Answers
Answer:
Step-by-step explanation:
= [tex]\int\limits^1_0 {5x\sqrt{x} } \, dx[/tex]
= [tex]\int\limits^1_0 {5xx^{1/2} } \, dx[/tex]
= [tex]\int\limits^1_0 {5x^{3/2} } \, dx[/tex]
= 5 [tex]\int\limits^1_0 {x^{3/2} } \, dx[/tex]
= 5*[tex]\frac{2}{5}[/tex]*[tex]x^{5/2}[/tex] |[tex]\left[\begin{array}{ccc}1\\0\\\end{array}\right] \left[/tex]
= 5*[tex]\frac{2}{5}[/tex]*[tex]1^{5/2}[/tex]
= 2
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]
Related Questions
khairul order one set meal at a restaurant which offer a 20% discount. there is a service charge of 10% and GST is at 7% given that he pays a total of 23.54 find the marked price of the set meal
Answers
Answer:
Market price of set = 25.14
Step-by-step explanation:
Given:
Discount percentage = 20%
Service charge = 10%
GST = 7%
Amount pays = 23.54
FInd:
Market price of set
Computation:
Assume;
Market price of set = a
Market price of set after discount = a(1-20%)
Market price of set after discount = 0.80a
Market price of set after discount + (Market price of set after discount)(Service charge) + (Market price of set after discount)(GST) = Amount pays
0.80a + (0.80a)(10%) + (0.80a)(7%) = 23.54
0.80a + 0.08a + 0.056a = 23.54
0.936a = 23.54
a = 25.14
Market price of set = 25.14
6. Write an equation of a line that is Parallel to the line: y = 3x -3
Answers
Answer:
3x - y -6 = 0
Step-by-step explanation:
We need to find the Equation of the line parallel to the given equation of line . The given equation of the line is ,
[tex]\rm\implies y = 3x - 3 [/tex]
Slope Intercept Form :-
[tex]\rm\implies y = mx + c [/tex]
where ,
m is slopec is y intercept .Therefore , the Slope of the line is 3 . Let the parallel line passes through ( 3,3) . We know that the parallel lines have same slope . Therefore the slope of the parallel line will also be 3 .
Using point slope form :-
[tex]\rm\implies y - y_1 = m ( x - x_1) \\\\\rm\implies y - 3 = 3( x - 3 ) \\\\\rm\implies y -3 = 3x -9 \\\\\rm\implies 3x -y -9+3=0\\\\\rm\implies \boxed{\rm\red{ 3x -y -6=0}}[/tex]
Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers
Answers
Answer:
8.8477344 km
Step-by-step explanation:
[tex] \because \: 1 \: ft = 0.000305 \: kilometre \\ \\ \therefore \: 29028 \: ft = 29028 \times 0.000305 \: km \\ \\ = 8.8477344 \: km[/tex]
Take -4 + 3a 2 from 7a - a 2.
Answers
Answer:
Refer to the attachment!~
John read 10 books in 12 months. What was his rate of reading in months per book?
Answers
Answer:
1.2 books per month
12/10
Step-by-step explanation:
In ∆ABC ,D and E are points on the sides AB and AC respectively such that DE is parallel to BC , 1) If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC. 2) If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm , find x 3) I f AD =2cm ,BD = 4cm , show that BC = 3 DE
Answers
Answer:
1). AC=8.25cm
2). DB=7cm & EC=14cm
3). See Explanation
Step-by-step explanation:
According To the Question,
Given That, In ∆ABC, D and E are points on the sides AB and AC respectively such that DE is parallel to BC.
1). If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC.
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD / BD = AE / EC
⇒ 2.5 / 3 = 3.75 / EC
On Solving we get,
⇒ EC * 2.5 = 3.75 * 3
⇒ EC * 2.5 = 11.25
⇒ EC = 11.25 / 2.5
⇒ EC = 4.5 cm
Thus,
AC = AE + EC
⇒ AC = 3.75 + 4.50
⇒ AC = 8.25 cm
Hence the measure of AC is 8.5 cm.
2). If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD / BD = AE / EC
⇒ 4 / (x-4) = 8 / (3x-19)
on solving we get,
⇒ 3x-19 = 2(x-4)
⇒ 3x-19 = 2x-8
⇒x=11
Thus, DB =x–4 ⇒ 11-4 ⇒ DB=7cm
And, EC =3x-19 ⇒ 3×11-19 ⇒ EC=14cm
3). If AD=2cm , BD= 4cm , show that BC = 3 DE
Thus, AB = AD + DB = 2+4 = 6cm
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD/AB = DE / BC
⇒ 2 / 6 = DE / BC
on solving we get
⇒ BC = 3 DE Hence, Proved
Use expression and the unit grid below to answer the question .
Answers
Your vacation cabin on the lake has three rooms. The bathroom is 12' X 6', the bedroom is 14' X 18' and the great room is 20' X 30'. The ceiling height is 10'. What is the total volume of your cabin? Group of answer choices 9420 Cubic Feet 9240 Cubic Feet 9240 Square Feet 9420 Square Feet
Answers
Answer: [tex]9240\ ft^3[/tex]
Step-by-step explanation:
Given
Dimension of the bathroom is [tex]12'\times 16'[/tex]
Dimension of the bedroom is [tex]14'\times 18[/tex]
Dimension of the great room is [tex]20'\times 30'[/tex]
Height of the ceiling is [tex]h=10'[/tex]
Total area of the cabin
[tex]\Rightarrow A=12\times6+14\times 18+20\times 30\\\Rightarrow A=72+252+600\\\Rightarrow A=924\ ft^2[/tex]
Volume of the cabin is [tex]V=A\times h[/tex]
[tex]\Rightarrow V=924\times 10\\\Rightarrow V=9240\ ft^3[/tex]
how do I set it up for this?
Answers
Answer:
CF = 8.5
Step-by-step explanation:
Given 2 intersecting chords, then
The product of the parts of one chord is equal to the product of the parts of the other chord, that is
CF × DF = BF × EF , substitute values
CF × 14 = 7 × 17
14CF = 119 ( divide both sides by 14 )
CF = 8.5
Re-write the following expression using ADDITION ONLY:
12- 3+16 - 37 - (-20)
Answers
=9+16-37-(-20)
=25-37-(-20)
=-12-(-20)
=8
(therefore ur answer would be 8)
Answer:
12- 3+16 - 37 -( 20)
=8
Step-by-step explanation:
Two negatives are a positive , this really helps
Someone help me please if you don’t mind
Answers
Answer:
Multiply to -63
and add to -2
Step-by-step explanation:
I'm a genius.
Answer:
(x - 9)(x + 7)
Step-by-step explanation:
Given
x² - 2x - 63
Consider the factors of the constant term (- 63) which sum to give the coefficient of the x- term, that is
numbers that multiply to give - 63 and add to give - 2
The factors are - 9 and + 7 , since
- 9 × 7 = - 63 and - 9 + 7 = - 2 , then
x² - 2x - 63 = (x - 9)(x + 7) ← in factored form
The sales tax rate in virginia is 5.3% . How much sales tax would be added to a group of items costing $83.75 ? HURRY .
Answers
Answer:
4.44
Step-by-step explanation:
Sales price x sales tax rate = sales tax
83.75 x .053(5.3%) =4.44
Solve the equation and enter the value of x below. 3(x+11) + 5= 68
Answers
[tex]\boxed{ \sf{Answer}} [/tex]
[tex]3(x + 11) + 5 = 68 \\ 3x + 33 + 5 = 68 \\ 3x + 38 = 68 \\ 3x = 68 - 38 \\ 3x = 30 \\ x = \frac{30}{3} \\ x = 10[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]3(x + 11) + 5 = 68 \\ 3 \times x + 3 \times 11 + 5 = 68 \\ 3x + 33 + 5 = 68 \\ 3x + 33= 68 - 5 \\ 3x + 33= 63 \\ 3x = 63 - 33 \\ 3x = 30 \\ x = \frac{30}{3} \\ x = 10[/tex]
(show your work!) i only got an hour left for this :c
Answers
Answer:
7 _> x
Step-by-step explanation:
28 - x _> 7(x-4)
28 - x _> 7x-28
28+28 _> 7x+x
56 _> 8x
7 _> x
28-x>_7x-28
then you’ll combine like terms. (-x and 7) and 28 and -28 )you’re equation is now
-8x>_ -56
divide both sides by -8 and flip your inequality sign your equation is now
x<_ 7 which is your final answer.
x is less than or equal to 7
hope this helps!
Which of the following is the logical conclusion to the conditional statements below? a arrow b mb arrow c
Answers
Answer:
B
Step-by-step explanation:
From what we have here;
if a implies b and b implies c
It simply means that we have a implying c
the correct representation here is given in the second option
And thus, we have it that;
a => c
A : B = 5 : 7 and B : C = 3 : 5 what is the ratio of A : B : C ?
Answers
Answer:
15:21:35 (I'm not sure, but this is my best guess)
Step-by-step explanation:
15:21 = A:B (plugging in 3 as a test)
21:35 = B:C
15:21:35 = A:B:C (can't simplify)
April measured her bed and made a scale drawing. The scale of the drawing was 1
centimeter = 6 inches. In the drawing, the bed is 10 centimeters long. What is the
length of the actual bed?
Answers
solve for:− 5 − 6 ≤ 8 − 8 − (show your work)
Answers
Answer:
hope it helps.
stay safe healthy and happy...f(x) = square root 32x
g(x) = square root 2x
Answers
Given:
The two functions are:
[tex]f(x)=\sqrt{32x}[/tex]
[tex]g(x)=\sqrt{2x}[/tex]
To find:
The [tex](f\cdot g)(x)[/tex]. Assume [tex]x\geq 0[/tex].
Solution:
We have,
[tex]f(x)=\sqrt{32x}[/tex]
[tex]g(x)=\sqrt{2x}[/tex]
Now,
[tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]
[tex](f\cdot g)(x)=\sqrt{32x}\cdot \sqrt{2x}[/tex]
[tex](f\cdot g)(x)=\sqrt{32x\times 2x}[/tex]
[tex](f\cdot g)(x)=\sqrt{64x^2}[/tex]
[tex](f\cdot g)(x)=8x[/tex]
Therefore, the correct option is A.
Please help asap!!! I'm in hurry please help
Answers
Step-by-step explanation:
so, what are we supposed to do with that ?
you forgot to tell us that.
adding them ?
transforming then into expressions of x and y ?
... ?
Which graph is that of the inequality shown below?
Answers
Answer:
Graph C
Step-by-step explanation:
Each graph has the same slope and points, but only C works for this inequality- since you’re looking for less than or equal to, and only graphs b and c show less than, you know it’s one of those. From there you know it’s less than or equal to, so you want the full line, not dotted, since dotted represents that those values are excluded from the solution.
Find the value of x. PLEASE HELP ASAPPPPPP
Answers
Answer:
5
Step-by-step explanation:
(38 + 6x - 6) ÷ 2 = 7x -4
multiply both sides by 2
(38 + 6x - 6 = 2( 7x - 4)
38 + 6x - 6 = 14x - 8
32 + 6x = 14x - 8
40 = 8x
x = 5
Midsegments are the average of both bases.
what is yhe measure of side IJ?
Answers
Answer:
Side IJ would be 15
Step-by-step explanation:
Since Triangle HIJ is dilated by a scale factor of 5, that means Triangle H'I'J' would have side measurements that are 5 times as much as Triangle HIJ.
They give you that side I'J' is 75
so you divide 75 by 5 and you'll end up with 15
Can someone help me with this
Answers
Answer:
a = 17
c = 9
Step-by-step explanation:
2a + 3c = 61
3a + 5c = 96
3a = 96 - 5c (solve for 'a'. Then you can substitute)
a = 32 - [tex]\frac{5}{3}[/tex] c
2(32 - [tex]\frac{5}{3}[/tex]c) + 3c = 61 (Substitute)
64 - [tex]\frac{10}{3}[/tex]c + 3c = 61 ([tex]\frac{10}{3}[/tex] = 3 [tex]\frac{1}{3}[/tex]. So subtracting, adding a negative, leaves [tex]\frac{-1}{3}[/tex])
-[tex]\frac{1}{3}[/tex] c= -3
c = 9
2a + 3(9) = 61
2a + 27 = 61
2a = 34
a = 17
Describe fully the graph which has equation x2 + y2 = 9
Answers
Answer:
The graph is a circle with a radius of 3 and a center of (0,0).
Step-by-step explanation:
Graph
The equation x² + y² = 9 represents a circle with center (0, 0) and radius = 3
What is equation?"It is a mathematical statement which consists of equal (=) symbol between two algebraic statements."
What is graph of a equation?"It is a set of points (x, y) which satisfy given equation."
For given question,
We have been given an equation x² + y² = 9
The graph of above equation as shown below.
We know, the equation of the circle with center (0, 0) and radius 'r' is, x² + y² = r²
We can write given equation as x² + y² = 3²
Comparing given equation with x² + y² = r² we have r = 3 units
The graph of above equation represents a circle with center (0, 0) and radius = 3
Therefore, the equation x² + y² = 9 represents a circle with center (0, 0) and radius = 3
Learn more graph of function here:
https://brainly.com/question/16957172
#SPJ2
PLZ HELPPP!!!!!!!!!! ASAP
Answers
Answer:
They are consecutive terms in the Fibonacci Sequence.
Step-by-step explanation:
The sequence goes 1,1,2,3,5,8,13,21,...
Since 13 and 21 are consecutive here, that is the answer.
Rudy rode a bike at the speed of 32 2/3 miles per 3 1/2 minutes. What is his speed in terms of miles per hours?
HELPPP
Answers
Answer:
[tex]32 \frac{2}{3 }miles- - - - 3 \frac{1}{ 2} minutes \\ \frac{98}{3} miles - - - - \frac{7}{2} minutes \\ \frac{2}{7} \times \frac{98}{3} miles - - - - 1minute \\ 60 \times \frac{2}{7} \times \frac{98}{3} miles - - - - 1 \: hour \\ 560 \: miles - - - - 1hour[/tex]
560 miles per hourA manufacturer knows that their items have a normally distributed length, with a mean of 10.2 inches, and standard deviation of 1.8 inches. If 25 items are chosen at random, what is the probability that their mean length is less than 9.8 inche
Answers
Answer:
P [ X ≤ 9.8 ] = 0.1335
Step-by-step explanation:
P [ X ≤ 9.8 ] = [ ( 9.8 - 10.2 )/1.8√25 ]
P [ X ≤ 9.8 ] = - 0.4*5/1.8
P [ X ≤ 9.8 ] = - 2 / 1.8
P [ X ≤ 9.8 ] = - 1.11
From z- table we get: α = 0.1335
P [ X ≤ 9.8 ] = 0.1335 or P [ X ≤ 9.8 ] = 0.1335
Simplify. Your answer should contain only positive exponents.
fraction numerator 2 b squared over denominator 2 b end fraction 2b^2/2b
A. fraction numerator 3 over denominator 4 b end fraction 3/4b
B. 3 b squared 3b^2
C. b
D. 3b
Answers
Answer:
D.6b C.v B.8squared 7b<9
Find the size of each of the unknown angles. Help me plz.
The answer is a=b=60 degree and c=120 degree. Give me solution plz
Answers
Answer:
a=60 b=60 c=120 is the answer
