The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A
Given the radius in the question = a
The integration of the total distance before dividing the volume will be =
⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a\cdot a^2\sin\theta\,da\,d\theta\,d\phi[/tex]
⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a^3\sin\theta\,da\,d\theta\,d\phi[/tex]
⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}\int_0^\pi \sin\theta\,d\theta\,d\phi[/tex]
⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}1\,d\phi[/tex]
⇒ [tex]\pi A^{4}[/tex]
Let us divide the average distance by the ball's volume,
⇒ [tex]\frac{\pi a^4}{(4/3)\pi a^3}[/tex]
⇒ [tex]{\frac{3a}4}[/tex]
By the use of the Parcly Taxel's way,
Let the radius of the ball be = A
f(x) = probability density function
Distance = D from the given point to the center.
P( D < a )
[tex]\begin{align}P(D\leq r)&= \frac{ \frac 43 \pi r^3 }{\frac 43 \pi R^3}=\frac {r^3}{R^3}, \ \ \ 0\leq r\leq R. \end{align}[/tex][tex]\frac{\frac{4}{3} \pi a^{3} }{\frac{4}{3} \pi A^{3} } = \frac{a^{3} }{R^{3} }[/tex]. 0 [tex]\leq[/tex] a [tex]\leq[/tex] A
Therefore, The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A
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Solve. Write answers as an imaginary number. 3x^2=-12
80 POINTS
Answer:
Step-by-step explanation:
3x^2 = -12
divide both side by 3x^2 = -4
Solve the square root.x = ±√-4
this equation has no real solutions
Answer:
x = {- 2i; 2i}-------------------------------
GivenEquation 3x² = 12Solve as below3x² = - 12x² = - 4x = √-4x = ± 2√-1x = ± 2iCalculate two-thirds of three-quaters of one half
Answer:
0.25
Step-by-step explanation:
Step 1: Convert all fractions to decimals
Two-thirds = 0.6666
Three-quarters = 0.75
One-half = 0.5
Step 2: Multiply all fractions
0.6666 * 0.75 * 0.5 = 0.25
Step 3: The answer is 0.25
Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Three-quarters of one half:
[tex]\implies \dfrac{3}{4} \times \dfrac{1}{2}=\dfrac{3 \times 1}{4 \times 2}=\dfrac{3}{8}[/tex]
Two-thirds of "Three-quarters of one half":
[tex]\implies \dfrac{2}{3} \times \dfrac{3}{8}=\dfrac{2 \times 3}{3 \times 8}=\dfrac{6}{24}=\dfrac{6 \div 6}{24 \div 6}=\dfrac{1}{4}[/tex]
A researcher needs to assign 10 subjects, numbered 0 to
9, to one of two treatment groups: A and B. Use the table
of random digits, starting with the first row and first
column, to carry out the random assignment.
Table of Random Digits
1 07581 34728 65182 58648 53252 83952
2 23290 98227 30144 83191 12167 90414
3 79486 99776 71793 95330 58256 71156
4 46354 09077 98202 03946 07455 39303
5 00472 20787 54571 73719 04368 41032
Select the correct random assignment using the table.
A: 0, 7, 5, 8, 1
A: 0, 2, 4, 6, 8
B: 3, 4, 7, 2, 8
B: 1, 3, 5, 7, 9
B: 2, 9, 1, 7, 4
OA: 0, 3, 6, 5, 8
A: 0, 7, 5, 8, 1
B: 3, 4, 2, 6, 9
In response to the question, we may say that As a result, the right answer expression is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To carry out the random assignment, we may utilise the following table of random digits:
Allocate the first ten topics to the table's rows, beginning with 0 and ending with 9.
Read the numerals from left to right, top to bottom, until 5 participants have been allocated to treatment A and 5 subjects have been assigned to treatment B.
We can get the following random assignment using this method:
A: 0, 3, 6, 5, 8 \sB: 1, 7, 4, 2, 9
As a result, the right answer is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.
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Answer:
A: 0, 7, 5, 8, 1 B: 3, 4, 2, 6, 9
Step-by-step explanation:
THE ANSWER IS D
in the morning there were t people at the beach. later at noon, 2/7 of the people left the beach and there were 30 people left on the beach. find t
Answer:
42
Step-by-step explanation:
If 2/7 left that means that 5/7 are still there.
