Answer:
Step-by-step explanation:
5 - 2 cannot be further simplified? No properties of exponents can be used due to already knowing the answer of the top of your head, it could be a mistype though, or I'm just very very d*mb.
Use the shell method to find the volume of the solid obtained by rotating the region bounded by the curves y=4x-2 and y=x^2+1 about the y-axis. Simplify your solution.
The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.
First, we determine the limits between the two curves. ([tex]f(x) = 4\cdot x -2[/tex], [tex]g(x) = x^{2}+1[/tex])
[tex]f(x) = g(x)[/tex] (1)
[tex]4\cdot x - 2 = x^{2}+1[/tex]
[tex]x^{2}-4\cdot x +3 = 0[/tex]
[tex](x-1)\cdot (x-3) = 0[/tex]
The lower and upper bounds are 1 and 3, respectively. It is to notice that [tex]f(x) > g(x)[/tex] for [tex]x \in (1, 3)[/tex]. Thus, we determine the volume of the solid of revolution by shell method, that is to say:
[tex]V = 2\pi \int\limits^a_b {x\cdot |f(x) - g(x) |} \, dx[/tex] (2)
If we know that [tex]a = 3[/tex], [tex]b = 1[/tex], [tex]f(x) = 4\cdot x - 2[/tex] and [tex]g(x) = x^{2}+1[/tex], then the volume of the solid of revolution is:
[tex]V = 2\pi \int\limits^3_1 {|4\cdot x^{2}-2\cdot x -x^{3}-x|} \, dx[/tex]
[tex]V = 2\pi\int\limits^3_1 {(4\cdot x^{2}-x^{3}-3\cdot x)} \, dx[/tex]
[tex]V = 8\pi \int\limits^3_1 {x^{2}} \, dx - 2\pi \int\limits^3_1 {x^{3}} \, dx -6\pi \int\limits^3_1 {x} \, dx[/tex]
[tex]V = 8\pi\cdot \left(\frac{3^{3}}{3}-\frac{1^{3}}{3} \right)-2\pi \cdot \left(\frac{3^{4}}{4}-\frac{1^{4}}{4} \right) - 6\pi\cdot \left(\frac{3^{2}}{2}-\frac{1^{2}}{2} \right)[/tex]
[tex]V = \frac{208\pi}{3} - 40\pi -24\pi[/tex]
[tex]V = \frac{16\pi}{3}[/tex]
The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.
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25. Which is a solution of the inequality y
(3,-5)
(2,-1)
(4,1)
(6,-4)
Step-by-step explanation:
B
D
A
с
2
2-1
1
2
3 4 5
2 1
2
2 4 5
A
B
2-1
1
2
B
5 4 3 2 1
1
2 3 4 5
The mass of a sheet of metal varies jointly with its area and its thickness. A sheet of metal of area 250cm2 and thickness 1mm has a mass of 200g. Find the formula which connects the mass M g, the area A cm2 and the thickness 1mm. Hence find the mass of a piece of metal of area 400 cm2 and thickness 3mm
The Formula of the relation is M = 8AT.
The mass of the metal sheet is 960 g.
The expression below shows the variation between the mass of the sheet (M), Area of the Sheet(A), and thickness (T).
Proportionality:
M ∝ ATRemoving the proportionality sign,
M = KATWhere:
K = constant of proportionality.make K the subject of the equation:
K = M/KT.................... Equation 1From the question,
Given:
M = 200 gA = 250 cm²T = 1 mm = 0.1 cmSusbtitute into equation 1
K = 200/(250×0.1)K = 8 g/cm³Formula:
M = 8AT................. equation 2Hence the formula of the relation is M = 8AT
If,
A = 400 cm²T = 3 mm = 0.3Substitute these values into equation 2
M = 8(400)(0.3)M = 960 gHence, the mass of the metal sheet is 960 g
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Juan has 6 times as many baseball cards as Nick. If Juan has 192 cards, how many does Nick have?
32
Step-by-step explanation:Divide 192 by 6, to find the amount of baseball cards Nick has.
192 ÷ 6 = 32
Check:32 · 6 = 192
192 ÷ 6 = 32
Nick has 32 baseball cards, which is 6 times less than Juan's amount.
If a plane travels 900kms in 3 hours what is its rate of speed expressed as a unit rate
Answer:
300kms
Step-by-step explanation:
900÷300 is 300. so then i think it would be 300kms
The following system of equations will be used to answer all remaining questions.
(8 - 12)
x + 2y = 11
2x + 3y = 18
=
Write the system as a matrix equation then identify the coefficient matrix.
The given equation above written in the form AX = b will be;
[tex]\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right][/tex]
Given the system of equation;
x + 2y = 11 2x + 3y = 18This equation can be represented in matrix form as [tex]AX = b[/tex]
where:
A is the coefficient of the matrixX is the variablesb is a column matrixThe given equation above written in the form AX = b will be;
[tex]\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right][/tex]
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Math help please!!!!!!!!!!!!!!
Answer:
x-1
correct me if im wrong
HELP!!
is {(-3,-6),(-2,-1),(-1,-0),(0,3),(1,15)} a function??
It's a function because we don't have any repeated x coordinates. Any given x input value leads to exactly one y output value.
The domain is {-3,-2,-1,0,1} which is the set of all x inputs.
The range is {-6, -1, 0, 3, 15} which is the set of y outputs.
Help help math math math
Answer:
[tex]slope = \frac{20 - 16}{5 - 3} [/tex]
[tex] = \frac{4}{2} [/tex]
[tex] = 2 \: is \: the \: answer[/tex]
The slope of the equation is 2.
What is the slope of an equation?The slope of an equation shows a gradient line that measures the steepness of the line.
It can be expressed by using the formula:
[tex]\mathbf{slope = \dfrac{\Delta y}{\Delta x}}[/tex]
[tex]\mathbf{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
From the parameters given;
The change in y distance from y2 to y1 The change in x distance from x2 to x1[tex]\mathbf{slope = \dfrac{20-16}{5-3}}[/tex]
[tex]\mathbf{slope = \dfrac{4}{2}}[/tex]
slope = 2
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Tim wants to create a circle graph showing the number of physicians whose specialty is aerospace medicine. He knows the following information.53 male physicians are under 35 years of age. 8 female physicians are under 35 years of age. 155 male physicians are between 35 and 44 years of age. 17 female physicians are between 35 and 44 years of age. 145 male physicians are between 45 and 54 years of age. 10 female physicians are between 45 and 54 years of age. 98 male physicians are over 54 years of age. 2 female physicians are over 54 years of age. If he wants to include each of the eight groups in his graph, how many degrees would he use for the central angle of the "45-54 year-old Males" sector? Express your answer to the nearest whole number.
Answer:
107 :)
Step-by-step explanation:
In total there are 53+8+155+17+145+10+98+2=488 physicians of aerospace medicine. 45-54 year-old males account for 145/488 of this population, so they should account for that fraction of the central angle of the circle graph also. Since there are 360 degrees in the central angle to divide up among the groups, the 45-54 year-old male group should get 145/488 x 360 which rounds to about 107 degrees.
Figure B is a scale image of Figure A, as shown.
7
2.5
Figure A
Figure B
Enter the scale factor applied to Figure A to produce Figure B.
Enter your answer as a fraction, like this: 42/53
Explanation:
Divide the side length for B over the corresponding side length for A.
scale factor = B/A = 7/(2.5) = 2.8
Let's now convert this to a fraction
2.8 = 2 + 0.8 = 2 + 8/10 = 20/10 + 8/10 = (20+8)/10 = 28/10
Then reduce that fraction
28/10 = (14*2)/(5*2) = 14/5
Note that 14/5 = 2.8
The cost C in dollars of producing a certain item is represented by the equation C = n/2+ 20. where n
represents the number of items produced. The revenue R, in dollars, from selling n items is represented by
the equation R=2n+ 5. For what value of n are the cost and revenue equal?
O 5
O 10
O 15
0 20
Considering the definition of equation, for a value of n of 10 the cost and revenue are equal.
What is equationA first degree equation is a mathematical equality with one or more unknowns.
Solving an equation consists of finding the value that the unknown must take so that equality is fulfilled.
The steps to solve an equation are as follows:
Group similar terms. That is, proceed to pass the terms containing variables from one side of the expression and the constants from the other side of the expression.Finally, the unknown is solved.Value of nThe cost C in dollars of producing a certain item is represented by the equation C = [tex]\frac{n}{2}[/tex]+ 20, where n represents the number of items produced.
The revenue R, in dollars, from selling n items is represented by the equation R=2n+ 5.
The cost and revenue are equal. Then:
[tex]\frac{n}{2}[/tex]+ 20= 2n+ 5
Solving:
When a term passes to the other side of equality, its sign changes (if it is positive it becomes negative and vice versa):
20 -5= 2n - [tex]\frac{n}{2}[/tex]
15= [tex]\frac{3}{2}n[/tex]
The X is cleared. Since the term in front of it is multiplying, it goes to the other side of the equation by dividing.
15 ÷[tex]\frac{3}{2}[/tex]= n
10= n
Finally, for a value of n of 10 the cost and revenue are equal.
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PLS HELP!!!!!! (again! XP)
Express each of these numbers, as a product of two fractions 2/25
Mr. Jefferson's and Mr. Hamilton's fifth grade classes sold brownies every day at school for 6 months. If
the pattern continues, which class will earn more at the end of week 8? Use the table to help solve the
problem.
Answer:
It is B
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST!
[tex]\huge \bf༆ Answer ༄[/tex]
Let's solve ~
[tex] \sf \sqrt{ {x}^{3} } [/tex][tex] \sf { ({x}^{3} ) }^{ \frac{1}{2} } [/tex][tex] \sf (x ){}^{3 \times \frac{1}{2 }} [/tex][tex] \sf{x {}^{ \frac{3}{2} } }[/tex]Hence, the required power in fractional form is ~
[tex] \sf \frac{3}{2} [/tex]what is 7 plus 56 divided by 4 tims 7
Answer:
107
Step-by-step explanation:
Answer:
The answer is 105
Step-by-step explanation:
hope its help:)
Find the equation of a line which contains the point (2, 5) and is parallel to the line y = 3x + 5.
Answer:
The equation of a line which contains the point (2, 5) and is parallel to the line y = 3x + 5 is
y = 3x - 1
A line is parallel to another when they both have the same slope.
The two equations above have a common slope of 3.
I hope this helped. Have a good new year!
Jeremiah buys 6 tacos and 8 enchiladas for 60 dollars. Kennedy buys 3 tacos and 2 enchiladas for 18 dollars.
Answer:
What's the question lol
WILL GIVE BRAINLYEST
PLZ HELPPP MEEEE
The height of a ball when it is thrown off a cliff can be represented by the equation $h=45-7t-6t^2$, where $t$ is time in seconds. In how many seconds will the ball reach a height of 25 feet?
You want to find t such that
45 - 7t - 6t² = 25
or
6t² + 7t = 20
Solve for t. By completing the square, we have
6t² + 7t = 20
t² + 7/6 t = 10/3
t² + 7/6 t + (7/12)² = 10/3 + (7/12)²
(t + 7/12)² = 529/144
t + 7/12 = ± 23/12
t = -7/12 ± 23/12
t = -5/2 or t = 4/3
We ignore the negative solution, so the ball reaches a height of 25 feet at t = 4/3 seconds, or about 1.33 seconds after being thrown.
What’s the difference for this equation!!!
Answer:
2x^2 + 11x – 1
Step-by-step explanation:
The position of a 2 kg object is given as x(t) = Bt2 +5, where x is in meters and t is in seconds. (a) Determine the force F responsible for this motion. (3) (b) If the force only results in a change in the kinetic energy of the object of 200 J between tı = 0 s and t2 = 5 s, determine the value of B. (3) (C) Without using kinematics (equations of motion), determine the displacement of the object during these 5 seconds referred to in part (b). (2)
(a) Given the position function
x(t) = (B m/s²) t² + 5 m
it's clear that the object accelerates at B m/s² (differentiate x(t) twice with respect to t), so that the force exerted on the object is
F(t) = (2 kg) (B m/s²) = 2B N
(b) Recall the work-energy theorem: the total work performed on an object is equal to the change in the object's kinetic energy. The object is displaced by
∆x = x(5 s) - x(0 s)
∆x = ((B m/s²) (5 s)² + 5 m) - ((B m/s²) (0 s)² + 5 m)
∆x = 25B m
Then the work W performed by F (provided there are no other forces acting in the direction of the object's motion) is
W = (2B N) (25B m) = 50B² J = 200 J
Solve for B :
50B² = 200
B² = 4
B = ± √4 = ± 2
Since the change in kinetic energy and hence work performed by F is positive, the sign of B must also be positive, so B = 2 and the object accelerates at 2 m/s².
(c) We found in part (b) that the object is displaced 25B m, and with B = 2 that comes out to ∆x = 50 m.
Melllissa owns 4 sets of jewelry. Each set contains 2 earrings, 1 neckles, 1 bracelet, 1 ring. How many pieces of jewelry does Melissa have all together?
Answer:
The answer is to the problem is 18.
you went to a coffee house with 2 friends and ordered an iced coffee and dessert which came to $12.96 how much is the tip if the rate is 15%
Answer:
its 1.944
Step-by-step explanation:
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.
What is the value of x?
O
O x = 32
O x = 36
x = 37
(x + 15)
xº
(4x - 20)
O x = 40
Answer:
x + (4x-20) = 180
by linear pair
therefore x= 70
Applying the definition of linear pair, the value of x is: D. 40.
What is a Linear PairA linear pair is a set of angles on a straight line.Straight line angle = 180 degrees.Linear pair of angles add up to 180 degrees.Therefore:
x + (4x - 20°) = 180°
Solve for x5x - 20 = 180
5x = 180 + 20
5x = 200
Divide both sides by 5x = 40
Therefore, applying the definition of linear pair, the value of x is: D. 40.
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If f (x) = 3x + 2 and g(x) = x2 – x, find the value.
-
f (2)+1
Answer:
......
Step-by-step explanation:
if your leg get cut off, where would you feel the pain if you got no leg. hehehe
Answer:
lol in your head , literally
Step-by-step explanation:
After one of your limbs is amputated, you may feel as if the limb is still there. This is called phantom sensation. You may feel: Pain in your limb even though it is physically not there.
Answer:
The nerve in your leg.
Explanation:
It's not your leg that will hurt but the nerve in your leg that'll hurt. So wherever the leg is cut, the nerves must be cut as well, but another thing is when one of your limbs is amputated, you may feel like the limb is still there. That's called phantom sensation. You might feel pain in your "limb" even though it's not physically there.
Simplify 4 to the seventh power over 5 squared all raised to the third power . (4 points)
a
4 to the tenth power over 5 to the fifth power
b
4 to the fourth power over 5
c
4 to the twenty-first power over 5 to the sixth power
d
12 to the seventh power over 15 squared
The answer is C, 4 to the 21st over 5 to the 6th power.
Fill in the missing numbers below.
5 feet + 12 inches =
yard(s)
inches = 1 foot + 1 yard
feet = 3 feet + 24 inches
Answer:
2
Step-by-step explanation:
5 feet + 12 inches = 2 yards
Therefore
5 feet + 12 inches = yard(2)
I solving for (s)
hope that helps
What are the domain and range of the function below? (In picture)
Answer:
Domain: [0 , ∞)
Range: (-∞ , 4]
Step-by-step explanation:
I) DOMAIN:For domain, look along the x axis.
The graph starts from x = 0 and it's ending point isn't given in the graph as it continues moving along the positive x axis.
Hence, it's ending point must be ∞
Domain of a function is:
[minimum point in x, maximum point in x]
=> [0, ∞)
"),(" is used for infinity.
"],[" for points that lie within the domain of the function.
II) RANGEFor range, look along the y axis.
The graph starts at y = 4, and continues moving downwards till infinity.
Range:
[minimum in y, maximum in y]
=> (-∞, 4]
For parenthesis, same rule as domain will be applied. 4 is naturally greater than all values in negative. Hence, maximum point will be 4 and minimum will be -∞.helpp anyone?? :(
No linkssss porfavorr plaesaaje cjkq
Answer:
127/100 = 1.27
1.4
1 whole and 1/3 = 1.5
Step-by-step explanation:
Hope this helps
May I get Braineist pls