f(x) = 4x3 − 9x2 − 30x 4 (a) find the intervals on which f is increasing or decreasing. (enter your answers using interval notation.)

The value of x on the unit circle in simplest form is -1/6√35

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

The point P = (x,-1/6) lies on the unit circle

The equation of a unit circle is

x² + y² = 1

In point P, we have

y = -1/6

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

x² + (-1/6)² = 1

So, we have

x² + 1/36 = 1

When evaluated, we have

x² = 35/36

Take the square root

x = -1/6√35

Hence, the value of x in simplest form is -1/6√35

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The value of x in simplest form is (√35)/6.

To find the value of x for the point P on the unit circle, you can use the Pythagorean theorem. The unit circle has a radius of 1.

The Pythagorean theorem for the unit circle is:

x² + y² = 1

You're given that the point P lies on the unit circle, and its y-coordinate is -1/6. Plug in the values:

x² + (-1/6)² = 1

Now, square (-1/6):

x² + 1/36 = 1

Subtract 1/36 from both sides:

x² = 1 - 1/36

x² = 36/36 - 1/36

x² = 35/36

Now, take the square root of both sides:

x = ±√(35/36)

x = ±(√35/√36)

Since it's a point on the unit circle, x must be between -1 and 1, so we take the positive square root:

x = √(35/36)

Now, simplify:

x = (√35)/(√36)

x = (√35)/6

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Answer:

-7a - 8y = 7

x = -7

Step-by-step explanation:

Answer:

4) [tex](x-1)^2 + (y - 1)^2 = 2[/tex]

Step-by-step explanation:

4) We can convert this polar equation to rectangular form using the following formulas:

We need to manipulate the equation so some of the terms match these formulas.

[tex]r=2\cos(\theta) + 2\sin(\theta)[/tex]

↓ dividing both sides by [tex]2[/tex]

[tex]r / 2=\cos(\theta) + \sin(\theta)[/tex]

↓ multiplying both sides by [tex]r[/tex]

[tex]\dfrac{r^2}{2}=r\cos(\theta) + r\sin(\theta)[/tex]

Now, we can apply the polar conversion formulas to get the equation:

[tex]\dfrac{x^2 + y^2}{2}=x + y[/tex]

This can be manipulated to get a circle standard form equation.

↓ multiplying both sides by 2

[tex]x^2 + y^2=2x + 2y[/tex]

↓ completing the square for [tex]x[/tex]

    ↓ moving the x's to one side

    [tex]x^2 -2x=-y^2 + 2y[/tex]

    ↓ adding (-2/2)², or 1, to both sides

    [tex]x^2 -2x + 1=-y^2 + 2y + 1[/tex]

    ↓ factoring the perfect square

    [tex](x-1)^2=-y^2 + 2y + 1[/tex]

↓ completing the square for [tex]y[/tex]

    ↓ factoring a (-1) out of the right side

    [tex](x-1)^2=-1(y^2 - 2y - 1)[/tex]

    ↓ adding (-1)(+2) to both sides

    [tex](x-1)^2 - 2=-1(y^2 - 2y - 1 + 2)[/tex]

    ↓ simplifying

    [tex](x-1)^2 - 2=-1(y^2 - 2y + 1)[/tex]

    ↓ factoring the perfect square

    [tex](x-1)^2 - 2=-(y - 1)^2[/tex]

↓ adding [tex](y-1)^2[/tex] to both sides

[tex](x-1)^2 + (y - 1)^2 - 2 = 0[/tex]

↓ adding 2 to both sides

[tex]\boxed{(x-1)^2 + (y - 1)^2 = 2}[/tex]

Answer:

[tex]\textsf{4)} \quad \textsf{A.}\;\;(x-1)^2+(y-1)^2=2[/tex]

[tex]\textsf{5)} \quad \textsf{A.}\;\;r=\cot \theta \csc \theta[/tex]

Step-by-step explanation:

A polar equation is a mathematical expression that relates the distance (r) and angle (θ) of a point (r, θ) in a polar coordinate system.

Rectangular form, also known as Cartesian form, is a way of representing numbers or equations using the coordinates (x, y) in a Cartesian coordinate system. It is a standard way of expressing values in a two-dimensional space using the horizontal axis (x) and the vertical axis (y).

[tex]\hrulefill[/tex]

To convert a polar equation to rectangular form, we can use the following relationships:

[tex]\boxed{\begin{aligned}r \cos \theta&=x\\\\r \sin \theta&=y\\\\r^2&=x^2+y^2\end{aligned}}[/tex]

Given polar equation:

[tex]r=2 \cos \theta+2 \sin \theta[/tex]

Multiply both sides of the equation by r:

[tex]r^2=2r \cos \theta+2r \sin \theta[/tex]

Substitute the expressions for r², r cosθ and r sinθ:

[tex]x^2+y^2=2x+2y[/tex]

This is an equation of a circle.

To write it in standard form, move all the terms to the left side of the equation:

[tex]x^2-2x+y^2-2y=0[/tex]

Add the square of half the coefficients of the x and y terms to both sides of the equation:

[tex]x^2-2x+\left(\dfrac{-2}{2}\right)^2+y^2-2y+\left(\dfrac{-2}{2}\right)^2=0+\left(\dfrac{-2}{2}\right)^2+\left(\dfrac{-2}{2}\right)^2[/tex]

[tex]x^2-2x+1+y^2-2y+1=2[/tex]

Factor the perfect square trinomials:

[tex](x^2-2x+1)+(y^2-2y+1)=2[/tex]

[tex](x-1)^2+(y-1)^2=2[/tex]

Therefore, the given polar form converted to rectangular form is:

[tex]\boxed{(x-1)^2+(y-1)^2=2}[/tex]

[tex]\hrulefill[/tex]

To convert an equation in rectangular form to polar form, we can use the following relationships:

[tex]\boxed{\begin{aligned}r \cos \theta&=x\\\\r \sin \theta&=y\\\\r^2&=x^2+y^2\end{aligned}}[/tex]

Given rectangular equation:

[tex]x = y^2[/tex]

Substitute the expressions for x and y:

[tex]r \cos \theta=(r \sin \theta)^2[/tex]

[tex]r \cos \theta=r^2 \sin^2 \theta[/tex]

Divide both sides of the equation by r sin² θ:

[tex]\begin{aligned}\dfrac{r \cos \theta}{r\sin^2 \theta}&=\dfrac{r^2 \sin^2 \theta}{r\sin^2 \theta}\\\\\dfrac{\cos \theta}{\sin^2 \theta}&=r\\\\r&=\dfrac{\cos \theta}{\sin^2 \theta}\\\\r&=\dfrac{\cos \theta}{\sin \theta}\cdot \dfrac{1}{\sin \theta}\end{aligned}[/tex]

Use the following trigonometric identities to simplify:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric Identities}\\\\$\cot \theta=\dfrac{\cos \theta}{\sin \theta}$\\\\\\$\csc \theta=\dfrac{1}{\sin \theta}$\\\end{minipage}}[/tex]

Therefore, the given rectangular form converted to polar form is:

[tex]\boxed{r=\cot \theta \csc \theta}[/tex]

Check the picture below.

(a) The value of divF is 1/2, -1/4.

(b) The value(s) of a making divF a minimum is -27/8.

What is the divergence?

The limit of the surface integral of F out of the closed surface of a volume V enclosing x0 to the volume of V as V shrinks to zero is the definition of the divergence of a vector field F(x) at a point x0.

Here, we have

Given: F = (24a²x+2ay²)i + (2z³−6ay)j−(3z+2x²+2y²)k

(a) we have to find the value of divF.

We know that divF = ΔF = (di/dx + dj/dy + dk/dz)F

divF = 24a² - 6a - 3 = 0

8a² - 2a - 1 = 0

Now, we find the roots of a and we get

a = (-(-2)±√4+32)/2×8

a = (2±6)/16

a = 2+ 6/16, 2-6/16

a = 1/2, -1/4

Hence, the value of divF is 1/2, -1/4.

(b) We have to find the value(s) of a making divF a minimum.

Let f(a) = divF = 24a² - 6a - 3

For maxima/Minima

f'(a) = 0

= 48a - 6 = 0

a = 6/48

a = 1/8

Now,

f"(a) = 48

At a = 1/8, f"(1/8) = 48>0

f has a minimum value at a = 1/8.

So,

minf = min divF = 24×1/64 - 6/8 - 3

min divF = 3/8 - 6/8 - 3

min divF = -27/8

Hence, the value(s) of a making divF a minimum is -27/8.

