Answers
The area under the curve (since the function of the parabolic expression is y = x - x²) is 1/6 square units.
What is a parabolic expression?A parabolic function has an expression represented as f(x) = ax² + bx + c, which allows solving for x using either the factorization method or applying the quadratic formula. By zeroing out this expression, it becomes possible to determine its roots as with any quadratic equation.
In the case of the above function:
To find the area under the curve, above the x-axis, we need to integrate the parabolic expression from 0-1
that is:
∫[0,1](x-x²)dx
This is evaluated using the power rule
∫[0,1](x-x²)dx = [1/2x² - 1/3x³) fro x= 0 to x = 1
inserting the limits of the integration, we have:
[1/2 (1) ² - 1/3 ( 1) ³] - [1/2 (0)² - 1/3 (0) ³]
Simplified, and we have :
Area = 1/2 - 1/3
Thus, Area under the curve = 1/6
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Related Questions
This data gives the length of the radius, in feet, of several circles.
Length (ft): 12, 316, 12, 12, 38, 38, 316, 12, 316, 716
Create a line plot to display this data.
To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
Radius of Circles
1/16
1/8
3/16
1/4
5/16
3/8
7/16
1/2
Length (ft)
0
1
2
3
4
5
6
7
8
9
10
Answers
Answer: on 1 = 0
on 2 = 0
on 3 = 3
on 4 = 0
on 5 = 0
on 6 = 2
on 7 = 1
on 8 = 4
Step-by-step explanation:
As the first, second, fourth and fifth do not have any numbers we will skip to the next number on the number line.
1/16 = 0
1/8 = 0
3/16 = 3
1/4 = 0
5/16 = 0
3/8 = 2
7/16 = 1
1/2 = 4
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC = 65
and DC = 6, what is the length of BC in simplest radical form?
Answer: =
B
65
6
C
Submit Answer
Answers
Applying the leg rule, the length of BC in simplest radical form is: x = x = √390
How to Apply the Leg Rule?The leg rule is used to find missing lengths in a right triangle when an altitude intersects the hypotenuse and form segments.
The leg rule is given as:
Hypotenuse / leg = leg / part
Thus, using the image given, we have:
Hypotenuse (AC) = 65
Part (DC) = 6
Leg = x
Plug in the values:
65 / x = x / 6
Cross multiply:
x * x = 6 * 65
x² = 390
x = √390
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It’s telling me to find ZL and IL but I’m not sure how
Answers
The length of ZL and IL is 297.72 ft and 283.15 ft respectively.
What is the length of ZL and IL?The lengths of ZL and IL is calculated by applying trigonometry ratio as follows;
SOH CAH TOA
SOH = sin θ = opposite /hypothenuse side
TOA = tan θ = opposite side / adjacent side
CAH = cos θ = adjacent side / hypothenuse side
The hypothenuse side = ZL and the adjacent side = IL.
tan 18 = 92/IL
IL = 92/tan (18)
IL = 283.15 ft
sin 18 = 92/ZL
ZL = 92/si 18
ZL = 297.72 ft
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Front Elementary School is putting in a new merry-go-round with a diameter of 10.4
10
.
4
feet on the playground. Before the piece can be installed, a solid circular pad of mulch must be put down which extends 3
3
feet beyond the edge of the merry-go-round.
image
What is the approximate area of the mulch around the merry-go-round? Use 3.14
3.14
for π
π
, if required.
Answers
The approximate area of the mulch around the merry-go-round is 126.228 feet².
Diameter of the merry go round = 10.4 feet
Radius is half of the diameter.
Radius of the merry go round = 10.4/2 = 5.2 feet
Before the piece can be installed, a solid circular pad of mulch must be put down which extends 3 feet beyond the edge of the merry-go-round.
