A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 24 feet across at its opening and 2 feet deep at its center, where should the receiver be placed?
Find the equation of the parabola?
How far above the vertex should the receiver be placed?
Answers
Equation of parabola: y =ax² and receiver should be placed 18 feet above vertex.
Explanation:
Considering satellite dish as parabola we can have vertex as origin and concave upward.
So, equation of parabola will be justifying structure of satellite dish i.e
y = ax² -------(1)
Two points other than (0,0) are (-12,2) and (12,2), unit being feet.
This points will satisfy equation of parabola, substituting them in equation 1, we will calculate the value of constant 'a'.
a = \(\frac{2}{12^{2} }\)
\(\frac{2}{2*6*12}\\ =\frac{1}{72}\)
Substituting value of a = 1/72 in equation 1 we get
72y = x²
As receiver need to be located at focus, so it will be places at a distance of 'p' above the vertex
4p = 72
Dividing both sides by 4, we get
p = 18 feet
So, receiver will be placed at a distance of 18 feet above vertex.
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Related Questions
Which set of mixed numbers has a difference less than 1?
Answers
the other answers gave a difference more than 1
A
Explanation
Others have a difference more than 1
I give Brainlest !!!!!!!
Answers
Answer:
40,000
Step-by-step explanation:
what type of scale is used on the map?
Answers
The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.
The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.
There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.
Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.
Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.
Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.
It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.
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HELP PLEASE!!
Quadrilateral CDEF is a rhombus. What is m
Answers
Answer:
∠ BDC = 29°
Step-by-step explanation:
the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then
∠ BCD = ∠ BED = 61°
• the diagonals are perpendicular bisectors of each other , then
∠ CBD = 90°
the sum of the 3 angles in Δ BCD = 180°
∠ BDC + ∠ CBD + ∠ BCD = 180°
∠ BDC + 90° + 61° = 180°
∠ BDC + 151° = 180° ( subtract 151° from both sides )
∠ BDC = 29°
Should the government print more currency to help the poor?
Answers
Answer:
Yes and No.
Step-by-step explanation:
The reasoning behind this is that the poor need to be helped, but it would also be bad because it would make drugs easier to come across, and they can ruin many people's lives.
can you help me find the answer
?
Answers
Answer:
15 is the answer
The distribution of monthly charges for cellphone plans in the United States is approximately normal with a mean of $62 and a standard deviation of $18. What percentage of plans have charges that are less than $83.60?
Answers
About 88.49% of cellphone plans have charges that are less than $83.60.
How to determine the percentage of plans have charges that are less than $83.60?To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.
z = (x – μ) / σ
where x = 83.60, mean, μ = 62 and standard deviation, σ = 18
Thus, the z-score of $83.60 is:
z = (83.60 - 62) / 18 = 1.2
Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).
Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.
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Stefan sells Jin a bicycle for $104 and a helmet for $17. The total cost for Jin is 110% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answers
The amount Stefan spent originally to buy the bike is; $100.91.
The amount Stefan made in profit by selling the bicycle and helmet to Jin is; $10.09.
How much did the bicycle cost originally?According to the task content;
Stefan sold the bicycle and helmet for a total of;
104 + 17 = $111.
Also, since the total cost ($111) for Jin is 110% of what Stefan spent to buy the bicycle and helmet, x originally; we have
110% × x = 111
x = (111 × 100) / 110
x = $100.91.
Therefore, Stefan spent $100.91 originally to buy the bike and helmet.
Consequently, the money Stefan made by selling the bicycle and helmet to Jin is; 111 - 100.91 = $10.09.
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6. If the equations kx - y = 2 and 6x - 2y = 3 have a solution then state the value of k a) K = 3 b) k 3 c ) K 0 d) k = 0 7.
Answers
Answer:
k ≠ 3Step-by-step explanation:
Given the system of equation;
kx - y = 2 ------------------- 1
6x - 2y = 3 -------------------- 2
Rewriting the equations in the format ax+by+c = 0
Equation 1 becomes kx - y - 2 = 0
Equation 2 becomes 6x - 2y - 3 = 0
where a₁ = k, b₁ = -1 and c₁ = -2 and a₂ = 6, b₂ = -2 and c₂ = -3
For the system of equation to have a unique solution the following must be true;
a₁/a₂ ≠ b₁/b₁
Substituting the coefficients into the condition, we will have;
k/6 ≠ -1/-2
k/6 ≠ 1/2
Cross multiplying we will have;
2k ≠ 6
k ≠ 6/2
k ≠ 3
This means that k can be any other real values except 3 for the system of equation to have a unique solution.
Elyas is on holiday in Greece.
He wants to buy a pair of sunglasses for €90
The exchange rate is €1 = £0.875
Elyas says, "The sunglasses cost less than £70"
Using a suitable approximation, show that Elyas is wrong.
Answers
Answer:
To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.
To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.
Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.
We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds
Step-by-step explanation:
Given AC and BD bisect each other at O prove AC is congruent to c
Answers
The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .
Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.
We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.
Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)
Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.
Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD
Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC
Therefore, AC is congruent to c .
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What is the 36th derivative of f(x)=cos2x?
Answers
The 36th derivative of f(x) = cos(2x) is \(2^{17}\)* cos(2x).
To find the 36th derivative of the function f(x) = cos(2x), we can apply the chain rule repeatedly. The chain rule states that if we have a composite function y = f(g(x)), then its derivative is given by dy/dx = f'(g(x)) * g'(x).
Let's start by finding the first few derivatives of f(x) = cos(2x):
f'(x) = -2sin(2x)
f''(x) = -4cos(2x)
f'''(x) = 8sin(2x)
f''''(x) = 16cos(2x)
We observe a pattern where the derivatives of cos(2x) alternate between sin(2x) and cos(2x), with the signs changing accordingly.
Based on this pattern, we can see that the 36th derivative will be:
f^(36)(x) =\((-1)^{17} * 2^{17} *\) cos(2x)
Simplifying this expression, we have:
f^(36)(x) = \(2^{17} * cos(2x)\)
Therefore, the 36th derivative of f(x) = cos(2x) is\(2^{17\) * cos(2x).
It's important to note that in this case, the number 36 is even, and since the derivatives of cos(2x) follow a repeating pattern every 4 derivatives, the sign (-1) raised to the power of 17 accounts for the change in sign in the 36th derivative.
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Will mark brainliest if correct
Answers
Answer:
\(mean = \frac{9 + 4 + 4 + 1 + 0 + 6 + 4}{7} = \frac{28}{7} = 4\)
\(mean \: deviation = \frac{ |9 - 4| + |4 - 4| + |4 - 4| + |1 - 4| + |0 - 4| + |6 - 4| + |4 - 4| }{7} = \frac{5 + 0 + 0 + 3 + 4 + 2 + 0}{7} = \frac{14}{2} = 7\)
How do you write equations in Point-slope form?
Answers
For a line with a slope a and a known point (h, k), the point-slope form is:
y = a*(x - h) + k
How to write an equation in point slope form?A general linear equation can be written in slope-intercept form as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that a line passes through a point (h, k), then the point-slope form of that line is:
y = a*(x - h) + k
Notice that particularly, the y-intercept can be written as (0, b), then the slope-intercept form is also a point-slope:
y = a*(x - 0) + b
y = a*x + b
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Country A has an exponential growth rate of 4.3% per year. The population is currently 4,079,000, and the land area of Country A is 19,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
Answers
The number of years it would it take for there to be one person for every square yard is 108,325.68 years.
How many years would it take for there to be one person for every square yard?When there is one person for every square yard, it means that the population and land area are equal in value.
Number of years = (In FV / PV) / r
FV = future populationPV = present populationr = rate of growth(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years
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What is -20/2(7 2/3)
Answers
The simplified form of -20/2(7 2/3) is -230/3.
To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.
First, let's convert the mixed number 7 2/3 to an improper fraction.
7 2/3 = (7 * 3 + 2) / 3 = 23/3
Now, let's substitute the value back into the expression:
-20/2 * (23/3)
Next, we simplify the multiplication:
-10 * (23/3)
To multiply a fraction by a whole number, we multiply the numerator by the whole number:
-10 * 23 / 3
Now, we perform the multiplication:
-230 / 3
Therefore, the simplified form of -20/2(7 2/3) is -230/3.
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Determine whether the following probabilities are best categorized as subjective, empirical, or classical probabilities.
a. Before flipping a fair coin, Sunil assesses that he has a 50% chance of obtaining tails. Subjective probability Empirical probability Classical probability
b. At the beginning of the semester, John believes he has a 90% chance of receiving straight A’s. Subjective probability Empirical probability Classical probability
c. A political reporter announces that there is a 46% chance that the next person to come out of the conference room will be a Republican, since there are 80 Republicans and 93 Democrats in the room. Subjective probability Empirical probability Classical probability
Answers
a) Classical. This is because there are 2 sides and 1/2 = 0.50 = 50% is the chance of landing on tails. Classical probability is also known as theoretical probability.
b) Subjective. This is based off John's belief and his gut feeling. There doesn't seem to be any empirical data to back him up, unless he's looking back at previous semesters.
c) Empirical. When you have a finite set of data and you compute the probability based on it like what we're doing here, we're computing empirical probability. Another example would be that if you flipped a coin 30 times and got 17 heads, then the empirical probability of getting heads is 17/30 = 0.5667 approximately. Note how this is slightly different from the theoretical probability 0.50
9 pt = How much fl oz
Answers
Answer:
9 pints would equal 144 ounces
Step-by-step explanation:
Pints
The US liquid pint is a unit of fluid volume equal to one-eighth of a gallon, one-half of a quart, or two cups. The liquid pint should not be confused with the dry pint (US) or the imperial pint, which are different units.
The pint is a US customary unit of volume. Pints can be abbreviated as pt; for example, 1 pint can be written as 1 pt.
Fluid Ounces
The US fluid ounce is a unit of volume equal to 1/16 of a pint or 1/8 of a cup. The fluid ounce is sometimes referred to as an "ounce" but should not be confused with the unit of mass. One fluid ounce is equal to just under 29.6 milliliters, but in nutrition labeling, one fluid ounce is rounded to exactly 30 milliliters.[1]
The fluid ounce is a US customary unit of volume. Fluid ounces can be abbreviated as fl oz, and are also sometimes abbreviated as fl. oz. or oz. fl.. For example, 1 fluid ounce can be written as 1 fl oz, 1 fl. oz., or 1 oz. fl..
Pint to Fluid Ounce Conversion Table
Pint measurements converted to fluid ounces
Pints Fluid Ounces
1 pt 16 fl oz
2 pt 32 fl oz
3 pt 48 fl oz
4 pt 64 fl oz
5 pt 80 fl oz
6 pt 96 fl oz
7 pt 112 fl oz
8 pt 128 fl oz
9 pt 144 fl oz
10 pt 160 fl oz
11 pt 176 fl oz
12 pt 192 fl oz
13 pt 208 fl oz
14 pt 224 fl oz
15 pt 240 fl oz
16 pt 256 fl oz
17 pt 272 fl oz
18 pt 288 fl oz
19 pt 304 fl oz
20 pt 320 fl oz
21 pt 336 fl oz
22 pt 352 fl oz
23 pt 368 fl oz
24 pt 384 fl oz
25 pt 400 fl oz
26 pt 416 fl oz
27 pt 432 fl oz
28 pt 448 fl oz
29 pt 464 fl oz
30 pt 480 fl oz
31 pt 496 fl oz
32 pt 512 fl oz
33 pt 528 fl oz
34 pt 544 fl oz
35 pt 560 fl oz
36 pt 576 fl oz
37 pt 592 fl oz
38 pt 608 fl oz
39 pt 624 fl oz
40 pt 640 fl oz
Please don't report this. :(
Select the equivalent expression. Select all that apply
2⁴/2⁵
A. 16/32
D. 2⁻¹
B. 1/2
E. 2⁴ × 2⁻⁵
C. 2⁹
F. 2¹
Answers
2^-1 = 1/2
2^4/2^5 = 2^(4-5) = 2^-1 = 1/2
16/32 = 1/2
1/2 = 1/2
What is the probability that a randomly chosen person from this group is a
sophomore and attended the jazz band concert?
