Answer:
V = 36Π cubic Centimetres
Step-by-step explanation:
Step(i):-
Volume of the solid
The Volume of the solid formed by revolving the region bounded by the curve y = f(x) and rotated around the x-axis defined by
[tex]V = \pi \int\limits^a_b {[f(x)]^{2} } \, d x[/tex]
Step(ii):-
Given two curves are y = x² and y = 9
The point of intersection of two curves
y = x²...(i)
and y = 9 ...(ii)
Equating both equations , we get
x² - 9 =0
⇒ x² - 3² =0
⇒ (x+3)(x-3) =0
⇒ x+3=0 and x-3=0
x = 3 ⇒ y = 9
x = -3 ⇒y = 9
The point of intersection ( -3,9) and (3,9)
Step(iii):-
[tex]V = \pi \int\limits^a_b {[(f(x)]^{2} } \, -[g(x)]^{2})d x[/tex]
The limits x- varies from -3 to 3
[tex]V =\pi (\int\limits^3_3 {x^{2} } \, dx +\int\limits^3_3{9} \, dx[/tex]
[tex]V =\pi (\frac{x^{3} }{3} -9 x)^{3} _{-3}[/tex]
[tex]V= \pi ( \frac{27}{3} - 9(3) - (\frac{-27}{3} -9(-3))[/tex]
V = π ( |-36| = 36Π cubic Centimetres
Final answer:-
The volume of the solid
V = π ( |-36| = 36Π cubic Centimetres
Find the midpoint of the segment with the following endpoints.
(5,9) and (0,3)
Answer:
(5/2, 6)
Step-by-step explanation:
(x, y)=[(5+0)/2, (9+3)/2]
(x, y)=[5/2, 12/2]
(x, y)=(5/2, 6)
The Midpoint of the Line Segment that has the endpoints (5,9) and (0,3) is (5/2,6).
What is the line segment?In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line that is between end points.
Now it is given that,
The endpoints of line segment is (5,9) and (0,3)
So, x₁ = 5
y₁ = 9
x₂ = 0
y₂ = 3
Let (x,y) be the midpoint of segment .
∴To find the midpoint of segment we have,
(x,y) = {[(x₁+x₂ )/2] , [(y₁+y₂ )/2]}
Put the values, we get
(x,y) = (5+0)/2 , (9+3)/2
solving them,
(x,y) = {(5/2) ,(12/2)}
or,
(x,y) = (5/2,6)
which is the required midpoint of the line segment.
Hence,the Midpoint of the Line Segment that has the endpoints (5,9) and (0,3) is (5/2,6).
To learn more about midpoint of line segment :
brainly.com/question/12774890
#SPJ2
write the sentence as a equation
b is 380 more than the quality y times 268
Use the map to find the distance between Brookline and Davenport to the nearest tenth
Answer:
8.5
Step-by-step explanation:
The distance between Brookline(8, 2) and Davenport(5, 10) can be calculated using the distance formula given as [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y1)^2} [/tex].
Let,
[tex] Brookline(8, 2) = (x_1, y_1) [/tex]
[tex] Davenport(5, 10) = (x_2, y_2) [/tex]
[tex] d = \sqrt{(5 - 8)^2 + (10 - 2)^2} [/tex]
[tex] d = \sqrt{(-3)^2 + (8)^2} [/tex]
[tex] d = \sqrt{9 + 64} = \sqrt{73} [/tex]
[tex] d = 8.5 [/tex] (nearest tenth)
Two angles are supplementary. One angle has a measure that is five less than four times the other. What is the measure of the larger angle?
Answer:
C
Step-by-step explanation:
4x-5+x=180. Add 5 to both sides
5x=185. Divide by 6
X=37
180-37=143
143
A survey of 500 farmers showed that of the farmers, 121 grew only wheat, 108 grew only corn, 92 grew only oats, 195 grew wheat, 59 grew wheat and corn, 48 grew wheat and oats, and 176 grew corn. Determine the number of farmers who a) grew at least one of the three, b) grew all three, c) did not grow any of the three, and d) grew exactly two of the three.
Answer:
The farmers in regions II, IV, and VI had exactly two of the three Summing the numbers in these regions 25 + 15 + 10 we find the that 50 farmers grew exactly two of the three.
forget this ever happened at all
Answer:
i- isnt it 2-
Step-by-step explanation:
1 + 1 is 2
i hope this helped?
Frank needs 3.6 meters of ribbon to wrap gifts for friends this year. If each spool contains 90 cm of ribbon,how many spools will Frank need to purchase?
Answer:a lot
Step-by-step explanation:
Alternate Interior Angles Theorem a. b. c. Corresponding Angles Flow Proof a. b. c. d. e. Proof Diagram a. b. c.
Answer:
Step-by-step explanation:
(1). m∠5 = 40° → (a) Given
m∠2 = 140° → (b) Given
∠5 and ∠2 are supplementary angles → (c) Interior angles on the same side of the transversal.
∠5 and ∠2 are the same side interior angles → (d) Both angles are supplementary
a║b → (e) By interior angles theorem of the parallel lines.
(2). Statements Reasons
1. l║n 1. Given
2. ∠2 ≅ ∠6 2. Corresponding angles
3. ∠4 ≅ ∠2 3. Vertical angles
4. ∠6 ≅ ∠4 4. Transitive property of equality
(3). Statements Reasons
1. ∠1 ≅ ∠5 1. Given
2. ∠4 ≅ ∠1 2. Vertical angles
3. ∠4 ≅ ∠5 3. Alternate interior angles
4. p║r 4. Definition of parallel lines
Another college precalculas question, please and thank you!
Answer:
B) (-∞,∞)
Step-by-step explanation:
The domain is the x-values, so it’s all real numbers in this graph.
I would use interval notation and choose B) (-∞,∞)
The range is the y-values, so it’s (2,-1), if that’s the next question.
Simplify the given expression below:
(-5 + 3i) times(1 - 2i)
Answer:
Step-by-step explanation:
Hello,
[tex](-5+3i)\times(1-2i)=-5(1-2i)+3i(1-2i)\\\\=-5+10i+3i-6i^2\\\\=-5+13i+6\\\\\boxed{=1+13i}[/tex]
Thanks
Answer:
Same answer as the other person, it is 1 + 13i
Step-by-step explanation:
They were first and is right so I don't think I have to put down a explanation! ^^
Please 5 stars and thank me if I'm right! -w-
9 and 26 find the LCM
Answer:
The answer is 234
Step-by-step explanation:
What is the y in the equation? 15-y-3y=17
Items 2-4. Points P, Q, and Sare
collinear.
(3x - 5)
0
(x + 1)
s
2. What is the value of x?
3. What is m ZPQR?
will
11. M
4. If a ray QT bisects ZRQS, what
will be the measure of one of the
resulting angles?
m
of
5. Points L, M, and N are collinear.
You are given LM = 5 and LN = 17.
What is a possible value of MN?
Flb
6. Ray BD bisects ZABC so that
mZDBC = x + 6 and
mZABD = 2x - 12. What is x?
Answer:
See below
Step-by-step explanation:
2......................
∠PQR and ∠RQS are supplementary, which add up 180°
∠PQR = 3x - 5∠RQS = x + 1Sum:
3x - 5 + x + 1 = 1804x - 4 = 1804x = 184x = 46°3......................
∠PQR = 3x - 5 = 3*46° - 5° = 138° - 5° = 133°4......................
From the picture and the value of x we got above:
∠RQS = x + 1 = 46 + 1= 47°QT bisects ∠RQS and we get two equal angles
Each will measure:
47°/2 = 23.5°5......................
LM = 5, LN = 17, MN = ?
If L is between M and N, then
MN = LM + LN = 5 + 17 = 22M is between L and N, then
MN = LN - LM = 17 - 5 = 125......................
Ray BD bisects ∠ABC, then formed angles are equal:
m∠DBC = x + 6 m∠ABD = 2x - 12m∠DBC = m∠ABD
x + 6 = 2x - 122x - x =6 + 12x = 18°historians label an event as a turning point when it
Answer:
F
Step-by-step explanation:
Answer:
Historians label an event as a turning point when it marks the beginning of a distant historical period
Step-by-step explanation:
(10x^4+5x^3+4x^2-9)(x-1)
Answer:
10x3 - 5x2 + 9x - 9
Step-by-step explanation:
10x4 + 5x3 + 4x2 - 9
Simplify ————————————————————
x + 1
Answer:
10x^5 - 5x^4 - x^3 - 4x^2 - 9x + 9
Step-by-step explanation:
(10x^4+5x^3+4x^2-9) × (x-1)
10^5 - 10x^4 + 5x^4 -5x^3 +4x^3 - 4x^2 -9x + 9
Collect Like terms
10^5 - 10x^4 + 5x^4 -5x^3 +4x^3 - 4x^2 -9x + 9
10^5 - 5x^4 -x^3 - 4x^2 -9x + 9
Final Answer
10x^5 - 5x^4 - x^3 - 4x^2 - 9x + 9
Which expression is equivalent to 1/2 x + (-70) - 2 1/4 x - (-2) *
Answer:
-7/4x-68
Step-by-step explanation:
Please answer the question. Thank you.
please answer thank you!
Answer:
C
Step-by-step explanation:
A rectangle is 5 times as long as it is wide. If the area is 45 square feet, find its perimeter.
Answer:
225 sq ft
Step-by-step explanation:
If the rectangle is 5 times as long as it is wide and the area is 45 sq ft then that would make it 225 sq ft. Happy to help!
Point U is located at (1,-4) on the coordinate plane. Point U is reflected on
-axis to create point U'. What ordered pair describes the location of U'?
Given :
A point U located at (1,-4) on the coordinate plane.
To Find :
The reflection of point U on x-axis.
Solution :
Reflection of any point ( h , k ) on x-axis is ( h , - k ) .
So , the reflection of point U i.e ( 1 , -4 ) is ( 1 , 4 ) .
Therefore , the ordered pair describes the location of U' is ( 1 , 4 ).
Hence , this is the required solution .
Temp went from -16 to 7.What was the change in temperature
Answer:
Change in temperature is +23 degrees.
Answer:
23 DegreesStep-by-step explanation:
To solve this, we set up an equation:
T = 7 - -16
This can be rewritten as:
T = 7 + 16
T = 23
___________________________________________________I AM ALWAYS HAPPY TO HELP :)Find the area of the parallelogram shown below.60 squ
Answer:
A
Step-by-step explanation:
The area for a parallelogram is given by the formula:
[tex]A=bh[/tex]
Where b is the base length and h is the vertical height.
The base length is 6 and the height is 10 (if you flip the figure 90 degrees). So:
[tex]A=6(10)[/tex]
Multiply:
[tex]A=60\text{ units}^2[/tex]
Our answer is A.
And we're done!
Help me please i dont understand :(
2/7+3/8= Please I don’t know what to do so can you help me
37/56 is the answer
you can cross multiply
Answer:
37/56
Step-by-step explanation:
Find the least common multiple of the denominators (56).
7x8=56
8x7=56
2x8=16
3x7=21
16+21=37
37/56
Write a story that includes both integers -10 and 12.
Answer:
In Alaska, it was -10 degrees in the morning and rose by 12 degrees.
Step-by-step explanation:
0.01 is...........0.01
Answer:
=
Step-by-step explanation:
0.01 is = to 0.01
what is the mathematical symbol for 0 is an integer
Answer:
0
Step-by-step explanation:
there is no symbol for 0
An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)?
Answer:
Step-by-step explanation:
The givens form a right triangle. The operational definition is The opposite over the hypotenuse, where the hypotenuse is the unknown.
sin(x) = 21000/hypotenuse
sin(55) = 21000 / hypotenuse
hypotenuse * sin(55) = 21000
hypotenuse = 21000/sin(55)
hypotenuse = 25636 feet.= 26000 feet rounded.
The answer does make sense. The hypotenuse is larger than the given height.
given the following functions f(x) and g(x), evaluate (gºf)(-2). Enter answer.
f(x)=2x^2+2x-5
g(x)=-1/-4x+6
Answer:
the composition results in [tex]\frac{23}{4}[/tex]
Step-by-step explanation:
Assuming that what you typed for function g is correct (looks a bit peculiar, but we will use it as typed):
[tex]g(x)=-\frac{1}{-4x} +6[/tex]
gof(-2) can be understood as: g(f(-2)), so what we need to do is to find the value for f(-2) using its given expression, and using then the obtained value as input for g(x):
[tex]f(x)=2x^2+2x-5\\f(-2)=2\,(-2)^2+2\,(-2)-5\\f(-2)= 8-4-5\\f(-2)= -1[/tex]
So, we now evaluate g(-1):
[tex]g(x)=-\frac{1}{-4x} +6\\g(-1)= -\frac{1}{-4(-1)} +6\\g(-1)= -\frac{1}{4} +6\\g(-1)=\frac{23}{4}[/tex]
Precalc Help me Please
We just need to solve for y when x = -2
Solution:
y = 2|-2 + 1|
y = 2|-1|
y = 2(1)
y = 2
Therefore, the answer is Option 3
Best of Luck!