Answer:
Either [tex]c = 12[/tex] or [tex]c = (-12)[/tex].
Step-by-step explanation:
Find the [tex]x[/tex]-coordinate of the intersection of the two curves by equating their [tex]y[/tex]-values and solving for [tex]x[/tex]:
[tex]x^{2} - c^{2} = c^{2} - x^{2}[/tex].
[tex]x^{2} = c^{2}[/tex].
[tex]x = c[/tex] or [tex]x = (-c)[/tex].
In other words, the two curves intersect both when [tex]x = c[/tex] and when [tex]x = (-c)[/tex].
Assume that [tex]c \ge 0[/tex]. The area enclosed would be over the range [tex](-c) < x < c[/tex]. Note that over this range, [tex]x^{2} \le c^{2}[/tex], so [tex]x^{2} - c^{2} \le 0 \le c^{2} - x^{2}[/tex]. The curve [tex]y = c^{2} - x^{2}[/tex] would be above [tex]y = x^{2} - c^{2}[/tex].
Integrate the upper curve minus the lower curve [tex](c^{2} - x^{2}) - (x^{2} - c^{2})[/tex] over this interval to find the area enclosed:
[tex]\begin{aligned}& \int\limits_{-c}^{c} \left((c^{2} - x^{2}) - (x^{2} - c^{2})\right)\, dx \\ =\; & \int\limits_{-c}^{c} \left(2\, c^{2} - 2\, x^{2}\right)\, dx \\ =\; & {\left[2\, c^{2}\, x - \frac{2}{3}\, x^{3}\right]}_{-c}^{c} && (\text{power rule}) \\ =\; & \left(2\, c^{2}\, c -\frac{2}{3}\, c^{3}\right) - \left(2\, c^{2}\, (-c) - \frac{2}{3}\, (-c)^{3}\right) \\ =\; & \frac{8}{3}\, c^{3} \end{aligned}[/tex].
In other words, assuming that [tex]c \ge 0[/tex], area enclosed between these two curves would be [tex](8/3)\, c^{3}[/tex]. Since this area is given, the value of [tex]c[/tex] can be found as:
[tex]\begin{aligned}c &= \sqrt[3]{\frac{3}{8}\, (\text{Area})} = 12\end{aligned}[/tex].
However, note that if [tex]c < 0[/tex], the order of limits of the integral would need to be reversed:
[tex]\begin{aligned}& \int\limits_{c}^{-c} \left((c^{2} - x^{2}) - (x^{2} - c^{2})\right)\, dx \\ =\; & \cdots \\ =\; & {\left[2\, c^{2}\, x - \frac{2}{3}\, x^{3}\right]}_{c}^{-c} \\ =\; & \left(2\, c^{2}\, (-c) - \frac{2}{3}\, (-c)^{3}\right) - \left(2\, c^{2}\, c -\frac{2}{3}\, c^{3}\right) \\ =\; & \left(-\frac{8}{3}\, c^{3}\right) \end{aligned}[/tex].
Hence, [tex]c = (-12)[/tex] would also be a solution to this question.
PLS HELP ME SOLVE THESE TWO QUESTIONS IM JUST NOT GETTING IT
Answer:
Below
Step-by-step explanation:
The two angles at U are equal....so the triangles have TWO equal angles: 72° and the angles at U
Answer A
Geometric mean is the square root of the two numbers after multiplying them sqrt ( 48* 12) = sqrt( 576) = 24
A church group set off from their
Church at 9:00a.m. The group had to change a tire at 9:38 a.m. the group noted that the trip took them 77 minutes to finish what time did the church group arrive at the canyon
Answer:
Below
Step-by-step explanation:
77 min is 1 hour 17 min...add this to the 9:00 start to find 10 :17 am
A trucker wanted to track how long it took to reach Bismarck. When she started out, her clock
read 7:00AM. When she refueled, the clock read 8:00AM. After reaching Bismarck, the clock read
10:00AM. How many hours did it take this trucker to reach Bismarck?
Answer:
Below
Step-by-step explanation:
From 7 to 10 AM is THREE hours (if the times are all on the same day)
Find the area of the rectangle
What is the area of the rectangle?
The area of the rectangle = 9x² +18x−16
What is the area of the rectangle?
The area of a rectangle is calculated by multiplying the height by the width. If the height of the rectangle is represented by h and the width is represented by w, then the area is given by:
A = h * w
In this case, the height of the rectangle is given as 3x - 2 yards, and the width is given as 3x + 8 yards. So, substituting these values into the formula:
A = (3x - 2) * (3x + 8)
A = (3x - 2)(3x + 8)
A = 9x² +18x−16
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The answer is:
9x² - 64Work/explanation:
To find the rectangle's area, we use the formula
[tex]\pmb{A=LW}[/tex]
Where A = area;
L = length;
w = width.
Plug in the data
[tex]\sf{A=(3x+8)(3x-8)}[/tex]
To multiply, use FOIL:
F = first
o = outside
i = inside
l = last
Multiply
[tex]\sf{3x\cdot3x=9x^2}[/tex]
[tex]\sf{3x\cdot(-8)=-24x}[/tex]
[tex]\sf{8\cdot3x=24x}[/tex]
[tex]\sf{8\cdot(-8)=-64}[/tex]
-------------------
[tex]\sf{9x^2-24x+24x-64}[/tex]
[tex]\sf{9x^2-64}[/tex]
Hence, the area is 9x² - 64.one ordered pair that is a solution of y is greater then or equal to 4
On solving the provided question, we can say that the inequality formed is 1 ≥ 2(3)-5 => 1 ≥ 1
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
The ordered pair is (3, 1)
Substitute (x, y)=(3, 1) in the given inequality, we get
the inequality formed is
1 ≥ 2(3)-5
1 ≥ 1
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1 6/11 ft of fabric is needed to make a rug? while 4 1/2 ft of fabric is required to make pillows/ Producing a rug is 2 2/7 times faster than pilliws/ How much more fabric is needed to make pillows versus a rug
2 21/22 feet of more fabric is required to make pillows versus a rug.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, 17/11 ft of fabric is needed to make a rug, while 9/2 ft of fabric is required to make pillows.
Also given that producing a rug is 16/7 times faster than pillows.
Therefore, The amount of extra fabric needed to make a pillow compared to a rug is,
= (9/2 - 17/11).
= (99 - 34)/22.
= 65/22 feet.
= 2 21/22 feet.
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At Hometown Hospital, the cancer registrar recorded the age (at the time of initial diagnosis) of patients diagnosed with lung cancer. A total of 68 cases were recorded. The ages are ranked from oldest to youngest.
91 86 83 82 81 80 80 79 78 77 76 75 75 74 74 73 73 72
72 72 71 71 70 70 70 70 69 69 68 68 67 67 67 66 66 66
66 66 65 65 65 64 64 63 63 62 62 61 61 61 60 60 59 59
59 58 58 57 57 57 56 56 55 54 53 53 52 51
Complete the frequency distribution table with the following data:
1. All score limit ranges
2. Frequency
3. Cumulative frequency
4. Relative frequency [round to two decimal places]
5. Frequency percentage [should be a whole percentage without decimals]
6. Graph your frequency distribution in a histogram [grouped data] Make sure to label the histogram and give it a title.
7. One paragraph [4-5 sentences] that would let your readers know what your table means/shows.
score limits f cf rel. f freq. %
91-95
51-55
Then determine the value for:
1) 1st decile
2) 3rd decile
3) 65th percentile
4) 85th percentile
5) Percentile for an age of 71
6) Average age at time of diagnosis
Answer:
First Class Group is given as 25-29 Class size = 29-25=4 Make the reminding classes of same size till 89-93 Count the values and write the frequency against the respective
What is the value of y?
