the radius of the new circle =5cm
5cm is your answer love
Evaluate the integral. 3 f(x) dx −4 where f(x) = 3 if −4 ≤ x ≤ 0 4 − x2 if 0 < x ≤ 3
It looks like you have
[tex]f(x) = \begin{cases} 3 & \text{if } -4 \le x \le 0 \\ 4 - x^2 & \text{if } 0 < x \le 3\end{cases}[/tex]
and the integral you want to compute is
[tex]\displaystyle \int_{-4}^3 f(x) \, dx[/tex]
Split the integral up at [tex]x=0[/tex]. Then
[tex]\displaystyle \int_{-4}^3 f(x) \, dx = \int_{-4}^0 f(x)\,dx + \int_0^3 f(x)\,dx \\\\ ~~~~~~~~~~~~ = \int_{-4}^0 3 \, dx + \int_0^3 (4 - x^2) \, dx \\\\ ~~~~~~~~~~~~ = 3(0 - (-4)) + \left(4\cdot3 - \frac{3^3}3\right) = \boxed{15}[/tex]
After evaluating the integral we get 15
Integral is the representation of the area of a region under a curve. We approximate the actual value of an integral by drawing rectangles. A definite integral of a function can be represented as the area of the region bounded by its graph of the given function between two points in the line.
Given,
f(x) = 3 if - 4 ≤ x ≤ 0
f(x) = 4 - [tex]x^{2}[/tex] if 0 < x ≤ 3
Then,
[tex]f(x) = \left \{ {{3} \atop {4-x^{2} }}[/tex]
We need to solve the integral -[tex]\int\limits^3_4 {f(x)} \, dx[/tex]
Elaborate the integral with x = 0
-[tex]\int\limits^3_4 {f(x)} \, dx[/tex]
= -[tex]\int\limits^0_4 {f(x)} \, dx + \int\limits^3_0 {f(x)} \, dx[/tex]
= -[tex]\int\limits^0_4 {3} \, dx + \int\limits^3_0 {4-x^{2} } \, dx[/tex]
= 3 ( 0 - (-4)) + (4.3 - [tex]\frac{3^{3} }{3}[/tex])
= 15
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Canceling units is also called: a. changing the value c. multiplication b. unit analysis d. making connections
Canceling units is also called unit analysis.
This is also called dimensional analysis.
What is a unit of analysis in statistics?
The unit of analysis is the entity that you're analyzing. It's called this because it's your analysis (what you want to examine) that determines what this unit is, rather than the data itself.Because it is the analysis you do in your study that determines what the unit is. For instance, if you are comparing the children in two classrooms on achievement test scores, the unit is the individual child because you have a score for each child.For example -
1 ft = 12 in
3 ft = [tex]3 ft * \frac{12 in }{1 ft}[/tex]
3 ft = ( 3 * 12 ) in ⇒ 36 in
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Suppose a researcher conducts an A-B-A-B study. She records baseline observations and then administers a treatment and records behavior during treatment. What will she do next
If we suppose a researcher conducts an A-B-A-B study. She records baseline observations and then administers a treatment and records behavior during treatment. Her next step would be administering the treatment again.
Reason Behind the Next Step of the Study
It is given the the researcher conducts an A-B-A-B study.
Her first step was recording the baseline observations.
Hence, first A indicates the first step here that is, recording the observations
In the next step of the study, she administers a treatment.
Thus, B denotes the administering treatment step.
Again, for the third step of the study, she again records behavior during the treatment.
This is again denoted by A.
Hence, we can conclude that in the A-B-A-B study, A denotes recording observation or behavior, B denotes administering a treatment.
Now, since, A, B, and A steps of the study have already been followed, the next phase is B which is concerned with reintroducing or re-administering the treatment.
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A square pyramid has a height of 6 units and a volume of 70 units3. if a square prism has the same base area and volume as the square pyramid, what is its height?
The height is 2 units.
What is a square pyramid?In terms of geometry, a square pyramid is a pyramid with a square base and four lateral faces. A pyramid is a polyhedron with three or more triangle faces that meet above its base. A square pyramid is a pentahedron, a three-dimensional form with a total of five faces.Find the area of the base of the square pyramid:
The volume of the square pyramid is equal to [tex]V=\frac{1}{3} BH[/tex]
B is the area of the base, and H is the height of the pyramid
[tex]H= 6 units[/tex]
[tex]V=70 units^{3}[/tex]
Solve: B
[tex]70=\frac{1}{3} B(6)\\ \\ B=\frac{70}{2} \\ \\ = 35units[/tex]
To find the height of the square prism:
The volume of the square prism is equal: [tex]V=Bh[/tex]
B is the area of the base and h is the height of the prism
[tex]B=35 units^{2}[/tex]
[tex]V=70units^{3}[/tex]
Solve: h
[tex]70=\frac{35}{h}[/tex]
[tex]h=2units.[/tex]
The height is 2 units.
