Answer:
m= 5/7
Step-by-step explanation:
y2-y1 / x2-x1
7-2/8-1
5/7
Calculate the area of the region bounded by y=6x and y=6x^2. And find the volume of the solid generated by revolving the region about the x-axis
Answer:
Hence, the Area is [tex]\frac{24}{5} \;\text {and the Volume of the bounded region is } \frac{24\pi}{5}[/tex]
Step-by-step explanation:
Concept :
Area of the region bounded by two curve :
[tex]\int_a^b(R^2-r^2)dx[/tex]
volume of the solid generated by revolving the region about the x-axis is :
[tex]\int_a^b\pi(R^2-r^2)dx[/tex] where [tex]R[/tex] is long radius of bounded region from x-axis and [tex]r[/tex] is short radius of bounded region from x-axis.
Given :
[tex]y=6x[/tex] and [tex]y=6x^2[/tex]
To find :
Area of the region bounded by [tex]y=6x[/tex] and [tex]y=6x^2[/tex] and volume of the solid generated by revolving the region about the x-axis.
Explanation :
[tex]\because y=6x\;\text{and}\;y=6x^2[/tex]
[tex]\therefore 6x=6x^2\\\Rightarrow x=1[/tex]
Area of the region bounded by [tex]y=6x[/tex] and [tex]y=6x^2[/tex] is :
[tex]\int_a^b(R^2-r^2)dx=\int_0^1((6x)^2-(6x^2)^2)dx\\[/tex]
[tex]\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=\int_0^1(36x^2-36x^4)dx\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\int_0^1(x^2-x^4)dx\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\left(\frac{x^3}{3}-\frac{x^5}{5}\right)_0^1\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\left(\frac{1}{3}-\frac{1}{5}\right)\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\times\frac{2}{15}\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=\frac{24}{5}[/tex]
Volume of the solid generated by revolving the region about the x-axis.
[tex]\int_0^1\pi((6x)^2-(6x^2)^2)dx=\int_0^1\pi(36x^2-36x^4)dx[/tex]
[tex]\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\int_0^1(x^2-x^4)dx\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\left(\frac{x^3}{3}-\frac{x^5}{5}\right)_0^1\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\left(\frac{1}{3}-\frac{1}{5}\right)\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\times\frac{2}{15}\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=\frac{24\pi}{5}[/tex]
If the Corner Bakery packages the muffins in the boxes of a 100 how many boxes of a 100 could they make
Answer:
24 muffins
240 muffins
2 boxes
Step-by-step explanation:
here is the complete question
Amy is baking muffins. Each baking tray can hold 6 muffins.
a. If Amy bakes 4 trays of muffins, how many muffins will she have in all?
b. The corner bakery produced 10 times as many muffins as Amy baked. How many muffins did the bakery produce?
If the Corner Bakery packages the muffins in the boxes of a 100 how many boxes of a 100 could they make
Number of muffins Amy has = number of trays x capacity of each tray
6 x 4 = 24 muffins
b. Muffins the bakery produces = 10 x 24 = 240 muffins
c. Number of boxes = 240 / 100 = 2. 4
that is 2 boxes of 100
What is the longest line segment that can be drawn in a right rectangular prism that is 14 cm long, 9 cm wide, and 7cm tall?
Answer:
This length is greater than the 12 cm side of the rectangle, so it confirms our initial guess, the longest line segment is 12.89 cm long.
3 Simplify 3e - e + 4e
Show me your thinking! This is not for marks but so that I get to know you more as a thinker
Determine the rule and the number of flowers at step 43.
Answer:
what do you mean
Step-by-step explanation:
can we see step 43
What is the equation of the line?
Answer:
The line equation is x=3 because the line covers all of the possible y values within the coordinate x=3.
find the sine of < I
Answer:
Step-by-step explanation:So for this question, you need to find side KI and you can find it with the pythagorean theorem
[tex]5^2+\sqrt{21}^2 = c^2[/tex]
25+21=c^2
46=c^2
c=sqrt46
c=6.78
sin(opposite/hypotnuse)
sin(sqrt21/ sqrt46) =.0117
Find the measure of
Need answer fast thx
Answer:
50
Step-by-step explanation:
10% of 100 is 10 so times it by 5
pls help me on number 1
Answer:
A. 25in.³
Step-by-step explanation:
Volume of a prism = area of base × height
Please help me with this
Answer:
Step-by-step explanation:
i think you have to multiply then divide
A student completed the problem below. Explain in your own words how to verify
if the answer is correct. *
2x^2 – 5x - 3 = (2x + 1)(x - 3)
7. What is the interquartile range for the following list of data?
1, 13, 15, 4, 1, 12, 6, 12, 6
Answer:
10
Step-by-step explanation:
1, 1, 4, 6, 6, 12, 12, 13, 15
[tex]LQ=\frac{9+1}{4} =2.5 term= \frac{1+4}{2}=\frac{5}{2}=2.5\\UQ= 3(\frac{9+1}{4}) =7.5 term= \frac{12+13}{2}=\frac{25}{2}=12.5\\IQR=UQ-LQ=12.5-2.5=10[/tex]
value of 4y when y = -3
Answer:
-12
Step-by-step explanation:
4y=4*(-3) 4*(-3)=-12
Answer:
It’s -12
Step-by-step explanation:
An isosceles triangle has two angles that measure 37 degrees. What is the measure of the third angle
Answer:
106°
Step-by-step explanation:
isosceles triangle has two sides equal meaning two sides measure 37 so
37+37=74
180-74=106
(total measurement of a triangle is 180)
SIMPLIFY (√2 + √5) ²
Answer:
7+2√10
Step-by-step explanation:
Answer:
7+2√10
Step-by-step explanation:
Which equation best represents the relationship between x and y in the graph?
A. y = 3x + 3
B. y = x + 3
C. y = 3x - 1
D. y = 13 - 1
15 points pls I need ASAP
Answer:
A. y = 3x + 3
Step-by-step explanation:
y=mx+b
b is the y-intercept (0,y) so lets start with that
We can see that the line touches 3 on the y intercept to get (0,3) meaning b=3
For the slope (m) I like to count rise over run so if we start from (0,3) and go up 3 over 1 we get 3/1 or 3 for m
The whole equation is y=3x+3
Write an expression in the form ax+b, where a and b represent rational numbers, that is equivalent to 6 (-1/2x + 2) + 1/4 (18x-12)
I need this answered by today, please!!
Answer:
[tex]6x + 6[/tex]
Step-by-step explanation:
Given
[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12)[/tex]
Required
Express as [tex]ax + b[/tex]
We have:
[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12)[/tex]
Open brackets
[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = 6 *-\frac{1}{2}x + 6*2 + \frac{1}{2} *18x-\frac{1}{2} *12[/tex]
Evaluate all multiplications
[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = -3x + 12 + 9x-6[/tex]
Collect like terms
[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = 9x-3x + 12-6[/tex]
[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = 6x +6[/tex]
Hence, the expression in form of [tex]ax + b[/tex] is [tex]6x + 6[/tex]
60 people were asked the colour of their car
A smartphone costs $260. Sales tax is 6%. What is the total cost, including tax?
The cost of the smartphone, with tax, is $
Answer:
Step-by-step explanation:
TAX CALCULATION: 260 x .06 = $15.6
Next, add the tax to the original price.
260 + 15.6 = $275.6
$275.6 is the final price including tax.
Use arrow notation to describe the translation of point P(8, –5) to point P'(15, –6).
Answer:
Step-by-step explanation:
From (-5,-4) to (-8, -7) is left 3 and down 3. In arrow notation: <-3 \/3
figure out what the x and y components of the translation are and then write the arrow to show the direction'
How many square feet of the carpet will the Smiths use for their family room.
Simplify
2/6
——-
2/3
Answer:
1/2
Step-by-step explanation:
You can change it to multiplication then solve
(2/6)*(3/2)=3/6=1/2
Step-by-step explanation:
You mean
╭☞2/6/2/3?
Ans:-[tex]╭☞ \sf \: \dfrac{2}{ \dfrac{6}{ \dfrac{2}{3} } } \\ ╭☞ \sf \: \frac{2}{6} \times \frac{3}{2} \\ ╭☞ \sf \: \frac{3}{6} \\ ╭☞ \bf \: \frac{1}{2} [/tex]
Find the value of x.
A.18
B.15
C.16
D.19
PLEASE HELP!!!!!
Answer:
x = 19
Step-by-step explanation:
123°+3x = 180°
3x = 180°-123°
3x = 57
x = 57/3
x = 19
The reason why we use 123° + 3x = 180° because both are adjacent angles. Adjacent angles add up to 180°
provide a correct answer to this problem quickly please.
A(n) is a written agreement between different parties.
A. contract
B. commitment
C. month-to-month
D. annual commitment
Answer:
A. contract
Step-by-step explanation:
Five packets of almonds cost 2m dollars. Mandy buys 3 packets of almonds.
How much change does she receive if she paid with a $10 bill?
Answer:
3 ($0.40) = $1.20
Step-by-step explanation:
find the square root of the following:
a. 1434/25
Answer:
7.57363849
Step-by-step explanation: square root of 57.36 = 7.57363849
Answer:
1434/25 is 57.36 the square root of 57.36 is 7.57
Find the derivative of f(x) = -5 divided by x at x = 11. (5 points)
AThe chosen topic is not meant for use with this type of problem. Try the examples below.
f (x) = 7x − 2, x = 6
f (x) = 3x − 2, x = 9
f (x) = x^2, x = 12
Answer:
I believe it is 2.2
Step-by-step explanation:
5 goes into 11. 2 times. 2times5= 10 and 11-10=1- 5 goes into 10 2 times- 2 times 5=10; 10-10=0. Therefore it would be 2.2. Hope this helps you. :)
Select ALL the expressions that have the same value as 9s
1. 9+s
2. 9*s
3. 3s + 6s
4. 3(3s)
5. s(5+4)
6. 3s * 3s
7. s+s+s+s+s+s+s+s+s
Answer:
1
Step-by-step explanation: