To keep a heavy box sliding across a carpeted floor at constant speed, a person must exert a force on the box. This force is used primarily to overcome which of the following forces?
A. Air resistance.
B. The weight of the box.
C. The frictional force exerted by the floor on the box.
D. The gravitational force exerted by the Earth on the box.
Answers
Answer:
D bcuz without gravity everything would be floating and you wouldn't get it anywhere
Answer:
It’s c
Step-by-step explanation:
Related Questions
Use Stokes´ Theorem to evaluate ∬s.curl F•nds. Assume that the Surface S is oriented upward.
F= (6yz)i+(5x)j+ (yz(e^(x^2)))k. ; S that portion of the paraboloid z=(1/4)x^2+y^2 for 0≤z≤4
Answers
The surface integral in terms of ρ and θ ∫∫S.((6y - 5)e^(x^2))
To evaluate ∬s.curl F•nds using Stokes' Theorem, we first need to find the curl of the vector field F and then compute the surface integral over the given surface S.
Given vector field F = (6yz)i + (5x)j + (yz(e^(x^2)))k, let's find its curl:
∇ × F = ∂/∂x (yz(e^(x^2))) - ∂/∂y (5x) + ∂/∂z (6yz)
Taking the partial derivatives, we get:
∇ × F = (0 - 0) i + (0 - 0) j + (6y - 5)e^(x^2)
Now, let's parametrize the surface S, which is the portion of the paraboloid z = (1/4)x^2 + y^2 for 0 ≤ z ≤ 4. We can use cylindrical coordinates for this parametrization:
r(θ, ρ) = ρcos(θ)i + ρsin(θ)j + ((1/4)(ρcos(θ))^2 + (ρsin(θ))^2)k
where 0 ≤ θ ≤ 2π and 0 ≤ ρ ≤ 2.
Next, we need to find the normal vector n to the surface S. Since S is oriented upward, the normal vector points in the positive z-direction. We can normalize this vector to have unit length:
n = (∂r/∂θ) × (∂r/∂ρ)
Calculating the partial derivatives and taking the cross product, we have:
∂r/∂θ = -ρsin(θ)i + ρcos(θ)j
∂r/∂ρ = cos(θ)i + sin(θ)j + (1/2)(ρcos(θ))k
∂r/∂θ × ∂r/∂ρ = (-ρsin(θ)i + ρcos(θ)j) × (cos(θ)i + sin(θ)j + (1/2)(ρcos(θ))k)
Expanding the cross product, we get:
∂r/∂θ × ∂r/∂ρ = (ρcos(θ)(1/2)(ρcos(θ)) - (1/2)(ρcos(θ))(-ρsin(θ)))i
+ ((1/2)(ρcos(θ))sin(θ) - ρsin(θ)(1/2)(ρcos(θ)))j
+ (-ρsin(θ)cos(θ) + ρsin(θ)cos(θ))k
Simplifying further:
∂r/∂θ × ∂r/∂ρ = ρ^2cos(θ)i + ρ^2sin(θ)j
Now, we can calculate the surface integral using Stokes' Theorem:
∬s.curl F•nds = ∮c.F•dr
= ∫∫S.((∇ × F)•n) dS
Substituting the values we obtained earlier:
∫∫S.((∇ × F)•n) dS = ∫∫S.((6y - 5)e^(x^2))•(ρ^2cos(θ)i + ρ^2sin(θ)j) dS
We can now rewrite the surface integral in terms of ρ and θ:
∫∫S.((6y - 5)e^(x^2))
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The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 23.5 for a sample of size 775 and standard deviation 12.2. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
Answers
The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:
\(22.6 < \mu < 24.4\)
How to obtain the confidence interval?The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:
\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)
Looking at the z-table, the critical value for a 95% confidence interval is given as follows:
z = 1.96.
The lower bound of the interval is then given as follows:
\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)
The upper bound of the interval is then given as follows:
\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)
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The product of 5 and the sum of 3 and a number is 20.
Answers
Answer:
The product of 5 and the sum of 3 and 1 is 20
Step-by-step explanation:
Equation:
5*(3+x)=20
15+5x=20
5x=5
x=1
You need to multiply 5 by three and x
5 (3 + x) = 20 5*3 = 15 5*x = 5x
Second step: Add 15 to both sides
15-15 = 0 20-15 = 5
15 + 5x = 20
-15 -15
Step three: Divide 5 from both sides
5x/ 5 = x
5/5 = 1
5x = 5
X= 1
An object has been heated to 200
degrees Celsius. After 5 minutes it
has cooled to 131 degrees. The
ambient temperature is 20 degrees.
Rounded to the nearest tenth, what
will the temperature of the object be
at the end of 9 minutes?
[?] degrees Celsius
Answers
We can use Newton's law of cooling to solve this problem:
T(t) = T_a + (T_0 - T_a) * e^(-kt)
where T(t) is the temperature of the object at time t, T_a is the ambient temperature, T_0 is the initial temperature of the object, and k is a constant. We can solve for k by using the information that the object cools from 200 degrees to 131 degrees in 5 minutes:
131 = 20 + (200 - 20) * e^(-5k)
Simplifying this equation, we get:
e^(-5k) = 0.625
Taking the natural logarithm of both sides, we get:
-5k = ln(0.625)
k = -ln(0.625) / 5
k ≈ 0.1078
Now we can use this value of k to find the temperature of the object after 9 minutes:
T(9) = 20 + (200 - 20) * e^(-0.1078 * 9)
T(9) ≈ 94.9 degrees Celsius
Therefore, the temperature of the object at the end of 9 minutes will be approximately 94.9 degrees Celsius.
You burn 4 Cal/min walking and 10 Cal/min running. You walk 10 to 20 min each day and run 30 to 45 min each day. You never spend more than an hour running and walking together. How much time should you spend on each activity to maximize the number of Calories you burn? Will you have exercised enough to burn off a 500-Calorie meal? A. 50 minutes running, 10 minutes walking; yes. B. 45 minutes running, 15 minutes walking; yes. C. 40 minutes running, 20 minutes walking; no. D. 30 minutes running, 30 minutes walking; no.
Answers
Answer:
I don’t know how to do the explanation but the answer is 15 min waking and 45 running. I got it right on the test
Step-by-step explanation:
Are all intersecting lines perpendicular? Draw a picture to help explain your answer
Answers
Not all intersecting lines are perpendicular.
What are perpendicular lines?Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.
Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.
As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.
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change 5 out of 19 to a percentage
Answers
Answer:
26.3%
Step-by-step explanation:
5 is divided by 19
That answer is then multiplied by 100.
You may round your answer to the nearest whole number.
Find the circumference of the circle.
The circumference is _____
mi.
Answers
c = 2•pi•4
c = 8pi
Answer:
The answer is 8 pi
Step-by-step explanation:
The formula is radius squared times pi!
I hope this helped!!
to determine that a item is not in an unordered array of 100 items, how many values must linear search examine on average? a) 7 b) 10 c) 100
Answers
To determine that an item is not in an unordered array of 100 items, total numbers of values which have to linear search examine on average is 100. The correct answer is C.
What is Linear Search?Linear Search is described as a sequential search algorithm which starts at one end and goes through each element of a list until the needed element is found, otherwise the search continues till the end of the data set. This is the simplest searching algorithm.
Starting at the beginning of the data set, each item of data is examined until a match is made. Once the item is found, the search ends.
Hence, in this case, since there are 100 items, then there will be 100 numbers of values.
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A projector displays a rectangular image on a wall. The height of the wall is x feet. The area in square feet of the projection is represented by x^2-12x+32. The width of the projection is (x-4) feet. a. Write a binomial that represents the height of the projection b. Find the perimeter of the projection when the height of the wall is 10 ft.
Answers
Given:
The area of the projection is
\(A=(x^2-12x+32)ft^2\)The width of the projection is w =(x-4) feet.
Let l be the height of the projection.
The shape of the projection is a rectangle.
Consider the formula for the area of the rectangle.
\(A=lw\)\(\text{ Sustitute }A=\mleft(x^2-12x+32\mright)\text{ and w=(x-4) in the formula.}\)\(x^2-12x+32=l(x-4)\)\(Use\text{ }-12x=-8x-4x.\)\(x^2-8x-4x+32=l(x-4)\)\(x(x-8)-4(x-8)=l(x-4)\)\((x-8)(x-4)=l(x-4)\)Cancel out the common factor.
\((x-8)=l\)Hence the height of the projection is (x-8).
b)
Given:
Height of the wall x=10 ft.
We know that the width of the projection w =(x-4) and height of the projection l=(x-8).
Substitute x=10 in the equation l and w, we get
\(w=10-4=6\text{ ft}\)\(l=10-8=2ft\)Consider the perimeter of the rectangle.
\(P=2(l+w)\)Substitute l=2 and w=10 in the formula, we get
\(P=2(2+4)=2\times8=16\text{ ft.}\)Hence the perimeter of the projection is 16 ft when the height of the wall is 10 ft.
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The supply and demand curves for a business dealing with wheat are:
Supply: p = 1.55 + 0.00014x^2
Demand: p = (2.358 - 0.007x)^2
where p is the price in dollars per bushel and x is the quantity in bushels per day. Use a graphing utility to graph the supply and demand equations and find the market equilibrium. (The market equilibrium is the point of intersection of the graphs for x > 0. Round your answers to 2 decimal places.)
x= ________ bushels
p = $_________
Answers
Given curves:
p = 1.55 + 0.00014x²p = (2.358 - 0.007x)²See the attached, where both curves and their intersection is shown.
According to this we have:
x = 96.05p = $2.84
Answer:
x = 96.05 bushels
p = $2.84
Step-by-step explanation:
Graph the two equations (see attachment).
The market equilibrium is the point of intersection of the graphs for x > 0.
From inspection of the graph, the point of intersection is (96.05, 2.84).
Therefore:
x = 96.05 bushelsp = $2.84
Secured debt usually has _____.
longer loan terms
collateral
lower interest rates
all of the above
Answers
“Secured debt generally has a lower interest rate, because the lender has a source of collateral if you don't make your payments,” says Brown.
Hope this helps, and it’s actually pretty convenient that I saw this today....
Answer:
all of the above
Step-by-step explanation:
Professor Cramer determines a final grade based on attendance, two papers, three major tests, and a final exam. Each of these activities has a total of 100 possible points. However, the activities carry different weights. Attendance is worth 7%, each paper is worth 9%, each test is worth 14%, and the final is worth 33%, (a) What is the average for a student with 64 on attendance, 82 on the first paper, 61 on the second paper, 72 on test 1, 64 on test 2, 93 on test 3, and 82 on the final exam? (Round your answer to one decimal place.) (b) Compute the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 29 on attendance. (Round your answer to one decimal place.)
Answers
The average for a student with 64 on attendance, 82 on the first paper, 61 on the second paper, 72 on test 1, 64 on test 2, 93 on test 3, and 82 on the final exam is 77.31% and the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 29 on attendance is 73.23%.
Averagea. Average:
Average: 82(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33
Average=5.74+5.49+10.08+8.96+13.02+27.06÷0.91
Average=70.35÷0.91
Average=77.31%
b. Average
Average= 29(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33
Average=2.03+5.49+10.08+8.96+13.02+27.06÷0.91
Average=66.64÷0.91
Average=73.23%
Therefore the average for both a and b is 77.31% and 73.23%.
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Suppose that a bike rents for $4 plus $1.50 per hour. Write an equation in slope-intercept form that models this situation. Then use the equation you wrote and fill out the table.
Answers
the slope-intercept should be in this form
\(y=mx+b\)where m should be the value that changes with time and b the fixed charges
\(y=1.5x+4\)replace in the equation like this
\(\begin{gathered} \text{when x=2} \\ y=1.5\cdot(2)+4 \\ y=3+4 \\ y=7 \end{gathered}\)\(\begin{gathered} \text{when x=}4 \\ y=1.5\cdot(4)+4 \\ y=6+4 \\ y=10 \end{gathered}\)\(\begin{gathered} \text{when x=}6 \\ y=1.5\cdot(6)+4 \\ y=9+4 \\ y=13 \end{gathered}\)\(\begin{gathered} \text{when x=}8 \\ y=1.5\cdot(8)+4 \\ y=12+4 \\ y=16 \end{gathered}\)replace values in the table
Drag the tiles to the correct boxes to complete the pairs.
Match each function with the graph of its inverse function. fx=5x-1 fx= 1/5 x fx=x-5 fx=7x+1
Answers
The inverse of the functions are solved
Given data ,
Let the inverse of the function be represented as f⁻¹ ( x )
a)
f(x) = 5x - 1
y = 5x - 1
x = 5y - 1
x + 1 = 5y
y = (x + 1)/5
Inverse: f⁻¹(x) = (x + 1)/5
b)
f(x) = (1/5)x
y = (1/5)x
x = (1/5)y
y = 5x
Inverse: f⁻¹(x) = 5x
c)
f(x) = x - 5
y = x - 5
x = y - 5
y = x + 5
Inverse: f⁻¹(x) = x + 5
d)
f(x) = 7x + 1
y = 7x + 1
x = 7y + 1
x - 1 = 7y
y = (x - 1)/7
Inverse: f⁻¹(x) = (x - 1)/7
Hence , the inverse of the functions are solved
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Almonds are priced at $7.50 for one pound in the bulk foods section. How many pounds of almonds could you purchase for $37.50?
Answers
$7.50 x 5 = $37.50
Alissa would like to make a deposit into her savings account. She filled out a deposit ticket and handed it to the teller at her bank. The teller apologizes to Alissa and explains that she cannot accept the deposit ticket in its current form. Determine what, if anything, Alissa will have to change in order for her deposit ticket to be accepted.
A deposit ticket. The amount deposited is 899 dollars and 86 cents and she is taking 260 dollars out as cash. The total on the slip is 629 dollars and 86 cents.
a.
The sub total is calculated incorrectly
b.
Alissa forgot to sign the deposit ticket for less cash back
c.
The total is calculated incorrectly
d.
Alissa forgot to date the deposit ticket
Answer is : C. The total is calculated incorrectly
Answers
Alisa should either fill out a new ticket or write the correct amount and append her signature beside it.
What is a deposit ticket?A deposit ticket is a little paper where you are required to fill in the details of the deposit that you seek to make into your savings account. All information in the ticket ought to be filled accurately.
here, we have,
The teller may have declined to receive the ticket due to incorrect total amount filled on the ticket. Alisa should either fill out a new ticket or write the correct amount and append her signature beside it.
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out of water park 243 out of 675 tickets were sold child tickets what percentage of the tickets were child tickets
Answers
Total ticket = 675
Child tickrt sold = 243
percentage of child tickets sold
\(\begin{gathered} =\text{ }\frac{243}{675}\text{ x 100\%} \\ \\ =\text{ }\frac{243\text{ x 100}}{675} \\ =\text{ }\frac{24300}{675} \\ =\text{ 36\%} \end{gathered}\)You are building a model sailboat. The plans show that the base of the main sail is 9 cm, the bottom acute angle in the sail is 52°, and the distance between the base of the sail and the deck is 2 cm. What is the height of the mast? a. 12.5 cm b. 11.2 cm c. 13.5 cm d. 11.5 cm
Answers
Answer:
c. 13.5 cm
Step-by-step explanation:
In the right triangle formed by the main sail.
Using the trigonometric function
\(\tan \theta =\dfrac{\text{Opposite}}{\text{Adjacent}} \\\tan 52^\circ =\dfrac{x}{9} \\x=9 \times \tan 52^\circ\\x=11.52$ cm\)
Therefore:
Height of the mast = 2+11.5=13.5 cm
The height of the mast is 13.5 cm.
Helpp. Mee\\\..........
Answers
Answer:
may not be exact
1- surveying every fifth student who walks in
2-randomly selected people of both genders
3-asking 8 random students from each second period
4-asking 4 girls and 4 boys from each~~
5-randomly choosing a page and counting the words
Step-by-step explanation:
1-explanation; the first one is skewed two 7th graders, the third one is skewed to volleyball players, the fourth one is skewed to eight graders
I would like to get help for number 10 please
Answers
ANSWER:
10:00 AM- 10:30 AM- 11:00 AM- 11:30 AM- 12:00 M- 12:30 PM- 1:00 PM- 1:30 PM- 2:00 PM- 2:30 PM- 3:00 PM- 3:30 PM- 4:00 PM- 4:30 PM- 5:00 PM
STEP-BY-STEP EXPLANATION:
The least common multiple of 10 min (chemistry presentation) and 6 min (recycling presentation) min is 30 min. So, the two presentations have the same starting time every half hour.
Therefore, presentations start at the same time at:
10:00 AM
10:30 AM
11:00 AM
11:30 AM
12:00 M
12:30 PM
1:00 PM
1:30 PM
2:00 PM
2:30 PM
3:00 PM
3:30 PM
4:00 PM
4:30 PM
5:00 PM
what's the answer for this? CLASS 6 MATHS I NEED HELP ASAP!!!
Answers
Answer:
20:
3 5/12 or 41/12
21:
-9 5/8 or -77/8
all the edges of a cube are expanding at a rate of 4 in. per second. how fast is the volume changing when each edge is 10in. long?
Answers
The rate at which the volume of the cube is changing is 1200 in³/seconds.
What is volume?Volume is the space occupied by a solid object.
To calculate the rate at which the volume of the cube is changing, we use the formula below.
Formula:
dV/dt = (dL/dt)×(dV/dL)................ Equation 1Where:
dV/dt = Rate at which the volume of the cube is changing dL/dt = Rate at which the edge of the cube is expandingdV/dL = Change in the volume of the cube with respect to the edge.From the question,
Given:
dL/dt = 4 in. per secondsL = 10 inIf, the volume of a cube is V = L³,
Then,
dV/dL = 3L² = (3×10²) = 300 in²Substitute these values into equation 1
dV/dt = 4×300dV/dt = 1200 in³/secondsHence, the rate at which the volume is changing is 1200 in³/seconds.
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Math work I hope you can see
Answers
What is the rationale for the above responses?
1) to obtain the value of x, we must equate AC and BD based on the diagonal properties of a rectangle. Note that a rectangle's diagonal divides it into two congruent right triangles.
A rectangle's diagonals are all the same length. A square is a quadrilateral whose diagonals bisect each other, intersect at right angles, and are congruent.
Thus,
Since BD = AC
2x + 19 = 5x - 2
To solve the equation 2x + 19 = 5x - 2, we need to isolate x on one side of the equation.
First, we can simplify both sides by combining like terms. Subtracting 2x from both sides gives:
19 = 3x - 2
Next, we can isolate x by adding 2 to both sides:
21 = 3x
Finally, we can solve for x by dividing both sides by 3:
x = 7
Therefore, the solution to the equation 2x + 19 = 5x - 2 is x = 7
b) The Properties of Parallel Lines Intersected by a Transverse Postulate states that when a transversal intersects two parallel lines, the corresponding angles are congruent, the alternate interior angles are congruent, and the same-side interior angles are supplementary. This means that
∠LMN + ∠MNK = 180°
Thus,
115 + ∠MNK = 180
∠MNK = 180 - 115
∠MNK = 65°
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The original price of a shirt is $18. The store is having a 50% off sale. Members get an extra 20% off the sale price. What is the cost of the shirt after the discounts?
A. $5.39
B. $14.39
C. $7.20
Answers
Answer:
A
Step-by-step explanation:
Hopefully this helps
The perimeter of the rectangle below is 166 units. Find the value of y.
4y + 2
Sy
Answers
The value of y is 9.
Perimeter is the total length of the boundary of any closed shape. It is basically the sum of all the sides of a given figure.
Perimeter of a rectangle is given by [ 2( l + b ) ] or (2 l + 2 b ) or
( l + l + b + b), here l and b represent the length and breadth of the given rectangle.
Perimeter of the given rectangle = 166 units ( given )
Length of the given rectangle = 5y ( given )
Breadth of the given rectangle = (4y + 2) ( given )
By putting values in the formula, we get
perimeter = 2 ( l + b )
166 = 2 [ (5y) + (4y + 2) ]
166 = 2 [ 5y + 4y + 2 ]
166 = 2 [ 9y + 2 ]
166 = 2*9y + 2*2
166 = 18y + 4
166-4 = 18y ( moving 4 to other side thus changing the sign to negative )
162 = 18y
162/18 = y ( moving 18 to other side for further solution )
y = 9
Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.
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The value of y is 9.
The whole length of any closed shape's boundary is known as its perimeter. In essence, it is the total of a given figure's sides.
A rectangle's perimeter can be calculated using [2(l + b)] or (2 l + 2 b) or
(l + l + b + b), where l and b stand for the provided rectangle's length and width
The rectangle's perimeter is 166 units ( given )
The rectangle's length is 5y ( given )
Given rectangle's width equals (4y + 2) ( given )
When we enter values into the formula, we obtain
perimeter = 2 ( l + b )
166 = 2 [ (5y) + (4y + 2) ]
166 = 2 [ 5y + 4y + 2 ]
166 = 2 [ 9y + 2 ]
166 = 2*9y + 2*2
166 = 18y + 4
166-4 = 18y ( moving 4 to other side thus changing the sign to negative )
162 = 18y
162/18 = y ( moving 18 to other side for further solution )
y = 9
Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.
Erika sells bicycles at a store. She is paid a monthly salary plus a bonus on each bike she sells. Her monthly pay is modeled in the table. Choose the linear equation below that best represents this data.
Answers
Answer: Show the table
Step-by-step explanation:
SHow the table
WINGSUIT A wingsuit flyer jumps off a tall cliff. He falls freely for a few seconds before deploying the wingsuit and -4.9x² +420, where y is = slowing his descent. His height during the freefall can be modeled by the function y the height above the ground in meters and x is the time in seconds. After deploying the wingsuit, the flyer's height is given by the function y = −3x + 200. deploy the wingsuit?
Answers
The total height of the flyer at any time after deploying the wingsuit would be;
y = -3x + 200 + (-4.9t² + 420),
Now, Based on the given information, we can use the two functions to determine the height of the wingsuit flyer at a particular time.
During the freefall, the height of the flyer can be calculated using the function
y = -4.9x² + 420.
Let's say the flyer falls freely for t seconds before deploying the wingsuit.
Therefore, the height at the moment of deploying the wingsuit would be,
y = -4.9t² + 420.
After deploying the wingsuit, the height of the flyer is given by the function
y = -3x + 200.
We can combine these two functions to get the total height of the flyer at any given time after deploying the wingsuit.
So, the total height of the flyer at any time after deploying the wingsuit would be;
y = -3x + 200 + (-4.9t² + 420),
where x is the time after deploying the wingsuit and t is the time of freefall before deploying the wingsuit.
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Find the area of the triangle having the indicated angle and sides. (Round your answer to one decimal place.)
B 128°, a 86, c = 37
Answers
The area of the triangle with angle B = 128°, side a = 86, and side c = 37 is approximately 2302.7 square units.
To find the area of a triangle when one angle and two sides are given, we can use the formula for the area of a triangle:
Area = (1/2) * a * b * sin(C),
where a and b are the lengths of the two sides adjacent to the given angle C.
In this case, we have angle B = 128°, side a = 86, and side c = 37. To find side b, we can use the law of cosines:
c² = a² + b² - 2ab * cos(C),
where C is the angle opposite side c. Rearranging the formula, we have:
b² = a² + c² - 2ac * cos(C),
b² = 86² + 37² - 2 * 86 * 37 * cos(128°).
By substituting the given values and calculating, we find b ≈ 63.8.
Now, we can calculate the area using the formula:
Area = (1/2) * a * b * sin(C),
Area = (1/2) * 86 * 63.8 * sin(128°).
By substituting the values and calculating, we find the area of the triangle to be approximately 2302.7 square units.
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