How do I do this step by step

The critical points are (t, y) = (t, 0) and (t, -4c/5).

To find the partial derivatives, we need to differentiate f(t, y) with respect to each variable separately.

f1(t, y) = ∂f/∂t = 0 (since there is no t term in the function)

fy(t, y) = ∂f/∂y = -12cy^3 + 15y^4

fz(t, y) = ∂^2f/∂t∂z = 0 (since there is no z term in the function)

fy(t, y) = ∂^2f/∂y∂z = 0 (since there is no z term in the function)

So, 2. - f1(,y) fy(x, y) = = frz(, y) = fry(x, y) = 0 - 12cy^3 + 15y^4 = 0  (since f1(,y) and frz(, y) and fry(x, y) are all 0)

Therefore, -12cy^3 + 15y^4 = 0

Factor out y^3:

y^3(-12c + 15y) = 0

This gives us two solutions: y = 0 or -4c/5.

So, the critical points are (t, y) = (t, 0) and (t, -4c/5).

Learn more about partial derivatives :https://brainly.com/question/31280533

#SPJ11

The probability that a randomly chosen student is a male who enjoys reading P(male and enjoys reading) ≈ 0.261

To calculate the probability that a randomly chosen student is a male who enjoys reading, you need the number of males who enjoy reading divided by the total number of students.

The probability that a randomly chosen student is a male who enjoys reading can be found by dividing the number of males who enjoy reading by the total number of students.

From the table, we see that there are 30 males who enjoy reading and a total of 115 students. Therefore, the probability is:

P(male and enjoys reading) = 30/115

Rounding to the nearest thousandth, we get:

Therefore, The probability that a randomly chosen student is a male who enjoys reading P(male and enjoys reading) ≈ 0.261

To know more about probability refer here:

https://brainly.com/question/30446665

#SPJ11

A histogram of the data distribution for the number of new plants is shown in the image below.

In this scenario and exercise, you are required to create a histogram to show the data distribution with respect to the number of new plants. First of all, we would determine the midpoint, absolute frequency, relative frequency, and cumulative frequency;

Midpoint                                      Absolute frequency      Rel. frequency

[0, 2] = (0 + 2)/2 = 1                        3 + 2 = 5                        0.128205

[2, 4] = (2 + 4)/2 = 3                        2 + 3 = 5                        0.128205

[4, 6] = (4 + 6)/2 = 5                        2 + 3 = 5                        0.128205

[6, 8] = (6 + 8)/2 = 7                                    2                        0.051282

[8, 10] = (8 + 10)/2 = 9                     3 + 4 = 7                        0.179487

[10, 12] = (10 + 12)/2 = 11                  4 + 3 = 7                        0.179487

[12, 14] = (12 + 14)/2 = 13                  1 + 2 = 3                        0.076923

[14, 16] = (14 + 16)/2 = 15                  3 + 2 = 5                        0.128205

Mathematically, the relative frequency of a data set can be calculated by using this formula:

Relative frequency = absolute frequency/total frequency × 100

Relative frequency = 5/39 × 100 = 0.128205

For the cumulative frequency, we have:

0.128205

0.128205 + 0.128205 = 0.25641

0.25641 + 0.128205 = 0.384615

0.384615 + 0.051282 = 0.435897

0.435897 + 0.179487 = 0.615385

0.615385 + 0.179487 = 0.794872

0.794872 + 0.076923 = 0.871795

0.871795 + 0.128205 = 1

Read more on histogram here: brainly.com/question/17046231

#SPJ4

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: x² + y²=6.25²

Step-by-step explanation:

Formula for a circle:

(x-h)²+(y-k)²=r²

where (h, k) is the center    yours: (0,0)

r is the raidus                                 r=6.25

Plug in:

x² + y²=6.25²

The total revenue over the two days is GH¢305.

We can represent the number of items sold and the cost for each item in matrices as follows:

[tex]\begin{equation}A = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix}\end{equation}[/tex]

Here, matrix A represents the number of items sold on each day, and matrix B represents the cost per item. To find the total revenue, we need to multiply the two matrices and then take the sum of all the elements in the resulting matrix:

[tex]\begin{equation}A \cdot B = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix} = \begin{bmatrix} 95 \ 140 \end{bmatrix}\end{equation}[/tex]

Therefore, the total revenue over the two days is GH¢(95 + 140) = GH¢305.