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The fourth person gains 25% in the price of the bracelet.

After deducting the gains experienced by the first three individuals, we must determine the overall percentage rise in the price of the golden bracelet.

Assume that the bracelet originally cost $100 for 100 units.

The price after the first person is 100 + 15% of 100 = 100 + 15 = 115 units since the first person makes a 15% profit.

The price after the second person is 115 + 20% of 115 = 115 + 23 = 138 units since the second person makes a 20% profit on the new price.

The price after the third person is 138 + 25% of 138 = 138 + 34.5 = 172.5 units since the third person makes a 25% profit on the new price.

The percentage increase between the original price and the final price (172.5 units) must now be calculated.

Percentage increase = (Final price - Original price) / Original price * 100

= (172.5 - 100) / 100 * 100

= 72.5%

The overall percentage increase in the price of the bracelet is 72.5%.

Since the bracelet's price increased by 85% overall, we can calculate the fourth person's percentage gain as follows:

Percentage gain by the fourth person = Total increase - Sum of gains by the first three persons

= 85% - (15% + 20% + 25%)

= 85% - 60%

= 25%

Therefore, the fourth person gains 25% in the price of the bracelet.

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Answer: The answer is 226.2 feet.

Step-by-step explanation: The formula to find the total surface area of a cylinder is 2[tex]\pi[/tex] x radius squared x height. If you use the formula you will get 226.19 feet as your answer and I rounded that to 226.2 feet.

UR MOM

The equation of the parabola is:

y = 3/5 (x² -2x -8)    

We can use the factored form of the equation of a parabola below:

y = a(x - x₁)(x - x₂)

where x₁ and x₂ are the x-intercepts

x₁ = -2 and x₂ = 4

Point (2, 7): x = -1, y = -3

Substituting:

y = a(x - (-2))(x - 4)

y = a(x + 2)(x - 4)

Substituting x and y:

-3 = a(-1 + 2))(-1 - 4)

-3 = a(1 )(-5)

-3 = -5a

a = 3/5

Substituting a = 0.6 into y = a(x + 2)(x - 4):

y = 3/5(x + 2)(x - 4)

In expanded form:

y = 3/5 (x² -2x -8)    

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Unconscious processing is a complex cognitive phenomenon that involves a wide range of mental activities that occur outside of our conscious awareness. It is not simply a group of answer choices or a set of predetermined responses that are guided by habit or well-established routines.

Rather, unconscious processing is a highly nuanced and multifaceted process that is guided by a variety of different factors, including our emotions, our past experiences, our cultural background, and our personal beliefs and values.

At the same time, it is important to note that unconscious processing is not entirely independent of our executive functions or our conscious awareness. While it may be composed of relatively specialized parts, such as our automatic reflexes and basic sensory processing systems, these parts are still intricately connected to the higher-level cognitive processes that govern our decision-making, problem-solving, and goal-oriented behavior.

In short, unconscious processing is a complex and dynamic process that involves a broad range of cognitive and emotional factors, and is intimately intertwined with our conscious awareness and executive functions.

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Answer:

-4

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

f(0) = -8

That eliminates choices C. and D.

f(1) = -11

A.

Try x = 1.

y = -3(1) - 8

y = -3 - 8 = -11

Answer: A.

The value(s) of λ such that the vectors v1 and v2 are linear dependent is (are): λ = 3 and λ = -1.

To find the value(s) of λ such that the vectors v1 and v2 are linearly dependent, we need to check if one of the vectors is a scalar multiple of the other. In other words, we need to see if we can find a non-zero scalar k such that:
v2 = k*v1
Expanding this equation, we get:
(2 - λ, -8, -4) = k*(-2 - 2λ, -4, -2)
Simplifying the right-hand side, we get:
(-2k - 2kλ, -4k, -2k)
Equating the corresponding components of both sides, we get a system of three equations:
2 - λ = -2k - 2kλ
-8 = -4k
-4 = -2k
Solving the second and third equations, we get:
k = 2
k = -2
Substituting these values of k into the first equation, we get:
2 - λ = -2(2) - 2(2)λ (for k = 2)
2 - λ = -2(-2) - 2(-2)λ (for k = -2)
Simplifying both equations, we get:
λ = 3
λ = -1

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Answer:

Step-by-step explanation:

The Angle across from a side correspond to each other so the angle is related to the side across from each other.