Round your answer to two decimal places.
A. 0.56
B. 0.52
C. 0.26
D. 0.31
Answers
Answer:
0.26 or C
Step-by-step explanation:
Basically you would do the sophomores that attended the jazz band concert (35) and divide that by the total number of students. (137) - - 35 ➗ 137 = .2554744526 round that to .26 or 0.26
The probability that a randomly chosen person from this group exists a sophomore and attended the jazz band concert is 0.31.
What is probability?Probability exists about calculating or estimating how possible or 'probable' something exists to occur.
Let A be the event that a person exists a sophomore.
B be the event that a person attended volleyball game.
A∩B denote the event that a person exists a sophomore and attend volleyball game.
P be the probability of an event.
We have to estimate the value of P(A∩B),
Given: A∩B = 42
P(A∩B) = 42/137 = 0.3065 approximately equal to 0.31
P(A∩B) = 0.31.
The probability that a randomly chosen person from this group exists a sophomore and attended the jazz band concert is 0.31.
Therefore, the correct answer is option D. 0.31.
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ASAPPPPP
PICTURE BELOW
WILL HAVE MORE OF THESE
Answers
Answer: -6m-n+3
Step-by-step explanation:
The answer is -6m-n+3 because -3
times 2m is -6m and -n stays the same its outside of the parenthesis
and lastly -3 times -1 is positive 3
so answer maches up with the last one
the answer is -6m-n+3
Hope this helps :)
Answer:
-6m-n+3
Step-by-step explanation:
-3 x 2 is -6m (n stays same)
-3 x -1 is whole or positive 3
put it together and u get -6m-n+3
hope this helps
The student activities office has four students who work part-time on a work-study program. Three of the students work
17 hours per week, 19 hours per week, and 16 hours per week. The office policy is that the average number of hours
students work per week in the student activities office is less than 17.5 hours. What is the restriction for the number of
hours that the fourth student can work?
Answers
Answer:
less than 18 hours
Step-by-step explanation:
You want the restriction on the fourth value such that the average of it and 17, 19, and 16 will be less than 17.5.
Average valueThe average of a set of numbers is their sum, divided by the number of numbers. The average of the four students' hours will be ...
(17 +19 +16 +h)/4 < 17.5 . . . . . . restriction on average hours
SolutionMultiplying by 4 gives ...
52 +h < 70
h < 18 . . . . . . . . subtract 52
The fourth student can work less than 18 hours.
Function and notaion.
Answers
Answer: 45
Step-by-step explanation:
Function notation: is another way of writing a function to make it easy to understandInstead of the independent and dependent variables being x and y they are now x and f(x)f(x) can be interpreted as the y value at a given x value in this case f(-5) must be solved for, essentially saying what is y when the x value is -5\(f(-5)=2(-5)^{2} -5\)
\(f(-5)= 2(25) -5\)
\(f(-5) = 50-5\)
\(f(-5) = 45\)
1 - Fill the space blanks
If we make a sequence selecting three elements from three different elements
{1, 2, 3} and we permit overlapped elements for the sequence, then the total
number of sequences is [ ] . If we do not take into account the order, the total
number of the selections is [ ] .
I'm totally lost in this, what is overlapped elements? This is about what math content? And what is the answer? Please i need help.
Answers
Answer:
The first part is of permutations.
We are selecting 3 elements from three different elements {1,2,3}
Points given:
We permit overlapped elements for the sequence. Here "overlapped elements" indicates that repetition is allowed.
So when repetition is allowed and order matters, we use permutations.
Formula to compute permutation is:
Lets say n is the three elements {1,2,3}
We have to select 3 elements so r = 3
Total number of selections using permutations = \(n^{r}\) = n × n × n
= 3³ = 3 * 3 * 3
= 27
This means if we have 3 different elements then we have have 3 choices each time for making a sequence.
Hence If we make a sequence selecting three elements from three different elements {1, 2, 3} and we permit overlapped elements for the sequence, then the total number of sequences is 27.
Step-by-step explanation:
The second part indicates combinations.
This is because the statement of the question: If we do not take into account the order.
When the order does not matter, we use combinations.
So when the order does not matter and repetition is allowed we use the following formula:
Total number of selections using combinations = (r + n - 1)! / r! (n - 1)!
= (3 + 3 - 1) ! / 3! (3 - 1)!
= (3 + 2) ! / 3! (2!)
= 5! / 3! 2!
= 5*4*3*2*1 / (3*2*1 ) (2*1)
= 120 / 6 * 2
= 120 / 12
= 10
So these are the number of combinations of 3 elements taken 3 at a time with repetition.
The total number that will be selected in the permutations is 27.
How to calculate the permutations?Based on the information given, the total number of permutations will be:
= n³
= 3 × 3 × 3
= 27
Also, the total number of selection using combination will be:
= (3 + 3 - 1)! / 3!(3 - 1)!
= 120 / (6 × 2)
= 120/12
= 10
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A rectangle has a length of 15 centimeters and a width of 7 centimeters. What is the area of the rectangle?
Answers
length= 15cm
width= 7cm
to find:area of the rectangle.
solution:area of rectangle= length × width
a= l × w
a= 15 × 7
= 105 cm^2
Answer:
105 cm²
Step-by-step explanation:
The formula to find the area of a rectangle is :
Area = length × width
Given that,
length ⇒ 15 cm
width ⇒ 7 cm
Let us solve it now.
Area = length × width
Area = 15 × 7
Area = 105 cm²
Absolute vale of x+2 if x is less than 2
Answers
Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).
Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).
plz help me it is do at 10:45
Answers
Answer:2+6+2+1+3+2+1+1+3+0+4+2=27
27 divided by 12=2.25
6863 in expanded form
Answers
Answer:
Expanded Notation Form:
6,863 =
6,000
+ 800
+ 60
+ 3
Expanded Factors Form:
6,863 =
6 × 1,000
+ 8 × 100
+ 6 × 10
+ 3 × 1
Expanded Exponential Form:
6,863 =
6 × 10^3
+ 8 × 10^2
+ 6 × 10^1
+ 3 × 10^0
Answer:
Six thousand eight hundred sixty three
Step-by-step explanation:
HELP QUICK PLEASE.
Luster, conductivity, and malleability are physical properties of metals. What makes these
properties different from chemical properties?
Answers
What is the equation of the graph that represents the parent function f(x)= x^4 stretched vertically by a factor of 2, then shifted down 3 spaces
Answers
The equation of the function is f"(x) = 2x^2 - 3
How to determine the equation?The parent function is given as:
f(x) = x^4
When it is stretched vertically by a factor of 2, the rule is
f'(x) = 2f(x)
So, we have
f'(x) = 2x^2
When shifted down 3 spaces, the rule is
f"(x) = f'(x) - 3
So, we have:
f"(x) = 2x^2 - 3
Hence, the equation of the function is f"(x) = 2x^2 - 3
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