Volume of cuboid =l×b×h
area of base of the cuboid =l×b
hence
volume of cuboid is = area of base × height
140=88×h
h=140÷88
h=5
Integrate the integral:
[tex]\int \frac{1}{\sqrt{x} \sqrt{1-x} }[/tex]
Answer:
[tex]\displaystyle \int {\frac{1}{\sqrt{x} \sqrt{1-x} } } \, dx = 2arcsin(\sqrt{x}) + C[/tex]
General Formulas and Concepts:
Calculus
U-SubstitutionIntegration Property: [tex]\int {cf(x)} \, dx = c\int {f(x)} \, dx[/tex]Arctrig Integration: [tex]\displaystyle \int\limits {\frac{1}{\sqrt{a^2-u^2} } } \, du = arcsin(\frac{u}{a} ) + C[/tex]Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int\limits {\frac{1}{\sqrt{x} \sqrt{1-x} } } \, dx[/tex]
Step 2: Identify
Set up variables for u-substitution and integral trig.
[tex]\displaystyleu = \sqrt{x}\\a = 1\\du = \frac{1}{2\sqrt{x}}dx[/tex]
Step 3: integrate
Rewrite Integral: [tex]\displaystyle 2\int {\frac{1}{2\sqrt{x} \sqrt{1-x} } } \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle 2\int {\frac{du}{\sqrt{1^2-(\sqrt{x})^2 } }[/tex][Integral] U-Sub Arctrig: [tex]\displaystyle 2\int {\frac{du}{\sqrt{1^2-u^2 } }[/tex][Integral] Arctrig: [tex]\displaystyle 2arcsin(\frac{u}{1}) + C[/tex]Simplify: [tex]\displaystyle 2arcsin(u) + C[/tex]Back-substitute: [tex]\displaystyle 2arcsin(\sqrt{x} ) + C[/tex]We are given the expression:
[tex]\int\limits {\frac{1}{\sqrt[]{x} }*\frac{1}{\sqrt[]{ 1-x^{2}}} } \, dx[/tex]
U-substitution:
let u = [tex]x^{1/2}[/tex] [So, x = u²]
[tex]\frac{du}{dx} = \frac{1}{2\sqrt[]{x}}[/tex] [differentiating both sides wrt x]
dx = du*2√(x)
dx = 2u(du) [Since u = √x]
Finding the Integral:
Plugging these values in the given expression:
[tex]\int\limits {u^{-1}*(1-u^{2})^{-1/2} } \, 2\sqrt[]{x}*du[/tex]
[tex]\int\limits {\frac{1}{u}*\frac{1}{\sqrt[]{ 1-u^{2}}}*2u } \, du[/tex]
The 'u' in the numerator and denominator will cancel out
[tex]\int\limits {\frac{1}{\sqrt[]{ 1-u^{2}}}*2 } \, du[/tex]
Since 2 is a constant
[tex]2\int\limits {\frac{1}{\sqrt[]{ 1-u^{2}}} } \, du[/tex]
Using the property: [tex]\int\limits {\frac{1}{\sqrt[]{1-x^{2}} }} \, dx[/tex] = ArcSin(x) + C
2*ArcSin(u) + C
Since u = √x :
2*ArcSin(√x) + C
Find three solutions to the linear equation 4x+y=20
Answer:
[tex](0,20),(1,16),(2,12)[/tex]
Step-by-step explanation:
[tex]We\ are\ provided\ with\ the\ equation:\\4x+y=20\\In\ order,\ to\ find\ solutions\ to\ a\ linear\ equation\ in\ two\ variables,\ we\\ usually\ substitute\ a\ value\ to\ either\ the\ abscissa or\ the\ ordinate\ to\ get\\ the\ corresponding\ ordinate\ or\ the\ abscissa.\\Hence,\\Here,[/tex]
[tex]Let's\ plug\ in\ simpler\ value's\ of\ 0,1,2\ as\ the\ x-co-ordinate\ to\ obtain\ it's\\ y-coordinate.\\Hence,\\Coming\ back\ to\ our\ equation:4x+y=20\\Substituting\ x=0,\\4*(0)+y=20\\y=20\\Hence,\\x=0,y=20\ or\ (0,20)\ is\ a\ solution\ of\ the\ equation.[/tex]
[tex]Substituting\ x=1,\\4*(1)+y=20\\4+y=20\\y=20-4=16\\Hence,\\x=1,y=16\ or\ (1,16)\ is\ also\ a\ solution\ of\ the\ equation.[/tex]
[tex]Substituting\ x=2,\\4*(2)+y=20\\8+y=20\\y=20-8=12\\ Hence,\\x=2,y=12\ or\ (2,12)\ is\ a\ solution\ of\ the\ equation\ too.[/tex]
[tex]Hence,\ collecting\ all\ the\ solutions\ of\ the\ equations:\\(0,20),(1,16),(2,12)\ are\ all\ solutions\ of\ the\ given\ equation.\\[/tex]
help me plz
Follow right steps
Here is the answer:
75 - 40 = t
Brainliest pls
Answer:
75=T+40
35
Step-by-step explanation:
75=T+40 subtract 40 from both sides and we get 35
Factor using the GCF method
8r3 + 16r2
Answer:
8r^2(r + 2)
Step-by-step explanation:
Factor 8r^3 + 16r^2
= 8r^2(r + 2)
Answer:
56 r
Step-by-step explanation:
8r x 3 + 16 r x 2
24 r + 32 r
56 r
Pls help my teacher sucks
What is the volume of this figure? Round to the nearest hundredth.
Answer:
I believe the volume is 80 cubic centimeters.
Step-by-step explanation:
V = volume
B = base
H = height
V = BH
V = (4) 20
V = 80
2(x + 5) = -10x + 34
Answer: X = 2
Step-by-step explanation: calculator
Solve for x; round to the nearest tenth of meter (please help will definitely give Brainliest❤️❤️)
Answer:
the first answer
Step-by-step explanation:
In SOHCAHTOA, we are using soh
sin(23)=2500/x
Hey there! I know this is prob really simple and I am beginning to understand it, but my problem is
Sec 60°
Now I know all the SOH CAO TOH stuff, and things like that, I just don't understand how to find the value because it changes all the time with the right triangle and the number of their sides.
Really just need the formula on how to solve stuff.
Answer:
sec(60) = 2
Step-by-step explanation:
sec(theta) = 1/cos(theta)
theta = 60o
cos(60) = 1/2 = 0.5
sec(theta) = 1/0.5 = 2
Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a flight had 52 passengers who paid $1360, how many first class and tourist class passengers were there?
There were 40 tourist class passengers and 12 first class passengers.
Explanation:
Let the number of passengers who booked for tourist class be
=
x
Then, number of passengers who booked for first class
=
52
−
x
According to question,
Total money paid = $25(tourist class)+$30(first class)
$
1360
=
$
25
(
x
)
+
$
30
(
52
−
x
)
1360
=
25
x
+
1560
−
30
x
1360
−
1560
=
25
x
−
30
x
−
200
=
−
5
x
x
=
−
200
−
5
x
=
40
So, there were 40 tourist class passengers.
Now first class passengers
=
52
−
x
=
52
−
40
=
12
∴
There were 40 tourist class passengers and 12 first class passengers.
As a check
Total money paid = $25(tourist class)+$30(first class)
R
H
S
=
$
25
(
40
)
+
$
30
(
12
)
$
1000
+
$
360
=
$
1360
L
H
S
=
$
1360
Hence verified.
The abbreviation for interquartile range is IQR.
A
False
B
True
Answer:
B, True
Step-by-step explanation:
Answer:
B)True
Step-by-step explanation:
IQR= Interquartile Range
Anybody wanna help volunteer?
Find the product. Your answer must be in simplest form.
7/8 of 56
Answer:
You probably know that the number above the fraction line is called the numerator and the number below it is called the denominator. To work out the fraction of any number, we first need to convert that whole number into a fraction as well.
Here's a little tip for you. Any number can be converted to fraction if you use 1 as the denominator:
56
1
So now that we've converted 56 into a fraction, to work out the answer, we put the fraction 7/8 side by side with our new fraction, 56/1 so that we can multiply those two fractions.
That's right, all you need to do is convert the whole number to a fraction and then multiply the numerators and denominators. Let's take a look:
7 x 56
8 x 1
=
392
8
In this case, our new fraction can actually be simplified down further. To do that, we need to find the greatest common factor of both numbers.
You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 392 and 8 is 8.
We can now divide both the new numerator and the denominator by 8 to simplify this fraction down to its lowest terms.
