Peter says, "If you subtract 13 from my number and multiply the difference by -3, the result is
- 69." What is Peter's number?

Answer:

\(\sqrt{\frac{3V}{\pi h} }=r\)

Step-by-step explanation:

The formula for volume of a cone is V = 1/3πr^2h, where V is the volume, r is the radius, and h is the height.

We can express r in terms of the other three parts of the formula by isolating it:

\(V=1/3\pi r^2h\\\\3V=\pi r^2h\\\\\frac{3V}{h\pi }=r^2\\ \\\sqrt{\frac{3V}{h\pi } }=r^\)

We can check first by choosing a value for r and h, which will allow us to find a volume.  Then, we can rearrange the numbers using the formula expressing r in terms of the volume, height, and pi

For example, using a radius that is 2 units and height that is 5\(V=1/3\pi (2)^2*5\\V=1/3\pi *4*5\\V=20/3\pi \\V=20.94395102\) units will give a volume of 20/3π (i.e., 20.94395102) units:

Now, we can plug in our numbers for the formula expressing r in terms of volume, height, and pi and check that we get a radius of 2:

\(\sqrt{(\frac{3*20/3\pi }{5\pi }) } =2\\\sqrt{(\frac{20\pi }{5\pi }) }=2\\ \sqrt{4}=2\\ 2=2\)

Thus, our formula expressing r in terms of V, h, and π is correct

The double intergral value is 288 units

By using symmetry, we can simplify the double integral to only consider the region where x is positive. Therefore, we can rewrite the integral as 2 times the integral of 9xyx⁴ over the region 0 ≤ x ≤ 2, 0 ≤ y. Evaluating this integral gives us 288.

Symmetry allows us to take advantage of the fact that the function 9xyx⁴ is an odd function in y, meaning that it flips signs when y is negated. Therefore, we can split the region of integration into two halves, one where y is positive and one where y is negative.

Because the integrand changes sign in the negative y half, we can ignore it and simply double the integral of the positive y half to get the total value. This simplifies the computation and reduces the possibility of errors.

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Answer:

I think it's d

Step-by-step explanation:

Nit 100% sure but if nit its b

The number sentence that matches the given word problem is:

A. 7-6 = 1

The word problem asks how much more weight the large crane can lift than the small crane. To find the difference, we subtract the weight capacity of the small crane (6 tons) from the weight capacity of the large crane (7 tons).

Therefore, 7 - 6 = 1, which means the large crane can lift 1 ton more than the small crane.

Answer:

12

Step-by-step explanation:

The median is the middle value when all values are listed in increasing order.

Here, there are 25 values.

The middle value is the 13th value.

There are 2 size 8.

Then there are 9 size 10.

2 + 9 = 11

That accounts for the first 11 values in increasing order.

Then there are 8 size 12.

Since we need the 13th value, and we already have 11 values, we need the second size 12.

The 13th value is size 12, so the median is size 12.

Answer: 12

The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.

Given parallelogram A B C D below, DE = 31 If EB = x - 7.

By the definition, then the equation is given as,

EB = DE

x - 7 = 31

Simplify the equation, then we have

x - 7 = 31

x = 31 + 7

x = 38

The value of the variable 'x' is 38.

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Answer:

c. the slope of the line

Step-by-step explanation:

because i just know

The direct variation has the same value or expression as that of the slope of a straight line given by - m = y/x.

The general equation of a straight line is -

y = mx + c

where m is slope of line

c is the y - intercept

Given is the direct variation of a quantity.

The direct variation of a quantity in the equation of a straight line is represented by the slope of a straight line. Mathematically, we can write -

y = mx + c

for y - intercept = [c] = 0, we can write -

y = mx

m = y/x

which is the representation of direct variation.

Therefore, the direct variation has the same value or expression as that of the slope of a straight line given by - m = y/x.

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Using the information provided, it appears that your neighbor will not save money by picking up the soil himself as its total cost is $103.86 as opposed to cost of delivery $30.

Here is a detailed breakdown of the calculations and assumptions made:

The area of the yard is estimated to be around 7,200 sq.ft. Assuming a 4 inch layer of topsoil, this requires 4 cubic yards (1 cubic yard = 27 cubic feet).

The cost of the soil delivery is $30 per truckload (up to 18 cubic yards). So the delivery cost for 4 cubic yards of soil would be $30.

The cost of topsoil per cubic yard is $18. Thus, the total cost of the topsoil is $72.

The weight of topsoil is 2000 pounds per cubic yard, so the total weight of the soil is 8,000 pounds (4 cubic yards x 2000 pounds).

The pickup truck's payload capacity is 1800 pounds, so the truck can only transport 1/4 of the total weight of the soil (1800/8000 = 0.225). Thus, it would require 4 trips to transport the soil, and the total trip distance is 36 miles (9 miles x 4 trips).

The truck gets 17 miles per gallon, so it would require 2.1 gallons of gas for each trip (36 miles/17 mpg = 2.12). The total amount of gas needed for the 4 trips is 8.4 gallons (2.1 gallons x 4 trips). The cost of gas per gallon is assumed to be $3.79, so the total cost of gas for the 4 trips is $31.86.

Thus, the total cost of picking up the soil himself is $31.86 + $72 = $103.86. This is higher than the cost of delivery which is only $30, so it would be better to pay for delivery.

To conclude, your neighbor will not save money by picking up the soil himself, and it is recommended that he pays for delivery.

Note: The question is incomplete. The complete question probably is: He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this. Here is (most of) the information you asked for:

Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery? Detail all your assumptions and calculations, and clearly write out your final conclusions.

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The true statement about the number 2^(-3) is that it is equal to 0.125, not -8

I'm sorry, but the statement "2-^3 is equal to -8" is not true. The correct calculation for 2 raised to the power of -3 is as follows:

2^(-3) = 1 / (2^3) = 1 / 8 = 0.125

The exponent of -3 signifies that we are calculating the reciprocal or inverse of the base number raised to the power of 3. In this case, the base number is 2, and raising it to the power of -3 results in the reciprocal, which is 1/8 or 0.125.

It's important to note that negative exponents indicate the use of fractions or decimals in the calculations. In this context, the negative exponent signifies the inverse or reciprocal of the base number raised to a positive exponent.

Therefore, the true statement about the number 2^(-3) is that it is equal to 0.125, not -8.

It's crucial to understand the concept of exponentiation and the rules associated with it. Negative exponents have specific meanings and should be handled correctly to avoid mathematical errors or misunderstandings.

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Answer:

1.25 hours.

68.75 miles from the city

Step-by-step explanation:

Eltan's train (E) is travelling 65mph west.

Dmitri's train (D) is travelling 55mph west.

In terms of vectors, we can write E as 65E and D as 55W

The miles travelled by each is a function of time, T, in hours.

Each train's distance is:

 E:  T*65E

 D:  T*55W

They are 150 miles apart.  They will meet with the combined miles travelled is 150 miles.

 150 miles = T*65E + T*55W

150 miles = T(120 miles/hour)

T = (150 miles/120 miles/hour)

T = 1.25 hours

Make Demitri's train mile 0 and Eitan's train at mile 150 at the start.

They will have travelled the following miles in 1.25 hours:

Demitri:  (1.25hr)(55 m/hr) = 68.75 miles

Eitan:      (1.25hr)(65 m/hr) = 81.25 miles

Total = 150 miles

Dimitri is headed away from the city.  After 1.25 hours, his train will have travelled 68.75 miles when he sees Eitan passing him on the adjacent track (hopefull) headed into the city.  They meet 68.75 miles from the city.

Answer:

question one is B and question 2 is C

Step-by-step explanation:

Answer:

y=4/3x +7

Step-by-step explanation:

4x - 3y = -21

Move 4x to the other side

-3y = -21 -4x

Next divide the other side by -3

y= 7 +4/3x

Move numbers around

y = 4/3x + 7

1. MULTIPLE-CHOICE CONSTRAINT - c.; 2. COREQUISITE CONSTRAINT - e.; 3. K OUT OF N ALTERNATIVES CONSTRAINT - b.; 4. CONDITIONAL CONSTRAINT - a.; 5. MUTUALLY EXCLUSIVE CONSTRAINT - d.

1. MULTIPLE-CHOICE CONSTRAINT - an example of the this is c. A constraint requiring that the sum of two or more binary variables equals one. Thus, any feasible solution makes a choice of which variable to set equal to one.

2. COREQUISITE CONSTRAINT - This is associated with e. A constraint requiring that two binary variables be equal and that they are both either in or out of the solution.

3. K OUT OF N ALTERNATIVES CONSTRAINT - This corresponds to b. A constraint requiring that the sum of n binary variables equals k.

4. CONDITIONAL CONSTRAINT - This matches with a. A constraint involving binary variables that does not allow certain variables to equal one unless certain other variables are equal to one.

5. MUTUALLY EXCLUSIVE CONSTRAINT - This fits the description of d. A constraint requiring that the sum of two or more binary variables be less than or equal to one. Thus, if one of the variables equals one, the others must equal zero. However, all variables could equal zero.

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Answer:

Obtuse

Step-by-step explanation:

x = missing angle

20+30+x=180

50+x=180

x=130

90<130

Thus, the triangle is obtuse

The matrix of a transformation for the reflection in the line y = -x is given by A = [ -1 0 0 -1 ] [ 0 1 -1 0 ] [ 0 -1 1 0 ] [ 0 -1 -1 0 ]. This matrix reflects points across the line y = -x and is known as a line reflection.

To understand how this matrix works, let's consider a point P(x, y). We can represent this point as a vector [x y]. To reflect this point across the line y = -x, we must multiply the vector by the transformation matrix A. This results in the vector [y -x]. Notice that this new vector is a reflection of the original vector in the line y = -x.

For example, let's consider points P(3, 4). We can represent this point as the vector [3 4]. To reflect this point across the line y = -x, we must multiply the vector by the transformation matrix A. This results in the vector [4 -3]. Notice that this new vector is a reflection of the original vector in the line y = -x.

Therefore, the matrix A of T for the given transformation (reflection in the line y = -x) is given by A = [ -1 0 0 -1 ] [ 0 1 -1 0 ] [ 0 -1 1 0 ] [ 0 -1 -1 0 ].

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Answer:

72

Step-by-step explanation:

If we find the average for both companies, it is 72, therefore there are two rows each with 72 cadets

Answer:

the answer is 16 please make me brainliest :> thx uuu

(a) Span (s) = {a₁v₁+a₂v₂+.........aₙvₙ} \(a_i\) ∈ field.

(b)  A basic for V is linearly independent spanning set of V.

(c) A subset of V which its self is a vector space is called subspace of V.

Let V be a vector space and S be a set of vectors on i. e.

s{V₁,V₂,V₃..........Vₙ} then,

(a) Span (S) is set of all possible linear combinations of vector in S i.e.

Span (s) = {a₁v₁+a₂v₂+.........aₙvₙ} \(a_i\) ∈ field

i. e. \(a_i\) are scalars from field on which vector space V is defined.

(b) A basic for V is linearly independent spanning set of V i.e.

Let B  be set of vectors in V. then B is a Basic of V if

(i) B is linearly independent set

(ii) Span (B) = V

(C) A subset of V which its self is a vector space is called subspace of V.

Therefore, Span (s) = {a₁v₁+a₂v₂+.........aₙvₙ} \(a_i\) ∈ field.

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Incomplete Question:

for a vector space v and a finite set of vectors s = {v1, · · · , vn} in v , copy down the definitions for

a) span(S).

b) a basis of b.

c) a subspace of V.

It is letter B, if you double this you will get this question

It is true to say that a subset of data values is a sample.

There are two types of sampling techniques:

Probability (simple random sampling, stratified sampling, etc.) and non-probability (snowball sampling, purposive sampling, etc.) sampling techniques.

Meanwhile, the population refers to the total number of items. It can be items, people, etc. For example, the population would be all the students in an area or all the employees in a company.

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Complete question is;

Maya is choosing between several pay plans for her new job. If she usually has monthly sales of about $5,000, which plan would allow Maya to earn the most money in a month?

Plan, Monthly base salary, Commission rate

A, $500, 8%

B, $600, 7%

C, $700, 6%

D, $800, 5%

Options:

A. plan A

B. plan B

C. plan C

D. plan D

Answer:

Option D - Plan D

Step-by-step explanation:

For plan A, at 8% commission rate,her monthly pay would be, 500 + 8%*5,000 = $900

For plan B, at 7% commission rate, her monthly pay would be; 600 + 7%*5,000 = $950

For plan C, at 6% commission rate, her monthly pay would be;700 + 6%*5,000 = $1000

For plan D, at 5% monthly commission rate, her monthly pay = 800 + 5%*5,000 = $1050

So the plan that allows maya earn the most is the highest which is plan D

Answer:

Plan D

Step-by-step explanation:

The areas of the four triangular sections in the trapezoidal cornfield in Iowa are: Section 1: 7200 sq m, Section 2: 10800 sq m, Section 3: 10800 sq m, Section 4: Approximately 14988.86 sq m

To find the areas of the triangular sections, we need to first find the lengths of the diagonals IW and OA.
Given that IO is parallel to WA, we can use the properties of trapezoids to find the length of the diagonal IW.
Since the area of the trapezoidal field is 18000 sq m, we can use the formula for the area of a trapezoid:
Area = (a + b) * h / 2
where a and b are the lengths of the parallel sides, and h is the height (the distance between the parallel sides).
In this case, a = 100 m, b = 150 m, and the area = 18000 sq m. We can plug these values into the formula and solve for the height:
18000 = (100 + 150) * h / 2
36000 = 250 * h
h = 36000 / 250
h = 144 m
Now that we have the height, we can use the properties of triangles to find the length of the diagonal IW.
In a right triangle with one leg being the height (h) and the hypotenuse being the diagonal (IW), we can use the Pythagorean theorem:
IW² = h² + b²
IW² = 144² + 100²
IW² = 20736 + 10000
IW² = 30736
IW ≈ 175.21 m
Similarly, we can find the length of the diagonal OA using the same steps:
OA² = h² + a²
OA² = 144² + 150²
OA² = 20736 + 22500
OA²= 43236
OA ≈ 207.93 m
Now, we can find the areas of the triangular sections.
Section 1: Triangle IOW
The base is IO, which is 100 m, and the height is h, which is 144 m. Using the formula for the area of a triangle:
Area1 = (base * height) / 2
Area1 = (100 * 144) / 2
Area1 = 7200 sq m
Section 2: Triangle IWA
The base is WA, which is 150 m, and the height is h, which is 144 m. Using the formula for the area of a triangle:
Area2 = (base * height) / 2
Area2 = (150 * 144) / 2
Area2 = 10800 sq m
Section 3: Triangle OWA
The base is WA, which is 150 m, and the height is h, which is 144 m. Using the formula for the area of a triangle:
Area3 = (base * height) / 2
Area3 = (150 * 144) / 2
Area3 = 10800 sq m
Section 4: Triangle OAI
The base is OA, which is approximately 207.93 m, and the height is h, which is 144 m. Using the formula for the area of a triangle:
Area4 = (base * height) / 2
Area4 = (207.93 * 144) / 2
Area4 ≈ 14988.86 sq m
The areas of the triangular sections are as follows:
- Section 1: 7200 sq m
- Section 2: 10800 sq m
- Section 3: 10800 sq m
- Section 4: Approximately 14988.86 sq m
To find the areas of the triangular sections in the trapezoidal cornfield in Iowa, we first need to find the lengths of the diagonals IW and OA. By using the formula for the area of a trapezoid, we can determine the height of the trapezoid, which is 144 m. Using the Pythagorean theorem, we can find the lengths of the diagonals IW and OA. IW is approximately 175.21 m, while OA is approximately 207.93 m. Next, we can calculate the areas of the triangular sections. Section 1 has a base of 100 m and a height of 144 m, resulting in an area of 7200 sq m. Section 2 and Section 3 both have a base of 150 m and a height of 144 m, resulting in areas of 10800 sq m each. Finally, Section 4 has a base of approximately 207.93 m and a height of 144 m, resulting in an area of approximately 14988.86 sq m.
In conclusion, the areas of the four triangular sections in the trapezoidal cornfield in Iowa are:
- Section 1: 7200 sq m
- Section 2: 10800 sq m
- Section 3: 10800 sq m
- Section 4: Approximately 14988.86 sq m

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Answer:

Y=8

Step-by-step explanation:

The difference between the number Alice hit and 6 is X - 6.  Twice that would be 2(X-6).  So Y = 2(X-6).  We also know that X + Y = 18 so we have 2 equations:

Y = 2(X-6)

X+Y = 18

Let's take the second equation and solve for Y in terms of X

Y = 18 - X

Now take that result and substitute that back into the first equation that starts with Y, because now you know that Y is also equal to 18 - X, now you have:

18 - X = 2(X - 6)

Let's solve for X

18 - X = 2X - 12

18 - 3X = - 12

- 3X = - 30

X = 10 <--number of home runs Alice Hit

That leaves us with Y = 8  <---number of home runs Peter hit

Go back to the original question and make sure the answer fits.  The difference between 10 and 6 is 4 and twice that is 8, the number Peter hit.  10 + 8 = 18.  Good to go!

Answer:

1996

Step-by-step explanation:

because the line chart started st 1996

Answer:

Step-by-step explanation:

(9). Reflection across the x-axis keeps the same x-coordinate and y-coordinate is the opposite to original ( x , y ) ------> ( x , - y )

(10).  Reflection across the y-axis keeps the same y-coordinate and x-coordinate is the opposite to original ( x , y ) ------> ( - x , y )

(11). Translation along the vector < 0, 2 >  means that each point of triangle moves 2 units UP  ( x , y ) ------> ( x , y + 2 )

(12). Translation along the vector < 3, - 4 >  means, that each point of triangle moves 3 units to the RIGHT and 4 units DOWN  ( x , y ) ------> ( x + 3 , y - 4 )

(13). ( x , y ) ------> ( - x , - y )

(14). ( x , y ) ------> ( - y , x )  

Answer:

Step-by-step explanation:

To find the surface area of a triangular prism, you need to calculate the areas of its individual faces and add them together. A triangular prism has five faces: two triangular bases and three rectangular lateral faces.

Here's how you can calculate the surface area step by step:

1.Calculate the area of one of the triangular bases:

Measure the length of the base of the triangle (b).

Measure the height of the triangle (h).

Use the formula for the area of a triangle: A = (1/2) * b * h.

Multiply the result by 2 since there are two triangular bases.

2.

Calculate the area of each of the three rectangular lateral faces:

Measure the length of one side of the triangle (a).

Measure the height of the triangle (h).

Multiply the length (a) by the height (h) to find the area of each rectangular face.

Sum up the areas of all three rectangular faces.

3.Add the areas of the two triangular bases and the three rectangular lateral faces to get the total surface area of the triangular prism.

The formula for the surface area (SA) of a triangular prism is:

SA = 2 * A_base + 3 * A_lateral

Where:

A_base is the area of one triangular base.

A_lateral is the combined area of the three rectangular lateral faces.

By following these steps and using the appropriate measurements, you can determine the surface area of a triangular prism.

The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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the Nash equilibrium is not necessarily the best or most desirable outcome for the players involved. It simply represents a stable state where no player has an incentive to unilaterally deviate from their chosen strategy.

To determine the Nash equilibria in a game, we need to analyze the strategies of each player and identify the combinations of strategies where no player has an incentive to unilaterally deviate.

Given the options:

1. (P1=Shot, P2=Shot)

2. (P1=No shot, P2=No shot)

3. (P1=Shot, P2=No shot)

4. (P1=No shot, P2=Shot)

Let's analyze each combination:

1. (P1=Shot, P2=Shot):

If both players choose to shoot, they both face the risk of being shot and getting injured. Neither player has an incentive to deviate from this strategy, as changing to "No shot" would expose them to the risk of being shot without being able to retaliate. Therefore, (P1=Shot, P2=Shot) is a Nash equilibrium.

2. (P1=No shot, P2=No shot):

If both players choose not to shoot, they avoid the risk of being injured. Again, neither player has an incentive to unilaterally deviate from this strategy, as changing to "Shot" would expose them to the risk of being injured without gaining any advantage. Therefore, (P1=No shot, P2=No shot) is a Nash equilibrium.