Radius of the merry go round with mulch = 5.2 + 3 = 8.2 feet
Total area of the merry go round with the mulch is,
Area = π (8.2)² = 67.24π feet²
Area of the merry go round = π (5.2)² = 27.04π feet²
Area of the mulch = 67.24π feet² - 27.04π feet² = 40.2π = 126.228 feet²
Hence the required area is 126.228 feet².
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The fifth-grade team ordered 325 shirts for Field Day. The company can package 21 boxes will they need to ship this order?
Answers
Result:
Yes, the fifth-grade team will need to ship the order of 325 shirts for Field Day. They will need to package them in 16 boxes to ship them.
How do we calculate the number of boxes needed for the shipment?To evaluate the number of boxes needed to ship the order, we need to divide the total number of shirts by the number of shirts that can fit in one box.
where:
Number of shirts per box = 21
Total number of shirts = 325
Number of boxes needed = Total number of shirts / Number of shirts per box
Number of boxes needed = 325 / 21
Number of boxes needed = 15.47619
Since we cannot have a fraction of a box, we would round up to the nearest whole number.
Therefore, the fifth-grade team will need to ship the order in 16 boxes.
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The minivan depreciates $3,000 in the first year. Write either a linear or exponential function to represent the value of the car x years after it was sold.
Answers
Answer:
Step-by-step explanation: However, say that the car loses 50% of its value every year. This means that if you originally bought a car for 2,000 dollars in 2015, in 2016 it would be world 2,000/2=1,000, 1,000/2=500 the year after that, and so on. We can try to put this into a linear function, but it's hard to put it into one equation because we're not subtracting or adding to the cost of the car by a specific amount each year. If we had our equation as y=-0.5*x+2000, this wouldn't work because it's adding to the original amount, not multiplying. However, if we used an exponential equation such as y=b(m^a), with y representing the end cost, b representing the starting cost, m representing the amount multiplied per year, and a representing the number of years. This works because we start with a value, and multiply it by an amount each year. Since 50%=0.5, we plug that into m to get y=2,000(0.5^a). Therefore, this works well here. If the minivan were to depreciate by 3,000 every year, starting at $29,248, this means that we first have to find out what we multiply by 29,248 by the first year to subtract 3,000. As, after one year, the value is 29,248-3,000=26,248, we have 26,248=29,248(m^1). Therefore, we can divide 29,248 by both sides to get around 0.9 as our answer form. Thus, our equation is y=29,248(0.9^a). This type of equation would not work if we subtracted an amount every year because we're not multiplying by the same amount then. For example, if a toy was valued at 3$ and gained a value of one dollar every year, we could multiply the toy by 4/3 the first year to get 4, but the next year we wouldn't get 5.
Luke is shipping another toy that has a volume of 34 cubic feet. The box he will use has a base of 15 square feet and a height of 3 feet. The rest of the box will be filled with packing material. B. What is the volume, in cubic feet, of the packing material Luke will need? Show or explain all your work.
Answers
The volume of the packing material that luke will need is: 11 cubic feet
How to find the volume of the box?The formula for the volume of a box is expressed as:
V = length * width * height
Now, we are given:
Area of base = 15 square feet
height = 3 feet
Thus:
Volume of box = 15 * 3 = 45 cubic feet
If he is going to ship a toy that is 34 cubic feet, then it means that:
Volume of packing material Luke needs = 45 - 34 = 11 cubic feet
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Solve for the following percentage
show with solution.
1. 20% of 80
2. 6% of 150
3. 30% of 200
4. 65% of 400
5. 50% of 150
Find the Base, show your solution
1. 28 is 4% of what number?
2. 25% of what number is 100?
3. 69 is 75% of what number?
4. 15% of what number is 9?
5. 12% of what number is 60
Find the Rate, show your solution
1. what percent of 200 is 50
2. what percent of 50 is 40?
3. what percent of 10 is 6?
4. 200 is what percent os 200?
5. what percent of 800 is 200?
help
Answers
Answer:
Step-by-step explanation:
20% of 80 is 16.
6% of 150 is 9.
30% of 200 is 60.