The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). In this example, the value "5" is the Y Coordinate.
HELP PLSS (show how to solve) for 59 points
Answer: Dude this is pretty easy!
Step-by-step explanation: Use the process of elimination.
Hint: It's just subtraction or addition. Trust me it's easy.
Answer:
Step-by-step explanation:
1/4 min, 15 sec
Describe a situation that you can model with 6m+3 = 27. Explain what the variable represents and solve the equation.
Answer:
Step-by-step explanation:
its 18+27 because you have to do 6x3 wich is 18 and add 27 to 18
Answer:
4
Step-by-step explanation:
Subtract 3 from both sides.Then divide both sides by 6 to give you your answer.Miguel bought a scarf. He paid $9.92 and received $0.01 in change. How much did the scarf cost?
Answer:
The scarf cost:
$9.91
Step-by-step explanation:
9.92 - 0.01 = 9.91
It took Mr. Black 2 hours to drive to his friend's house. On the way back the traffic was heavy, and Mr. Black drove 20 mph slower. The trip back took 1 hour longer. What was Mr. Black's speed to his friend's house?
Mr. Black was driving at 60 mph to his friend's house.
What was Mr. Black's speed to his friend's house?Let's call Mr. Black's speed to his friend's house "x".
The trip back took x - 20 mph, since he was driving 20 mph slower.
The trip back took 1 hour longer, so it took 2 + 1 = 3 hours.
Using the formula for distance = rate x time, we can set up the equation:
x * 2 = (x - 20) * 3
Expanding and simplifying, we get:
2x = 3x - 60
Subtracting 2x from both sides:
0 = x - 60
Adding 60 to both sides:
x = 60 mph
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I need this for math homework anyone on tonight to help? 5/8 = x/12 x=
What is the estimated answer of 0.93 x 2.6
Answer:
2.5!
Step-by-step explanation:
round 0.93 up to 1 and 2.6 down to 2.5
1*2.5 = 2.5
Answer:like 3
Step-by-step explanation:
Factor out the greatest common factor.
2x³ + 8x² - 4x
Answer:
[tex]2x(x^2+4x-2)[/tex]
Step-by-step explanation:
We can factor out 2x:
[tex]2x^3+8x^2-4x=2x(x^2+4x-2)[/tex]
QUESTION 9 1 POINT
Determine the interval(s) for which the function shown below is decreasing.
A function is decreasing if as x-values increase, the y-values decrease. Graphically this means that if you move from left-to-right, the graph goes down.
The downhill portion of this curve is on the interval [tex](1,\infty)[/tex].
3. Which expressions have the same solution as -4.
a.
-4.5
-3 -7
-5/?
Select all that apply.
4(-6), 6(-4), and 12(-2). (-2). Each one adds up to -24. I am aware of this because if you multiply the two numbers and one of the numbers is negative, the result will also be negative. The item will be favorable if there are just two drawbacks.
What is meant by negative numbers?Describe how a negative number is similar to having no money at all and owing someone money. It is a negative number. Therefore, the value is less or less, the larger the numeral. If a number is more than zero, it is positive. Less than zero makes a number negative. If a number is higher than or equal to 0, it is considered to be non-negative. Any number that is less than or equal to zero is considered non-positive. Around 200 BCE, China was the first place to use negative numbers. They stood in for the cost of an item being bought or a debt. In any mathematical work, Diophantus was the first to discuss negative numbers.To learn more about negative numbers, refer to:
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G
Identifying Exponential Growt
Which is an exponential growth funcion
0f3=61025/
04-0295254
0f=423
0fx)=(-1257
Answer:
The exponential growth function 0f3=61025/ 04-0295254 0f=423 0fx)=(-1257 is not a valid equation.
Step-by-step explanation:
A telephone company charges $30 a month and gives the customer 200 free minutes. After the 200 min, the company charges $0.03 a minute.
(a) Write the function using function notation.
