For the function f(x) and g(x) given in the graph. Find f(g(2))
Answer:
f(g(2)) = 4
Step-by-step explanation:
find g(2) then substitute the value obtained into f(x)
locate x = 2 on the x- axis, go vertically up to meet g(x) at (2, 5 )
locate x = 5 on the x- axis, go vertically up to meet f(x) at (5, 4 )
then f(g(2)) = 4
Evaluate the surface integral ∫sf⋅ ds where f=⟨2x,−3z,3y⟩ and s is the part of the sphere x2 y2 z2=16 in the first octant, with outward normal orientation away from the origin
Parameterize S by the vector function
[tex]\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle[/tex]
with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.
Compute the outward-pointing normal vector to S :
[tex]\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle[/tex]
The integral of the field over S is then
[tex]\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv[/tex]
[tex]\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv[/tex]
[tex]\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}[/tex]
Jayne Stopped to get gas before going on a road trip the tank already had 4 gallons of gas in it which equation relates the total amount of gasoline in the tank y to the number of gallons that she put in the tank X
a.) y=4+x
b.) y = x - 4
c.) y = 4 . x
d.) y = x / 4
Answer: A.) y=4+x
Step-by-step explanation:
What is the first step in the solution of 3x2+6x=12 by completing the square?
A: r3+r=2
B: r2+2r=4
C: 3r2+6r+9=12+9
D: 3r2+6r+36=12+36
Answer:
B: r² + 2r = 4
Explanation:
[tex]\rightarrow \sf 3x^2+6x=12[/tex]
divide both sides by 3
[tex]\rightarrow \sf x^2+2x=4[/tex] ← This is the result of the first step.
factor out the common term
[tex]\rightarrow \sf x(x+2) = 4[/tex]
set to 0
[tex]\rightarrow \sf x = 4, \ x+2 = 4[/tex]
simplify
[tex]\rightarrow \sf x = 4, \ x= 2[/tex]
Divide all terms by a i.e 3
We get
x²+2x=4Or
r²+2r=4Option B is correct
-33 + 8x = -3 (3x+6) + 2
Answer:
x = 1
Step-by-step explanation:
-33 + 8x = -9x - 18 + 2
8x+ 9x = -18 + 2 + 33
17x = -16 + 33
17x = 17
x = 1
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hope this helps :)
A giant pie is created in an attempt to break a world record for baking. The pie is shown below: What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
78.13 ft
82.43 ft
86.31 ft
91.98 ft
if the "d"iameter of the pie is 30, then its radius must be half that, or 15.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=15\\ \theta =42 \end{cases}\implies \begin{array}{llll} A=\cfrac{(42)\pi (15)^2}{360}\implies A=\cfrac{105\pi }{4} \\\\\\ \stackrel{using~\pi =3.14}{A\approx 82.43} \end{array}[/tex]
7) Heather records the number of winners of the three Ring Toss game in the table below.
Number of Number of
Players
Winners
Game 1
123
52
Game 2
155
63
Game 3
172
65
Based on the data recorded in the table, how many winners should Heather expect if there
are 750 players?
The number of winners that Heather can expect is 300.
How many winners can be expected?The first step is to determine the total number of winners to the total number of players using the information in the table.
Total number of winners = 52 + 63 + 65 = 180 Total number of players = 123 + 155 + 172 = 450Ratio = 180 / 450 = 0.40
Number of winners if there are 750 players = 0.40 x 750 = 300 winners
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A cone has a height of 9 feet and a radius of 8 feet. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth.
please help me i dont get it. :(
Anthony shines a beam of light on the surface of a solution of glycerol at a certain angle. if the angle of refraction is 38°, what is the angle of incidence? the index of refraction of glycerol is 1.47, while that of air is 1.00. a. 38° b. 45° c. 55° d. 65° e. 70°
Answer:
D) 65°
Step-by-step explanation:
Use Snell's Law
[tex]n_1\sin\theta_1=n_2\sin\theta_2\\\\1.00\sin\theta_1=1.47\sin38^\circ\\\\\sin\theta_1=1.47\sin38^\circ\\\\\theta_1=\sin^{-1}(1.47\sin38^\circ)\\\\\theta_1\approx64.83^\circ[/tex]
Thus, the angle of incidence is D) 65°
1 pound is equivalent to ____ grams.
Answer: 453.592 grams
Step-by-step explanation:
I searched it up online. But if you're going to use this to calculate. Use 454 grams.
Answer:
453.592 rounded would be 454* grams witch is equal to 1 pound
Step-by-step explanation:
1 pound is equivalent to __453.592 or just say 454*__ grams.
Had to fix that hehehe
Hope This Helped
What is the value of the expression when n = 3?
6 (n² + 2)
n
O 16
O22
O 30
O 66
Answer:
66
Step-by-step explanation:
6(n² + 2)
6(3² + 2)
6(9 + 2)
6(11)
66
Find the minimum point(s) of f(x) = x - 2x² + 1 given that f'(x) = 4x³ - 4x.
Answer: f(x) = x - 2x² + 1
x=-b/2a
(1/4,9/8
2. f'(x) = 4x³ - 4x
((\sqrt(3))/(3),-(8\sqrt(3))/(9))is a local minima
(-(\sqrt(3))/(3),(8\sqrt(3))/(9))is a local maxima
Step-by-step explanation: hopes this help
please mark me as a brainliest
Round of to the nearest thousand 741,543
Answer:
The correct answer is 742,000
Step-by-step explanation:
Answer:
742,000
Step-by-step explanation:
Please give me brainlist
elo guys can u guys help me on these i have 20 min
I used exemplar. the mean means add all the numbers and divide it buy how many there are.
5 + 7 + 9 = 21
21/3 = 7
0 3 4 6 6 7 7 7 9
Median = 6 (the middle number)
Mode = 7 (the most common number)
Range = 9 (Biggest number - smallest number)
Hope this helps!
If not then let me know!
James defines a circle as the set of all the points equidistant from a given point. His statement is not precise enough because he should specify that.
A circle has a center, radius, diameter and points in a plane. Depending on the context, the definition of a circle must contain at least one of the following terms:
Center
Radius
Diameter
Points in a plane
The complete question is as follows:-
James defines a circle as "the set of all the points equidistant from a given point." His statement is not precise enough
because he should specify that
A circle includes its diameter
The set of points is in a plane
A circle includes its radius
The set of points is collinear
What is a circle?A circle is a two-dimensional geometry on the plane having a center point and the circular line is drawn equidistant from the center point.
Based on James' definition of a circle, he needed to specify that the points are in a plane (option c).
As presented in his definition "the set of all the points" can be interpreted in several ways. Some of which are:
the set of points on a line
the set of points in a plane
the set of points in a region
Etc
Of these numerous possible interpretations, James should have specified that the set of points is in a plane
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A rectangular piece of iron has sides with lengths of 7.08 × 10–3 m, 2.18 × 10–2 m, and 4.51 × 10–3 m. what is the volume of the piece of iron? 6.96 × 10–7 m3 6.96 × 107 m3 6.96 × 10–18 m3
The volume of the rectangular piece with sides of lengths of 7.08 × 10–3 m, 2.18 × 10–2 m, and 4.51 × 10–3m is 6. 96 × 10^ -7 m
What is volume?Volume is defined as the amount of space or capacity occupied by a three-dimensional shape.
It is represented in cubic units.
How to determine the volume of a rectangleFormula:
Volume, V = length × breadth × height
Given the values;
7. 08 × 10 ^-3m , 2.18 × 10^ -2m and 4. 51 × 10^-3m
Multiply all the lengths
Volume = 7. 08 × 10 ^-3 × 2.18 × 10^ -2 × 4. 51 × 10^-3
= 69.6 × 10^-8
= 6. 96 × 10^ -7 m
Therefore, the volume of the rectangular piece is 6. 96 × 10^ -7 m
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Answer:
A
Step-by-step explanation:
trust
The functions f and g are defined as follows.
f(x)=2x²-3x
g(x) = -4x-1
Find f(-2) and g (7).
Simplify your answers as much as possible.
f(-2) =
믐
X
9 (7) =
Ś ?
Answer:
f(-2) = -14g(7) = -29Step-by-step explanation:
~1
Given Polynomial:
f(x)=2x²-3xTo Find:
f(-2)Solution:
f(x)=2x²-3xSubstitute x = -2 onto the given polynomial,as we need to find f(-2),so x = -2.
f(6) = 2(-2)² -3(-2)Simplify using PEMDAS,then.
f(6) = -8 - 6f(6) = -14Hence, f(6) = -14
[tex] \rule{225pt}{2pt}[/tex]
~2
Given polynomial:
g(x) = -4x-1To Find:
g(7)Solution:
g(x) = -4x-1
Substitute x = 7 onto the given polynomial,as we need to find g(7),so x = 7.
g(7)= -4(7) - 1Simplify using PEMDAS.
g(7) = -28 - 1g(7) = -29Hence, g(7) = -29.
[tex] \rule{225pt}{2pt}[/tex]
Find the 50th term of the sequence: 65536,49152,36846,27648
Step-by-step explanation:
first you should check whether the sequence is arithmetic and geometric .as you see the sequence is arithmetic with the common difference of -16384.
Find the measure of the missing angle.
112°
a
The measure of angle b is 112° and the measure of angle c is 68°
Calculating the measures of anglesFrom the question, we are to determine the measures of the missing angles
From the diagram,
b = 112° (Vertically opposite angles)
∴ b = 112°
Also,
112° + c = 180° (Sum of angles on a straight line)
c = 180°- 122°
∴ c = 68°
Hence, the measure of angle b is 112° and the measure of angle c is 68°
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Pippa has a box containing n pens.
there are only black pens and red pens in the box.
the number of black pens in the box is 3 more than the number of red pens.
pippa is going to take at random 2 pens from the box.
the probability that she will take a black pen followed by a red pen is
9
35
find the possible values of n.
show clear algebraic working.
The possible values of N from the given probability parameters is; N equals 15 or 21
How to Solve Algebra Problems?We are told that;
Number of pens in the box = N
Let the number of red pens be x
Thus; number of black pens = x + 3
Thus;
x + x + 3 = N
x = (N - 3)/2
The probability that she will take a black pen followed by a red pen is;
P(she will take a black pen followed by a red pen) = (x + 3)/N * x/(N - 1)
Plugging in he relevant values and solving for N gives ;
Solving for N gives N equals 15 or 21
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My age this year is a multiple of 7. Next year it will be a multiple of 5. I am more than 20 years of age but less than 80. How old will I be 6 years from now?
Answer:
You will be 55
Step-by-step explanation:
Can anyone please help me with this I been working on this for hours
Write an equation of the parabola in vertex form that passes through ( 3 , -2 ) and has a vertex of ( 5,8 )
Answer:
Parabola in vertex form: y = a(x - h)2 + k
Vertex: (h, k) = (3, 2) and (x, y) = (13, 8)
y = a(x - h)2 + k
y = a(x - 3)2 + 2 <== with substitution (h, k) = (3, 2)
8 = a(13 - 3)2 + 2 <== with substitution (x, y) = (13, 8)
8 = a(10)2 + 2
100a = 8 - 2 ==> 100a = 6 ==> a = 6/100 ==> a = 3/50
Parabola in vertex form: y = a(x - h)2 + k
y = (3/50)(x - 3)2 + 2 (Final Answer - Parabola in vertex form)
Step-by-step explanation:
Answer:
Hi,
Step-by-step explanation:
Parabola has the equation:
y=k*(x-5)²+8
if x=3, y=-2: -2=k*(-2)²+8 ==> 4k=-10==> k=-5/2
So y=-5/2(x-5)²+8
The sun of two numbers is 7 and a different 1 what are the two numbers
Answer:
3 and 4
Step-by-step explanation:
given that the difference is 7, two numbers that add up to 7 are 3 and 4.
Nevaeh models the volume of a popcorn box as a right rectangular prism. Its dimensions are 5 in by 3 in by 7 1/4 in. How many cubic inches of popcorn would it hold when it’s a quarter full? Round your answer to the nearest tenth if necessary.
The cuboid can hold 27.2 cubic inches of popcorn
What is a right rectangular prism?A right rectangular prism is also called the cuboid. it is a solid three dimensional shape with 6 faces, 12 edges and 8 vertices.
Analysis:
Volume of cuboid = length x width x height
= 5 x 3 x 29/4 = 108.75 cubic inches
When it is quarter full, volume = 1/4 x 108.75 = 27.2 cubic inches
In conclusion, the volume of the cuboid is 27.2 cubic inches.
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y=4(3)^x complete a table showing y values for values of x from 0 to 5
To solve this problem, we just have to substitute the values into the exponential equations and solve.
Exponential EquationIn the given exponential equation, we simply need to plug in the values of x from 0 to 5
[tex]y = 4(3)^x[/tex]
when x = 0
[tex]y = 4(3)^x\\y = 4(3)^0\\y = 4[/tex]
when x = 1
[tex]y = 4(3)^x\\y = 4(3)^1\\y = 12\\[/tex]
when x = 2
[tex]y = 4(3)^2\\y = 36[/tex]
when x = 3
[tex]y = 4(3)^3\\y = 108[/tex]
when x = 4
[tex]y = 4(3)^4\\y = 324[/tex]
when x = 5
[tex]y = 4(3)^5\\y = 972[/tex]
From the calculations above, the value of y when x is from 0 to 5 are
x(0) = 4x(1) = 12x(2) = 36x(3) = 108x(4) = 324x(5) = 972Learn more on exponential equations here;
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Denise is designing the seating arrangement for a concert at an outdoor theater. to give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. explain to denise how to create an equation to predict the number of seats in any row. then, using your equation, show your work to determine the number of seats in row 18
An equation is formed of two equal expressions. The number of seats in row 18 will be 119.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
A.) Given the number of seats that the first row can have is 11, while the number of seats that the next row should have is six more than the previous one. Therefore, the number of seats will increase linearly.
Thus, the equation for the number of seats in any row can be given as y=11+6x, where y is the number of seats and x is the number of row.
B.) The number of seats in row 18 will be equal to,
y = 11 + 6x
y = 11 + 6(18)
y = 11 + 108
y = 119
Hence, the number of seats in row 18 will be 119.
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Chelsea wants to rearrange her room. She makes a scale drawing of the room and cuts out pieces of paper to represent her furniture. The paper representing her desk is 1 1/4 inches by 2 1/4 inches. What are the actual dimensions of her desk?
A: 1 3/4 feet by 3 feet
B: 2 1/2 feet by 5 feet
C: 2 1/4 feet by 4 1/4 feet
D: 2 1/2 feet by 4 1/2 feet
Since the paper representing her desk is 1 1/4 inches by 2 1/4 inches, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft
To answer the question, we need to know what scale is
What is a scale?A scale is the ratio of two dimension and it is given on a scale drawing.
Given that Chelsea makes a scale drawing of the room and cuts out pieces of paper to represent her furniture, and the paper representing her desk is 1 1/4 inches by 2 1/4 inches.
Since on the scale, we have 1/2 in = 1 foot ⇒ 1 in = 2 ft
Actual dimensions of deskSo, the actual dimensions of her desk are
1 ¹/₄ in by 2 ¹/₄ in = 5/4 in by 9/4 in
= 5/4 × 1 in by 9/4 × 1 in
= 5/4 × 2 ft by 9/4 × 2 ft
= 5/2 ft by 9/2 ft
= 2 ¹/₂ ft by 4 ¹/₂ ft
So, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft
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HELP ASAP!! ANSWER QUESTION IN PICTURE BELOW!!!
Answer:
a
Step-by-step explanation:
anything less than 18 is wrong
What is the area of an isosceles right triangle whose hypotenuse is 5 √2 m long?
Answer:
Sides other than hypotenuse of an isosceles triangle are equal.
Let the other two sides be x each.
Using pythagoras theorem
x
2
+x
2
=(5
2
)
2
2x
2
=50
⇒x
2
=25
⇒x=5cm
So the other two sides are 5cm each.