65% of 400 is 260.
50% of 150 is 75.
1 Let x be the unknown number. Then we have the equation:
0.04x = 28
Solving for x, we divide both sides by 0.04:
x = 28 ÷ 0.04 = 700
Therefore, 28 is 4% of 700.
2. Let x be the unknown number. Then we have the equation:
0.25x = 100
Solving for x, we divide both sides by 0.25:
x = 100 ÷ 0.25 = 400
Therefore, 25% of 400 is 100.
3 Let x be the unknown number. Then we have the equation:
0.75x = 69
Solving for x, we divide both sides by 0.75:
x = 69 ÷ 0.75 = 92
Therefore, 69 is 75% of 92.
4 Let x be the unknown number. Then we have the equation:
0.15x = 9
Solving for x, we divide both sides by 0.15:
x = 9 ÷ 0.15 = 60
Therefore, 15% of 60 is 9.
5. Let x be the unknown number. Then we have the equation:
0.12x = 60
Solving for x, we divide both sides by 0.12:
x = 60 ÷ 0.12 = 500
Therefore, 12% of 500 is 60.
(3)
1 Let x be the percent, then we can set up the equation:
x/100 * 200 = 50
Solving for x, we get:
x = 25
Therefore, 50 is 25% of 200.
2 Let x be the percent, then we can set up the equation:
x/100 * 50 = 40
Solving for x, we get:
x = 80
Therefore, 40 is 80% of 50.
3 Let x be the percent, then we can set up the equation:
x/100 * 10 = 6
Solving for x, we get:
x = 60
Therefore, 6 is 60% of 10.
4. 200 is 100% of itself, so the percent is 100.
5. Let x be the percent, then we can set up the equation:
x/100 * 800 = 200
Solving for x, we get:
x = 25
Therefore, 200 is 25% of 800.
Help me please this question is too tricky for me
Answers
the answer does not exist thats the answer. “the answer to this problem does not exist”
Huai takes out a $3700 student loan at 6.8% to help him with 2 years of community college. After finishing the 2 years, he transfers to a state university and borrows another $12,00 to defray expenses for the 5 semesters he needs to graduate. He graduates 4 years and 4 months after acquiring the first loan and payments are deferred for 3 months after graduation. The second loan was acquired 2 years after the first and had an interest rate of 7.4%. Find Huai's monthly payment when regular payments begin. Calculate the monthly payment on the loan (community college). Round your answer to two decimal places, if necessary.
The monthly payment on loan 1 (community college) is :
Part: 0 / 30 of 3 Parts Complete
Please provide the honest answer here I can't do it and I need your help, okay thank you
To calculate the monthly payment for each loan, we need first to calculate the total amount
Answers
Huai's monthly payment for the community college loan is $89.72 and $235.35.
To calculate the monthly payment for each loan, we need first to calculate the total amount borrowed and the total interest paid for each loan.
For the first loan
Total amount borrowed = $3700
Total interest paid = $3700 x 0.068 x (4 + 4/12 + 3/12) = $1,271.12
Total amount repaid = $3700 + $1,271.12 = $4,971.12
To find the monthly payment, we can use the formula for a loan payment
P = (r(PV))/(1-(1+r)⁻ⁿ)
Where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan, and n is the total number of payments.
For the first loan, r = 0.068/12, PV = $3700, and n = 48 (4 years x 12 months/year). Substituting these values into the formula, we get
P = (0.068/12 * $3700)/(1-(1+0.068/12)⁻⁴⁸) = $89.72
Therefore, the monthly payment on the first loan is $89.72.
For the second loan
Total amount borrowed = $12,000
Total interest paid = $12,000 x 0.074 x (3/12) = $222.00
Total amount repaid = $12,000 + $222.00 = $12,222.00
The second loan was acquired 2 years after the first, so the total repayment period is 5 x 12 - 2 x 12 - 3 = 51 months.