5/7x = 30 Multiple both sides by 7/5
x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]
x = 42
Find the area of a rectangle with the sides of x+7 and 3x-4
The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.
Define area of rectangle.Any shape's area can be calculated by counting how many unit squares will fit inside of it. A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area. Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangle floor's area.
Given
Sides = x+7 and 3x-4
Area of rectangle
Length ×Breadth
(x + 7) (3x - 4)
Multiplying,
x(3x - 4) + 7(3x - 4)
3x² - 4x + 21x - 28
3x² + 17x - 28
The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.
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Subtract 7x-9 from 2x² - 11.
O 2x²-7x-20
02x²-7x-2
O 2x²+7x-20
O 2x²+7x-2
The required, subtraction of 7x-9 from 2x² - 11 is 2x²-7x-2. Option B is correct.
What is arithmetic?Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
Here,
To subtract 7x-9 from 2x² - 11, we need to distribute the negative sign across 7x and 9, and then combine like terms.
=2x² - 11 - (7x - 9)
= 2x² - 11 - 7x + 9
= 2x² - 7x - 2
Therefore, the answer is 2x²-7x-2.
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Can someone solve this please
Answer: B
Step-by-step explanation:
The two equations have the same slope, but different points. This means that the lines are parallel to one another and will not intersect.
The answer is B: No solution
Answer: No solution.
Step-by-step explanation: I graphed the two given functions below. It looks like there is no solution to the given functions.
Hope this helps! :)
to specify that x1 must be at most 75% of the blend of x1 , x2 , and x3 , we must have a constraint of the form
The linear constraint form of the variables is X1 =< 0.75(X1 + X2 + X3)
The term linear refers the algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Here we have given that x1 must be at most 75% of the blend of x1 , x2 , and x3 ,
Abd here we must have to find the linear constraint of the form of the variables.
While we looking into the given question we have identified the three are three variables are given they are x1, x2 and x3.
And we have also given that x1 must be greater than 75% when we convert this into decimal then we get the value 0.75.
Here the term of blend refers the sum of the terms,
Then the linear constraint form of the variables is written as,
=> X1 =< 0.75 (X1 + X2 + X3)
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How to calculate rate of change of y=4x-3
Answer:
4
Step-by-step explanation:
Answer:
The rate of change is 4
Step-by-step explanation:
The rate of change is the slope.
Since the equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 4x-3
The slope is 4 and the y intercept is -3
I need a little bit of help with this one
Step-by-step explanation:
boy come ladies yer wait for you
hvb-amor-jon
Check the binomial distribution to see whether it can be approximated by the normal distribution. Round p and q to 1 decimal place, as needed. n = 95 P = 0.96 9 -0.04 np - and ng Is a normal approximation appropriate ? Yes No
As per the binomial distribution, the value of the normal approximation is 0.6573
The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.
Here we have given that n = 95 P = 0.96 and q = 0.04
Now, here we have to check the binomial distribution to see whether it can be approximated by the normal distribution.
While we looking into the given question we know that the value of n = 95 P = 0.96.
Then as per the binomial distribution formula, the normal distribution is calculated as,
=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴
When we simplify this one then we get the value as 0.6573
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The linear regression equation for the data set is...
Answer: C
Step-by-step explanation: Because
Status
Review
A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Range ($)
0 - 10,000
10,001 - 50,000
50,001 - 100,000
Progressive
Tax Rate
3%
5%
5.5%
Calculate the state income tax owed on a $50,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Enter
h
Answer:
final answer would be $6,550
Step-by-step explanation:
To calculate the state income tax owed on a $50,000 per year salary, we can use the progressive tax rate provided in the question. We can divide the salary into three ranges, corresponding to the three tax rates:
Income Range: $0 - $10,000
Progressive Tax Rate: 3%
Tax Owed: $0 - $10,000 * 3% = $0 - $300
Income Range: $10,001 - $50,000
Progressive Tax Rate: 5%
Tax Owed: $10,001 - $50,000 * 5% = $500 - $2,500
Income Range: $50,001 - $100,000
Progressive Tax Rate: 5.5%
Tax Owed: $50,001 - $100,000 * 5.5% = $2,750 - $5,500
Thus, the total state income tax owed on a $50,000 per year salary would be $300 + $2,500 + $2,750 = $6,550. This amount should be rounded to the nearest whole dollar amount, so the final answer would be $6,550.
