Answer:
volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx
Step-by-step explanation:
Given the data in the question and as illustrated in the image below;
R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)
from the image;
the equation of AB will be;
y-b / b-0 = x-0 / 0-a
(y-b)(0-a) = (b-0)(x-0)
0 - ay -0 + ba = bx - 0 - 0 + 0
-ay + ba = bx
ay = -bx + ba
divide through by a
y = [tex]\frac{-b}{a}[/tex]x + ba/a
y = [tex]\frac{-b}{a}[/tex]x + b
so R is bounded by y = [tex]\frac{-b}{a}[/tex]x + b and y =0, 0 ≤ x ≤ a
The volume of the solid revolving R about x axis is;
dv = Area × thickness
= π( Radius)² dx
= π ( [tex]\frac{-b}{a}[/tex]x + b )² dx
V = π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx
Therefore, volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx
The volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].
Equation of the line AB
[tex]y-0 = \frac{b-0}{0-a} (x-a)[/tex]
[tex]y = \frac{-b}{a} (x-a)[/tex]
What is the volume generated when a curve f(x) is generated about the x-axis?The volume generated when a curve f(x) is rotated about the x-axis in x∈(c,d) is given by:
[tex]V=\int\limits^d_c {y^2} \, dx[/tex]
So, the volume generated when line AB is rotated about the x-axis will be [tex]V=\int\limits^b_0 ({\frac{-b}{a} (x-a))^2} \, dx[/tex]
[tex]V=\frac{b^{5} }{3a^{2} }[/tex]
Therefore, the volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].
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If it is completely impossible to put a contract in writing, which of the following would be the best substitute?
a. having a friend witness the verbal agreement
a video or audio recording of the verbal agreement
the words "I promise" spoken in a verbal recitation of the contract
d. a firm hand-shake between all those involved in the contract
C.
Please select the best answer from the choices provided
Answer:
B
Step-by-step explanation:
Because the the contract will be in verbal form. no matter if it is videotaped or recorded or both a "videoed verbal contract" not just written. so like paper thst is notarized or not this is still the same bc the the same rules apply the contract is still valid. the rest of the options are more like what they call gentlemens agreements which would be the handshake type of thing. and no matter what any agreement someone has to witness the transaction or contract. so definitely the answer is B
A group of friends hiked 7 miles in 2 hours at this same rate what is the total number of miles they can hike in 8 hours
How much water do you add to make 12% sugar syrup using 5g sugar.
Answer:
You know that 5 g of sugar form 12%. Let x g be the amount of water needed. The total amount of syrup will be x+5 g. Then
5 g - 12%,
x+5 g - 100%.
mathematically you can write a proportion;
5/x+5=12/100
=>500=12(x+5)
,500=12x+60
,12x=400,
x=440/12
=110/3
=36 2/3g of water36.66 grams of water is added to make 12% sugar syrup using 5g sugar.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Let the amount of water is added be 'x'.
Amount of sugar = 5 g
We need to make 12% of sugar syrup.
x grams of water is added to 5 g of sugar, to 12% of sugar syrup.
5/5+x=12/100
Apply cross multiplication
5×100=12(5+x)
500=60+12x
Subtract 60 from both sides
440=12x
Divide both sides by 12
x=36.66
Hence, 36.66 grams of water is added to make 12% sugar syrup using 5g sugar.
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Write an equation in slope intercept form that is perpendicular to 3x + 2y equals 12 and passes through the point (1,2)
Answer:
The equation is y = (2/3)x + (4/3).
Step-by-step explanation:
First, you have to change the equation into slope-intecept formula to find its gradient (slope) :
[tex]3x + 2y = 12[/tex]
[tex]2y = - 3x + 12[/tex]
[tex]y = - \frac{3}{2}x + 6[/tex]
Given that when a line is perpendicular to the other line, their slope value multiplied, will form -1. Next, we have to find the slope for line :
[tex]m1 \times m2 = - 1[/tex]
[tex] - \frac{3}{2} \times m2 = - 1[/tex]
[tex]m2 = - 1 \div - \frac{3}{2} [/tex]
[tex]m2 = \frac{2}{3} [/tex]
Lastly, we have to subatitute the x and y values into the equation, to find its intercept value :
[tex]y = \frac{2}{3}x + b[/tex]
[tex]let \: x = 1,y = 2[/tex]
[tex]2 = \frac{2}{3} (1) + b[/tex]
[tex]b = 2 - \frac{2}{3} [/tex]
[tex]b = \frac{4}{3} [/tex]
[tex]y = \frac{2}{3} x + \frac{4}{3} [/tex]
There is a line that includes the point (-5, 2) and has a slope of -3. What is its equation in slope-intercept form?
Answer:
y=-3x-13
Step-by-step explanation:
Answer:
1 .
Step-by-step explanation:
7. Write an equation of the line that passes through the points (1, 4) and (-2, 10), in point-slope form.
Answer:
y = -2x + 6
Step-by-step explanation:
This has sort of the same concept as your earlier question
Use the equation y = mx + b
To find the slope, take the second y value and subtract the first y value. Then take the second x value and subtract the first x value. Divide the answers. You'd get -2 in this case. -2 would be your slope (m).
The substitute any set of x and y values (either (1, 4) or (-2, 10)) and the slope into y = mx + b. You'd get 6 as your y-intercept (b).
4+8= 2 x (6-3)
Can somebody help me ASAP
Answer: 12≠6
False
Step-by-step explanation:
Evaluate the expression 6x for x 6.
6x = blank when x=6
Step-by-step explanation:
[tex] \underline{ \underline{ \text{Given}}} : [/tex]
x = 6[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]
Value of 6x[tex] \underline{ \underline{ \text{Solution}}} : [/tex]
~ Plug the value of x and then multiply !
⇾ [tex] \tt{6x = 6 \times 6 \times = \boxed{36}}[/tex]
[tex] \red{ \boxed{ \boxed{ \text{Our \: final \: answer : \boxed{ \tt{36}}}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day / night ! ツ
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Can someone please help
Answer:
340
Step-by-step explanation:
Factor the expression. d2 + 10d + 25
Answer:
(d+5)^2
Step-by-step explanation:
PLEASE ANSWER THIS QUESTION RIGHT.What do we call the graph of a quadratic?
Answer:
parabola
Step-by-step explanation:
Please help if you can!!!!!!
Answer:
Perpendicular
(03.05 HC)
In a dance competition, a participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round. Steward scored 5 points in the first round. He then went on to score additional points in the second, third, and fourth rounds. In each of those rounds, his score was identical. Which inequality best shows the number of points, p, that Steward scored in each of the second, third, and fourth rounds if he earned a place in the finals? (1 point)
a
5 + 3p ≥ 30
b
5 + 3p ≤ 30
c
5p + 3 ≥ 30
d
5p + 3 ≤ 30
Given:
Score in first round = 5 points
Score in second, third and fourth rounds was identical.
A participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round.
To find:
The inequality for the given problem.
Solution:
Let p be the number of points, p, that Steward scored in each of the second, third, and fourth rounds.
Score in first 4 rounds = Score of 1st round + Score of 2nd round + Score of 1s 3rd round + Score of 4th round
Score in first 4 rounds [tex]=5 + p + p + p[/tex]
[tex]=5 +3p[/tex]
A participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round. It means the total score in first 4 rounds must be greater than or equal to 30.
[tex]5+3p\geq 30[/tex]
Therefore, the correct option is A.
Answer:
A
Step-by-step explanation:
The area of the square above is 36. What is the value of x?
A) 2
B) 4
C) 6
D) 9
I think it is A)2 because 3^2 = 9 and 9×4 = 36
Derrick needs to sell a minimum of 100 orders each month to make it into the sales winners circle. He has already sold 45 orders this month. He still needs to sell s more orders.
Which inequality can be used to find the possible values for s?
If and are the radi of two concentric circles and (r. > r.). If the chord
of the larger circle AB touches the inter circle. Find the value of AB
Answer:
r1 and r2 are the radii of two concentric circles
To find:
The length of the chord of the larger circle.
Solution:
We have given the two concentric circles which means both the circles have the same centre.
The chord of the larger circle toches the inner circle so the chord of the larger circle will be the tangent of the smaller circle.
And we know that the radius of the circle is perpendicular to the tangent of the circle.
Let 2x be the length of the chord of the circle.
r1 is the radius of the larger circle.
r2 is the radius of the smaller circle.
So by the Pythagoras theorem,
The length of the half of the chord is given by:
r1² = x² + r2²
x² = r1² - r2²
x = √r1² - r2²
So,
The length of the chord will be 2x = 2√r1² - r2² units
Step-by-step explanation:
solve the inequality and graph the solution on the line provided.
Answer:
x [tex]\geq[/tex] 5
Step-by-step explanation:
step 1: subtract 6 from both sides
step 2: divide both sides by 7
answer: x [tex]\geq[/tex] 5
interval notation: [5,∞)
What is the height of the cone below?
Answer:
Where's the cone at and I might be able to help
Step-by-step explanation:
Answer: Please put a picture of the cone underneath the question!
Step-by-step explanation:
which statement about these triangles is true?
Answer:
I think it's D
Step-by-step explanation:
Answer:
i think it's a or d
but d is more have percent