y\)       --------(1)

The surface area, S = 2\(x^{2}\) + 4xy .   -------(2)

S =  2\(x^{2}\) + 4xy and  8000/ \(x^{2}\) =y     -------( from 1 and 2)

so, S= 2\(x^{2}\) + 4x(8000/ \(x^{2}\))

S= 2\(x^{2}\) + 32000/x

to find the least amount of material to be used, we will differentiate the surface area w.r.t x.

ds/dx= 0 = 4x - 32000/\(x^{2}\)

therefore, we have, 4x = 32000/\(x^{2}\)

                                 4\(x^{3}\) =32000

                                   \(x^{3}\) =8000

                                     x=20

Hence, The dimensions of the closed rectangular box with a square base and volume of 8000 cubic centimeters that can be constructed with the least amount of material are 20 cm.

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Answer:

Below in bold.

Step-by-step explanation:

The general form of a linear function can be written as:

n(p) = kp + C      where k and C are constants.

So substituting the given data:

8000 = 3k + C

5200 = 5k + C    Subtract

2800 = -2k

k = -1400

and C = 8000 - 3(-1400) = 12200

a. So the equations is:

n(p) = -1400p + 12200

b.

For a charge p of $6.50;

n(p)  = -1400*6.5 + 12200

= 3100 balls.

The radius of the circle can be determined using the Pythagorean theorem. Since the chord is 5 units away from the center of the circle, a right triangle can be formed where one leg is half the length of the chord (5 units) and the hypotenuse is the radius of the circle. Using the Pythagorean theorem, we can solve for the radius as follows:

r^2 = (10/2)^2 + 5^2

r^2 = 25 + 25

r^2 = 50

r = sqrt(50) = 5sqrt(2) units

Therefore, the radius of the circle is 5sqrt(2) units.

To further explain, the Pythagorean theorem 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 chord is a line segment connecting two points on the circle and is perpendicular to the radius passing through the midpoint of the chord. Since the chord is 10 units long and 5 units away from the center of the circle, the length of one leg of the right triangle is 5 units (half the length of the chord), and the length of the other leg is the radius of the circle. Using the Pythagorean theorem, we can solve for the unknown length of the radius.

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