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The height of the square pyramid exists 2 units.
How to estimate the area of the base of the square pyramid?Volume of the square pyramid
[tex]$V = \frac{1}{3}BH[/tex]
where B exists in the area of the base H lives at the height of the pyramid
we have H = 6 [tex]$$unit^3[/tex]
V = 70 [tex]$$unit^3[/tex]
substitute in the formula and solve for B, we get
[tex]$70 = \frac{1}{3}B(6)[/tex]
B = [tex]$\frac{70}{2}[/tex]
= 35 [tex]$$unit^3[/tex]
To estimate the height of the square prism
Volume of the square prism = Bh
Where B exists the area of the base
h exists the height of the prism
we have B = 35 and V = 70
substitute in the formula and solve for h
70 = (35)h
h = 2 units.
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Factor the polynomial completely
10³ -25r² - 12r + 30
Find the value of x
a. 13 b. 14/5 c. 5 d. 8
Answer:
C. 5
Step-by-step explanation:
The product of chord segment lengths is the same for the two crossing chords.
ApplicationOne chord has segment lengths 4 and 10; the other has segment lengths x and 8.
(4)(10) = (x)(8)
40/8 = x = 5 . . . . . . . divide by the coefficient of x
The value of x is 5, making option C the right choice, using the chord theorem.
The chord theorem, also known as the intersecting chords theorem, is a statement in basic geometry that explains the relationship between the four line segments formed by two intersecting chords inside of a circle. According to this statement, the products of the line segment lengths on each chord are equal.
In the question, we are asked to find the value of x.
Using the chord property, we know that:
8*x = 4*10,
or, 8x = 40,
or, x = 40/8,
or, x = 5.
Thus, the value of x is 5, making option C the right choice, using the chord theorem.
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If ph term of A.P. is q and qth term is p, then (p+q) term is??
If the pth term of an arithmetic progression is q and qth term is p then the (p+q) th term is 0.
Given that the p th term of an A.P is q aand q th term is p.
We are required to find the (p+q) th term of that A.P.
Arithmetic progression is a sequence in which all the terms have common difference between them.
N th term of an A.P.=a+(n-1)d
p th term=a+(p-1)d
q=a+(p-1)d-------1
q th term=a+(q-1)d
p=a+(q-1)d---------2
Subtract equation 2 by 1.
q-p==a+(p-1)d-a-(q-1)d
q-p=pd-qd-d+d
q-p=d(p-q)
d=(p-q)/(q-p)
d=-(p-q)/(p-q)
d=-1
Put the value of d in 1.
q=a+(p-1)(-1)
q=a-p+1
a=q+p-1
(p+q) th term=a+(n-1)d
=q+p-1+(p+q-1)(-1)
=q+p-1-p-q+1
=0
Hence if the pth term of an A.P is q and qth term is p then the (p+q) th term is 0.
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PLEASE HELP IM STUCK
The completed equations are:
2x + 3y = 80 equation 1
x + y = 37 equation 2
What are the completed equations?
In order to determine the number of each type of shots made, two equations would be derived based on the information provided in the question. These equations would be solved simultaneously in order to determine the required values.
[(type of basket made)x ]+ [(type of baskets made)y] = total number of points
2x + 3y = 80
x + y = total number of baskets
x + y = 37
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If r varies jointly as s and t, and r = 8 when s = 6 and t = 4, find s when t = 16 and r = 24.
The value of s for the given conditions is 9/2.
What is a quadratic equation ?Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.
According to the given information:r = k*s*t
k = constant of proportionality
r = 8
s = 6
t = 5
Putting the value in the equation:
8 = k x (6) x (4)
8 = 24k
k = 8 /24
k = 1/3
Now,
t = 16
r = 24
Putting the value in the equation:
r = k*s*t
24 = 1/3( x (s) x (16))
((24) x (3) )/ 16 = s
((3) x (3))/2 = s
s = 9/2
The value of s for the given conditions is 9/2.
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The sum of three numbers is 134. The second number is 8 less than the first. The third number is 4 times the second. What are the numbers?
Answer:
29, 21, 84
Step-by-step explanation:
Let the first number be x.
The second number is x - 8.
The third number is 4(x - 8).
Their sum is 134.
x + (x - 8) + 4(x - 8) = 134
x + 5(x - 8) = 134
x + 5x - 40 = 134
6x = 174
x = 29
x - 8 = 29 - 8 = 21
4(x - 8) = 4(29 - 8) = 4(21) = 84
sixteen thousand, four hundred eighty-two. Write this number in standard
In a recent year, the population of Springfield, Illinois was one hundred
form. Show your work in the space below. Remember to check your solutic
Answer:
16482 this is the answer
[THESE ARE NOT THE RIGHT ANSWERS I JUST GUESSED]
Consider the graph of function f.
у
OA.
-2
OB.
6+
4
2
2
S
Which is the graph of the function g(x) = f(-x)?
9
N
6
44
2
y
2
4
6
y
6
-
40
X
IN
on
4
X
The parent function of the function represented in the table is exponential.
Note if you subtract 10 from each output, you get [tex]f(x)=3^x[/tex].If function f was translated down 4 units, the f(x) values would be decreased by 4.
See attached image.A point on the table for the transformed function would be (4, 87).
[tex]f(4)-4=87[/tex]The figure shows a square, a regular pentagon and a regular hexagon put together. What is the measure of ∠BAC
Answer:
42
Step-by-step explanation:
One angle of a regular pentagon = 108°
One angle of a regular hexagon = 120°.
One angle of a square = 90°
∴ ∠BAC = 360 – (108 + 20 + 90) 360 – 318 = 42°
PLEASE I NEED THIS FAST there are 3 denominations of bills in a wallet: $1, $5, and $10. there are 5 fewer $5-bills than $1-bills there are half as many $10-bills if there is $115 altogether, find the number of each type of bill in the wallet
The number of $1, $5 and $10 are 49, 44 and 22 respectively.
How to use equation to find the number of bills?There are 3 denominations of bills in a wallet: $1, $5, and $10.
There are 5 fewer $5-bills than $1-bills.
let
x = number of $1 bills
Hence,
number of $5 bills = x - 5
There are half as many $10-bills as $5-bills.
number of $10 bills = 1 / 2 (x - 5)
Therefore,
x + x - 5 + 1 / 2 (x - 5) = 115
2x - 5 + 1 / 2 x - 5 / 2 = 115
2x + 1 / 2 x - 5 - 5 / 2 = 115
5 / 2 x - 7.5 = 115
2.5x = 115 + 7.5
x = 122.5 / 2.5
x = 49
Number of $1 bills = 49
Number of $5 bills = 49 - 5 = 44
Number of $10 bills = 1 / 2 (49 - 5) = 22
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The selling price, s, of an item is s = c mc, where c is the cost of the item and m is the percent markup based on cost. what is the formula solved for m? m = startfraction s minus c over c endfraction m = startfraction s c over c endfraction s minus c = m s c = m
Answer:
s - c over c = m or (s-c)/c = m
Step-by-step explanation:
s = c * mc
s -c = mc
(s - c) / c = m
Answer:
A ) m=s-c/c
Step-by-step explanation:
A regular hexagon has an apothem of 14.7 inches and a perimeter of 101.8 inches. what is the area of the hexagon? square inches
Answer:
748.23 in^2.
Step-by-step explanation:
Area = 1/2 * apothem * perimeter
= 1/2 * 14.7 * 101.8
= 748.23 in^2.
Answer:
748.23
Step-by-step explanation:
please please please please please please please please please please please please please please please please please help mey,
Answer:
See below
Step-by-step explanation:
REMEMBER sec = 1/cos ...so the left side is
[1/cos -1] / [1/cos +1 ]
get common denominator for numerator and denominator
[ (1 -cos) /cos ] / [ (1+cos) / cos ]
now flip the bottom fraction and multiply to get
[(1-cos/cos) ] * [ cos / (1+cos) ] which simplifies to ( the 'cos' term cancels)
(1-cos) / (1+cos) done !
The data in the table represents the volume of helium, in cubic feet, inside a balloon relative to the elapsed time in minutes.
The interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the slope?From the table of values, we have the following points
(x, y) = (5, 5.5) and (10, 5)
The slope of the table of values is calculated as:
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (5 - 5.5)/(10 -5)
Evaluate the difference
m = -0.5/5
Evaluate the quotient
m = -0.1
This means that the slope is -0.1
From the table of values, we have
x represents the elapsed time and y represents the volume of helium
So, the interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute
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Which of the graphs below represents the equation 4x+y=7
An amusement park sells adults' and
children's passes. An adult's pass is $25,
and a child's pass is $15. A group spent
$440 on 20 passes. How many children's
passes did the group purchase?
A
Answer:
6 children passes
Step-by-step explanation:
a = adult and c = children
25a + 15c = 440 and a + c = 20
c = 20 - a
25a + 15(20-a) = 440
25a + 300 - 15a = 440
25a - 15a = 440 - 300
10a = 140
a = 140/10
a = 14 and this is 14 adult tickets
Now we plug the a value into the equation to find the c value
14 + c = 20
c = 20 - 14
c = 6
Verify answer:
25(14) = 15(6) = 440
350 + 90 = 440
440 = 440
Instructions: Find the length of the arc. Round your answer to the nearest tenth.
Answer:
7
Step-by-step explanation:
The length of the arc can be calculated via a simple proportion:
2 pi r : 360° = x : 45°
Where r is the radius of the circumference and x the length of the arc we want to know. Isolating the x:
x = (2 pi r : 360) * 45 = (2 pi * 9 : 180) * 45 = 18 pi : 360 * 45 = 18pi : 8 = 7
Maria was shopping for a camera and found one that was on sale for 30% off. As she went to pay for it, the store announced an instant sale that took an additional 10% off all items. If the final price Maria paid was $207.27, what was the original price (before all discounts) of the camera? Possible Answers: $290.18 $329.00 $518.18 $767.67 $82.91
Answer:
$329.00
Step-by-step explanation:
Let the original price be $x, then
x - 0.30x - 0.10(x - 0.30x) = 207.27
x - 0.30x - 0.10x + 0.03x = 207.27
0.63x = 207.27
x = 329.00.
cosa/2-tana +sina/1-cota=cosa+sina
Answer:
Cosa/2-tana+sina
Step-by-step explanation:
Cosatana
3. What is the missing term in the sequence below?
3, 6, 11, ?, 27, 38, 51
The combination for opening a safe is a four-digit number made up of different digits. How many different combinations cna you make, using only odd digits?
Answer:
120
Step-by-step explanation:
My choices are: 1, 3, 5, 7, 9. I cannot repeat any of the numbers.
The first spot, I have 5 choices. The second spot, I have 4 choices, the third spot, I have 3 choices and the final spot has only 2 choices.
5x4x3x2 = 60
David's car was valued at $38,000 in the year 2007. If it is continuously depreciating in value by 6% every year, how much will it be worth in 2017
The car will be worth $20467 in 2017
How to determine the worth in 2017?The given parameters are:
Initial value, a = 38000
Depreciation rate, r = 6%
The value of the car after x years is represented by the following exponential equation
V(x)= a(1 - r)^x
Substitute the known values in the above equation
V(x) = 38000 * (1 - 6%)^x
2017 is 10 years from 2007
This means that x = 10
So, we have:
V(x) = 38000 * (1 - 6%)^10
Evaluate
V(x) = 20467
Hence, the car will be worth $20467 in 2017
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HELPPP ASAP 25PTS! Find the area of the shape
Answer:
480
Step-by-step explanation:
can someone help me with these kind of fractions
[tex]\frac{1}{2} of \frac{2}{3}[/tex]
Answer:
[tex]\frac{2}{6}[/tex] or [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
To find a fraction of a fraction simply multiply the numerators and denominators into another fraction:
[tex]\frac{1}{2}*\frac{2}{3} = \frac{2}{6} = \frac{1}{3}[/tex]
Answer:
1/3.
Step-by-step explanation:
'of' means multiply. so
1/2 of 2/3
= 1/2 * 2/3
= 1*2 / 2*3
= 2/6
= 1/3.
Determine whether the following series converges or diverges using any test. Be sure to clearly state what test(s) you are using and check any conditions needed to apply that test.
According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.
How to determine whether a series converges by ratio criterioHerein we have a series in rational form, whose convergence can be proved by the ratio criterion, whose defintion is shown below:
x = lim (n → ∞) |aₙ/aₙ₊₁| (1)
The series converges if x < 0 and diverges when x > 1. If x = 1, the criterion cannot be used and another criterion must be used instead. Now we proceed to apply it on the expression behind the series:
|aₙ/aₙ₊₁| = [(2 · n + 1) · (2 · n + 2)] / [5 · (n + 1)²]
|aₙ/aₙ₊₁| = [4 · n² + 5 · n + 2] / [5 · n² + 10 · n + 5]
Then, by applying the limit property for rational equations we find that limit of the expression within the series is:
L = 4 / 5
According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.
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By the ratio test, the series diverges.
[tex]\displaystyle \lim_{k\to\infty} \left| \frac{5^{k+1} ((k+1)!)^2}{(2(k+1))!} \cdot \frac{(2k)!}{(5^k (k!)^2}\right| = 5 \lim_{k\to\infty} \frac{(k+1)^2}{(2k+2)(2k+1)} = \frac54 > 1[/tex]
Lou received requests for 150 tickets for their art show. The number of requests was 120% of the number of tickets they had. How many tickets do they have?
Answer:
180
Step-by-step explanation:
If she received requests for 150 tickets, and that is 120% of what they have, you would find 20% of 150. You would do this because 100% of 150 is 150, now you need to add the other 20%, so you have to find 20% of 150. Which is 30. You would then add that to 150 sine it is 120% of what they have. So, they have 180 tickets
