PLEASE HELP WILL MARK BRAINLIEST..Write a polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.
x= -2, x=7
P(x)=
Answers
A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²-5x-14
What is a polynomial function?A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.
A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.
x= -2, x=7
Given,
P(x) = 0
This polynomial function has the roots,
x= -2, x=7
So,
(x+2)(x-7)
We have to multiply both of them we get,
P(x)=(x+2)(x-7)
0=x²-5x-14
x²-5x-14=0
Therefore, P(x)=x²-5x-14 is the polynomial function.
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Related Questions
Find the missing length.
c=√?
Pythagorean Theorem: a²+b²=c²
Answers
After using the Pythagorean theorem the missing length of c is √148
What is the Pythagorean theorem in plain English?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
How may the Pythagorean Theorem be demonstrated the simplest way?
Angles CAB, AC'B, and AB'C must be equal in order for AC2 + AB2 to equal BC(CB' + BC'). Triangles ABC, AC'B, and AB'C are indeed comparable. Since AB/BC' = BC/AB and AC/CB' = BC/AC, we have the necessary identity right away. Theorem reduces to Pythagorean proposition and proof if angle A is correct.
Pythagorean Theorem: a²+b²=c²
so (12)^2+(2)^2 = 144+4 = 148
c²=148
c=√148
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The graph displaying the prices of laptops at two different stores is shown. You are helping your friend Marcus decide how much money to spend on a laptop. Which of the following statements are true? Pls help
Answers
b,d and e option are correct
What is statement?
A statement, like "Pizza is tasty," is a declaration that something is true. In the fields of law, finance, and government, there are more types of statements. Every statement makes a claim or a point.
These statements are true:
The least Marcus would pay for a laptop from electro's is $500
Marcus can accept to pay about $700 for a laptop from electro's and $1500 for a laptop from bits and bytes.
The middle 50% of laptops from electro's are priced between $500 and $900.
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Question content area left
Part 1
On a math test Ali needs to describe the motions which map ΔEFG to ΔMNO. The coordinates of ΔEFG are E(6,5), F(9,5), and G(6,10). The coordinates of ΔMNO are M(0,0), N(−3,0), and O(0,5). He says there is a translation 6 units to the left and 5 units down, followed by a reflection across the x-axis. Describe the sequence of rigid motions. What is Ali's likely error?
-10
-5
5
10
-10
-5
5
10
x
y
E
F
G
M
N
O
x y graph
.
.
.
Question content area right
Part 1
Which of the following is the description of the rigid motions which maps ΔEFG to ΔMNO?
A.
A translation 6 units to the left and 5 units down, followed by a reflection across the x-axis
B.
A translation 6 units to the left and 5 units down, followed by a reflection across the y-axis
C.
A translation 5 units to the left and 4 units down, followed by a reflection across the y-axis
Part 2
What is Ali's likely error?
A.
He reflected the triangle across the wrong axis.
B.
He did not move the correct units down.
C.
He did not move the correct units to the left.
Answers
There is a translation 6 units to the left and 5 units down, followed by a reflection across the x-axis is the description of the rigid motions which maps ΔEFG to ΔMNO and he reflected the triangle across the wrong axis is the Alis error.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
The coordinates of ΔEFG are E(6,5), F(9,5), and G(6,10).
The coordinates of ΔMNO are M(0,0), N(−3,0), and O(0,5)
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis
Reflections of graphs involve reflecting a graph over a specific line. Reflecting functions are functions whose graphs are reflections of each other.
There is a translation 6 units to the left and 5 units down, followed by a reflection across the x-axis is the description of the rigid motions which maps ΔEFG to ΔMNO and he reflected the triangle across the wrong axis is the Alis error.
Hence, there is a translation 6 units to the left and 5 units down, followed by a reflection across the x-axis is the description of the rigid motions which maps ΔEFG to ΔMNO and he reflected the triangle across the wrong axis is the Alis error.
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pls help me with math i’ll give you brainlist :)))
Answers
The required number of candles Marcella has in the starting is 56.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
As mentioned in the question,
She has some candles in the starting before she starts collecting the candles, let x be the candle she had in the starting,
Now,
According to the question she is buying 13 candles every week, at the end of 8 weeks she has 160 candles,
So.
x + 13(8) = 160
x + 104 = 160
x = 160 - 104
x = 56
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Each year caronline deposited a certain amount of money in an account which pays an annual interest rate of r so that at the end of each year, the balance in the account is multiplied by a growth factor of x=1+r. $600 is deposited at the start of the first year, and $200 at the start of the following year. Write an expression for a value of the account at the end of three years in terms of growth factors x. Find the value at the end of 3 years if the interest rate is 4%.
Answers
balance = previous balance * growth factor
At the start of the first year, the balance is 600$ and the growth factor is x = 1 + r. At the start of the second year, the balance is the value of the account at the end of the first year, and the growth factor is still x = 1 + r. At the start of the third year, the balance is the value of the account at the end of the second year, and the growth factor is still x = 1 + r.
Therefore, the balance at the end of three years can be expressed as:
balance = 600 * x * (200 * x)
If the interest rate is 4%, the growth factor is x = 1 + 0.04 = 1.04. Plugging this value into the equation for the balance, we find that the balance at the end of three years is:
balance = 600 * 1.04 * (200 * 1.04)
= 648 * 288
= 186368
So the balance at the end of three years is $186368.
A football player throws a ball down the side line. The ball's height above the
ground is modeled by the equation h=-8t^2+24t+4, where h is the height
in feet and t is the time in seconds.
At what two times will the ball be at a height of 16 feet?
Answers
Answer: t₁=1.5-0.5√3 c ≈0.634 c t₂=1.5+0.5√3 c ≈2.366 c
Step-by-step explanation:
h=-8t²+24t+4 h=16 feet t₂=?
[tex]16=-8t^2+24t+4\\\\16-16=-8t^2+24t+4-16\\\\0=-8t^2+24t-12\\[/tex]
Divide both parts of the equation by -4:
[tex]0=2t^2-6t+3[/tex]
Thus,
[tex]2t^2-6t+3=0[/tex]
a=2 b=-6 c=3
D=b²-4ac
D=(-6)²-4(2)(3)
D=36-24
D=12
√D=√12
√D=√(4*3)
√D=2√3
[tex]t=\frac{-bб\sqrt{D} }{2a} \\\\t=\frac{-(-6)б2\sqrt{3} }{2(2)} \\\\t=\frac{6б2\sqrt{3} }{4} \\\\t_1=1.5-0.5\sqrt{3}\ c \\\\t_2=1.5+0.5\sqrt{3}\ c[/tex]
PLEASE HELP ME ASAP!!!! PLEASE I WILL GIVE YOU BRAINLIST!!!
Answers
LM is translated 5 units right and 2 units up to LM' as the graph shows the move in positive direction.
What is graph?In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty). In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
Here,
As the graph indicates a move in the right direction, LM is translated 5 units right and 2 units up to LM'.
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pls help i will give brainliest
The table represents a quadratic function C(t).
t C(t)
2 4
3 1
4 0
5 1
6 4
What is the equation of C(t)?
C(t) = −(x − 4)2
C(t) = (x − 4)2
C(t) = −x2 + 4
C(t) = x2 + 4
Answers
The quadratic equation of the function C(t) is; C(t)= (x - 4)²
How to find the quadratic function?
We are given the coordinates as;
When t = 2, C(t) = 4
When t = 3, C(t) = 1
When t = 4, C(t) = 0
When t = 5, C(t) = 1
When t = 6, C(t) = 4
The general formula formula for quadratic equation is;
y = ax² + bx + c
where c is y-intercept
We are given that x = 4, when y = 0. Thus, x = 4 is a root of the equation.
Put x = 2and y = 4 into the equation to get;
4a + 2b + c = 4 -----(1)
Put x = 3 and y = 1 into the equation to get;
9a + 3b + c = 1 -----(2)
Put x = 4 and y = 0 into the equation to get;
16a + 4b + c = 0 -----(3)
Using simultaneous equation solver gives;
a = 1, b = -8 and c = 16. Thus, our equation is;
y = x² - 8x + 16
By factorization;
y = x² - 4x - 4x + 16
y = x(x - 4) - 4(x - 4)
y = (x - 4)²
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One of the same side interrier angles of two paralell lines is 20 degrees less than the other sameside interior angle. Find the measures of the two angles.
Answers
Interior angles on the same side are supplementary, which means they add up to 180°. We can write the equation as follows and refer to the two angles as x° and (x + 20)°.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
According to our question-
x + x + 20 = 180
2x + 20 = 180
2x = 160
If x = 80, the angles are 80° and 80 + 20 = 100°, respectively.
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I Need help on this problem! please!
Answers
The pairs of triangles that are congruent are;
A. Δ1 and Δ5
B. Δ1 and Δ2
C. Δ2 and Δ3
D. Δ3 and Δ5
E. Δ1 and Δ3
F. Δ3 and Δ4
G. Δ1 and Δ4
H. Δ4 and Δ5
What are congruent triangles?Congruent triangles are triangles that have all three sides and all three angles on each triangle having the same length and the same measure.
The congruent angles are indicated by the number of markings
The angles in the figures are;
Angle with one arc
Angles with two arcs marks
Angles with three arc marks
The congruent sides are indicated by one dash, and two dashes
Therefore;
Δ2 s congruent to Δ1 is congruent to Δ3 by Angle-Side-Angle rule of congruency
Similarly, we have;
Δ3 is congruent to Δ4 by Angle-Side-Angle congruency postulate
Therefore;
Triangle Δ2 is congruent to Δ3 by Angle-Side-Angle congruency postulate
From the diagram, the one arc, two arcs, and three arc angles form a linear pair, therefore;
Therefore, Δ4 is congruent to Δ5
Δ1 is congruent to Δ4
Δ2 is congruent to Δ5, therefore; Δ3 is congruent to Δ5
Similarly;
Δ1 is congruent to Δ3
Δ1 is congruent to Δ2, therefore , therefore, Δ1 is congruent to Δ5
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How far can an object be pushed if 22 J is used with 17.5 N of force? *
A 1.25 meters,
B 0.80 meters
C 4.5 meters
D 385 meters
Answers
Answer:
[tex]\huge\boxed{\sf d = 1.25\ m}[/tex]
Step-by-step explanation:
Given Data:Work = W = 22 J
Force = F = 17.5 N
Required:Distance = d = ?
Formula:W = Fd
Solution:Put the given data in the above formula.
22 = 17.5 (d)
Divide 17.5 to both sides
22/17.5 = d
1.25 m = d
d = 1.25 m[tex]\rule[225]{225}{2}[/tex]
ents
Select all of the triangles that are congruent to triangle A by the SSS postulate.
A
B
HHH
A A
G
O Triangle H
O Triangle D
O Triangle I
O Triangle C
O Triangle F
O Triangle B
O Triangle E
O Triangle G
À l
H
HE
Answers
Answer:
Triangle B
Step-by-step explanation:
The triangles have three pairs of congruent sides.
Please answer correctly It's pre-calculus
Answers
Initial size of bacteria is 313, population of bacteria after 5 hours is 3.346 ×10¹¹.
What is bacterial growth?here growth means increases in the number of bacterial populations with respect to time. Generally, the rate of growth of bacteria is occurred exponentially. We use the following exponential equation to calculate the number of bacteria.
N= N° e∧(kt)
How to calculate the initial sizes of bacteria and the population after certain time period?In the above equation, N and N° denotes the number of populations after t minutes and initial time respectively.
k is a constant of proportion
t is the time in minutes
as per given data, the number is doubled after 10 min
N=2N°, t=10
2N°=N° e∧(k10)
2= e∧(k10)
㏑2 = k10 [we took ㏑ in both side]
k= 0.0693
after t= 80 min, the population N= 80000
now using the equation, 80000=N° e∧(k80)
as k=0.0693, N°= 313
the initial number is 313'
after t=5 hours =300 min, the population will be
N= 313 e∧ (0.0693x300)
N = 3.346×10¹¹
hence, initial population is 313 and the number increase to 3.346×10¹¹ after 5 hours.
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Kelly recorded the following data while observing the temperature, in degrees Fahrenheit, of a chemical liquid cooling in her science class.
What is the rate of change for the temperature of this liquid?
Answers
The rate of change of temp w.r.t time is -1.875°F
What is rate of change?
The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time. When discussing momentum, the term "rate of change" (ROC) is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another; visually, the rate of change is represented by the slope of a line. The Greek letter delta () is frequently used to represent the ROC.
The term "rate of change" (ROC) describes the rate at which something changes over time.
Thus, it is not the amount of individual changes themselves but rather the acceleration or slowdown of changes (i.e., the pace).
Time Temperature Difference
4 89.5 -
10 78.25 78.25 - 89.5 = -11.25
16 67.00 67 - 78.25 = -11.25
There is a common difference of -11.25 in each successive term.
Therefore, cooling of a chemical represents a linear function.
Rate of change of temp from 4 min to 10 min
=78.25 - 89.5 = -11.25
= -11.25/6
=-1.875
So, the rate of change of temp w.r.t time is -1.875°F
which means temperature is decreasing continuously when the time is increasing
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The points (d, 7) and (0, 10) fall on a line with a slope of 1/3. What is the value of d?
Answers
The value of missing coordinate d of the point (d, 7) in the line such that its slope is 1 / 3 is - 9.
What are the missing coordinates that satisfies a given slope?
In this problem we must determine the value of the missing coordinates of a point in a line such that its slope is 1 / 3. The slope of the line can be determined by means of the secant line formula:
m = Δy / Δx
Where:
Δx - Change in the x-coordinates.Δy - Change in the y-coordinates.If we know that (x₁, y₁) = (d, 7), (x₂, y₂) = (0, 10) and m = 1 / 3, then the missing coordinate is:
1 / 3 = (10 - 7) / (0 - d)
1 / 3 = - 3 / d
d = - 9
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what is 50% of 950? Hint: We can think of 50% as a common fraction.
Answers
Answer:
Step-by-step explanation:
To find 50% of 950, you can multiply 950 by 0.50. 50% is the same as 0.50.
The calculation is: 50% * 950 = 0.50 * 950 = <<50*.01*950=475>>475
So, 50% of 950 is 475.
Find sin D, sin E, cos D, and cos E. Write each answer as a fraction in simplest form.
Answers
Answer:
7 5 15 22
step,by step explanation: yes
Mr. Hansen has three sticks that measure 5 inches, 10 inches and 17 inches. If he connects the sticks ends, will the three sticks form a triangle?
Answers
The three sticks will not form a triangle.
What is the triangle inequality theorem?
The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.
Given, Mr Hansen has three sticks that measure 5 inches, 10 inches and 17 inches
From the above definition of the Triangle inequality theorem,
Sum of two sides = 5 + 10 = 15 which is less than
the length of the third side = 17
So, the three sticks will not form a triangle.
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g(t)=3t+4 Find g(-3)
Answers
Let's compare
5/8 and 7/10
Answers
Answer:
5/8=25/40 7/10=28/40
Step-by-step explanation:
5/8<7/10
IfGH=72- 1andBC=4z- 3,whatisGH?
Answers
The length of the line segment GH is 34 units
How to determine the length GH?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
GH= 7z - 1
BC = 4z - 3
Also from the question, we understand that the line segment BC is half the line segment GH
This can be represented mathematically as follows
BC = 1/2 * GH
Substitute the known values in the above equation, so, we have the following representation
4z - 3 = 1/2(7z - 1)
Multiply through by 2
8z - 6 = 7z - 1
Collect the like terms
8z - 7z = 6 - 1
Evaluate the like terms
z = 5
Recall that
GH= 7z - 1
Substitute the known values in the above equation, so, we have the following representation
GH= 7 * 5 - 1
Evaluate
GH= 34
Hence, the length is 34 units
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Complete question
The line segment BC is half the line segment GH
If GH = 7z- 1 and BC=4z- 3,
What is GH?
Of the 400 students in the 8th grade, four-fifths have purchased tickets for the end of year trip. If there needs to be two chaperones for every 75 students, how many chaperones are needed?
Answers
The number of chaperones that are needed is 128/15.
What is unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given that the number of students in 8th grade is 400.
Four fifth of total number of students go for trip.
The number of student who goes for the trip is 400 × 4/5
= 320.
To carry 75 students, we need 2 chaperones.
Apply unitary method:
To carry 1 student, we need 2/75 chaperones.
To carry 320 students, we need (2 ×320)/75 chaperones.
= (2 × 64)/15
= 128/15
= 8.533
= 9
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Given ∠3≅∠4
Which of the following statements cannot be proved
∠1≅∠2
∠F≅∠2
∠1+∠4≅∠2+∠3
∠1+∠2≅∠3+∠4
Answers
Answer:
∠1+∠2≅∠3+∠4 cant be proven because sum of two obtuse angles is sure to be greater than sum of two acute angles of a triangle.
Arturo compro una calculadora, para venderla recargó el precio que le costo en 30%. Al momento de venderla a su amiga Carmen, le hizo una rebaja de 30% pensando que con esta rebaja iba a vender el precio que habia comprado, pero sin embargo quedó peerjudicado en s/ 54.¿ A qué precio se vendio?
Answers
Answer:
5.46
Step-by-step explanation:
precio original = x
0.7(1.3x) = x - 0.54
0.91x - x = -0.54
x = 6
6 + 30% de 6 = 7.8
7.8 - 30% de 7.8 = 5.46
Arturo compró por 6.
Aumentó 30% para 7.80.
Bajó 30% para 5.46.
6 - 5.46 = 0.54
What is m/1?
68°
49°
Answers
x=measure of angle 1
68+49+x=180
117+x=180
x=180-117
x=63.
Therefore, the measure of angle 1 is 63.°
We can check our work: 117+63=180
how do i get an equation perpendicular to 5/4x + 2 that passes through the point (-6,2)
Answers
Answer: -4/5x - 22/5
Step-by-step explanation:
To find an equation of a line that is perpendicular to a given line and passes through a given point, we need to first find the slope of the given line. The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate of any two points on the line. For example, the slope of the line 5/4x + 2 is 5/4.
To find the equation of a line that is perpendicular to a line with slope m, we need to use the equation:
y - y1 = -1/m(x - x1)
where (x1, y1) is the given point that the line passes through. In this case, the given line has slope 5/4 and the given point is (-6,2), so the equation of the line perpendicular to 5/4x + 2 that passes through (-6,2) is:
y - 2 = -1/((5/4))(x + 6)
y - 2 = -4/5(x + 6)
y - 2 = -4/5x - 24/5
y = -4/5x - 22/5
Therefore, the equation of the line perpendicular to 5/4x + 2 that passes through (-6,2) is -4/5x - 22/5 (option "-4/5x - 22/5").
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Use cylindrical coordinates. Evaluate E(x+y+z)dV where E is the solid in the first octant that lies under the paraboloid z=4x2y2.
Answers
Evaluation of E(x+y+z)dV where E is the solid in the first octant that lies under the paraboloid z = 4 - x² - y² is [tex]\frac{128}{15} + \frac{8\pi}{3}[/tex]
Cylindrical coordinates are a set of three coordinates used to locate a point in the cylindrical coordinate system.
When the polar coordinates are extended to a three-dimensional plane, an additional z coordinate is added.
These three measurements combine to form cylindrical coordinates. The coordinates describe two distances and one angle.
According to the question,
We have to find the area under paraboloid
Given : E is a region that lies under paraboloid z = 4 - x² - y² and in the first octant.
The intersection of this paraboloid with the xy plane will give z = 0,
z = 4 - x² - y² , z = 0, that is a circle x² +y² = 4 with radius 2
Therefore , 0 ≤ z ≤ 4 - r²
Therefore, the region E in cylindrical coordinates is
[tex]E = ( r , \theta , z ) | 0 \leq \theta \geq \frac{\pi}{2} , 0 \leq 4 \geq , 0 \leq z \geq 4 - r^2[/tex]
f(x , y ,z ) = x + y + z
=> f(x , y ,z ) = rcosθ + rsinθ + z
=> f(x , y ,z ) = r(cosθ + sinθ) + z
Integration ,
[tex]{\int \int \int }\limits_E {z} \,dv[/tex]
=> [tex]\int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 \int\limits^{4 - r^2}_0 {[r ( cos \theta + sin \theta) + z] r \, dzdrd\theta[/tex]
simlifying,
[tex]= \int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 \int\limits^{4 - r^2}_0 {[r^2 ( cos \theta + sin \theta) + rz] \, dzdrd\theta\\= \int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 [r^2 ( cos \theta + sin \theta)z + r\frac{z^2}{2}] \, drd\theta[/tex]
=> [tex]\int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 [(4r^{2} - r^{4})( cos \theta + sin \theta) + \frac{r(4 - r^2)^2}{2}] \, drd\theta[/tex]
=> [tex]\int\limits^{\frac{\pi}{2}}_0 [(\frac{4}{3} r^{3} - \frac{r^{5}}{5})( cos \theta + sin \theta) + \frac{(4 - r^2)^3}{12}]^{2}_{0} \, d\theta[/tex]
Putting the limit and solving,
=> [tex]\int\limits^{\frac{\pi}{2}}_0 [(cos \theta + sin\theta )\frac{64}{15} + \frac{16}{3} \theta ]\, d\theta[/tex]
=> [tex][(sin\theta - cos\theta )\frac{64}{15} + \frac{16}{3} \theta ]^\frac{\pi}{2} _0[/tex]
Evaluating the limits,
[tex]\int\int\int\limits_E {x + y +z } \,dV = \frac{128}{15} + \frac{8\pi}{3}[/tex]
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Simplify the following equation:
17/6 = -1 2/3 + x
Answers
Answer: x=27/6
Step-by-step explanation:
-1 2/3 = -5/3
17/6 = -5/3 + x
x = 17/6 + 5/3
x = 17/6 + 10/6
x = 27/6
Match the amplitude, midline, period, and frequency for the cosine equation.
Answers
Amplitude is 5, midline is 3, period is π and the frequency is 2
We can describe the cosine function as y = Acos(B(x + C )+ D
where,
amplitude is A
Frequency is B
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
Step 1:
Identify
5 cos(2x) + 3 → Acos(B(x + C )+ D
Hence
A = 5 = Amplitude
B = 2.C = 0. So,
Period = 2π / B
= 2π / 2 = π
Period = π
Frequency = B = 2
Vertical shift = D = 3
Step 2:
Midline
The equation of the midline of periodic function is the average of the maximum and minimum values of the function.
a) we have a maximum when
cos(2x) = 1
x =0, because (cos 0) = 1 Now, replace
y = 5 cos(2x) + 3
y = 5cos(2. 0 ) +3
= 5.1 + 3
= 8
So, the maximum is 8
b) we have a minimum when
cos(2x) = -1
x = π/2 , because
cos(2.π/2) = cos(π) = -1
Now, replace
y = 5cos(2.π/2) + 3
= 5. (-1) + 3
= -5+3
= -2
So, the midline is the average of 8 and -2
Midline = y = [8 + (-2)] / 2
= 6/2
y = 3
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A movie theater has a seating capacity of 317. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 2298, and the theater was filled to capacity, how many children, students, and adults attended?
Answers
The total ticket sales was $ 2298, and the theater was filled to capacity
Children: 158
Students: 158
Adults: 79
What exactly is a math area?The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. Draw a square on a piece of paper using a pencil. A 2-D figure, that is. The term "Area" refers to the area that a shape occupies on paper. Now picture that your square is composed of smaller unit squares.
Where is the usage of area?According to Study.com, area is a mathematical concept that is defined as the two-dimensional space occupied by an item. Area is used in many real-world contexts, including building, farming, architecture, science, and even determining how much carpet you'll need to cover your home's rooms.
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