For more questions like Matrix click the link below:

https://brainly.com/question/28180105

#SPJ11

Answer: 15 feet

Step-by-step explanation:

The percent change in carbon dioxide in the atmosphere between 2015 and 2019 is 3 %

the percent change in carbon dioxide According to a WMO report in 2019 greenhouse gas concentrations, it was discovered that carbon dioxide growth rates were nearly 20% higher than the previous five years and that the percentage increase from 2015 and 2019 was approximately 2.88%. which is approximately 3 %.

carbon dioxide in the atmosphere in 2015 = 399 parts per million

carbon dioxide in the atmosphere in 2019 = 410.5 parts per million

Percentage change can be calculate by using

% change = [tex]\frac{Final - initial }{initial}[/tex] × 100

% change = [tex]\frac{410.5 - 399}{399} \[/tex] × 100

% change = 2.88 %

Hence, the percent change in carbon dioxide in the atmosphere between 2015 and 2019 is 3%

To know more about percentage change click here :

https://brainly.com/question/31060287

#SPJ4

The correct answer is b. 3%.

To answer this question, we need to compare the concentration of carbon dioxide in the atmosphere between 2015 and 2019. The concentration of carbon dioxide is measured in parts per million (ppm). In 2015, the concentration of carbon dioxide in the atmosphere was around 400 ppm, while in 2019, it was around 414 ppm.

To calculate the percent change between these two years,

Percent Change = [(New Value - Old Value) / Old Value] x 100%

Percent Change = [(414 - 400) / 400] x 100%

Percent Change = 3.5%

Therefore, the correct answer is b. 3%.

To know more about atmosphere here

https://brainly.com/question/22732099

#SPJ4

You would have to receive an approximately 8.696% increase in pay to regain your original salary after an 8% decrease.

To find the percentage increase in pay needed to regain your original salary after an 8% decrease, follow these steps:

1. Assume your original salary is 100%. After an 8% decrease, your salary becomes 100% - 8% = 92%.

2. Calculate the difference between your original salary (100%) and your current salary (92%). The difference is 100% - 92% = 8%.

3. To find the percentage increase needed to regain your original salary, divide the difference (8%) by your current salary (92%): 8% / 92% = 0.08696.

4. Multiply the result by 100 to convert it to a percentage: 0.08696 (100) = 8.696%.

So, you would have to receive an approximately 8.696% increase in pay to regain your original salary after an 8% decrease.

To know more about "Percentage" refer here:

https://brainly.com/question/10893287#

#SPJ11

2.25 liters of solution in all is there in the test tubes. So, the correct option is 2.25 l.

The total volume of solution in the 15 test tubes can be calculated by multiplying the volume of one test tube by the number of test tubes:

Total volume = 15 test tubes × 150 milliliters/test tube

Total volume = 2,250 milliliters

However, the question asks for the answer in liters, so we need to convert milliliters to liters by dividing by 1,000:

Total volume = 2,250 milliliters ÷ 1,000

Total volume = 2.25 liters

Therefore, there are 2.25 liters of solution in all the test tubes.

Know more about solution here:

https://brainly.com/question/25326161

#SPJ11

Answer:

Step-by-step explanation:

5^2 + x^2 = 8^2

25 + x^2 = 64

x = 6.2

Answer :The maximum profit is $1,650 when making 5 organza dresses and no lace dresses per week.

Explanation:

Let x represent the number of organza dresses, and y represent the number of lace dresses.

The time constraint for cutting:
3x + 6y ≤ 30

The time constraint for sewing:
6x + 3y ≤ 33

The profit function to maximize is:
P(x, y) = 330x + 190y

Using these constraints,
3x + 6y ≤ 30
6x + 3y ≤ 33
x ≥ 0
y ≥ 0

Optimal solution:

The corner points of the feasible region are (0,0), (0,5), (3,3), and (5,0). Calculate the profit for each point:

P(0,0) = 0
P(0,5) = 950
P(3,3) = 1,320
P(5,0) = 1,650

The maximum profit is $1,650 when making 5 organza dresses and no lace dresses per week.

Answer:

There is an outlier at 28.

Tina received $12.30 for recycling her cans last week.

To find how much money Tina got for her cans last week, we need to find the total number of cans she collected and then multiply that by 0.05 (since she gets 5 cents per can).

On Wednesday and Thursday, Tina collected 37 cans each day, for a total of 2 x 37 = 74 cans.

On Tuesday, Friday, Saturday, and Sunday, she collected 43 cans each day, for a total of 4 x 43 = 172 cans.

The total number of cans collected is 74 + 172 = 246 cans.

To find the total amount of money Tina received, we multiply 246 by 0.05, which gives us:

246 x 0.05 = $12.30

Therefore, Tina received $12.30 for recycling her cans last week.

Learn more about Money

brainly.com/question/28784237

#SPJ11

The fraction of the cookies do they still need to made after Cameron and Lindsey made 80 cookies is 1/2.

Fractions are referred to as the components of a whole in mathematics. A single thing or a collection of objects might be the entire. When we cut a slice of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Roman. "Fractus" means "broken" in Latin.

The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form. A piece or sector of any quantity is another name for the fraction.

Total cookies to be made is 160

Out of which Cameron made 2/5 of the cookies so,

2/5 x 160 = 64 cookies are made by Cameron

Lindsey made 16 cookies

So total cookies that still need to be made is,

= 160 - (64 + 16) = 80

The fraction of cookies still need to made is 80/160 = 1/2 .

Learn more about Fraction of cookies:

https://brainly.com/question/17447744

#SPJ4

In linear equation, The sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches.

What in mathematics is a linear equation?

An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation.

                           The above is sometimes called a "linear equation in two variables" where x and y are variables. Equations in which the variable is power 1 are called linear equations. axe+b = 0 is a one-variable example where a and b are real numbers and x is a variable. 

A triangle with sides 12 feet, 16 feet, and 18 feet on a drawing where 1 inch = 2 feet.

Then, 1 feet of original triangle = 1/2 inch on drawing.

Now, the sides of the triangle on the drawing are

12 feet = 1/2 * 12 = 6 in

12 feet = 1/2 * 16 = 8 in

12 feet = 1/2 * 18 = 9 in

Hence, the sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches..

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

The radius of convergence R is 1/4 and the interval of convergence is (-6.25, -5.75) for the power series

∑((-4[tex])^n[/tex]) * (-(x + 6[tex])^n[/tex]) / sqrt(n)
To find the radius of convergence (R) and interval of convergence for the power series ∑((-4[tex])^n[/tex]) * (-(x + 6[tex])^n[/tex]) / sqrt(n)

where n starts from 1 to infinity,

We can use the Ratio Test.
Step 1: Apply the Ratio Test
We want to find the limit as n approaches infinity of the absolute value of the (n+1)th term divided by the nth term:
lim (n→∞) |((-4[tex])^{(n+1)[/tex] * (-(x + 6)^(n+1)) / sqrt(n+1)) / ([tex](-4)^n[/tex] * (-(x + 6[tex])^n[/tex]) / sqrt(n))|
Step 2: Simplify the expression
The limit simplifies to:
lim (n→∞) |((-4)(x + 6))/sqrt((n+1)/n)|
Step 3: Find when the limit is less than 1
For the series to converge, the limit must be less than 1:
|(-4)(x + 6)| / sqrt((n+1)/n) < 1
As n approaches infinity, (n+1)/n approaches 1, so the expression simplifies to:
|-4(x + 6)| < 1
Step 4: Determine the radius of convergence (R)
Divide both sides by 4:
|-(x + 6)| < 1/4
The radius of convergence, R, is 1/4.
Step 5: Determine the interval of convergence
To find the interval of convergence, solve for x:
-1/4 < (x + 6) < 1/4
-1/4 - 6 < x < 1/4 - 6
-6.25 < x < -5.75
Thus, the interval of convergence is (-6.25, -5.75).
In summary, the radius of convergence R is 1/4 and the interval of convergence is (-6.25, -5.75).

To know more about Power series:

https://brainly.com/question/29888415

#SPJ11

A graph of the function p(x) and the function p(x + 2) is shown below.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided above, we can determine the value of a as follows:

f(x) = a(x - h)² + k

0 = a(-3 - 0)² + 4

0 = 9a + 4

a = -4/9

Therefore, the required quadratic function is given by:

f(x) = a(x - h)² + k

p(x) = y = -4/9(x - 0)² + 4

p(x + 2) = -4/9(x + 2)² + 4

Read more on vertex here: brainly.com/question/14946018

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The type of bankruptcy that typically affects a person's credit score for seven years is Chapter 7 bankruptcy.

Chapter 7 bankruptcy involves the liquidation of assets to pay off debts, and it remains on a person's credit report for up to seven years from the filing date. This can have a significant negative impact on a person's credit score and their ability to obtain credit in the future.

Chapter 9 bankruptcy is specifically designed for municipalities such as cities, towns, and counties, and it does not apply to individuals or affect personal credit scores.

Chapter 11 bankruptcy is primarily used by businesses to reorganize their debts and continue operating. While it can affect a business owner's personal credit if they have personal liability for the business debts, it does not have a specific time frame for how long it remains on a credit report. The impact on an individual's credit score can vary depending on the circumstances and how the bankruptcy is structured.

Hence the answer is Chapter 7.

Learn more about bankruptcy click;

https://brainly.com/question/30628707

#SPJ12

Answer:

Chapter 13

Step-by-step explanation:

it’s not on there but that’s the answer

Round the answer to the nearest mile: She is 398 miles from her starting position.

To solve this problem, we'll use the Law of Cosines.

Here are the steps to find the distance from the starting position:

1. Convert the given time to hours: 1 hour 45 minutes = 1.75 hours 2 hours 15 minutes = 2.25 hours

2. Calculate the distance traveled in each direction:

Distance1 = Speed × Time1 = 235 mi/h × 1.75 h = 411.25 miles

Distance2 = Speed × Time2 = 235 mi/h × 2.25 h = 528.75 miles

3. Use the Law of Cosines to find the distance between the starting position and her final position:

Distance = √(Distance1² + Distance2² - 2 × Distance1 × Distance2 × cos(35°))

4. Plug in the values and solve for the distance:

Distance = √(411.25² + 528.75² - 2 × 411.25 × 528.75 × cos(35°))

Distance ≈ 397.69 miles

5. Round the answer to the nearest mile: She is 398 miles from her starting position.

Learn more about Law of Cosines,

https://brainly.com/question/30766161

#SPJ11

(a) Discount amount is $6. (b) Maturity value is $2,200. (c) Current yield is 0.27%.

Here, we have,

A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.

A product may, for instance, be discounted by $10 from its list price or by 10% from its list price. A sales discount is a lower price that a company offers on a good or service.

Find out how to add discounts to invoices. A sales discount, usually referred to simply as a "discount," offers clients of a business a lower price on one or more of the goods or services being provided.

(a) Discount amount

= Maturity (face) value - Purchase price

=$2,200 - $2,194

=$6

(b) Maturity value

=Face value

=$2,200

(c) Current yield

=Discount amount / Purchase price

=$6 / $2,194

=0.0027, or 0.27%

Learn more about Discount amount here

brainly.com/question/20129073

#SPJ1

The tumor was approximately 1.47 grams six months before the first measurement. It would not have been detected by the instrument at that time.

Let M(t) be the mass of the tumor at time t (in months) since the first measurement. Since the rate of growth is proportional to the size of the tumor, we have the differential equation dM/dt = kM, where k is the proportionality constant. The general solution to this differential equation is M(t) = Me^(kt), where M is the initial mass of the tumor.

Using the given data, we have M(0) = 4.0 and M(4) = 6.76. Substituting these values into the equation M(t) = Me^(kt), we get the system of equations M = 4.0 and 6.76 = Me^(4k). Solving for M and k, we get M = 4.0 and k = ln(6.76/4.0)/4 ≈ 0.153. Thus, the equation for the mass of the tumor is M(t) = 4.0e^(0.153t).

To find the mass of the tumor six months before the first measurement (i.e., when t = -6), we plug in t = -6 into the equation M(t) = 4.0e^(0.153t) to get M(-6) ≈ 1.47 grams.

Finally, we check whether the tumor would have been detected at that time. Since the mass of the tumor was less than 1 gram at that time, the instrument would not have detected it.

For more questions like Differential equation click the link below:

https://brainly.com/question/14598404

#SPJ11

Each portion of Grace weighs 1/8 pound.

It gauges how much gravity is pulling on a body.

If Robert has 3/4 pound of Grace and he wants to divide it into six equal portions, we can find the weight of each portion by dividing 3/4 by 6:

(3/4) / 6 = (3/4) * (1/6) = 1/8

So each portion of Grace weighs 1/8 pound.

Learn more about division on:

https://brainly.com/question/25289437

#SPJ4

The null hypothesis (H0) for this situation would be that there is no difference in the proportion of male and female students with an overall GPA of 3.5 or higher.

The alternative hypothesis (Ha) would be that there is a difference in the proportion of male and female students with an overall GPA of 3.5 or higher.

Formally, we can write the hypotheses as:

H0: p_male = p_female (where p_male represents the proportion of male students with an overall GPA of 3.5 or higher, and p_female represents the proportion of female students with an overall GPA of 3.5 or higher)

Ha: p_male ≠ p_female

The president of the university can test these hypotheses using a hypothesis test for the difference in proportions. She can calculate the test statistic using the sample proportions and sample sizes for male and female students, and then compare it to the appropriate critical value or p-value based on the desired level of significance.

If the test results provide strong evidence against the null hypothesis, she can reject it and conclude that there is a statistically significant difference in the proportion of male and female students with an overall GPA of 3.5 or higher. If the test results do not provide enough evidence to reject the null hypothesis, she can fail to reject it and conclude that there is not enough evidence to suggest a difference in grades between males and females.

To learn more about null hypothesis refer here:

https://brainly.com/question/31525353

#SPJ11

Unfortunately, we don't have enough information to determine the area of the garden. We would need to know the dimensions of the backyard and/or the garden to calculate their areas.

To know more about calculating areas refer here:

https://brainly.com/question/30656333

#SPJ11

The volume of the cone with a height and radius both of 7 units is 359.24 cubic units.

In Mathematics and Geometry, the volume of a cone can be determined by using this formula:

V = 1/3 × πr²h

Where:

By substituting the given parameters into the formula for the volume of a cone, we have the following;

Volume of cone, V = 1/3 × 3.142 × 7² × 7

Volume of cone, V = 1/3 × 3.142 × 49 × 7

Volume of cone, V = 359.24 cubic units.

Read more on cone here: brainly.com/question/1082469

#SPJ1

Answer:

343/3

Proof of answer is in the image, please give brainliest

Answer:

Step-by-step explanation:

A. Sales Budget:

To prepare the sales budget, we need to multiply the unit sales by the sales price per unit for each month. The sales budget for July, August, September, and the total quarter is as follows:

Jones Corporation Sales Budget

Month Unit Sales Sales price Total sales dollars

July 20,000 $180 $3,600,000

August 35,000 $180 $6,300,000

Sept 25,000 $180 $4,500,000

Total 80,000 $180 $14,400,000

B. Production Budget:

To prepare the production budget, we need to calculate the number of units to be produced each month to meet the sales demand and maintain the desired ending inventory level. The production budget for July, August, September, and the total quarter is as follows:

Jones Corporation Production Budget

Month Unit Sales Add: Desired Ending Inventory Total Units Needed Less: Beginning Inventory Units to be Produced

July 20,000 4,000 24,000 - 24,000

August 35,000 5,000 40,250 20,000 20,250

Sept 25,000 7,000 28,750 15,250 13,500

Total 80,000 16,000 93,000 35,250 57,750

Note: The desired ending inventory for finished goods for each month is calculated as 20% of the unit sales for the next month. For materials, the desired ending inventory for September is given as 25,200 pounds.

Therefore, we can calculate the total materials needed for September and subtract the desired ending inventory to find the materials to be purchased for September.

The production budget takes into account the inventory levels for both finished goods and materials.

We can now calculate the total direct materials needed, direct labor hours needed, and total manufacturing overhead costs for the quarter.

C. Direct Materials Budget:

To prepare the direct materials budget, we need to calculate the total materials needed for production and deduct the beginning inventory and desired ending inventory levels to determine the materials to be purchased each month.

The direct materials budget for July, August, September, and the total quarter is as follows:

Jones Corporation Direct Materials Budget

Month Units to be Produced Materials required per unit Total Materials Needed Add: Desired Ending Inventory Total Materials Required Less: Beginning Inventory Materials to be Purchased

July 24,000 3 72,000 - 72,000 20,700 51,300

August 20,250 3 60,750 7,500 68,250 51,300 16,950

Sept 13,500 3 40,500 25,200 65,700 36,300 29,400

Total      

To know more about Sales Budget refer here

https://brainly.com/question/31165239#

#SPJ11

The function may still be continuous.

The lack of differentiability only implies that the function is not smooth at that point.

Here are three scenarios in which the derivative of a function may not exist, along with a sketch of each situation:

Corner: A function may not be differentiable at a corner, where the graph abruptly changes direction.

At a corner, the left and right-hand limits of the derivative do not match. Here is a sketch of the situation:

                   /

                  /

                 /

                /

               /

---------------/----------------

Cusp: A function may not be differentiable at a cusp, where the graph has a sharp point.

At a cusp, the left and right-hand limits of the derivative approach different values. Here is a sketch of the situation:

           /

          /

         /

        /

       /

------/--------

      \

       \

        \

         \

          \

Vertical tangent: A function may not be differentiable at a vertical tangent, where the graph has a vertical line tangent to the curve.

At a vertical tangent, the derivative is either infinite or undefined. Here is a sketch of the situation:

     |

     |

------|-------

     |

     |

Note that in all three of these situations, the function may still be continuous.

The lack of differentiability only implies that the function is not smooth at that point.

Learn more about existance of derivative

brainly.com/question/30365299

#SPJ11

The solution to the equation 30 + q = 43 is q = 13.

Given the equation in the question:

30 + q = 43

To determine the value of q in the equation 30 + q = 43, isolate q on one side of the equation by performing the same operation on both sides of the equation.

30 + q = 43

q + 30 = 43

Next, we can isolate q by subtracting 30 from both sides of the equation:

q + 30 - 30 = 43 - 30

q = 43 - 30

Subtract 30 from 43

q = 13

Therefore, the value of q is 13.

Learn to solve more equations here: https://brainly.com/question/9236233

#SPJ1

Answer:

Let's start by drawing a diagram of the cornfield with the plowed strip around it:

markdown

Copy code

_____________________________

|                             |

|                             |

|                             |

|                             |

|        _____________________|__

|       |                       |

|       |                       |

|       |                       |

|       |                       |

|_______|_______________________|

The plowed strip has a uniform width, which we'll call w. We want to find w such that half of the cornfield is plowed.

The total area of the cornfield is:

Copy code

12 km x 9 km = 108 km^2

If we plow a strip of width w around the cornfield, the new dimensions of the cornfield will be:

scss

Copy code

(12 + 2w) km x (9 + 2w) km

The area of the plowed strip is the difference between the area of the new cornfield and the area of the original cornfield:

scss

Copy code

(12 + 2w)(9 + 2w) - 12(9) = 108 + 42w + 4w^2

We want half of the cornfield to be plowed, so we set the area of the plowed strip equal to half the area of the original cornfield:

scss

Copy code

108 + 42w + 4w^2 = (1/2)(108)

Simplifying, we get:

Copy code

4w^2 + 42w - 54 = 0

We can solve this quadratic equation using the quadratic formula:

css

Copy code

w = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 4, b = 42, and c = -54. Substituting these values, we get:

scss

Copy code

w = (-42 ± sqrt(42^2 - 4(4)(-54))) / 8

arduino

Copy code

w = (-42 ± sqrt(1936)) / 8

makefile

Copy code

w = (-42 ± 44) / 8

So we have two possible solutions:

makefile

Copy code

w = 1/2 km (discarded since it does not satisfy the given condition)

or

makefile

Copy code

w = 11/2 km

Therefore, the width of the plowed strip is 11/2 km = 5.5 km if half of the cornfield is plowed.

To know more about plowed refer here

https://brainly.com/question/2852405#

#SPJ11

The area of the shaded portion in the given triangle of the attached diagram with given measurements is equal to 30 square centimeters.

In triangle ABC ,

Base 'AB' = 3+ 6 + 3

                = 12cm

In the attached figure.

Let the perpendicular line passing through C intersect on AB at point D.

Height of the triangle ABC  'CD' = 12 -2

                                                     = 10 cm

Area of triangle ABC = ( 1/2) × AB × CD

                                   = ( 1/ 2) × 12 × 10

                                   = 60 cm²

Area of triangle excluding shaded portion = ( 1/2 ) × 6 × 10

                                                                       = 30cm²

Area of the shaded portion

= Area of triangle ABC - Area of triangle excluding shaded portion

= 60 - 30

= 30 square centimeters.

Therefore, the area of the shaded portion of the triangle in the attached figure is equal to 30 square centimeters.

learn more about triangle here

brainly.com/question/13149571

#SPJ4

The above question is incomplete, the complete question is:

The figure below is not drawn to scale. The height of the triangle ABC is 2 cm shorter than its base. Find the area of the shaded portions.

Attached figure.