93 is what percent of 124
Answer: 75%
Step-by-step explanation:
93 is 75 percent of 124.
Explained in the picture attached...
Hope that helps...
choose the answer that best describes the statement. probality can be used to determine the likelihood of specific .
The statements best describe probability as the relative likelihood that an event will occur. It is a number between 0 and 1 inclusive.
Probability
A mathematical tool used to examine unpredictability is probability. It discusses the likelihood that an event will occur. For instance, you might not get two heads and two tails if you flip a fair coin four times. But if you flip the same coin 4,000 times, you'll get results that are almost evenly split between heads and tails. The theoretically predicted chance of heads in any given toss is 12, or.5. There is a predictable pattern of results when there are numerous repetitions, even though the results of a few repetitions are unknown. One of the authors tossed a coin 2,000 times after reading about the English statistician Karl Pearson, who threw a coin 24,000 times and got 12,012 heads. The outcome was 996 heads. The expected chance of 5 is quite near to being reached by the fraction of 9962,000, which is equivalent to 498.
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Denominator is 3 more than numerator. If both are increased by 2, the result is 2/3.
Eqn 1:
Eqn 2:
Answer:
Step-by-step explanation:
let numerator=x
denominator=x+3
again
[tex]\frac{x+2}{x+3+2} =\frac{2}{3} \\3(x+2)=2(x+5)\\3x+6=2x+10\\3x-2x=10-6\\x=?[/tex]
x=4
number is
[tex]\frac{4}{4+3} \\=\frac{4}{7}[/tex]
Amy and three friends are renting a house near the campas for $2400 per month. She plays 1/4 of the rent. What is her monthly rent?
Answer:
Amy has to pay $600 every month for rent.
Step-by-step explanation:
To take 1/4 of a number is to multiply 1/4 and said number.
So you can do 0.25*number
or number/4.
For this problem, the number is 2400 because Amy is going to pay 1/4 of 2400 for rent.
[tex]rent = 2400/4\\rent = 600[/tex]
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Solve each equation. Round to the nearest ten-thousandth.
17(0.3x+5)
Answer:
first option
Step-by-step explanation:
using the property of logarithms
ln [tex]x^{n}[/tex] = nlnx ( ln is the natural logarithm )
given
[tex]17^{(0.3x+5)}[/tex] = 12
take the ln of both sides
ln [tex]17^{(0.3x+5)}[/tex] = ln 12 , then
(0.3x + 5) ln 17 = ln 12 ( divide both sides by ln 17 )
0.3x + 5 = [tex]\frac{ln12}{ln17}[/tex] ≈ 0.877063 ( subtract 5 from both sides )
0.3x ≈ - 4.12293 ( divide both sides by 0.3 )
x = [tex]\frac{-4.12293}{0.3}[/tex] ≈ - 13.7431 ( to the nearest ten thousandth )
Which quantity is multiplied by pi in the formula for the area of a circle?
The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius
How to determine the multiplied quantity?From the question, we have the following parameters that can be used in our computation:
Area of a circle
The formula for the area of a circle is represented as
A = πr²
Express the formula as a product
So, we have the following representation
A = π * r²
In the above formula, we can see that the square of r is multiplied by pi
Hence, the required quantity is the square of the radius of the circle
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3. What type of angle is angle A?
obtuse
acute
right
straight
The angle A is an obtuse angle of the regular polygon.
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The interior angle of a polygon is [(n-2)180°]/n.
Where n is the number of sides of the polygon.
The number of sides of the polygon is 8.
The measure of the interior of the polygon is [(8-2)180°]/8
= 135°
The obtuse angle is an angle that more than 90°.
Therefore angle is an obtuse angle.
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Give expressions for the following:-
1) x is multiplied by -10 and then 5 is added to the result
2) 5 is multiplied by p and the result is subtracted from 26
3)y is multiplied by -5 and the result is added to 6
Answer:
1) -10x + 5
2) 5p - 26
3) -5y + 6
A man is in a boat 2 miles from the nearest point on the coast. He is to go to point Q, located 3 miles down the coast and 1 mile inland (see figure). He can row at a rate of 1 mile per hour and walk at 3 miles per hour. Toward what point on the coast should he row in order to reach point Q in the least time? (Round your answer to two decimal places.) 0.84 mile(s) down the coast
Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.
As given in the question,
Nearest point on the coast is 2 miles far away
rate of the row = 1mile per hour
Walk at the rate of 3 miles per hour
Let 'x' hours be the least time to reach point Q.
Time = distance / speed
Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3
Time taken to reach the coast = (√ 4 + x² ) / 1
Total time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3
To find least time dt/dx = 0
t = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3
⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )
⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )
Squaring both the side we get,
x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )
⇒3x² -24x +36 =0
⇒ x² -8x + 12 = 0
⇒ x = 2 or 6 hours
Therefore , the least time taken to reach the point Q is equal to 2 hours.
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Use Figure 1 to evaluate the trigonometric function.
A right triangle with side a of length 13 opposite of angle A, and side b of length 6 opposite of angle B.136
Figure 1
Enter the exact answer.
tanB=
Change entry mode
Show your work and explain, in your own words, how you arrived at your answer. Answers with no relevant explanations may receive reduced or no credit.
third side, AB= 14.318 Units and tanB = 0.461
How to find the value of tanB and third side?given:
BC=13 units
AC=6 units
solution:
using pythagoras theorem, we get
AB² = BC² + AC²
AB² = 13² + 6²
AB² = 169 + 36
AB² = 205
AB = 14.318 units
tanB = side opposite/side adjacent
tanB = AC/BC
tanB = 6/13
tanB = 0.461
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Using Pythagoras theorem, Third side, AB= 14.318 Units and tanB = 0.461
What is the Pythagoras theorem theory?The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.
How to find the value of tanB and third side?given:
BC=13 units
AC=6 units
solution:
using pythagoras theorem, we get
AB² = BC² + AC²
AB² = 13² + 6²
AB² = 169 + 36
AB² = 205
AB = 14.318 units
tanB = side opposite/side adjacent
tanB = AC/BC
tanB = 6/13
tanB = 0.461
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s formula to find a quadratic approximation of at the origin. estimate the error in the approximation if and .
A quadratic equation of at the origin, estimate the error = 0.000859M
The approximation is valid because is very small.
Calculation of concentration:
Since
0.85 M 0 0
(0.85-x)M x x
Now the value of x should be
x = 0.0000229
So based on this, the above concentration should be determined.
In order to demonstrate that the same value of x may be achieved either way, you will now solve using the quadratic formula rather than iterations. What are the values of a, b, and c and x, where a, b, and c are the coefficients in the quadratic equation [tex]ax^{2} +bx+c=0[/tex] and x is [h3o+], when using the quadratic equation to determine [h3o+] in 0.00250 m hno2? Keep in mind that ka=4.5104.
a : 1
b : 4.5x[tex]10^{-4}[/tex]
c : 1.125x[tex]10^{-6}[/tex]
[[tex]H_{3} O^{+}[/tex]] = 0.000859M
As [tex]HNO_{2}[/tex] is a weak acid, its equilibrium in water is:
[tex]HNO_{2} (aq)+H_{2} O(I)[/tex] ⇄ [tex]H_{3} O^{+} (aq)+N_{2} O^{-} (aq)[/tex]
Equilibrium constant, ka, is defined as:
ka = 4.5x[tex]10^{-4}[/tex] = [[tex]H_{3} O^{+}[/tex]] [NO₂⁻] / [HNO₂] (Equation-1)
Equilibrium concentration of each specie are:
[HNO₂] = 0.00250M - x
[H₃O⁺] = x
[NO₂⁻] = x
Replacing in (1):
4.5x[tex]10^{-4}[/tex] = [tex]\frac{x*x}{0.00250M-x}[/tex]
1.125x10⁻⁶ - 4.5x10⁻⁴x = x²
0 = x² + 4.5x10⁻⁴x - 1.125x10⁻⁶
As the quadratic equation is ax² + bx + c = 0
Coefficients are:
a: 1
b: 4.5x10⁻⁴
c: 1.125x10⁻⁶
Now, solving quadratic equation:
x = -0.0013 → False answer, there is no negative concentrations.
x = 0.000859
As [H₃O⁺] = x; [H₃O⁺] = 0.000859M
Therefore,
A quadratic equation of at the origin, estimate the error = 0.000859M
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A line is graphed on the coordinate grid to the right.
Which equation describes the line?
A.y=x/2+1/3
B.y = x/3+1/2
C.y=x/2+15 1/2
D.y=x/3+15 1/2
The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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whats the domain,range, and y-intercept and tell me if its exponential or linear.
k(x)=50(1.3)^x
0.3% is the percentage rate of increase in exponential function.
What exactly makes a function exponential?
A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.
The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
We have,
y = 50( 1.3)ˣ
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is
y(x)= a(1-r)^x such that r is the growth percent.
1 + r = 1.3
r = 0.3 ⇒ 0.3%
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expresa 1405 en base 7 a base 10
1405 in base 7 = 544 in base 10
What is base-7 number system ?
The heptimal system is another name for base-7 numbers. Base 7 numbers are represented by the digits 0, 1, 2, 3, 4, 5, and 6.
The digits of a Base 10 number, on the other hand, are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If there isn't a subscript at the supplied number, Base 10 is used to write that number. The decimal system is sometimes known as base-10 numbers. Currently, in daily life, we frequently use numbers in the base 10 range.
base 7 to base 10 conversion:
Multiply each digits by the powers of 7 as follows:
Base 7 digits: 1 4 0 5
Multiply by: 7^3 7² 7^1 7^0
( 1*7^3) + (4*7² ) + (0* 7^1 )+ ( 5 * 7^0)
= 343 + 196 + 0 + 5
= 544
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The parabola of y= has a vertex of (3, - 2) and a focus of (3, - 2 1/16) opens downward
The equation of the parabola is y = -1/4 x² + 3/2 x - 17/4. Where the vertex of the equation is at (3, -2) and the focus is at (3, -2 2/16) that opens downwards.
What is the equation of a parabola?The equation of the parabola with vertex at (h, k) is
y = a(x - h)² + k
The focus of the parabola is represented by (h, k + 1/4 a).
Calculation:It is given that, the vertex of the parabola is (h, k) = (3, -2)
And the focus of the parabola is (h, k + 1/4 a) = (3, -2 1/16)
From the focus point, we can calculate the value of 'a'.
(h, k + 1/4 a) = (3, -2 1/16)
⇒ k + 1/4 a = -2 1/16 = -33/16
⇒ -2 + 1/4 a = -33/16
⇒ 1/4 a = -33/16 + 2
⇒ 1/4 a = -1/16
⇒ a = -1/16 × 4
∴ a = -1/4
Since a is negative the parabola is downwards.
Now, the equation of the parabola is
y = a(x - h)² + k
On substituting the values, we get
y = -1/4(x - 3)² - 2
= -1/4(x² - 6x + 9) - 2
= -1/4 x² + 3/2 x -9/4 - 2
= -1/4 x² + 3/2 x - 17/4
Therefore, the equation of the parabola is y = -1/4 x² + 3/2 x - 17/4.
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Find the least common denominator of these fractions.
3/8 5/18
Answer: 72
Step-by-step explanation
Let's just look at the denominators for this problem.
8 and 18
8 can go into 24, 3 times but 18 does not multiply into 24
18 can go into 36, 2 times but 8 does not multiply into 36
Therefore 72 is the least common denominator.
8 times 9 = 72
18 times 4 = 72
72 is the least common denominator.
A recipe for a sports drink calls for 5/8 cup of powder for every 2 quarts of water. If Dionne uses 3 quarts of water, how many cups of powder are needed?
Answer: i think 15/8 but, im not sure
Step-by-step explanation:
