Answers
Answer:
2 ( Option A )
Step-by-step explanation:
The given integral to us is ,
[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]
Here 5 is a constant so it can come out . So that,
[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]
Now we can write √x as ,
[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]
Simplify ,
[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]
By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,
[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]
On simplifying we will get ,
[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]
Answer:
A)2
Step-by-step explanation:
we would like to integrate the following definite Integral:
[tex] \displaystyle \int_{0} ^{1} 5x \sqrt{x} dx[/tex]
use constant integration rule which yields:
[tex] \displaystyle 5\int_{0} ^{1} x \sqrt{x} dx[/tex]
notice that we can rewrite √x using Law of exponent therefore we obtain:
[tex] \displaystyle 5\int_{0} ^{1} x \cdot {x}^{1/2} dx[/tex]
once again use law of exponent which yields:
[tex] \displaystyle 5\int_{0} ^{1} {x}^{ \frac{3}{2} } dx[/tex]
use exponent integration rule which yields;
[tex] \displaystyle 5 \left( \frac{{x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1} \right) \bigg| _{0} ^{1} [/tex]
simplify which yields:
[tex] \displaystyle 2 {x}^{2} \sqrt{x} \bigg| _{0} ^{1} [/tex]
recall fundamental theorem:
[tex] \displaystyle 2 ( {1}^{2}) (\sqrt{1} ) - 2( {0}^{2} )( \sqrt{0)} [/tex]
simplify:
[tex] \displaystyle 2 [/tex]
hence
our answer is A
Related Questions
plz answer!!!!!!!!!!!!!
Answers
Answer:
That's cheating my guy...................
What is the least common multiple of 50, 41, and 30?
Answers
Hello!
[ 50; 41; 30 ] = ?
50 | 2 × 5
5 | 5 => 50 = 2 × 5²
1 |
41 | 41 => 41 = 41
1 |
30 | 2 × 5
3 | 3 => 30 = 2 × 3 × 5
1 |
[ 50; 41; 30 ] = 2 × 3 × 5² × 41 = 2 × 3 × 25 × 41 = 6 × 25 × 41 = 150 × 41 = 6150
Good luck! :)
17.27. How many Social Security numbers (see Exercise 8.12) have their nine digits in strictly increasing order
Answers
Answer:
"10 possibilities" is the appropriate response.
Step-by-step explanation:
The numbers will be:
⇒ [tex]123 \ 456 \ 789[/tex]
Now anyway we commence with right and afterwards remove nine from eight and seeing as maintain the sequence growing.
then,
[tex]012345678[/tex][tex]012345679[/tex][tex]012345689[/tex][tex]012345789[/tex][tex]012346789[/tex][tex]012356789[/tex][tex]012456789[/tex][tex]013456789[/tex][tex]023456789[/tex]Thus, the above is the correct answer.
Please help me with this one!!
Answers
Answer:
[tex]21 in^{2}[/tex]
Step-by-step explanation:
The square in the middle has a length and width of 3, so multiply. 9.
All of the triangles have a base of 3 and a height of 2. The area equation for triangles is
[tex]A=bh\frac{1}{2}[/tex]
So base*height is 6. Divide that by 2 or multiply by 1/2.
You get 3. There are 4 triangles, so multiply that by 4. 12.
Add 12 and 9 together, and you get:
[tex]21 in^{2}[/tex]
I hope this helps!
What is the hardest math problem ever?
Answers
Step-by-step explanation:
this is the hardest I think
Goldbach's Conjecture Creative Commons. ...
The Twin Prime Conjecture. ...
The Riemann Hypothesis. ...
The Birch and Swinnerton-Dyer Conjecture. ...
The Kissing Number Problem. ...
The Unknotting Problem. ...
The Large Cardinal Project.
(c) The perimeter of a rectangle with length 2r cm and width 5 m is 14 m.
Answers
A lighthouse casts a 128-ft shadow. A nearby lamppost that measures 5
feet casts an 8-foot shadow. What is the height of the light house, rounded
to the nearest foot? *
Answers
Answer: 80 feet
Step-by-step explanation:
We can write these as fractions and do cross multiplication with the numerator being the height of the object while the denominator being the length of the shadow:
5 * 128 = 8x
640 = 8x
80 = x
Thus, the height of the lighthouse is 80 feet tall.
9. Consider the line y = 4x+9. If a second line is perpendicular to this one, what is its slope? please show your work, i will mark brainliest!
Answers
Answer:
Slope of the line perpendicular to the given line = [tex]- \frac{1}{4}[/tex]
Step-by-step explanation:
If two are lines are perpendicular to each other,
the product of their slopes = - 1 .
That is ,
[tex]m_ 1 \times m_2 = -1[/tex]
Slope of the given line :
[tex]m_ 1 = 4[/tex]
Hence slope of the line perpendicular to it :
[tex]4 \times m_ 2 = - 1 \\\\\frac{4}{4} \times m_2 = - \frac{1}{4} \\\\1 \times m_2 = - \frac{1}{4}\\\\m_ 2 = \frac{-1}{4}[/tex]
The slope of the line perpendicular to the equation y = 4x + 9 is m = -1/4
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = 4x + 9 be equation (1)
The equation is of the form y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
Slope m = 4
Now , the second line is perpendicular to the line A , the product of slopes of the lines will be -1
So , m₁ x m₂ = -1
4 x m₂ = -1
Divide by 4 on both sides of the equation , we get
m₂ = -1/4
Therefore the value of m₂ is -1/4
Hence , the slope of the line is m₂ = -1/4
To learn more about equation of line click :
https://brainly.com/question/14200719
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Let A = {a, b, c}, B = {b, c, d}, and C = {b, c, e}. (a) Find A ∪ (B ∩ C), (A ∪ B) ∩ C, and (A ∪ B) ∩ (A ∪ C). (Enter your answer in set-roster notation.)
Answers
Answer:
(B n C) = {b,c}
A = {a,b,c}
B= {b,c,d}
C= {b,c,e}
A u (B n C) = {a,b,c}
(A u B) = {a,b,c,d}
(A u B) n C = {b,c}
(A u C) = {a,b,c,e}
(A u B) n (A u C) = {a,b,c}
B n C = {b,c}
A = {a,b,c}
A U (B n C) = {a,b,c} U {b,c} = {a,b,c}
b. A U B = {a,b,c} U {b,c,d} = {a,b,c,d}
c. (A U B) n (A U C)
A U B= {a,b,c,d}
A U C= {a,b,c,e}
(A U B) n ( A U C)
➡️ {a,b,c,d} n {a,b,c,e}
➡️ {a,b,c}
Solve for x.
-9x + 7 < 25
Answers
I don't know I don't know I don't know I don't know I don't know I don't know I don't know
f () = 6x + 4. Find the inverse of f(x).
Answers
Answer:
F-1 (x)=1/6x-2/3
Step-by-step explanation:
Use substitution, Interchange the variables, Swap the sides, movthe constant to the right, Divide both sides, Use substitution, and youll find your solution. By the way the -1 is in scientific notation!
find the area of the kite. please help thank you
Answers
Answer:
1/2×d1×d2
=1/2× (4+4)(6+3)
=36
This is my last question, I hope to get the right answer
pls and ty :>
Answers
Answer:
Options A , D , E
Step-by-step explanation:
Triangle has angles 27° and 45°
The third angle = 180 - 27 - 45 = 108°
Therefore, the angles of ABC are 27° , 45° , 108°
=> ABC is Scalene triangle .
Option A :
Triangle DEF :
3x + 5x + 12x = 180°
20x = 180°
x = 9
Therefore , the angles of DEF = 27° , 45° , 108°
Satisfies
Option B:
Triangle GHI is Isosceles triangle with one angle 108°
But ABC is scalene , therefore not similar.
Does not satisfy.
Option C :
Triangle JKL with one of the angle = 72°
But none of the angles of ABC is equal to 72° .
Therefore, not similar.
Does not satisfy.
Option D :
Triangle MNO have angles 45° and 108°.
Sum of angles of triangles = 180°
So the third angle of MNO = 27°
Therefore , MNO is similar to ABC.
Satisfy.
Option E:
Angles of triangle PQR are 45° , x° , 4x°
Lets find all the angles .
45 + x + 4x = 180°
5x = 180 - 45
5x = 135
x = 27
Therefore, the angles of PQR = 45° , 27° , 108°
Hence similar to triangle ABC.
Satisfy
Option F :
Angles of triangle STU (5x + 3)°, (9x)° , (21x + 2)°
Sum of the angles => 5x + 3 + 9x + 21x + 3 = 180°
=> 35x = 180 - 5
=> 35x = 175
=> x = 5
Therefore, the angles are
5x + 3 = 5( 5) + 3 = 25 + 3 = 28°
9x = 9 ( 5 ) = 45°
21x + 2 = 21(5) + 2 = 105 + 2 = 107°
The angles are not congruent to the angles of Triangle ABC
does not satisfy.
The ages of Sohail, Afzal and Bilal are 17, 16 and 12 respectively. If the age of Aslam also included the average of the ages is increased by 5. What is the age of Aslam?
Answers
Sohail=17
afzal=16
Bilal=12
Aslam=16+5=21
What is the missing reason for the 3rd
step in the proof below?
Answers
Answer:
Multiplication property of the equality
which statement is correct?
Answers
Answer:
Option 3 is correct
tex]\frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]
Step-by-step explanation:
1.[tex]\frac{1 in}{2.54 cm}=\frac{7 in}{17.68 cm}[/tex]
1 in=2.54 cm
[tex]7 in=2.54\times 7=17.78 cm[/tex]
[tex]\frac{1 in}{2.54 cm}=\frac{1 in}{1 in}=1[/tex]
[tex]\frac{1 in}{2.54 cm}\neq \frac{7 in}{17.68 cm}[/tex]
Hence, it is not correct.
2.[tex]\frac{1 ft}{12 in}=\frac{7ft}{74 in}[/tex]
1 foot=1 2in
[tex] 7ft=7\times 12=84 foot[/tex]
[tex]\frac{1 ft}{12 in}=1[/tex]
[tex]\frac{7ft}{74 in}\neq 1[/tex]
[tex]\implies \frac{1 ft}{12 in}\neq \frac{7ft}{74 in}[/tex]
Hence, it is not correct.
3.[tex]\frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]
1 yd=36 in
[tex]\frac{1yd}{36 in}=\frac{36}{36}=1[/tex]
[tex]7yd=7\times 36=252 in[/tex]
[tex]\frac{7yd}{252 in}=\frac{252 in}{252 in}=1[/tex]
[tex]\implies \frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]
Hence, it is correct.
4.[tex]\frac{1 m}{3.28ft}=\frac{7m}{22.86ft}[/tex]
1 m=3.28 ft
[tex]\frac{1 m}{3.28ft}=\frac{3.28}{3.28}=1[/tex]
[tex]7m=7\times 3.28=22.96 ft[/tex]
[tex]\frac{7m}{22.86ft}\neq 1[/tex]
[tex]\frac{1 m}{3.28ft}\neq \frac{7m}{22.86ft}[/tex]
Hence, option is not correct.
Maths assignment
a^4-16
Answers
Answer:
[tex]a^4-16[/tex]
[tex]\left(a^2\right)^2-4^2[/tex]
[tex]\left(a^2+4\right)\left(a^2-4\right)[/tex]
[tex]=\left(a^2+4\right)\left(a+2\right)\left(a-2\right)[/tex]
------------------------
Hope it helps...
Have a great day!!
Step-by-step explanation:
The difference of squares: a² - b² factors to (a - b) (a + b)
Let x⁴ = (x²)²
Let 16 = 4²
Now by difference of squares x⁴ - 16 factors as (x² - 4)(x² + 4)
The front factor, (x² - 4), can factor by difference of squares again as (x - 2)(x + 2)
The relationship between miles and kilometers is shown in the table below.
Miles
Kilometers
18.2
29.12
29.5
47.20
34.1
54.56
52.8
84.48
How many miles are in 19.08 kilometers?
11.925
17.48
20.68
30.528
Answers
Answer:
Step-by-step explanation ithink your are correct because that there 19.08+18.3=11.925
Answer:
11.925
Step-by-step explanation:
Triangle MNO is isosceles. Find the value of y and the measure of Angle O. Y=______
Angle O=_______degrees
Answers
Answer:
y = -5
o = 35 degrees
Step-by-step explanation:
If you replace y with -5, the statement 7y = 4y - 15 is correct. You get -35 = -35. Hope this helped!
help.........................
Answers
Answer:
solution
here,
Step-by-step explanation:
f={(2,1/2), ( 3, 1/3) , (4, 1/4)}
Range = { / (\ frac 12\) , \ (\ frac 13\) ,
\( \ frac 14\ )}
Inverse function ( f-^1 ) = {( 1/2, 2) ,( 1/3 ,3) , 1/4, 4 )} is the required answer
What is the height of the parallelogram?
+
A=56 m2
8 m
Answers
Answer:
7 m
Step-by-step explanation:
A = base x height
56 = 8 x h
56/8 = h
h = 7
Find the surface area or volume of each rectangular prism. (Show work pls)
Answers
Answer:
496 in.²
346 mm²
880 in.²
168 cm³
960 m³
420 yd³
Step-by-step explanation:
SA = 2(wl + hl + hw)
SA = 2 · (8 · 16 + 5 · 16 + 5 · 8)
SA = 496
SA = 2(wl + hl + hw)
SA = 2 · (5 · 13 + 6 · 13 + 6 · 5)
SA = 346
SA = 2(wl + hl + hw)
SA = 2 · (4 · 20 + 15 · 20 + 15 · 4)
SA = 880
V = whl
V = 4 · 7 · 6
V = 168
V = whl
V = 10 · 8 · 12
V = 960
V = whl
V = 14 · 3 · 10
V = 420
What degree of rotation about the origin will cause the triangle below to map
onto itself?
A.90
B.270
C.360
D.180
Answers
Neeeeed helpppppppppp
Answers
Answer:
The answer is x = -3.
Step-by-step explanation:
To solve for (x), start by realizing that line segment IJ and line segment JK sum up to line segment IK, which equals 5. These line segments can then be turned into an equation, and the equation will look like [tex]7+x+2x+7=5[/tex].
Next, begin to solve the equation by combining like terms, which will look like [tex]3x+14=5[/tex]. Then, subtract 14 from both sides of the equation, which will look like [tex]3x=-9[/tex], and divide both sides by 3 and simplify, which will look like [tex]x=-3[/tex]. The final answer is x = -3.
Find two positive numbers so that twice their sum equals their product and one number is 10 times the other number. Enter the smaller number first.
Answers
Answer:
Step-by-step explanation:
We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:
y = 10x
Now on to the first statement about the numbers: "twice their sum" is 2(x + y) and "equals their product" is = xy. Putting that all together:
2(x + y) = xy and we know that y = 10x so
2(x + 10x) = x(10x) and
[tex]2(11x)=10x^2[/tex] and
[tex]10x^2-22x=0[/tex] and
x(10x - 22) = 0 so
x = 0 or 10x - 22 = 0 which makes
x equal to [tex]\frac{22}{10}=2.2[/tex]
So x = 2.2 and y = 22.
Write the number in standard notation. 9.07 x 10−2
Answers
Answer:
Yeah, so that is right, just put it into a formula.
[tex]9.07*10x^{-2}[/tex]
Can someone help me with this math homework please!
Answers
Answer:
1. [tex]x=2[/tex]
2. Simplify by combining like terms
3. [tex]x=1[/tex]
4. [tex]k=0.5[/tex]
5. [tex]y=3[/tex]
Step-by-step explanation:
1. [tex]2.5(6x-4)=10+4(1.5+0.5x)[/tex]
Distribute within the parenthesis
[tex]15x-10=10+6+2x[/tex]
Combine like terms
[tex]15x-10=16+2x[/tex]
Isolate the variable expression by using the addition/subtraction properties of equality
[tex]13x=26[/tex]
Isolate the variable by using the division/multiplication properties of equality
[tex]x=2[/tex]
2. Like terms are always combined as soon as possible but never before the distributive property is applied.
3. You can find the solution by comparing the tables.
4. [tex]6k+10.5=3k+12[/tex]
Apply the addition/subtraction properties of equality
[tex]3k=1.5[/tex]
Apply the division/multiplication properties of inequality
[tex]k=0.5[/tex]
5. [tex]y+3=-y+9[/tex]
Addition/subtraction properties
[tex]2y=6[/tex]
Division/Multiplication properties
[tex]y=3[/tex]
Help and explain ( solve using the substitution method )
Answers
Answer:
you are posting unvisibile photo pls fix it
Step-by-step explanation:
help please what is the median
Answers
Answer:
The median is 9
Step-by-step explanation:
The median is the number in the middle. The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.
please help me please help me
Answers
Answer:
the answer is 1
Step-by-step explanation:
(√4 / √6) + (√6 / √4)
(2 / 2√3) + (2√3 / 2)
√3 / √3
= 1