392/8 = 49
8/8 = 1
When we put that together, we can see that our complete answer is:
49
1
The complete and simplified answer to the question what is 7/8 of 56 is:
49
Hopefully this tutorial has helped you to understand how to find the fraction of any whole number. You can now go give it a go with more numbers to practice your newfound fraction skills.
Step-by-step explanation:
Answer:
forty nine
Step-by-step explanation:
convert 56 into a fraction (56/1) then multiply 7/8 × 56/1. it equals out to 392/8. then find the GCF of 392 and 8, which is 8. now divide boht the new numerator and denominator by 9 to simplify it to lowest terms. 49 is the answer
Select from the drop-down menus to correctly complete each statement An arithmetic sequence represents a _____ function because it has a constant rate of change. As the sequence progresses, each value an in the sequence increases or decreases by a specific amount For example, the arithmetic sequence 9, 13, 17, 21, represents a ______ function because as n increases by 1, each value an increases by _____ Therefore, this arithmetic sequence ______a function
1st line :linear or nonlinear
2nd line:linear or nonlinear
3rd line: 1 , 4 or different amounts
4th line:represents or does not represent
Answer:
1st line: linear
2nd line: linear
3rd line: 4
4th line: represents
Step-by-step explanation:
Arithmetic sequences increase by the same number each time. This means they are linear, as linear functions also increase by the same number each time.
So, the first and second lines have the answer of linear.
In the arithmetic sequence given, 4 is added to the previous number as it progresses. This represents a function.
So, the third line has the answer of 4, and the fourth line has the answer or represents.
Using arithmetic sequence concepts, it is found that the lines are:
1st: linear.2nd: linear.3rd: 4.4th: representsWhat is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of the sequence is given by:
[tex]a_{n+1} = a_1 + (n-1)d[/tex]
Hence, an arithmetic sequence is also a linear function with rate of change d.
In this problem:
The sequence is: 9, 13, 17, 21.The rate of change is of 4, as when n increases by 1, each value increases by 4.Hence, the lines are completed by:
1st: linear.2nd: linear.3rd: 4.4th: representsYou can learn more about arithmetic sequence concepts at https://brainly.com/question/25433204
HELP PLEASE I WILL MARK BRAINLIEST
Answer:
M<1 = 131
M<2 = 49
Step-by-step explanation:
1. Alternate interior angles theorem
2. 180-131 = 49
A bottle contains 15 marbles: 9 are white and 6 are green. What is the
probability of picking a white?
Answer: 3/5
Step-by-step explanation:
Fist find out how many whites are there and divide it by the total to find the probability.
9/15 simplify it to 3/5
This is an absolute value problem with LETTERS?! Absolute madness (no pun intended)
Answer:
a
Step-by-step explanation:
sjejeneissbebdejjesj
A restaurant borrowed
$15,000 to remodel.
The loan is for 7 years and
the yearly interest rate is
4.25%. How much interest
will the restaurant pay?
Answer:
$4462.50
Step-by-step explanation:
simple interest =principal × rate × time\100
This question has two parts. First, answer Part A. Then, answer Part B. Part A Fill in the blanks to complete the sentence. A taxi service charges $5.00 to ride in the vehicle and then $1.00 for each mile. Complete the table with the missing information. Distance Traveled (mi) 10 $
14 $
20 $
85 $
Listen to the complete question
Part B
Complete the statement about whether the relationship between distance traveled and the price of the trip is proportional.
The relationship , 1 of 2. proportional because the ratio of price to distance traveled is , 2 of 2. the same.
Answer:
85
Step-by-step explanation:
Can someone help me find X for number 4
Joe is running after Bob. In a minute Joe does 60 steps, which makes up 3/16 of the number of steps, which Bob does in a minute. The length of Bob's step is 25 cm which makes up 5/24 the length of joe's step. With what speed do Bob and Joe run with what speed does the distance between them change? what will it become in 10 minutes, if right now bob is in front of joe by ten meters?
Joe is going with a speed of ____
cm per minute. Bob is going with a speed of ____
cm per minute. The distance between them changes with ____
cm per minute. The distance will become _____
cm in 10 minutes. _____
Answer:
Joe is going with a speed of 7200
cm per minute. Bob is going with a speed of 8000
cm per minute. The distance between them change with 800
cm per minute. The distance will become 9000
cm in 10 minutes
Answer:
7200 8000 800 and 9000
Step-by-step explanation:
L
ABCD is a parallelogram, find the value of y
Answer:
33
Step-by-step explanation:
angles A and B should add up to 180, so A must be 40, and because it is a parallelogram the anlge across from it should also equal 40. 33+7=40.
A circle of radius 90 inches has a central angle that intercepts an arc of length 120 inches. Explain whether the measure of the central angle is 34 radians
A. The measure is not 34 radians. The measure is 32 radians because the angle measure in radians is the diameter divided by the arc length.
B. The measure is not 34 radians. The measure is 43 radians because the angle measure in radians is the arc length divided by the radius.
C. The measure of the angle is 34 radians because the angle measure in radians is the radius divided by the arc length.
D. The measure is not 34 radians. The measure is 23 radians because the angle measure in radians is the arc length divided by the diameter.
Answer:
D
Step-by-step explanation:
I really don't know not smart
Please help me! I WILL MARK BRAINLIEST
Answer:
B because you add each time starting from 3
Step-by-step explanation:
10.You can buy 5 stickers for $3. How many stickers could you buy for $12 if the price remains proportional?
20
12
10
15
1.) Multiply 2ab(−a+2b+3).(1 point)
8a2b2
−2a +2ab+3b
8ab
−2a2b+4ab2+6ab
2.) Simplify the polynomial using multiplication.
xy(3x2+2x−3y)
(1 point)
3x3y+2x2y−3xy2
3x3+2xy−3y
2x3y2
3x3+2x2−3y2
The area of a rectangle is given by the expression (x+3)(4x−2). Which of the following is an equivalent expression for the area?(1 point)
13x−2
4x2+14x+6
4x2+10x−6
14x−6
Multiply (x+2)(x2−3x +4)(1 point)
x3+5x2+10x+8
x3−x2−2x+8
x2−2x+6
2x2−6x+8
Simplify the polynomial using multiplication.
−5b(2a−3a2)
(1 point)
−10ba+15ba2
10ba−15ba2
−10a+3ba2
−5b+2a−3a2
Answer:
(x+3)(4x−2) = 4x2+10x−6
(x+2)(x2−3x +4) = x3−x2−2x+8
Step-by-step explanation:
What is the opposite of -|-32|
Find the area of the shape below.
11 cm
14 cm
9 cm
20 cm
Answer: A = 235 cm²
Step-by-step explanation: The figure has not a regular shape, but we can divide it to other figures that are easier to calculate the area.
For example, we can divide this figure in 2:
1) A square of side 9;
2) A rectangle of sides 14 and 11;
The image below represents what it is described.
Area of quadrilateral is calculated as A = length x width
Since both rectangle and square are quadrilateral, area of each will be
[tex]A_{square}[/tex] = 9.9
[tex]A_{square}[/tex] = 81
[tex]A_{rectangle}[/tex] = 11.14
[tex]A_{rectangle}[/tex] = 154
The area of the shape is the sum of each part we calculated:
[tex]A_{total}[/tex] = 154 + 81
[tex]A_{total}[/tex] = 235
The area of the shape is 235 cm².
Bill sees two boxes of baseball cards at a card show. The first box has 150 cards for $12.55.The second box has 120 cards for $9.60. The cards in which box are cheaper?
Answer: Cards in second box are cheaper.
Step-by-step explanation:
We are told that the first box has 150 cards for $12.55. Therefore, the cost of one card would be:
= $12.55 / 150
= $0.084.
The second box has 120 cards for $9.60. Therefore, the cost if one card would be:
= $9.60 / 120
= $0.08
Therefore, the cards in the second box are cheaper.
I'm not quite sure how to solve this problem. Note I do understand the problem if it was like this 7π/4 because you would do 7/4 times 180 which would be 315. But now since there is not an number in from of π/-12 i'm confused.
Answer:
the answer is -90degrees
Step-by-step explanation:
DO substitite 180 for pie and do -180/2 and get -90 degrees
simplify the expression -1\2(-5\6+1\3)
please helpppp
Answer:
1/4
Step-by-step explanation:
1. Solve the parentheses
(-5/6+1/3)
(-5+2/6) 6 is common multiple for 3 and 6
-3/6
-1/2
2. Multiply
-1/2*-1/2
1/4
Hope this helps
Have a great day!