6)   the red lines indicate that those 2 sides opposite the red line are equal to each other.  So the angles across equal each other.   So the angles of the triangle are 54, 54 and <2

All the angles added of a triangle =180

54+54+<2=180                >Substitute <2

54+54+x+78=180            >add numbers on left side

186 + x = 180                   >subtract 186 from both sides

x = -6

8)  The red lines say those to sides are equal so the sides on opposite sides of those lines are equal 72 and 72

<2 = the 2 angles on the other end

<2=72+72

x+150 = 144

x = -6

a) Written as a mixed number, we will get N = 1 + 2/3.

b) Written as a improper fraction, we will get N = 5/3.

a) First we want to write the number as a mixed number, this is written as a sum between a whole number and a proper fraction.

The circle in the left is a whole number, we can write it as 1.

The circle in the left has 4 out of 6 regions shaded, so it is 4/6 = 2/3.

Then the mixed number is N = 1 + 2/3.

b) Now we want to write this as a improper fraction, this is just a fraction where the numerator is larger than the denominator, so we can rewrite this as:

1 + 2/3 = 3/3 + 2/3 = 5/3

That is the improper fraction.

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The total measure of the jump is 11/2 feet and the number line is plotted

Given data ,

To calculate the total distance Vulcan jumped, we need to add the distances in yards and feet.

Now , the fractions to a common unit, which is feet :

1 yard is equal to 3 feet.

Therefore, Vulcan jumped:

(7/8) yard = (7/8) * 3 feet = 21/8 feet  

Next, we add the distance in feet:

(2 7/8) feet = 2 feet + (7/8) feet = 2 + (7/8) = 16/8 + 7/8 = 23/8 feet

Now, let's add the distances:

(21/8) feet + (23/8) feet = (21 + 23) / 8 feet = 44/8 feet

Simplifying the fraction:

44/8 feet = 22/4 feet = 11/2 feet

Hence , Vulcan jumped a total of 11/2 feet or 5 1/2 feet

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We are given the random variable N with the PMF P_N(n) = c, where n ∈ {0, 1, 2} and P_N(n) = 0 otherwise.

(a) To find the value of the constant c, we need to remember that the sum of all probabilities in a probability distribution must equal 1. Therefore, we can set up the following equation:

P_N(0) + P_N(1) + P_N(2) = 1

c + c + c = 1

Now we can solve for c:

3c = 1

c = 1/3

So, the value of the constant c is 1/3.

(b) To find P[N ≤ 1], we need to calculate the probability of N being 0 or 1. Using the PMF we found in part (a), we have:

P[N ≤ 1] = P_N(0) + P_N(1)

= (1/3) + (1/3)

= 2/3

Therefore, P[N ≤ 1] = 2/3.

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The inverse of the function f(x) = 1/4(x - 1)⁴ - 2 is y = ∛√(4(x + 2)) + 1.

The inverse of the function f(x) = 1/4(x - 1)⁴ - 2, we can follow these steps:

Replace f(x) with y:

y = 1/4(x - 1)⁴ - 2

Swap x and y:

x = 1/4(y - 1)⁴ - 2

Solve for y:

4(x + 2) = (y - 1)⁴

Take the fourth root of both sides:

∛√(4(x + 2)) = y - 1

Add 1 to both sides to isolate y:

y = ∛√(4(x + 2)) + 1

Hence, the inverse of the function f(x) = 1/4(x - 1)⁴ - 2 is given by y = ∛√(4(x + 2)) + 1.

To verify the inverse, we can compose the original function with its inverse:

f(f⁽⁻¹⁾(x)) = 1/4((∛√(4(x + 2)) + 1) - 1)⁴ - 2

Simplifying further:

= 1/4(∛√(4(x + 2)))⁴ - 2

= 1/4(√(4(x + 2)))² - 2

= 1/4(2(x + 2)) - 2

= 1/2(x + 2) - 2

= 1/2x + 1 - 2

= 1/2x - 1

The composition of the original function with its inverse results in the identity function.

This confirms that the inverse function undoes the action of the original function.

The inverse of the function f(x) = 1/4(x - 1)^4 - 2 is y = ∛√(4(x + 2)) + 1.

