Let's divide the shaded region into two areas:
area 1: x = 0 ---> x = 2
ares 2: x = 2 ---> x = 4
In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.
Area 1:
[tex]A\frac{}{1} = ∫g(x)dx = ∫xdx = \frac{1}{2} {x}^{2} | \frac{2}{0} = 2[/tex]
Area 2:
[tex]A\frac{}{2} = ∫(g(x) - f(x))dx[/tex]
[tex]= ∫(x - {(x - 2)}^{2} )dx[/tex]
[tex] = ∫( - {x}^{2} + 5x - 4)dx[/tex]
[tex]= ( - \frac{1}{3}{x}^{3} + \frac{5}{2} {x}^{2} - 4x) | \frac{4}{2}[/tex]
[tex] = 2.67 - ( - 0.67) = 3.34[/tex]
Therefore, the area of the shaded portion of the graph is
A = A1 + A2 = 5.34
[tex]\int\limits^a_b {\frac{1}{xln(x)} } \, dx[/tex]
Step-by-step explanation:
Let u = ln x
du = dx/x
[tex]\int {\frac{1}{x \ln(x)} }\: dx = \int \frac{du}{u}[/tex]
[tex]= \ln |u| + k[/tex]
or
[tex]\int_b^a {\frac{1}{x \ln(x)} }\:dx= \ln |\ln|x|| _b^a[/tex]
[tex]=\ln|\ln(a)| - \ln|\ln(b)|[/tex]
Solve the inequality -3x+1 <7?
x > -2
x < -2
x > 2
Pls help meeeee
Answer:
x<-2 ^;;:%%^^^::"%%^::::%^&&;::%^^^;::^^^&;;:%^_
this please help me
9514 1404 393
Answer:
y = 2·3^x
Step-by-step explanation:
The shape of the graph appears exponential. The horizontal asymptote appears to be y=0, so there is no vertical offset. The y-intercept seems to be 2 (we can't really read the numbers), and the y-value seems to increase by a factor of 3 for each additional unit of x.
The multiplier is 2, and the base of the exponential factor is 3. That gives us ...
y = 2(3^x)
URGENT.. pls help NO links
Answer:
.83
Step-by-step explanation:
we want
(sports∩Senior)/Senior
we can see that sports∩senior= 25
and senior= 25+5+5=30
25/30= .83
If mAB = 30° and mCD = 110°, find mLE.
D
110°
А
30°
E
с
B
O 15°
O 30°
O 40°
O 70°
Answer:
40
Step-by-step explanation:
Use the Outside Angles Theorem,
[tex] \frac{110 - 30}{2} = 40[/tex]
FIND THE LENGTH of X triangle (Look at picture easy and brainlest)
Answer:
resizing by the factor of 5/7
x = 3.5 * 5/7
= 17.5/7
= 2.5
If you know how to solve this, Please answer it. Thank You
Please show your work and the steps.
The first one to answer the question right, will get Brainlist!
I PROMISE!!!!!
The answer is in the picture. Click on it.
side lengths and angle measures in similar figures
Step-by-step explanation:
You can see the full detailed explanation in the attached files
I really need help! Please find the area of the polygon?
Answer:can you help me
write a letter to your friend about important of reading books?
Answer:
Area = 189 m^2
Step-by-step explanation:
This is a trapezium with height h=9m, base, b = 24, top, t = 18.
The area is given by
A = (base+top)*height/2
= (24+18)*9/2
= 189 m^2
a patient is advised to supplement her diet with 3g of calcium per day. The calcium tablets she purchases 300mg per tablet. How many tablets should the patient take per day?
Answer:
Number of tablet needed = 1 tablet
Step-by-step explanation:
Given:
Amount of calcium per day needed = 3 gram
Amount of calcium in a tablet = 300 mg
Find:
Number of tablet needed
Computation:
Number of tablet needed = Amount of calcium per day needed / Amount of calcium in a tablet
Number of tablet needed = 3gram / 300 milligram
Number of tablet needed = 300 milligram / 300 milligram
Number of tablet needed = 1 tablet
Calculate a positive co-terminal angle for θ=40°
Answer:
400
Step-by-step explanation:
angles that are coterminal with the angle 400? => 4000 and 7600 are two positive coterminal angles.
QUESTION 5 of 10: You have a choice of a $2,000 rebate on a $13,000 vehicle or 18% off. Which is better?
O a) Rebate
Ob) 18% off
Submit
C2021 Knowledge Matters, Inc.
Lesson
Estimated time: 60 minutes
Answer:
18% off
Step-by-step explanation:
i just took the test
The area of a rectangle is 28 m', and the length of the rectangle is 1 m more than twice the width. Find the dimensions of the rectangle.
Answer:
8m ×3.5m
Step-by-step explanation:
Area of rectangle= length ×width
Let the length and width of the rectangle be L and W meters respectively.
Area of rectangle= LW
LW= 28 -----(1)
L= 2W +1 -----(2)
Subst. (2) into (1):
(2W +1)(W)= 28
Expand:
2W² +W= 28
-28 on both sides:
2W² +W -28= 0
Factorise:
(W +4)(2W -7)= 0
W +4=0 or 2W -7=0
W= -4 (reject) or W= 3.5
Substitute W= 3.5 into (2):
L= 2(3.5) +1
L= 7 +1
L= 8
∴ The dimensions of the rectangle is 8m ×3.5m.
Solve the system of equations given below. y - 15 =3x and -2 + 5y = -3
Answer:
y-15=3x balakaksnzujsbhzbskndh
Answer:
x = - 6 , y = - 3
Step-by-step explanation:
y - 15 = 3x => y = 3x + 15 ------- ( 1 )
-2x + 5y = - 3 --------- ( 2 )
Substitute ( 1 ) in ( 2 ) :
-2x + 5 ( 3x + 15) = - 3
-2x + 15x + 75 = - 3
13x = - 3 - 75
13x = - 78
x = - 6
Substitute x in ( 1 ) :
y = 3x + 15
= 3 ( - 6 ) + 15
= - 18 + 15
y = - 3
PLEASEEEE HELPPPPP IM BEGGING SOMEONE HELPPP PLEASEEEEEEEEE PLEASEEEEEEEE
Answer:
x = -1
y = 6
Step-by-step explanation:
We can multiply the second equation by two, so we can have opposite y terms:
2 (3x - 2y = -15)
6x - 4y = -30
Now, we can add the equations, and the y terms can cancel out:
7x + 4y = 17
+ 6x - 4y = -30
13x = -13
x = -1
Now, we can plug in x:
3(-1) - 2y = -15
-3 - 2y = -15
-2y = -12
y = 6
Your checking account is in debt $20. You use this account to make a $10 purchase. Then, you deposit $38 into the account. What is the balance of the checking account?
Answer: 8
Step-by-step explanation
Answer:
$8
Step-by-step explanation:
If we just keep track of the money in the account, we can solve this pretty quickly. If the balance is -20, and we subtract another 10 from it, it gives us -30. $38 is then deposited into the account, giving us a balance of $8.
[tex]-20-10+38=8[/tex]
What is the slope of the line that is parallel to the y-axis and passes through the point (–1, 5)?
–1
0
5
undefined
Undefined.
All lines that are parallel to the y-axis have an undefined slope.
Answer:
This is an Undefined Slope
Please help i’ll rate brainliest too
Answer:
- 4
Step-by-step explanation:
h(x) = sin x
f(x) = | 3x - 4 |
g(x) = 2x² - 6
h( [tex]\frac{\pi }{2}[/tex] ) = sin ( [tex]\frac{\pi }{2}[/tex] ) = 1
f ( 1 ) = | 3 × 1 - 4 | = 1
g ( 1 ) = 2( 1² ) - 6 = - 4
g ( f ( h ( [tex]\frac{\pi }{2}[/tex] ) ) ) = - 4
the Satya Vansh become an important dynasty in the world of
Answer: it’s 352425262625251452 is 4th of July and I am present
Step-by-step explanation:
3 cm
8 cm
Find surface area of cylinder
Answer: [tex]66\pi \text{ cm}^{2[/tex]
Step-by-step explanation:
[tex]S=2\pi(8)(3)+2\pi(3)^{2}=\boxed{66\pi \text{ cm}^{2}}[/tex]
WILL MARK YOU IF YOU HELP ME PLEASE!!
Answer:
84
Step-by-step explanation:
180-72-24
so the answers is 84
Answer:
84
Step-by-step explanation:
In all triangles, once the angles are added up the total will be 180° and so in this case first add then subtract.
72+24=96
180-96=84
What is the length of DF?
Answer:
-DE+EF
Step-by-step explanation:
this is because DE is a negative vector because we are moving against the direction
MT is a diameter of OE. Calculate the measure of ZMTH.
A. 17°
B. 34°
C. 68°
D. 146
NEED HELP please, check the picture
Answer:
A. 17°
Step-by-step explanation:
Recall: measure of an inscribed angle = ½(intercepted arc)
Inscribed angle = m<MTH
Intercepted arc = arc MH = 34°
Therefore,
m<MTH = ½(Arc MH)
Substitute
m<MTH = ½(34)
m<MTH = 17°
(2x-7)/4=(x+3)/3
someone help me?
=
3
3
2
hope it's helpful for you
Answer:
x=33/2
Step-by-step explanation:
[tex]\frac{2x-7}{4}[/tex]=[tex]\frac{x+3}{3}[/tex]
do cross multiplication
4(x+3)=3(2x-7)
4x+12=6x-21
12+21=6x-4x
33=2x
33/2=x
Sylvia is twice as old as her brother. Find their ages now if in seven years her brother will be what her age was last year.
Answer:
sylvia is 14 and brother is 7
Step-by-step explanation:
theres a seven year difference, and sylvia is twice as old as him, so that means that sylvia is 14 and her brother is 7
The function f (t) = 310(0.2)24t represents the change in a quantity over 7 days,
What does the constant 0.2 reveal about the rate of change of the quantity?
the rate percentage
Answer:
80% decrease in the quantity over 7 days
Step-by-step explanation:
Given data
We have the function
f (t) = 310(0.2)24
the above function is similar to the exponential function
f (t) = P(1±r)^t
Now the value 0.2
This means that there is 80% decrease in the quantity over 7 days
I got zero, but that’s wrong.
I multiplied-25,000 x 40% and 25,000 x 25% and 40,000 x 35%
They all were zero. Can you help me figure out where I went wrong?
Answer:
Expected value is 4,000
Step-by-step explanation:
To find expected value ⇒ multiply the value by it's probability
40% × ( -25,000 ) = - 10,000
Breaking means neither add nor subtract a given amount
20% × 0 = 0
35% × 40,000 = 14,000
∴ Expected value = -10,000 + 14,000 = 4,000
LOSS: -10,000
BREAK EVEN: 0
WIN: 14,000
Expected value is 4,000
hope this helps....
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Answer:
the answer is 31°...........
PLZ SOLVE. DONT BE WRONG PLEASEEEE I NEDD ED THIS
Answer:
288
Step-by-step explanation:
Take the area of every individual section, and add them together.
24
24
100
80
60
how do u solve this problem 1 1/4 x 42/3
Answer:
17.5
Step-by-step explanation:
{ 1 [tex]\frac{1}{4}[/tex] = 5/4 }
1 [tex]\frac{1}{4}[/tex] * 42/3 = 5/4 * 42/3
= 210/12
= 17.5