3. (P1=Shot, P2=No shot):

If Player 1 chooses to shoot while Player 2 chooses not to shoot, Player 1 has an advantage and can potentially eliminate Player 2 without being injured. In this scenario, Player 2 may have an incentive to deviate from "No shot" and switch to "Shot" to protect themselves. Therefore, (P1=Shot, P2=No shot) is not a Nash equilibrium.

4. (P1=No shot, P2=Shot):

Similarly, if Player 1 chooses not to shoot while Player 2 chooses to shoot, Player 2 has an advantage and can potentially eliminate Player 1 without being injured. In this scenario, Player 1 may have an incentive to deviate from "No shot" and switch to "Shot" to protect themselves. Therefore, (P1=No shot, P2=Shot) is not a Nash equilibrium.

Based on the analysis, the Nash equilibria in this game are:

- (P1=Shot, P2=Shot)

- (P1=No shot, P2=No shot)

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For the function f(z) = z² + z - 2, the poles are found, and the residues at each pole z = -3/2 is a pole of order 6.

In part (a), we will evaluate the integral of the function x²+x+1. To do this using contour integration, we need to find a contour C that encloses the singularities of the function. However, this particular function is a polynomial, which means it is entire and has no singularities. Therefore, the integral of x²+x+1 over any closed contour C is zero.

In part (b), we are given the function f(z) = (3+2sinθ)/(2z+3)^6 and asked to evaluate the integral of f(z) over a circle with radius 4 (|z| = 4). To accomplish this, we can use the residue theorem. First, we need to find the poles of the function, which occur when the denominator (2z+3)^6 is equal to zero. Solving this equation, we find that z = -3/2 is a pole of order 6.

To determine the residues at each pole, we can expand the function f(z) in a Laurent series around the pole z = -3/2. The residue can be found by taking the coefficient of the (z - (-3/2))^-1 term. Once the residues are calculated, we can apply the residue theorem, which states that the integral of f(z) over the circle C is equal to 2πi times the sum of the residues. By substituting the values into the formula, we can evaluate the integral over the given contour.

In conclusion, using contour integration, we evaluated the integral of x²+x+1 and found it to be zero. We also determined the poles and residues for the function f(z) = z² + z - 2 and used the residue theorem to evaluate the integral of f(z) over a circle with radius 4.

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The area of the region enclosed by the given curves is 85.25.

The region enclosed by the given curves and the decision of whether to integrate with respect to x or y are shown below:

To find the area of the region enclosed by the given curves, we'll integrate with respect to y since the curves are defined in terms of y.

So, we use the following formula to find the area of the region:

∫[b,a] f(y)dy, where b and a are the y-coordinates of the intersection of the curves.

2y = 4√x

Squaring both sides: (2y)² = (4√x)²4y² = 16x, we get;

x = y²/4 …(1)

y = 3 is a horizontal line so we can use this to find the intersection with curve (1).

Substituting y = 3 in equation (1), we get;

x = 3²/4

= 2.25y + 1/2

x = 5

Substituting x = 5 - 2y in equation (1)

2y = 4√(5 - 2y)

Squaring both sides of the equation:

(2y)² = (4√(5 - 2y))²

4y² = 16(5 - 2y)

4y² = 80 - 32y

4y² + 32y - 80 = 0

Dividing by 4: y² + 8y - 20 = 0

Using the quadratic formula; y = (-b ± √(b² - 4ac))/2a;

where a = 1, b = 8, and c = -20

We get; y = (-8 ± √144)/2

= (-8 ± 12)/2

= -10 or 2

Therefore, the y-limits are from -10 to 3.

To find the area, we integrate using the limits found above.

∫[3,-10] (y²/4)dy

=(1/12)y³[3,-10]

=(1/12)[(3)³ - (-10)³]

=(1/12)(27 + 1000)

= 85.25

Therefore, the area of the region enclosed by the given curves is 85.25.

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Answer:

1/3 of 6=2

1/4 of 20 =5

Step-by-step explanation:

You divide them