Using the same formula as before, but with r = 0.074/12, PV = $12,000, and n = 51, we get
P = (0.074/12 * $12,000)/(1-(1+0.074/12)⁻⁵¹) = $235.35
Therefore, the monthly payment on the second loan is $235.35.
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The coordinates of ΔRGB are R(‒3, 2), G(3, 4) and B(1, 1). Under a series of transformations, the resulting figure ΔUNA has the following coordinates: U(2, ‒3), N(‒4, ‒3) and A(‒1, ‒1).
Which statement is not true?
RB has the same length as UA.
GB is congruent to AN.
The measure of ∠R is the same as ∠N.
The original triangle ΔRGB is congruent to ΔUNA.
Answers
The statement that is not true is (c) The measure of ∠R is the same as ∠N.
Selecting the false statement
From the question, we have the following parameters that can be used in our computation:
The coordinates of ΔRGB are R(‒3, 2), G(3, 4) and B(1, 1). The coordinates of ΔUNA are U(2, ‒3), N(‒4, ‒3) and A(‒1, ‒1).Looking at the above coordinates, we can see that the transformation rule is (x, y) = (-x, -y)
This is a rigid transformation
And so, the side lengths and the corresponding angle measures are equal
However, angles R and N are not corresponding angles
So, the false statement is (c) The measure of ∠R is the same as ∠N.
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Use the long division method to find the result when x³ + 7x² + 15x + 25 is divided by x+ 5.
Answers
```
-x² - 2x + 5
x + 5 | x³ + 7x² + 15x + 25
-x³ - 5x²
-----------
2x² + 15x
2x² + 10x
-----------
5x + 25
5x + 25
--------
0
```
Therefore, the result when x³ + 7x² + 15x + 25 is divided by x + 5 is:
x² - 2x + 5
What does the box represent in a box plot? Select all that apply.
Select 2 correct answer(s)
A)The lower 50% of the data
B)The upper 50% of the data
C)The median
D)The range
E) The middle 50% of the data
F) The interquartile range
Answers
The box in a box plot represents the middle 50% of the data (E) and the interquartile range (F).
Team People on Each Team A 7 B 3 C 7 D 5 E 6 F 7 G 8 H 5 I 3 J 5 K 7 Think about a line plot using the data from the table. Which statement is true?
Think about a line plot using the data from the table. Which statement is true?
A. The greatest value with a dot above it is 11.
B. There will be 11 dots in total.
C. There will be 4 more dots above 7 than above 8.
D. There will be 5 dots above 7.
Answers
Statement " There will be 5 dots above 7" is true. Therefore, option D is the correct answer.
A line plot is an effective way to visualize and compare data in a table. In this case, the line plot would show the total number of people on each team, with dots representing the values.
The greatest value in the table is 11, but this would not be represented with a dot in the line plot. There will be 11 dots in total, representing the 11 teams listed in the table.
There will be 4 more dots above 7 than above 8, since there are 4 teams with 7 people on each team and only 3 teams with 8 people on each team.
Finally, there will be 5 dots above 7, since there are 5 teams with 7 or more people on each team.
Therefore, option D is the correct answer.
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S is the midpoint of RT. R has the coordinates (13,-8), and S has the coordinates (9,5). Find the coordinates of T.
Please help (Image Attached)
Answers
The coordinates of endpoint T are (5,18).
What is the coordinates of point T?The midpoint formula is expressed as:
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.
Let's call the coordinates of point T (x,y).
Since S is the midpoint of RT, we can use the midpoint formula to find the coordinates of S:
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
((13+x)/2, (-8+y)/2) = (9,5)
Solving for x:
(13+x)/2 = 9
13 + x = 2 × 9
13 + x = 18
x = 18 - 13
x = 5
Solving for y, we get:
(-8+y)/2) = 5
-8 + y = 5 × 2
-8 + y = 10
y = 10 + 8
y = 18
Therefore, the coordinates are (5,18).
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find the equation of the line best fit for the following data. pls explain im kind of lost lol
Answers
The equation of the line of best fit for the set of data is given as follows:
y = 4.24773x - 0.32726
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
From the table in this problem, the points are given as follows:
(0.9, 3.51), (1.7, 6.61), (3, 12.27), (0.1, 0.15), (2.3, 9.59), (1.3, 5.35), (0.5, 1.65), (2.1, 8.8).
Inserting these points into a calculator, the line of best fit is given as follows:
y = 4.24773x - 0.32726
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Find the volume of this sphere.
Use 3 for TT.
V≈ [?]cm³
V = πr³
6 cm
Answers
The volume of the sphere with a diameter of 6cm is 108 cm³.
What is the volume of the sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The volume of a sphere is expressed as:
Volume = (4/3)πr³
Where r is the radius of the sphere and π is the mathematical constant pi
Given the data in the question:
Diameter d = 6cm
Radius is half of diameter
Radius r - 6cm/2
Radius r = 3cm
Also, π = 3
Plug the given values into the above formula.
Volume = (4/3)πr³
Volume = (4/3)π3³
Volume = (4/3)(3)(27)
Volume = 108 cm³
Therefore, the volume is 108 cm³.
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For the position function s(t)20/t+1, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 0.
Answers
Answer:So the instantaneous velocity at t = 0 is -20. This means that the object is moving in the negative direction at a rate of 20 units per second at t = 0.
Look at the Photo
CAN SOMONE HELP WITH THIS QUESTION?
Answers
a) The height of the stone 5 seconds later is: 90 feet
b) The time at which the stone hits the ground is: 7.66 secs
c) The velocity of the stone when it hits the ground is: 227 ft/sec
How to solve Projectile Motion Problems?We are given:
Height above ground: h = 800 feet
Initial speed: u = 18 feet per second
(A.) Height of the stone at t = 5 seconds.
g = -32feet/sec²
t = 5 sec.
Since the stone is thrown vertically upward from some height X = 800 feet, so the total height will be:
h = X + ut + 1/2at²
h = 800 + (18*5) + ¹/₂ * (-32) * (5²)
h = 90 feet
(B.) At what time did the stone hit the ground, that means height, h = 0.
0 = 800 + (18t) + ¹/₂ * (-32) * (t²)
16t² - 18t - 800 = 0
t = 18 ± √-18² - 4 * 16 * (-800)/2*16
t = 7.66 sec
So at t = 7.66 secs, the stone hits the ground.
(C.) The velocity when the stone hits the ground.
Using the energy conservation theorem,
Initial total energy = Final total energy.
¹/₂mu² + mgh = ¹/₂mv² + 0
u² + 2gh = v²
v² = 18² + 2*32*800
v=√18² + 2*32*800
v = 227 ft/sec
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(3x-2y+7)-(x+8xy-1)+(10x-xy)
Answers
Simplifying the expression, (3x - 2y + 7) - (x + 8xy - 1) + (10x - xy), the solution we would get by combing like terms can be expressed as: 12x - 2y + 7xy + 6.
How to Simplify an Expression?Given the expression, (3x - 2y + 7) - (x + 8xy - 1) + (10x - xy), to simplify it, follow the steps shown below:
(3x - 2y + 7) - (x + 8xy - 1) + (10x - xy) [given]
Open the bracket by applying the distributive property:
3x - 2y + 7 - x + 8xy - 1 + 10x - xy
Combine like terms together:
3x - x + 10x - 2y + 8xy - xy + 7 - 1
12x - 2y + 7xy + 6
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Given: ABCD is a trapezoid,
AD=10, BC=8,
CK-altitude of ΔACD=30
Find: Area of ABCD
Answers
The area of the given trapezoid is 270 square units.
A trapezoid is a four-sided geometric shape that has two parallel sides (called the bases) and two non-parallel sides (called the legs). The area of a trapezoid is the amount of space inside the shape and can be calculated using the formula:
A = (a + b)h/2
Where:
a and b are the lengths of the two parallel sides of the trapezoid, and
h is the height (perpendicular distance) between the two parallel sides.
The area will be calculated as,
A = ( 10 + 8) x 30 /2
A = 270 square units
Therefore, the area is 270 square units.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
By evaluating the function related to the second derivative f''(x) = - 25 · sin 5x is equal to f(π / 5) = (14π - 50) / 25.
How to find the function related to a second derivative
In this question we find the definition of the second derivative of a function, this function must be found by integrals and initial values. First, write the entire function:
f''(x) = - 25 · sin 5x
Second, determine the first derivative:
f'(x) = (1 / 5) · cos 5x + C₁
f(0) = (1 / 5) · cos 0 + C₁
3 = 1 / 5 + C₁
C₁ = 14 / 5
f'(x) = (1 / 5) · cos 5x + 14 / 5
Third, determine the function:
f(x) = (1 / 25) · sin 5x + (14 / 5) · x + C₂
f(0) = (1 / 25) · sin 0 + (14 / 5) · 0 + C₂
- 2 = (1 / 25) · sin 0 + (14 / 5) · 0 + C₂
- 2 = C₂
f(x) = (1 / 25) · sin 5x + (14 / 5) · x - 2
Fourth, evaluate the function:
f(π / 5) = (1 / 25) · sin π + (14 / 5) · (π / 5) - 2
f(π / 5) = 14π / 25 - 2
f(π / 5) = (14π - 50) / 25
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Two homebuilders are working to get the windows installed on their homes. Tom uses the formula 42 = 7x + 2 to model the number of windows he is installing on his home and Suzanne uses the formula 37 = 6x + 5 to model the number of windows she is installing on her home. In each formula, x represents the number of days that Tom and Suzanne work on installing windows.
Answers
Tom is installing 6 windows each day and Suzanne is installing 6 windows each day as well.
To find the number of days it takes for each homebuilder to install the windows, we need to solve for x in each equation.
Tom's equation: 42 = 7x + 2
Subtracting 2 from both sides:
40 = 7x
Dividing both sides by 7:
x = 5.71 ≈ 6
So it will take Tom approximately 6 days to install the windows on his home.
Suzanne's equation: 37 = 6x + 5
Subtracting 5 from both sides:
32 = 6x
Dividing both sides by 6:
x = 5.33 ≈ 6.
So it will take Suzanne approximately 6 days to install the windows on her home.
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Question 6
A square is placed within a rectangle. Find the area of the shaded region.
Select one:
O
✪
✪
O
559 ft²
640 ft²
721 ft²
604 ft²
32 ft
19A
9 ft
20 ft
Answers
The area of the shaded region is 559 ft².
How to find the area of the shaded region?In order to find the area of the shaded region, we will subtract the area of the square from the area of the rectangle. That is:
area of the shaded region = area of rectangle - area of square
area of the shaded region = (32 * 20) - (9 * 9)
area of the shaded region = 640 - 81
area of the shaded region = 559 ft²
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Complete Question
See attached image
Question
Find the equation of the line shown.
-4-3
9 10
3
2
O-
27
-5
1 2 3 4
Answers
The equation of the line for the given points is y= (1/2)x - 3.
An equation of a line can be written in slope-intercept form, which is:
y = mx + b
where:
y and x are the coordinates of any point on the line.
m is the slope of the line (the rate at which y changes with respect to x).
b is the y-intercept of the line (the y-coordinate of the point where the line intersects the y-axis).
The slope of the line is calculated as,
m = ( y₂ -y₁) / (x₂ - x₁)
m = ( -2+1) / (2-4)
m = 1/2
The y-intercept is calculated as,
y = mx + c
-1 = (1/2)x 4 + c
c = -3
The equation of the line will be,
y = mx + c
y = (1/2)x - 3
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A farmer saw some chickens and pigs in a field. He counted 53 heads and 138 legs. Determine exactly how many chickens and pigs he saw.
Answers
The number of chickens and pigs the farmer saw on the field are 37 and 16 respectively.
How many chickens and pigs he saw?Let
Number of chickens = x
Number of pigs = y
x + y = 53
2x + 4y = 138
From (1)
x = 53 - y
Substitute x = 53 - y into (2)
2x + 4y = 138
2(53 - y) + 4y = 138
106 - 2y + 4y = 138
- 2y + 4y = 138 - 106
2y = 32
divide both sides by 2
y = 32/2
y = 16
Substitute y = 16 into
x + y = 53
x + 16 = 53
x = 53 - 16
x = 37
Therefore, there are 37 chickens and 16 pigs respectively.
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Casey rolls a fair number cube twice. If she rolls the same number twice in a row, then she gets to roll again. If she rolls a six on the third roll, she wins. How many outcomes are in the sample space that shows Casey wins
Answers
There are 6 such paths, so there are 6 outcomes in the sample space that show Casey winning.
We can use a tree diagram to visualize the different outcomes of Casey's rolls:
Each branch of the tree represents one roll of the number cube.
The first two rolls are independent and equally likely to be any of the six numbers.
If the first two rolls are the same number, then Casey gets to roll again. If the third roll is a 6, she wins.
We can count the number of outcomes in the sample space that show Casey winning by counting the number of paths in the tree that lead to a 6 on the third roll.
These are:
1-1-6
2-2-6
3-3-6
4-4-6
5-5-6
6-6 (rolls again)-6
Therefore, the answer is 6.
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For the given polynomials, find the sum of the squares of the real roots. :
P(x) = x^{3} - x^{2} - 18x + k
Answers
The sum of the squares of all the real roots of the polynomials = 1² + (-71) = -70
How to find the real roots of the polynomials?Using Vieta's formulas, the sum of the roots of the polynomials is 1, so the sum of the two non-positive roots is -1. Let's call these roots r and s. Then we have:
Let r and s be the non-positive roots of the polynomial P(x) = x³ - x² - 18x + k. Then we have:
r + s = -1
rs + k = 18
The sum of the squares of these roots:
r² + s² = (r + s)² - 2rs = 1 - 2(18 - k) = -35 + 2k
For the non-positive roots to be real, the discriminant of the polynomial must be non-negative, i.e.,
D = 18² - 4(1)(-k) = 72 + 4k ≥ 0
Solving for k, we get:
4k ≥ -72
k ≥ -18
So, the smallest value of k that makes the non-positive roots real is -18, and the sum of their squares is:
r² + s² = -35 + 2(-18) = -71
Finally, the sum of the roots of P(x) = 1 (by Vieta's formulas).
Therefore, the sum of the squares of all the real roots of the polynomials = 1² + (-71) = -70
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The table shows the number of bikes sold by a company from January to June of last year.
Answers
The mean number of bikes sold by the company from January to June was 146.17.
What is the mean number of bikes sold?
The mean, also called average refers to data set found by adding all numbers in the data set and then dividing by the number of values in the set.
Given data: 110 158 112 176 119 202
The total number of bikes sold is:
= 110 + 158 + 112 + 176 + 119 + 202
= 877
The number of months (Jan - Jun) = 6
The mean number of bikes sold will be:
= Ef/x
= 877 / 6
= 146.166666667
= 146.17
Full question "The table shows the number of bikes sold by a company from January to June of last year.
Find the mean number of bikes sold by the company from January to June.
January February March April May June
110 158 112 176 119 202"
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Find the surface area of a square pyramid with side length 1 km and slant height 2 km.
Answers
Answer: 5km
Step-by-step explanation:
The formula for Surface area of a square pyramid
SA= [tex]L^{2} + 2Ls[/tex] where L is the length on the bottom and s is the slant height
L=1 km s=2 km
SA = [tex]1^{2} +[/tex] 2(1)(2)
=1+4
=5km