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Check the picture below.

now, ∡SPQ is a bit ambiguous, it could be ∡SRQ or ∡STUQ, anyhow we'll be doing the green one in the picture, ∡STUQ

[tex]86+x+x+60+154~~ = ~~360\implies 2x+300=360\implies 2x=60 \\\\\\ x=\cfrac{60}{2}\implies x=30\hspace{9em}\stackrel{ \measuredangle STUQ }{86+30+30}\implies \text{\LARGE 146}^o[/tex]

The graph of the quadratic function f(x) = 2x² + x - 3 and the linear function f(x) = x + 5 is given below.

Given two functions.

Quadratic function : f(x) = 2x² + x - 3

Linear function : f(x) = x + 5

We have to draw the graph of each function.

Since the domain is not completely said, assume the domain to be -3 ≤ x ≤ 3.

The vertex of the quadratic function of general form ax² + bx + c is (-b/2a, f(-b/2a)).

-b/2a = -1/4

f(-b/2a) = 2 (-1/4)² - 1/4 + 3 = 23/8 = 2.875

This is the vertex.

For the linear function,

y = x + 5

Slope = 1 and y intercept = 5

Other points are (0, 5), (1, 6), (2, 7), ...

Hence the line passes through these points.

Hence the graph of these is given below.

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The probability that a  randomly selected point within the circle falls in the red square is approximately 64%.

To find the probability that a randomly selected point within the circle falls in the square, we need to compare the areas of the square and that of  the circle.

Area of the square is  8 x 8 = 64Units²

The area of the  circle can be found using the formula for the area of a circle.

A = πr²

⇒ π x (4 √2 )² = 32π units²

The  probability is then given by the ratio of the area of the square to the area of the circle

Probability = Area of  Square / Area of Circle

= 64 / (32 π)

= 2 / π

≈ 0.6366

Rounded to the nearest hundredth, the  the probability that a randomly selected  point within the circle falls in the red square is about 0.64 or 64%.

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The correct answer will be A) yes, a measure of an interior angle is 60

Tessellation refers to the tiling of a flat surface or plane by one or more geometric surfaces. No overlapping or gap or unevenness which is left during tessellation, all the shapes fit perfectly to the plane or flat surface. There are three geometric shapes which can be used for tessellation.

These shapes are:

Square

Triangle

Hexagon

As in given , the polygon given is square

So YES the tessellation of the plan is possible and the as the interior angle of the square is 90 degrees

Hence, A is the correct complete answer i.e. yes, the measure of interior angle is 60.

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The probability of an event and the probability of its complement always sum to 1.

The probability of an event and its complement refers to the likelihood of either the event occurring or its opposite (not occurring). In any probability space, the sum of these two probabilities must always equal 1.

This can be understood using the concept of the sample space, which represents all possible outcomes of an experiment. The event and its complement together cover the entire sample space, leaving no room for other outcomes. Therefore, the sum of their probabilities must account for the entire probability space, which is equal to 1.

In other words, if the probability of an event occurring is P(A), then the probability of its complement (not A) occurring is 1 - P(A). Adding these probabilities together yields 1:

P(A) + P(not A) = P(A) + (1 - P(A)) = 1

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the expression that could represent p is,

⇒ p (x) = (x + 4) (x + 2/3) (x) (x - 9)

We have to given that;

The polynomial p is a function of x.

And, The graph of p has four zeros at -4 , -2/3 , 0 , and 9.

Now, We get;

All the factors of polynomial are,

⇒ (x - (- 4)) , (x - (- 2/3)) , (x - 0), (x - 9)

⇒(x + 4), (x + 2/3),  (x),  (x - 9)

Hence, the expression that could represent p is,

⇒ p (x) = (x + 4) (x + 2/3) (x) (x - 9)

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The measure of angle ACD is given as follows:

m < ACD = 143º.

Similar triangles are triangles that share these two features listed as follows:

The similar triangles for this problem are given as follows:

ABC and ADC.

Two equivalent angles are given as follows:

<ACB and <ACD.

On similar triangles, equivalent angles are congruent, hence the measure of angle ACD is given as follows:

m < ACD = 143º.

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The compound value interest is solved and term life policy is a better value

Given data ,

To determine which policy is the better value, we need to compare the total cost and potential returns of each option.

For the whole life policy:

Premium per year: $3008

Number of years: 20

Total cost: $3008 * 20 = $60,160

For the term life policy:

Premium per year: $185

Number of years: 20

Total cost: $185 * 20 = $3,700

Now, let's calculate the potential returns from investing the difference in premiums ($3008 - $185 = $2823) in a mutual fund with a 3.75% interest rate compounded annually over 20 years.

Future value of the investment:

Principal (difference in premiums): $2823

Interest rate: 3.75%

Number of years: 20

Using the compound interest formula:

FV = PV * (1 + r)^n

FV = $2823 * (1 + 0.0375)^20

FV = $2823 * (1.0375)^20

FV ≈ $5986.27

Therefore, the potential future value of the investment after 20 years is approximately $5986.27.

To determine the better value, we compare the total cost of each policy and subtract the potential future value of the investment from the cost of the whole life policy:

Better Value = Total Cost of Term Life - (Total Cost of Whole Life - Future Value of Investment)

Better Value = $3,700 - ($60,160 - $5,986.27)

Better Value = $3,700 - $54,173.73

Better Value = -$50,473.73

The result is negative, indicating that the term life policy is a better value by approximately $50,473.73 over 20 years

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Answer: if i'm right 6.5 meters is the answer!

p.s. you don't have to give me anything i'm just here to help!! <3

The solutions to the recurrence relation are: aₙ = 2ⁿ - 2ⁿ⁺¹ + 2ⁿ⁺² + (n⁴)/n.

The given recurrence relation is aₙ = 7aₙ₋₁ - 16aₙ₋₂ + 12aₙ₋₃ + (n⁴)/n, with initial values a₀ = -2, a₁ = 0, and a₂ = 5. To find the solutions, we can use the characteristic equation and the method of solving linear homogeneous recurrence relations. After solving the characteristic equation, we obtain the roots 2, -1, and -2.

Thus, the general solution is aₙ = C₁ * 2ⁿ + C₂ * (-1)ⁿ + C₃ * (-2)ⁿ. Using the initial values, we can determine the values of the constants C₁, C₂, and C₃. The resulting solutions are aₙ = 2ⁿ - 2ⁿ⁺¹ + 2ⁿ⁺² + (n⁴)/n. This formula provides the values of aₙ for any n.

Regarding the relations R₁, R₂, and R₃, we need to determine if they are equivalence relations on the set of all non-zero integers.

a. R₁: The relation R₁ states that (x, y) ∈ R₁ if and only if x ≥ y². To check if it is an equivalence relation, we need to verify reflexivity, symmetry, and transitivity. It is reflexive since for any integer x, x ≥ x². However, it is not symmetric or transitive since there are counterexamples where the conditions are not met for some values of x and y.

b. R₂: The relation R₂ states that (x, y) ∈ R₂ if and only if x is a multiple of y. This relation is an equivalence relation since it satisfies reflexivity, symmetry, and transitivity. Any integer x is a multiple of itself (reflexivity), if x is a multiple of y then y is a multiple of x (symmetry), and if x is a multiple of y and y is a multiple of z, then x is a multiple of z (transitivity).

c. R₃: The relation R₃ states that (x, y) ∈ R₃ if and only if xy ≥ 1. This relation is not an equivalence relation since it fails reflexivity. For example, when x = 0, xy = 0 for any y, and 0 is not greater than or equal to 1.

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Answer:A) To determine which box holds more cereal, we can calculate the volume of each box.

The original box has dimensions of 8cm by 3cm by 11cm, so its volume is:

Volume of original box = 8cm * 3cm * 11cm = 264 cm³

The new box has dimensions of 10cm by 10cm by 3cm, so its volume is:

Volume of new box = 10cm * 10cm * 3cm = 300 cm³

Therefore, the new box holds more cereal, as it has a larger volume of 300 cm³ compared to the original box's volume of 264 cm³.

B) To determine which box requires more material to make, we can calculate the surface area of each box.

The original box has dimensions of 8cm by 3cm by 11cm, so its surface area is:

Surface area of original box = 2(8cm * 3cm) + 2(8cm * 11cm) + 2(3cm * 11cm) = 330 cm²

The new box has dimensions of 10cm by 10cm by 3cm, so its surface area is:

Surface area of new box = 2(10cm * 10cm) + 2(10cm * 3cm) + 2(10cm * 3cm) = 340 cm²

Therefore, the new box requires more material to make, as it has a larger surface area of 340 cm² compared to the original box's surface area of 330 cm².

Step-by-step explanation: