The equation of parabola becomes y = -2/25(x-3)^2 + 4.
According to the statement
we have given a graph and from this graph we have to find the equation of parabola in the general form.
So,
we know that the equation of parabola in general form is
y = a(x-h)^2 +k - (1)
From the graph we have:
a point on the graph is (x,y) = (-2,2)
the vertex of the graph is (h,k) = (3,4)
Now, substitute these values in the equation number (1)
Then
y = a(x-h)^2 +k
2 = a(-2-3)^2 +4
2 = a(-5)^2 +4
2 = a(25) +4
25a = -2
a = -2/25.
Now put a = -2/25 and (h,k) = (3,4) in the equation(1).
Then
the equation of parabola becomes y = -2/25(x-3)^2 + 4
So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.
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The segments shown below could form a triangle.
A
5
с
B
8
B
6
Based on the triangle inequality theorem, the statement that the given segments will form a triangle is TRUE.
What is the Triangle Inequality Theorem?If a, b, and c are lengths of a triangle, then,
a + b > c
a + c > b
b + c > a
Given the segments:
AC = 6
CB = 5
BA = 8
6 + 5 > 8 [true]
6 + 8 > 5 [true]
5 + 8 > 6 [true]
Therefore, it is true that the segments given could form a triangle.
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The volume of a solid revolution generated by rotating the curve y = f(x) and x = f(y) between x = a and x = b , y = a and y = b through 360 degrees about the x-axis and y-axis is given
[tex]V_{x} =\int\limits^b_a {\pi y^{2} } \, dx[/tex] and [tex]V_{y} =\int\limits^b_a {\pi x^{2} } \, dy[/tex]
The diagram shows the line y = 1, the line y = 4 and part of the curve [tex]y=3x^2[/tex]. The shaded region is rotated through 360 degrees about the y-axis. Find the exact value of the volume of revolution obtained. Leave your answer in pi.
Answer:
[tex]\dfrac{5}{2}\pi[/tex]
Step-by-step explanation:
Rotation about the y-axis
[tex]\textsf{Volume}=\displaystyle \int^b_a \pi x^2\:\text{d}y[/tex]
where:
b = upper limita = lower limitx is a function of yGiven function of y: [tex]y = 3x^2[/tex]
Rewrite the given function as a function of y:
[tex]\implies x^2=\dfrac{1}{3}y[/tex]
Substitute the values into the formula:
[tex]\implies \displaystyle \int^4_1 \dfrac{1}{3}\pi y\:\:\text{d}y[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ay^n\:\text{d}y=a \int y^n \:\text{d}y$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $y^n$}\\\\$\displaystyle \int y^n\:\text{d}y=\dfrac{y^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
Take out the constant and integrate:
[tex]\begin{aligned}\implies \dfrac{1}{3}\pi\displaystyle \int^4_1 y\:\:\text{d}y & = \dfrac{1}{3}\pi \left[\dfrac{1}{2}y^2\right]^4_1\\\\& =\dfrac{1}{3}\pi \left[\dfrac{1}{2}(4)^2-\dfrac{1}{2}(1)^2\right]\\\\&=\dfrac{1}{3}\pi\left[8-\dfrac{1}{2}\right]\\\\&=\dfrac{5}{2}\pi \end{aligned}[/tex]
Therefore, the exact value of the volume of revolution is:
[tex]\dfrac{5}{2}\pi[/tex]
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Grass the line with the given slope and y-intercept. slope = -4, y-intercept =-5
There will be no change to the grass because the exponential of the function remains the same.
According to the questions,
slope = -4 and y-intercept = -5
Equation of straight line y = mx + c
y = -4x - 5
In order to grass line, there will be no change to the grass because the exponential of the function remains the same.
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A football field is 160 feet wide and 360 feet in length. what is the distance around the field?
Answer:
Step-by-step explanation:
Distance around = 2*160 + 2*360
= 320 + 720
= 1080 feet.
The distance around the field is 1040 feet.
It is required to find the distance around the field.
What is rectangle?A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.
Given that:
A football field is 160 feet wide and 360 feet in length.
A football field is in the shape of rectangle.
So, we know that ,
Perimeter of rectangle= 2(length +breadth)
Distance around
= 2(160 + 360)
=2(520)
= 1040 feet.
Hence, the distance around the field is 1040 feet.
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Page 3. Calculate the semi inter quartile range and its coefficients from the table Marks (below) 20 30 40 50 60
No of students 5 12 27 40 50
SOMEONE HELP ME
1. The semi inter quartile range is 10
2. The coefficient of quartile deviation is 0.2
1. How to determine the semi inter quartile rangeMark: 20, 30, 40, 50, 60Freq: 5, 12, 27, 40, 50Com. freq: 5, 17, 44, 84, 134Semi inter quartile range =?1st quartile (Q₁) = (134 + 1) / 4 = 33.75th = 40
3rd quartile (Q₃) = 3 (134 + 1) / 4 = 3 × 33.75 = 101.25th = 60
Semi inter quartile range = (Q₃ - Q₁) / 2
Semi inter quartile range = (60 - 40) / 2
Semi inter quartile range = 10
2. How to determine the coefficient1st quartile (Q₁) = 403rd quartile (Q₃) = 60Coefficient of quartile deviation =?Coefficient of quartile deviation = (Q₃ - Q₁) / (Q₃ + Q₁)
Coefficient of quartile deviation = (60 - 40) / (60 + 40)
Coefficient of quartile deviation = 0.2
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You can fine the run by subtracting the __ coordinate of the lead point from that of the right point
You can find the run by subtracting the _x_ coordinate of the lead point from that of the right point.
The "slope formula" for a straight line connecting any two locations is another name for the rise over run formula. The rise is the difference between the y-coordinates of the two locations. The run is the difference between the x-coordinates of two locations. Divide the rise by the run to find the slope.
The rise over run formula is also known as the slope formula because the fraction consists of a rise, whether the line is moving up or down, divided by the run, which can be either left or right. The slope of the line dictates the direction of the line as well as its steepness.
Thus, "You can find the run by subtracting the _x_ coordinate of the lead point from that of the right point".
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MATH HELP!!! 100PTS!!!
Write the parametric equations
x=5sinθ,y=3cosθ,0≤θ≤π
in the given Cartesian form.
(y^2)/9=
with x≥0.
Answer:
[tex]\dfrac{y^2}{9}=1-\dfrac{x^2}{25}[/tex]
Step-by-step explanation:
When converting parametric equations that involve trig functions to Cartesian equations, use trig identities to eliminate the parameter.
Given parametric equations:
[tex]x=5 \sin \theta, \quad y=3 \cos \theta, \quad 0\leq \theta\leq \pi[/tex]
Square the equation for x:
[tex]\implies x^2=(5 \sin \theta)^2=25 \sin^2 \theta[/tex]
Use the identity [tex]\sin^2 x+\cos^2x =1[/tex] to write [tex]x^2[/tex] in terms of cos:
[tex]\implies x^2=25(1-\cos^2 \theta)[/tex]
Isolate [tex]\cos^2 \theta[/tex] :
[tex]\implies \dfrac{x^2}{25}=1-\cos^2 \theta[/tex]
[tex]\implies \cos^2 \theta=1- \dfrac{x^2}{25}[/tex]
Square the equation for y:
[tex]\implies y^2=(3 \cos \theta)^2=9 \cos ^2 \theta[/tex]
Replace [tex]\cos^2 \theta[/tex] with the found equation involving [tex]x^2[/tex] :
[tex]\implies y^2=9\left(1-\dfrac{x^2}{25}\right)[/tex]
Divide both sides by 9:
[tex]\implies \dfrac{y^2}{9}=1-\dfrac{x^2}{25}, \quad \textsf{with }x\geq 0[/tex]
help please a.-5 b.-1/5 c1/5 d.5
Answer:
-5
Step-by-step explanation:
Slope is rise over run. The graph decreases by 5 units every 1 unit to the right, so the slope is -5.
Please answer the question below..
The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The area of big sector = (60/360) * π(10)² = (50π /3) cm²
Area of small sector = (60/360) * π(x)² = (x²π /6) cm²
Unshaded area = (x²π /6) cm²
Shaded area = (50π /3) - (x²π /6) = (100π - x²π) /6
Shaded area = unshaded area
(100π - x²π) /6 = (x²π /6) cm²
x = 7.07
The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.
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The length of x in the sector is 7.08 cm.
How to find area of a sector?area of a sector = ∅ / 360 × πr²
where
r = radiusTherefore,
area of a sector = 60 / 360 × π × 10²
area of a sector = 60 / 360 × π × 100
area of a sector = 6000 / 360 π
Hence,
area of the unshaded portion = 6000 / 360 π ÷ 2 = 6000π / 720 = 26.1666666667 = 26.2 cm
Hence,
26.2 = 60 / 360 × 3.14 × x²
x² = 26.2 / 0.52333333333
x = √50.0637261552
x = 7.07557064836
x = 7.08 cm
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The marks obtained by 10 student in a test are as follows: 3,7,6,2,8,5,9,1,4 and 10. find the mean mark
Answer:
[tex]5.5[/tex]
Step-by-step explanation:
Mean:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is
[tex]\mu = \frac{{\sum}x}{N}[/tex]
The formula for the mean of a sample is
[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:
[tex]\frac{55}{10} = 5.5[/tex]
I need help please! This is urgent!
Answer:
first 35 out of 100 then second person 34 out of 99
Step-by-step explanation:
Rewrite the ratio 15: 39 as an equivalent ratio of the form 1 : n.
Give any decimals in your answer to 1 d.p.
Answer:
n = 2.6
Step-by-step explanation:
Hello!
We can create an equation with equivalent fractions. Remember that a ratio can also be represented as a fraction.
[tex]a:b = \frac ab[/tex]We can create two fractions that are equivalent to each other given the ratios.
[tex]\frac{15}{39} = \frac 1n[/tex]Solve for n[tex]\frac{15}{39} = \frac 1n[/tex][tex]\frac{5}{13} = \frac 1n[/tex][tex]5n = 13[/tex][tex]n = \frac{13}{5}[/tex][tex]n = 2.6[/tex]The value of n is 2.6.
Can someone help me with this and show work pleaseee!!!
Answer:
10 units and 157.84 units
Step-by-step explanation:
4
substitute t = 1 into the equation
h = - 16(1)² + 6 = - 16 + 6 = - 10
the value is negative since the ball travels down
the ball has travelled 10 units after 1 second
5
substitute t = 3.2 into the equation
h = - 16(3.2)² + 6 = - 16(10.24) + 6 = - 163.84 + 6 = - 157.84
the well is 157.84 units deep
Given A(2, 3) B(1, 4) C(1, 3) D(-2, 2). How are AB and CD related?
The vector AB is not related with the vector CD as k is not the same for each pair of components.
Are two vectors similar?In this question we must prove if the vector AB is a multiple of the vector CD, that is:
[tex]\overrightarrow{AB} = k \cdot \overrightarrow {CD}[/tex]
[tex]\vec B - \vec A = k \cdot [\vec D - \vec C][/tex]
(1, 4) - (2, 3) = k · [(- 2, 2) - (1, 3)]
(- 1, 1) = k · (- 3, - 1)
Hence, the vector AB is not related with the vector CD as k is not the same for each pair of components.
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A coffee shop gives the customer a free cup of coffee after the purchase of 5 cups: a.) industrial marketing program b.) loyalty marketing program c.) product sampling program d.) cooperative marketing program
PRE-FINAL REVIEW
LINDA WAS SELLING TICKETS TO THE HOMECOMING GAME
SHE SOLD 15 MORE STUDENT TICKETS THAN FACULTY TICKETS
AND SHE SOLD TWICE AS MANY ALUMI TICKETS AS FACULTY TICKETS.
LET S REPRESENT THE NUMBER OF STUDENT TICKETS
F-FACULTY TICKETS
A-ALUMNI TICKETS
A. WRITE AN EXPRESSION TO REPRESENT THE NUMBER OF STUDENT TICKETS SOLD
BALUMIE TICKETS
SOLD
STUDENT TICKETS COST $5, FACULTY TICKETS COST $2
AND ALUMNI TICKETS COST $10. LINDA MADE $2170.
CWRITE AN EQUATION TO REPRESENT THE TOTAL TICKET SALES.
The equation that can be used to represent total tickets sales is 2170 = 5s + 2f + 10a
Equationlet
Number of students tickets = sNumber of faculty tickets = fNumber of alumni tickets = aExpression for number of students tickets sold;
s = f + 15
Expression for number of faculty tickets sold;
f = 2a
Expression for number of alumni tickets sold;
f = 2a
a = f/2
Cost of students tickets = $5Cost of faculty tickets = $2Cost of Alumni tickets= $10Total revenue = $21702170 = 5s + 2f + 10a
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Note: Figure is not drawn to scale.
The object above is symmetrical through Z. If Y = 14 inches, Z = 14 inches, and H = 10 inches, what is the area of the object?
The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The area of kite = (product of diagonals)/2
Area of kite = (10 * 14) / 2 = 70 in²
The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².
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In the figure pq is parallel to Ed the length of to is 4 cm the length of pt is 16 the length of qt is 20 what is the length of sq
By applying the basic proportionality theorem (BPT), the length of side SQ is equal to 5 cm.
How to calculate the length of side SQ?In order to determine the length of side SQ, we would apply basic proportionality theorem (BPT) as follows:
Since PQ ǁ RS, PT = 16
PT/RP = QT/SQ
16/4 = 20/SQ
Cross-multiplying, we have:
16SQ = 20 × 4
SQ = 80/16
SQ = 5 cm.
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Complete Question:
In the figure, PQ is parallel to RS. The length of RP is 4 cm; the length of PT is 16 cm; the length of QT is 20 cm. What is the length of SQ?
Please help ASAP!! Conner and Jana are multiplying (3⁵6⁸)(3⁹6¹⁰).
Conner's Work: (3⁵6⁸)(3⁹6¹⁰) = 3⁵ + ⁹ 6⁸ + ¹⁰ = 3¹⁴6¹⁸
Jana's Work: (3⁵6⁸)(3⁹6¹⁰) = 3⁵⋅⁹ 6⁸⋅¹⁰ = 3⁴⁵6⁸⁰
Is either of them correct? Explain your reasoning. (i do think jana is incorrect but im not sure how to answer for conner)
Answer:
Step-by-step explanation:
Write it out in expanded form and you will see why Connor is correct.
3^5 means 3x3x3x3x3
6^8 means 6x6x6x6x6x6x6x6
3^9 means 3x3x3x3x3x3x3x3x3
6^10 means 6x6x6x6x6x6x6x6x6x6
These numbers are all multiplied together, so how many of each number do we have?
3x3x3x3x3x6x6x6x6x6x6x6x6x3x3x3x3x3x3x3x3x3x6x6x6x6x6x6x6x6x6x6
3^14 6^18
If there are seven points on a plane and no three points are on the same line, how many lines can the points make?
The number of lines that the points can make is; 21 lines
How to find Collinear Points?We are given that;
- There are 7 points on a Plane
- No 3 points on the plane are on the same line
Thus;
No 3 points are collinear and as such the number of lines that the points can make is found from the combination formula;
C(7,2);
C(7,2) = 7!/(7 - 2)!*2!
= (7 × 6)/(2 × 1)
= 42/2
=21
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Alissa is analyzing an exponential growth function that has been reflected across the y-axis. She states that the domain of the reflected function will change because the input values will be the opposite sign from the reflected function. Simon disagrees with Alissa. He states that if an exponential function is reflected across the y-axis, the domain will still be all real numbers.
Which student is correct and why?
Alissa is correct because the domain will change from negative to positive x-values.
Alissa is correct because a reflection across the y-axis will change the possible input values of the reflected function.
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.
Neither student is correct.
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input for an exponential growth function.
Verification of Choice
Let us consider the following exponential growth function.
y = Aeˣ ...........................(1)
This equation changes when it is reflected across the y axis and becomes,
y = Ae⁻ˣ ...........................(2)
Here, the set of all x values for which y is defined is known as the domain of this exponential growth function.
Therefore, the domain of exponential growth function 1 is the set of all real numbers, given by, x ∈ [-∞,∞]
The domain of function 2, which is a reflection of function 1, will also consist entirely of real numbers and will be given by x ∈ [-∞,∞ ]
Therefore, between Alissa and himself, Simon is right when he asserts that even if an exponential growth function is reflected across the y-axis, the domain will still consist only of real values.
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which number produces a rational number when multiplied by 1/3
A. 2
B. -√17
C. 0.166
D. 2/3
Please could you answer this one decently quick for me? thanks!
The number which produces a rational number when multiplied by 1/3 is; Choice A; 2.
What is a rational number?It follows from the definition of rational number that they can be represented as the quotient a/b of two integers such that b ≠ 0.
On this note, it follows that when 1/3 is multiplied by 2; the result is 2/3 which is a rational number.
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find the equation of the straight line with the following gradient point c) 5, (-1,-3)
Answer:
y = 5x + 2
Step-by-step explanation:
Standard form of Equation of line: y = mx + c
where m = slope or gradient,
c = y-intercept
From the question we know that:
x = - 1
y = - 3
m = 5
We will substitute these values into the equation to find c.
- 3 = (5)(- 1) + c
- 3 = - 5 + c
c = - 3 + 5 = 2
Therefore the equation of this line is: y = 5x + 2
Help with this question please.
Answer:
Step-by-step explanation:
A basketball league’s average score is 58 points per game. Coach McGee tracks a team’s average for five weeks and compares it to the league’s average. The table shows the variances in scores for five weeks.
Points Above/Below Average
Week 1
Week 2
Week 3
Week 4
Week 5
2 and StartFraction 1 Over 8 EndFraction
1.6
Negative 2 and StartFraction 1 Over 8 EndFraction
–1.8
Negative 1 and StartFraction 4 Over 5 EndFraction
Which comparison is true? Use the number line to help you.
A number line going from negative 5 to positive 3 in increments of 1.
Week 1 = Week 3
Week 4 = Week 5
Week 2 < Week 4
Week 5 < Week 3
The correct option for the inequality is
Week 4 = Week 5. Option B. This is further explained below.
What is inequality?Generally, the relationship between two expressions that do not have the same value is denoted by a sign such as, which means "not equal to," >, which means "greater than," or, which means "less than."
In conclusion, When converted to decimal form, Week 5's score comes out to -1.8, which is the same as Week 4's score.
Week 4 = Week 5
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Answer:
The Answer Is B
Step-by-step explanation:
Week 4 = Week 5
An equilateral triangle and a square both have perimeters of 48 inches. What is the ratio of the length of the side of the triangle to the length of the side of the square
Answer: 4:3
Step-by-step explanation:
The side length of the triangle is 48/3 = 16.
The side length of the square is 48/4 = 12.
So, the ratio is 16:12 = 4:3.
What is the degree of the polynomial? 5x² + 8x³ + 4- 6x² - 3x5
Answer:
The degree of polynomial is 5.
Step-by-step explanation:
I suppose the polynomial is [tex]\displaystyle{5x^2+8x^3+4-6x^2-3x^5}[/tex]. To find the which degree this polynomial is, we consider the highest exponent of the term which is [tex]\displaystyle{3x^5}[/tex], the 5 is our highest degree of the term and thus, 5 is our highest degree of polynomial.
Answer:
5
Step-by-step explanation:
I'm assuming that the 5 in "3x5" is supposed to be a exponent. The degree of the polynomial is the greatest of the exponents (powers) of its various terms.
Consider figures 1 and 2 shown in the coordinate plane. Figure 1 has been translated to produce figure 2.
Graph shows 2 quadrilaterals plotted on coordinate plane. Quadrilateral 1 in quadrant 2 has vertices at (minus 6, 3), (minus 5.5, 5), (minus 3.5, 5), (minus 3, 3). Quadrilateral 2 in quadrant 1 has vertices at (2, 1), (2.5, 3), (4.5, 3), (5, 1).
This translation can be described by
,
).
Answer:
A translation 8 units right and 2 units down
A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true?
Based on the calculations, the true statements are:
A. The angular velocity is 10π rad/sec.
E. The angular velocity is 600π rad/min.
How to calculate the angular velocity?Mathematically, angular velocity can be calculated by using this formula:
ω = θ/t
Where:
ω is the angular velocity.θ is the angle.t is the time.Note: 1/2 revolution = 0.5 × 2π = π radians.
Substituting the given parameters into the formula, we have;
ω = θ/t
ω = π/0.1
ω = 10π rad/s.
Next, we would convert the time in seconds to minutes:
ω = 10π × 60
ω = 600π rad/min.
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Complete Question:
A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true? Check all that apply.
A. The angular velocity is 10π rad/sec.
B. The angular velocity is 10π rad/min.
C. The angular velocity is 60π rad/min.
D. The angular velocity is 600π rad/sec.
E. The angular velocity is 600π rad/min.
Answer:
A,
Step-by-step explanation:
Edge202
Derivatives with the functions of multiplication, division and rule of the chain. derive the following algebraic functions using all the basic formulas of algebraic derivatives (it is important to do the procedure) y=2x3+5x4x-9 y=3x+2x2+5 y=(5x2-9)6
The derivatives of y=[tex]2x^{3}+5x^{2} +4x-9[/tex] is [tex]6x^{2} +10x+4[/tex], derivative of y=[tex]2x^{2} +3x+5[/tex] is 4x+3, derivative of [tex](5x^{2} -9)6[/tex] is 60x.
Given three functions y= [tex]2x^{3}+5x^{2} +4x-9[/tex], y=[tex]2x^{2} +3x+5[/tex], y=[tex](5x^{2} -9)6[/tex].
We have to find the derivative of functions.
Derivative of a function of a real variablemearsures the sensitivity to change of the function value with respect to a chaneg in its argument. Derivatives are a fundamental tool of calculas.
First function: y=[tex]2x^{3}+5x^{2} +4x-9[/tex], derivative can be as under:
dy/dx=2*3[tex]x^{2}[/tex]+2*5x+4 (derivative of x is 1)
(d[tex]x^{n}[/tex]/dx=n[tex]x^{n-1}[/tex])
dy/dx=6[tex]x^{2}[/tex]+10x+4
Second function: y=[tex]2x^{2} +3x+5[/tex], derivative can be as under:
dy/dx=2*2x+3
=4x+3
Third function:y=[tex](5x^{2} -9)6[/tex]
dy/dx=5*2x*6
=10x*6
=60x
Hence the derivative of first function is [tex]6x^{2} +10x+4[/tex], second function is 4x+3, third function is 60x.
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