(b) Find the cost for talking 350 min in a month
(c) Find the number of minutes used if the monthly charge is $34.68
Answer:
(a)
f(x) = 30, for x ≤ 200
f(x) = 0.03(x - 200) + 30, for x > 200
(b) $34.50
(c) 356
Step-by-step explanation:
Let x = number of minutes.
(a)
f(x) = 30, for x ≤ 200
f(x) = 0.03(x - 200) + 30, for x > 200
(b)
Here, x = 350, so x > 200.
f(x) = 0.03(x - 200) + 30
f(350) = 0.03(350 - 200) + 30
f(350) = 0.03(150) + 30
f(350) = 4.5 + 30
f(350) = 34.5
$34.50
(c)
f(x) = 0.03(x - 200) + 30
0.03(x - 200) + 30 = 34.68
0.03(x - 200) = 4.68
x - 200 = 156
x = 356
Examine the triangle below, find the m
mZM=The length of NP is 6.28 cm
What do you mean by triangle?A triangle is a two-dimensional geometric shape with three sides and three angles. It is one of the basic shapes in geometry and has many different properties that can be studied. Triangles can be classified into several different types based on the length of their sides and the size of their angles.
The most basic type of triangle is an equilateral triangle, which has three sides of equal length and three equal angles. Another common type of triangle is the right triangle, which has one right angle (90 degrees) and two other angles that add up to 90 degrees. Scalene triangles have no sides or angles of equal length, while isosceles triangles have at least two sides of equal length.
Triangles have many interesting and useful properties that can be used in geometry and other areas of mathematics. For example, the Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side. This theorem can be used to find the length of a missing side in a right triangle.
To find angle P and angle M, we can use the fact that the sum of the angles in a triangle is 180 degrees.
angle P + angle M + 46 = 180
angle P + angle M = 134
Next, we can use the law of cosines to find angle P. Let's call the length of NP "x".
cos(angle P) = (MN² + MP² - x²) / (2 × MN × MP)
We can use the formula for cosine to solve for angle P:
angle P = arccos((MN² + MP² - x²) / (2 × MN × MP))
Substituting in the values for MN and MP:
angle P = arccos((4² + 7² - x²) / (2 × 4 × 7))
Next, we can use the Pythagorean theorem to find x:
x^2 = MN^2 + MP^2 - 2 * MN * MP * cos(angle P)
x^2 = 4^2 + 7^2 - 2 * 4 * 7 * cos(angle P)
x² = 49 - 56 × cos(angle P)
Substituting in the value we found for angle P:
x² = 49 - 56 × cos(arccos((4² + 7² - x²) / (2 × 4 × 7)))
Solving for x, we get:
x = sqrt(49 - 56 × cos(arccos((4² + 7² - x²) / (2 × 4 × 7))))
x = sqrt(49 - 56 × cos(arccos(33 / 28)))
x = √(49 - 56 × (33 / 28) / √(33² + 28²))
x = √(49 - 56 × 33 / 28 / √(33^2 + 28^2))
Finally, we can use the value we found for x to find angle M:
angle M = 134 - angle P
angle M = 134 - arccos((4² + 7² - x²) / (2 × 4 × 7))
So the final answers are:
angle P = arccos((4² + 7² - x²) / (2 × 4 × 7)) = 68.93 degrees
angle M = 134 - angle P = 65.07 degrees
length of NP = x = sqrt(49 - 56 × 33 / 28 / √(33² + 28²)) = 6.28 cm
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Two cars start from towns 660 mi apart and travel toward each other. They meet after 6 hr. Find the speed of each car if one travels 10 mph faster than the other.
The speed of the cars are 50mph and 60mph
How to determine the speed of each carLet's call the speed of the slower car "x". The faster car is traveling at "x + 10 mph".
The total distance both cars travel is 660 miles, and the time it takes for them to meet is 6 hours.
Using the formula for distance = rate x time, we can set up the equation:
x * 6 + (x + 10) * 6 = 660
Expanding and simplifying, we get:
12x + 60 = 660
Subtracting 60 from both sides:
12x = 600
Dividing both sides by 12:
x = 50 mph
So the slower car is traveling at 50 mph and the faster car is traveling at 60 mph.
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Someone help me with this math problem.
Answer:
Good luck man.
Step-by-step explanation:
Ima be honest, I got no idea.
v= u + at
work out the value of v
Answer:
I don’t even know
Step-by-step explanation:
Choose if simple or compound. If compound which type: *Conjunction *Disjunction *Conditional *Biconditional a. Twilight is my favorite time to set on the porch (simple or compound) b. I will get coffee if and only if I want to stay awake. c. Lemons are yellow and limes are green.
We can classify them as -
Twilight is my favorite time to set on the porch : Simple.I will get coffee if and only if I want to stay awake : Conditional.Lemons are yellow and limes are green : Conjunction.What are the types of propositional logics?There are six primary statement forms in Propositional Logic -
SimpleConjunctionDisjunctionConditionalBiconditionalNegationGiven are the statements as -
Twilight is my favorite time to set on the porch.I will get coffee if and only if I want to stay awake. Lemons are yellow and limes are green.We can classify them as -
Twilight is my favorite time to set on the porch : Simple.I will get coffee if and only if I want to stay awake : Conditional.Lemons are yellow and limes are green : Conjunction.Therefore, we can classify them as -
Twilight is my favorite time to set on the porch : Simple.I will get coffee if and only if I want to stay awake : Conditional.Lemons are yellow and limes are green : Conjunction.To solve more questions on propositional logics, visit the link below-
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A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional
minute.
(a)Write a function to represent the cost, C, of a call as a function of its length tin minutes.
b)State the domain and range of the function.
c)Determine the cost of a call that lasts 12minutes.
(d)Determine the cost of a call that lasts 1 hour.
Answer:
a) Let's call the length of a call "t" (in minutes). The cost of a call can be represented as follows:
C(t) = 0.99 if t <= 20
C(t) = 0.99 + 0.07(t - 20) if t > 20
b) The domain of the function is all non-negative real numbers (t >= 0), since a call can have any non-negative length in minutes. The range of the function is all non-negative real numbers, since the cost of a call can never be negative.
c) If a call lasts 12 minutes, then the cost would be 0.99:
C(12) = 0.99
d) If a call lasts 1 hour (60 minutes), then the cost would be:
C(60) = 0.99 + 0.07(60 - 20) = 0.99 + 0.07(40) = 0.99 + 2.80 = 3.79
Step-by-step explanation:
if cos theta =3/4 find sin (90°-0)
Answer:
Below
Step-by-step explanation:
sin (90 -0) = sin (90) = 1
Remember sin^2 + cos^2 =1
for theta sin2 + (3/4)^2
sin^2 = 1 - 9/16 = 7/16
sin (theta) = ± sqrt(7) /4
pilar said that the expressions -4x + 3x + 2 and -x + 2 are equivalent. is pilar correct. explain
Yes, this is correct. If you solve the first equation it equals the second equation.
Please help me with my math
Answer:
square 3. Multipky the result by -2 and then subtract 4.
Step-by-step explanation:
comment if u need explanation
11. Check for Reasonableness Santiago wants to display categorical data
in a circle graph. He divides the circle graph into 5 equal sections because
the data set has 5 groups. Do you agree? Justify your answer,
Answer: Not necessarily. Dividing the pie chart into 5 equal sections might be a way to display categorical data if the number of categories is 5. However, dividing it into 5 sections might not be the best way to display the data if the number of categories is different than 5 or if any category has a significantly higher or lower proportion than the others. In this case, it may be more appropriate to use a different scale to display the correct ratio. It is important to consider data distribution and visualization clarity before choosing how to display categorical data.
Graphing
100 POINT FOR HELP!!