Answer: 32
Step-by-step explanation:
We will use the Order of Operations. First, we will do parentheses (), then brackets [], then lastly the braces {}, then lastly add 12.
Given:
{[2+(11+9)]-2)+12
Add 11 to 9:
{[2+20]-2)+12
Add 2 to 20:
{22-2)+12
Subtract 2 from 20:
20 + 12
Add 20 and 12:
32
Describe at least two differences between constructing parallel lines and constructing perpendicular lines.
By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.
What is the parallel lines?
Parallel lines are two lines in a plane that never intersect.
1. Orientation of Lines:
Parallel lines are lines that never intersect and remain equidistant from each other at all points.
When constructing parallel lines, the lines are drawn in the same direction and maintain the same distance between them throughout their entire length. They do not meet or cross each other.
On the other hand, perpendicular lines are lines that intersect at a right angle (90 degrees). When constructing perpendicular lines, the lines are drawn so that they intersect at a right angle, forming four right angles at the point of intersection.
2. Tools/Methods Used:
Constructing parallel lines and constructing perpendicular lines may require different tools or methods.
To construct parallel lines, one common method is to use a straightedge and a compass. A straightedge is used to draw a straight line, and a compass is used to measure and transfer distances to create additional parallel lines.
Therefore, By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.
To learn more about parallel lines from the given link:
https://brainly.com/question/16701300
#SPJ1
Is each number rounded correctly to the nearest hundred thousand?
yes is answer for all option .we can check it by rules of rounding off numbers .
what is rounding ?
Rounding is the process of approximating a number to a nearby value that is easier to work with or more appropriate for a given context. When rounding, we take a number with many decimal places or significant figures and adjust it to a simpler or more convenient value with fewer decimal places or significant figures.
In the given question,
Yes, each number is rounded correctly to the nearest hundred thousand based on the rules of rounding.
To round to the nearest hundred thousand, we look at the digit in the hundred thousand place and the digit to its right (i.e., in the ten thousand place).
If the digit in the ten thousand place is 5 or greater, we round up the digit in the hundred thousand place by adding 1.
If the digit in the ten thousand place is less than 5, we leave the digit in the hundred thousand place as it is.
Using these rules, we can see that:
350000 rounded to the nearest hundred thousand is 400000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.
555555 rounded to the nearest hundred thousand is 560000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.
137998 rounded to the nearest hundred thousand is 200000 because the digit in the ten thousand place is 7, so we round up the digit in the hundred thousand place.
792314 rounded to the nearest hundred thousand is 800000 because the digit in the ten thousand place is 3, so we leave the digit in the hundred thousand place as it is.
To know more about rounding , visit:
https://brainly.com/question/29878750
#SPJ1
You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
Therefore, it will take 173 months to pay off the loan, or approximately 14 years and 5 months.
What is percentage?A percentage is a way of expressing a number as a fraction of 100. The symbol for a percentage is "%". For example, 50% is the same as 50/100 or 0.5 as a decimal. Percentages are often used to express a portion or share of a whole. For instance, if you scored 90% on a test, it means you got 90 out of 100 possible points. In finance, percentages are commonly used to express interest rates, returns on investments, or changes in stock prices.
First, we need to convert the monthly interest rate from a percentage to a decimal by dividing by 100.
0.25% / 100 = 0.0025
Now we can plug in the values into the formula:
N= (-log (1-0.0025*70000/250))/ (log (1+0.0025))
Simplifying the equation in the parentheses:
N= (-log (1-175))/ (log (1.0025))
N= (-log (0.9964))/ (0.002499)
N= 172.9
Rounding up to the nearest whole number since we can't make partial payments:
N= 173
To learn more about percentage, visit
https://brainly.com/question/29306119
#SPJ1
I'LL MARK THE BRAINLIEST TO THE USER THAT GETS IT RIGHT!
A} 38
B} -7
C} -18
D} 11
Answer:
the answer will be A
Step-by-step explanation:
for the explanation the picture will do the best
mark me branliest as you promised
Harry owns a gaming arcade in his neighborhood. He recorded the number of people who visited his arcade every month in the table below. Month, x 0 1 2 3 4 Number of People, f(x) 115 182 229 313 358 Use technology to determine the exponential equation that best represents the data. Then, predict the number of people who might visit Harry’s arcade after 6 months.
The function is f(x)=115.[tex](1.58)^x[/tex] and number of people after 6 months is 1789.
What is exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
Here according to the table initial people f(0) = 115
Now using exponential formula
=> f(x) = f(0).[tex](1+r)^x[/tex]
If x = 1 then f(1)= 182 then,
=> 182 = 115.[tex](1+r)^1[/tex]
=> 1+r = 182/115
=> 1+r = 1.58
=> r = 1.58-1=0.58
Then the exponential function is
=> f(x)=115.[tex](1.58)^x[/tex]
Now x=6 then,
=> f(6) = 115.[tex]1.58^6[/tex] = 1789
Hence number of people after 6 month is 1789.
To learn more about exponential function refer the below link
https://brainly.com/question/2456547
#SPJ1
Histogram from the other post like I said it would be great if someone could look this over for me thanks!
This is an image of a histogram representing the number of hours a group of students spent studying for a test. The horizontal axis shows the number of hours studied, and the vertical axis shows the frequency or number of students who studied that number of hours.
What is histogram?A histogram is a graphical representation of data that displays the frequency distribution of a set of continuous or discrete data. It consists of a series of adjacent rectangular bars, where the area of each bar represents the frequency of occurrences of a particular range of values.
Based on the histogram, it appears that the majority of students studied for 5-7 hours, with a frequency of 14 students. Additionally, it appears that 8 students studied for 2-4 hours, and 10 students studied for 8-10 hours. Finally, it appears that only 1 student studied for more than 10 hours.
Histograms are a useful way to display and analyze data because they allow us to quickly see the distribution and frequency of the data. In this case, we can see that the data is roughly symmetric around the 5-7 hour range, with fewer students studying for fewer or more hours.
To know more about histogram visit:
https://brainly.com/question/28164315
#SPJ1
Identify the domain and range of the function. y=√x-4
A. Domain: x≥−4, Range: y≥0
B. Domain: x≥4, Range: y≥0
C. Domain: x≤4, Range: y≤0
D. Domain: x≥0, Range: y≥4
The domain of the function y=√x-4 is restricted by the square root of a non-negative number, which means that x-4 must be greater than or equal to zero. Thus, we have:
x-4 ≥ 0
x ≥ 4
Therefore, the domain of the function is x≥4.
The range of the function is determined by the output values of the function. Since the square root of any non-negative number is always non-negative, the output values of the function y=√x-4 will always be non-negative. Thus, the range of the function is y≥0.
Therefore, the correct answer is A. Domain: x≥−4, Range: y≥0.
positive.
an remove
3√5a-8√/35a2
PLEASE HELP DUE TODAY ASAP
im pretty sure the answer is B Please tell me if im correct ASAP!
Question 3(Multiple Choice Worth 1 points)
(08.07 LC)
The function g(x) is shown on the graph.
The graph shows an upward opening parabola with a vertex at negative 4 comma 3, a point at negative 6 comma 7, and a point at negative 2 comma 7.
What is the equation of g(x) in vertex form?
g(x) = (x − 4)2 − 3
g(x) = (x − 4)2 + 3
g(x) = (x + 4)2 − 3
g(x) = (x + 4)2 + 3
Step-by-step explanation:
Vertex at -4,3 would result in vertex form of parabola
g(x) = (x+4)^2 + 3
$2000 are invested in a bank account at an interest rate of 5 percent per year.
Find the amount in the bank after 7 years if interest is compounded annually.
Find the amount in the bank after 7 years if interest is compounded quaterly.
Find the amount in the bank after 7 years if interest is compounded monthly.
Finally, find the amount in the bank after 7 years if interest is compounded continuously.
The amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
Simple interest calculation.
Using the formula A = P(1 + r/n)^(nt), where:
A = the amount in the account after t years
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
a) If interest is compounded annually:
A = 2000(1 + 0.05/1)^(1*7) = $2,835.08
b) If interest is compounded quarterly:
A = 2000(1 + 0.05/4)^(4*7) = $2,888.95
c) If interest is compounded monthly:
A = 2000(1 + 0.05/12)^(12*7) = $2,905.03
d) If interest is compounded continuously:
A = Pe^(rt) = 2000e^(0.05*7) = $2,938.36
Therefore, the amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
Learn more about simple interest below.
https://brainly.com/question/25793394
#SPJ1
Which statement is true about the value of ( ✔27 − 3) ∙ 9?
Question 3 options:
It is rational, because the product of two rational numbers is rational.
It is rational, because the product of a rational number and an irrational number is rational.
It is irrational, because the product of two irrational numbers is irrational.
It is irrational, because the product of an irrational number and a rational number is irrational.
Answer:
It is irrational, because the product of an irrational number and a rational number is irrational.
Step-by-step explanation:
sqrt 27 is irrational =5.19615.......
3 is rational
subtracting 3 from the irrational number just creates a smalller irrational number ....then multiplying by 9 just creates a larger irrational number
Find the deductions and the net pay. Social Security is 6.2 percent of the first $90,000. Medicare is 1.45 percent of all income. $90,000. For Problems 3-7, the state tax is 2 percent of gross pay and the local tax is 1.5 percent of gross pay.
The minimum value of Jeri Dammers' total deductions is $200.68.
What is the deductions?Based on the given information, we can calculate the total deductions for Jeri Dammers as follows:
Social Security: Jeri pays 6% of the first S$90,000 of her gross pay towards Social Security. As her gross pay is only $735.00, her Social Security deduction will be:
Social Security = 6% of $735.00 = $44.10Medicare: Jeri pays 1.45% of all her income towards Medicare. As her gross pay is $735.00, her Medicare deduction will be:
Medicare = 1.45% of $735.00 = $10.65Federal Income Tax: To calculate the federal income tax, we need to refer to the tax tables provided by the IRS. As the gross pay is only $735.00, Jeri's federal income tax deduction will be very minimal or possibly none.
State Tax: Jeri pays 2% of her gross pay towards state tax. As her gross pay is $735.00, her state tax deduction will be:
State = 2% of $735.00 = $14.70Local Tax: Jeri pays 1.5% of her gross pay towards local tax. As her gross pay is $735.00, her local tax deduction will be:
Local = 1.5% of $735.00 = $11.03Medical: Jeri has a deduction of $32.00 towards medical expenses.
Union Dues and Others: No information is given about Jeri's union dues or other deductions.
Therefore, the total deductions for Jeri Dammers will be:
Total Deductions = Social Security + Medicare + Federal Income Tax + State Tax + Local Tax + Medical + Union Dues + OthersTotal Deductions = $44.10 + $10.65 + $0 + $14.70 + $11.03 + $32.00 + Union Dues + OthersTotal Deductions = $112.48 + Union Dues + OthersWe cannot calculate the exact value of Total Deductions without information about Union Dues and Others.
However, the minimum value of Total Deductions would be:
Total Deductions (minimum)= $44.10 + $10.65 + $88.20 + $14.70 + $11.03 + $32.00
= $200.68
Therefore, the minimum value of Jeri Dammers' total deductions is $200.68.
Read more about deductions here:
https://brainly.com/question/29307306
#SPJ1
See full text below
Find the total deduction The person pays Social Security 6 percent of the first S90,000. Medicare is 1.45 percent of all income Use the tax tables for federal tax The state tax is 2 percent of gross pay and the local tax is 1.5 percent of gross pay. (Remember to add the Medical; Union Dues, and Others for total deduction: FIT Federal Income Tax, FICA Social Security) .4. Jeri Dammers is married and claims 3 allowances.
Dept
Employee
Check Number -3205
Gross Pay -$735.00
Net Pay
44B Jeri Dammers
Tax Deductions
Other Deductions
FIT
FICA
Medicare
State
Local
Medical -32.00
Union
Dues
Others
The count in a bateria culture was initially 300, and after 35 minutes the population had increased to 1600. Find the doubling period. Find the population after 70 minutes. When will the population reach 10000?
LONG PROBLEM PLEASE HELP CORRECTIONS DUE ASAP GIVING 50 POINTS AND BRAINLY
Sin angel L =
Cos angel L =
Tan Angel L =
Cos < ___ = y/x
Tan< ___ = y/x
Sin < ____ = y/x
The trigonometric ratios for this problem are given as follows:
sin(L) = y/x.cos(L) = z/x.tan(L) = y/z.What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For the triangle, we have that:
x is the hypotenuse.z is the adjacent side to angle L.y is the opposite side to angle L.More can be learned about trigonometric ratios at brainly.com/question/24349828
#SPJ1
Look at the equations below. Find a pair of
equations whose lines are perpendicular.
Click on the correct answer.
y = x +6;y = −6x + 4
y = 5x-4; y = 5x +5
y = -5x + 6; y = -10x + 4
1
y=-x-4; y = −5x+5
The equations of line that are perpendicular to each other are:
A: y = (1/6)x + 6; y = -6x + 4
How to find perpendicular equations?The general formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
Now, for two equations to be perpendicular, it means that their slope must be negative reciprocals of each other. Thus:
Looking at the equations, we can say the only ones that have slopes that are negative reciprocals of each other is option A.
Read more about Perpendicular Equations at: https://brainly.com/question/7098341
#SPJ1
if f(x)=7x-5, determine f^-1(18)
To find the inverse of the function f(x) = 7x - 5, we need to solve for x in terms of y (or f^(-1)(x)). First, let's replace f(x) with y:
y = 7x - 5Now, we need to solve for x:
1. Add 5 to both sides:
y + 5 = 7x2. Divide both sides by 7:
(x = (y + 5) / 7)Now we have the inverse function, f^(-1)(x) = (x + 5) / 7. We can use this to find f^(-1)(18):
f^(-1)(18) = (18 + 5) / 7f^(-1)(18) = 23 / 7So, f^(-1)(18) = 23/7.Find tan(Q).
A 1
3 9
"5
135°
P
para os a
was a s
Save and Exit
Next
Submit
Answer:
tanQ = 1
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ OPQ is an exterior angle of the triangle , then
∠ R + ∠ Q = 135°
90° + ∠ Q = 135° ( subtract 90° from both sides )
∠ Q = 45°
Then
tanQ = tan45° = 1
what is 15 to the power of 12
Answer:
1.2974634e+14
Step-by-step explanation:
ye
multiply the equations: 1: (3√p-5)(√p+5√5) ? 2: (3√2-8)(3√2+8) *show explanation please*
Based on the information, the product of the first equation is 9p-75, and the product of the second equation is -47.
How to calculate the product of equations?We can use the formula:
(a - b)(a + b) = a² - b²Where a and b can be any expressions. Substituting the first expression into the formula:
(3√p-5)(√p+5√5)(3√p - 5)(√p + 5√5) = (3√p)^2 - (5√5)^2= 9p - 75Substituting the second equation into the formula:
(3√2 - 8)(3√2 + 8) = (3√2)^2 - (8)^2= 9(2) - 64= -47Therefore, the product of the first equation is 9p-75 and the product of the second equation is -47.
Find out more about equations at:
https://brainly.com/question/22688504
#SPJ1
A conic has vertices at (0,8) and (0,-8) and foci at F(0, √48) and F(0,-√48). (a) Write the standard form of the equation of this conic.
The standard form of the equation of the conic is x² + y² - 16x - 16y - 192 = 0.
What is conic?It is a type of curve with a curved line in the middle and two straight lines on the sides. Conic sections include circles, ellipses, parabolas, and hyperbolas.
The standard form of the equation of a conic is
Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E, and F are constants.
In this case, the equation of the conic is x² + y² - 16x - 16y - 192 = 0.
To derive this equation, we'll use the distance formula to calculate the distance between the vertices and the foci. The distance between the vertices and the foci is given by
d = √((x_1 - x_2)² + (y_1 - y_2)²)
where (x_1, y_1) is the coordinates of the first vertex and (x_2, y_2) is the coordinates of the first foci.
For the first vertex, (x_1, y_1) = (0, 8). For the first foci, (x_2, y_2) = (0, √48). Thus, the distance between the two points is
d = √((0 - 0)² + (8 - √48)² )
= √(0 + (-8 - √48)² )
= √(-16 - 2√48 + 48)
= √(32 -2√48)
= 2√(16 - √48)
= 2√(16 - 6.9)
= 2√(9)
= 2(3)
= 6
So, the distance between the vertices and the foci is 6.
The equation of the conic can then be written as x² + y² - 16x - 16y - (-8)² = 0, which simplifies to x² + y² - 16x - 16y - 192 = 0.
Thus, the standard form of the equation of the conic is x² + y² - 16x - 16y - 192 = 0.
For more questions related to conic
https://brainly.com/question/29132297
#SPJ1
PLEASE HELEPEPPEE QUICKKK ILL GIVE U
Answer:
21, 22, 23 or
-23, -22 , -21
Step-by-step explanation:
The 3 consecutive integers are x, x + 1, and x + 2
Sum of the squares of the 3 consecutive integers:
x² + (x+1)² + (x+2)² = 1454 Expand this equation
x² + x² + 2x + 1 + x² + 4x + 4 = 1454 Combine like terms
3x² + 6x + 5 = 1454
3x² + 6x + 5 - 1454= 0
3x² + 6x - 1449 = 0
Use quadratic equation to solve for the roots of x: (a = 3, b = 6,
c= -1449)
x = 21, -23
The consecutive numbers are: x, (x + 1), (x + 2)
21, 22, 23
-23, -22 , -21
the current of a river is 2 miles per hour. a boat travels to a point 24 miles up stream and back in 5 hours . what is the speed of the boat in still water
Let's denote the speed of the boat in still water as "b", and let's denote the distance between the two points as "d" (in this case, d = 24 miles).
When the boat is traveling upstream against the current, its effective speed is b - 2 mph (since the current is working against the boat). When the boat is traveling downstream with the current, its effective speed is b + 2 mph (since the current is helping the boat).
We know that the boat travels a total distance of 24 miles upstream and then 24 miles downstream, for a total distance of 48 miles. We also know that the total time it takes for the boat to make this round trip is 5 hours. So we can set up the following equation:
24/(b-2) + 24/(b+2) = 5
Multiplying both sides by (b-2)(b+2), we get:
24(b+2) + 24(b-2) = 5(b-2)(b+2)
Simplifying and rearranging, we get:
10b^2 - 96b - 208 = 0
We can solve this quadratic equation using the quadratic formula:
b = (-(-96) ± sqrt((-96)^2 - 4(10)(-208))) / (2(10))
b = (96 ± sqrt(96^2 + 8320)) / 20
b = (96 ± sqrt(9024)) / 20
b = (96 ± 96) / 20
So the possible values of b are b = 9.6 or b = -0.8. We can discard the negative value since it doesn't make sense as a speed, so we have:
b = 9.6 mph
Therefore, the speed of the boat in still water is 9.6 miles per hour
One hundred adults were asked to name
their favorite sport, and the results are
shown in the circle graph. What percent of
adults preferred soccer or baseball?
Volleyball, 3
Other, 4
Golf, 7
Soccer. 11.
Baseball, 14
Football,39
Basketball, 22
Total percentage of adults who preferred soccer or baseball: is 25%
what is percentage ?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, 50% means 50 out of 100, or 50/100 as a fraction.
In the given question,
The circle graph shows the percentage of adults who preferred each sport. To find the percentage of adults who preferred soccer or baseball, we need to add the percentages for soccer and baseball.
Soccer: 11%
Baseball: 14%
Total percentage of adults who preferred soccer or baseball: 11% + 14% = 25%
Therefore, 25% of adults preferred soccer or baseball.
To know more about percentage , visit:
https://brainly.com/question/31060287
#SPJ1
What kind of angle is
∠mah?
What is the value of x?
What is the measure of
∠mat ?
What is the measure of
∠tah ?
So according to the given figure ∠mah is right angle(90°), The value of x is 17, ∠mat is 38° and ∠tah is equal to 52°.
What is the source of this answer and define a graph?(A) ∠mah is right angle(90°) [GIVEN IN THE FIGURE]
(B) (2x+4)+(3x+1) = 90
5x+5 = 90
x= 17
(C) 2x+4 = 2×17 + 4 = 38°
(D) 3X + 1 = 3 × 17 + 1 = 52°
A graph is a visual representation or diagram that displays facts or values in an organised manner in mathematics. The points on a graph are typically used to depict the relationships between two or more things.
A graph in discrete mathematics is made up of vertices, which are groups of points, and edges, which are the connections between those vertices. There are numerous different types of graphs besides linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs.
To know more about Graph, visit:
https://brainly.com/question/30444906
#SPJ1
Différenciation implicit function containing product and quotient. d/dx (2y/5x)
Answer:
To differentiate the given expression, we will need to use both the product rule and the quotient rule.
Let's first rewrite the expression using the reciprocal identity for x:
2y/5x = 2y * (5x)^(-1)
Now we can use the product rule and the quotient rule to find the derivative with respect to x:
d/dx [2y * (5x)^(-1)] = 2y * d/dx[(5x)^(-1)] + (5x)^(-1) * d/dx[2y]
Using the chain rule, we can find the derivative of (5x)^(-1) with respect to x:
d/dx[(5x)^(-1)] = -1/(5x)^2 * 5 * (dx/dx)
d/dx[(5x)^(-1)] = -1/(5x)^2
Using the chain rule again, we can find the derivative of 2y with respect to x:
d/dx[2y] = 2 * (dy/dx)
Substituting these expressions back into the original equation, we get:
d/dx [2y/5x] = 2y * (-1/(5x)^2) + (5x)^(-1) * 2 * (dy/dx)
Simplifying this expression, we get:
d/dx [2y/5x] = -2y/(5x)^2 + 2/(5x) * (dy/dx)
Therefore, the derivative of 2y/5x with respect to x is -2y/(5x)^2 + 2/(5x) * (dy/dx).
Find the length of the triangle.
The length of the unknown side of the triangle is __________
Answer:
The answer is 2√10
Step-by-step explanation:
Hyp²=opp²+adj²
let hyp be x
x²=6²+2²
x²=36+4
x²=40
square root both sides
√x²=√40
x=2√10
consider a collection of enveloped consisting of 2 red, 1 blue, 2 green envelopes, and 2 yellow envelopes. If two envelopes are selected at random, with replacement, determine the probability that at least one envelope is a yellow envelope.
Can I get a detailed answer so that I can use it to study?
Answer:
The probability of picking a yellow envelope is 2/7
Step-by-step explanation:
red envelope =2
blue " " =1
green " "=2
yellow " " =2
Total envelope =2+1+2+2=7
Probability thay at least one envelope will be yellow
P=number of yellow envelope/Total envelope
P=2/7
A package is weighed at 11 kg to the nearest kg. Find the largest possible weight for the package.
Answer:11.4999...
Step-by-step explanation:
Any number when rounding that starts with 1, 2, 3 4 will be rounded down. All numbers above will be rounded up. Therefore, you find the largest number that will still round down.
PLEASE HELP!!!!
A parabola can be drawn given a focus of (0,7) and a directrix of y=−7. Write the equation of the parabola in any form.
Answer:
y = 1/28(x²)
Step-by-step explanation:
Not totally sure about this, but here's what I think is the answer:
focus (0,7)
directrix y = -7
Always a good idea to plot the point (0,7) and the line y = -7 so you can visualize what the parabola looks like.
From the graph, you can see that p = 7 (halfway between the focus and the directrix).
The vertex of this parabola is (0,0), which are your (h, k) values. You can see that from the graph. The parabola opens UP.
4p(y-k) = (x-h)² → 4p(y-0) = (x-0)²
4py = x²
y = x²/4p = x²/4(7) = x²/28
y = 1/28(x²)
sorry if this isn't the right answer, but I tried (I'm not a paid expert, just a fellow student trying to learn math)!
The reflector of a flashlight is in the shape of a paraboloid of revolution. Its diameter is 8 centimeters and its depth is 4 centimeters. How far from the vertex should the light bulb be placed so that the rays will be reflected parallel to the axis?
Answe: The distance of light bulb can be calculated using equation of parabola. The parabola is a plane curve which is U-shaped.
Step-by-step explanation: