The volume of the buoy is the sum of volume of hemisphere and volume of cone which is 0.504m³
What is volume of the buoyTo calculate the volume of the buoy, we need to find the volume of the hemisphere and the volume of the cone.
The volume of a hemisphere can be calculated using the formula:
V = (2/3) * π * (r^3)
where "r" is the radius of the hemisphere.
So, the volume of a hemisphere with radius "r" is equal to (4/3) times π times the cube of the radius.
The base is 0.95 and the radius is half the length of the base.
radius = 0.95 / 2 = 0.475m
The volume of the hemisphere = 2/3 * 3.14 * 0.475³
volume of hemisphere = 0.224m³
The volume of the cone = 1/3 πr²h
The volume of the cone = 1/3 * 3.14 * 0.475² * 1.2
The volume of the cone = 0.28m³
The volume of buoy = volume of sphere + volume of cone
The volume of buoy = 0.224 + 0.28 = 0.504m³
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In the figure, the octagon is formed by two overlapping squares. The overlapping region is also a square. The larger square has a length of 6cm. The smaller square has one corner at the center of the larger square and the smaller square has a length of 4cm. How many centimeters is the permeter of the octagon?
So the perimeter of the octagon is approximately 45.25 centimeters (rounded to two decimal places).
What is perimeter ?In geometry, a shape's perimeter is sometimes referred to as its total length. By adding up the lengths of all of an object's sides and borders, one can determine the circumference of something such as a form. The perimeter of a form can be calculated by adding up all of the edges' lengths. For instance, a rectangular with dimensions of 24 yards long as well as 15 yards wide will have a 78 yard perimeter.
Here,
To find the perimeter of the octagon, we need to determine the length of each side of the octagon.
First, let's find the length of the diagonal of the smaller square. We can use the Pythagorean theorem:
d²=4² + 4²=
d² = 16+16 =32
d = √32
=> d = 4√2
This diagonal of the smaller square is also the side length of the overlapping square.
Next, let's find the length of one of the sides of the larger square that overlaps with the smaller square. Since the length of the larger square is 6cm, the side length of the overlapping region (part of the larger square that overlaps with the smaller square) is:
6 - 4√2
Finally, the length of one of the sides of the octagon is the sum of the side lengths of the two squares that overlap, minus the side length of the overlapping square (since this side is counted twice):
=> 6 + 6 - 4√2 - 4√2 - (6 - 4√2)
Therefore, the perimeter of the octagon is:
=>8 (12 - 6√2) = 96 - 48√2
So the perimeter of the octagon is approximately 45.25 centimeters (rounded to two decimal places).
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To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points � B and � C. He measures � � AD, � � DB, and � � DE as marked. Find the distance across the lake ( � � ) (BC), rounding your answer to the nearest hundredth of a meter.
The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.
We can use similar triangles to find the distance across the lake (DE). Since triangle CGF is similar to triangle CED, we can use ratios of the sides to find DE.
Let's call DE = x. Then, we have:
CE/FG = x/142.1
Solving for x, we have:
x = (CE * 142.1) / FG
CE = CF + FD = 130 + 60 = 190m
x = (190 * 142.1) / 142.1 = 190m
The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.
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The complete question is :
To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter.
Which of the following expressions is equivalent to -1/4 - 5/3
Step-by-step explanation:
the first one because positive (+) x negative (-) = negative (-), so it give you the negative sign in the middle
Let △ABC be a right triangle with m∠C = 90°. Given tan ∠B = 0.25, find tan ∠A. tan ∠A =
The solution of the given problem of triangle comes out to be tan ∠A = 0.25.
What exactly does a triangle mean?Triangles are called polygons if they have four quadrants or more. Its form is a simple geometric figure. When put together, the characters ABC create a right-angled triangle. When the boundaries are incompatible, Euclidean geometry generates a new rectangle with square corners. Triangles are regarded as polygons because they have three edges and three corners.
Here,
Since △ABC is a right triangle with m∠C = 90°, we know that m∠A + m∠B = 90°.
Using the fact that tan ∠B = opposite/adjacent, we can set up a ratio using a common factor, x, for the opposite and adjacent sides of ∠B:
tan ∠B = 0.25 = opposite/adjacent = x/4x
Simplifying the right side, we get:
0.25 = x/4x = 1/4
Multiplying both sides by 4x, we get:
x = 4
So the opposite side of ∠B has length x = 4, and the adjacent side has length 4x = 16.
Using the Pythagorean theorem, we can find the length of the hypotenuse of △ABC:
c² = a² + b²
c² = 4²+ 16²
c² = 256
c = √256
c = 16
Now, we can use the fact that tan ∠A = opposite/adjacent to find tan ∠A:
tan ∠A = opposite/hypotenuse = 4/16 = 1/4
Therefore, tan ∠A = 0.25.
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ASAP pls
The graph shows two accounts with the same principal and annual interest rate. Use the graph to estimate the answer to each question. Show your workAbout how much more compound interest than simple interest is earned after 35 years? Remember to show your work. About how much more compound interest than simple interest is earned after 45 years? Remember to show your work.
About $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.
What is a graph ?
A graph is a visual representation of data that shows the relationship between two or more variables. It is a way of presenting information in a clear and concise manner that makes it easy to interpret and understand.
Graphs can be used to show trends over time, compare different groups or categories, or illustrate the relationship between two or more variables.
Since the graph shows the balance for two accounts with the same principal and annual interest rate, we can assume that one account is earning simple interest while the other is earning compound interest.
To estimate the amount of compound interest earned after 35 years, we can look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 35 years is approximately $4,000, while the balance for the compound interest account is approximately $10,000. Therefore, the amount of compound interest earned after 35 years is approximately:
$10,000 - $4,000 = $6,000
To estimate the amount of compound interest earned after 45 years, we can again look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 45 years is approximately $5,500, while the balance for the compound interest account is approximately $18,000. Therefore, the amount of compound interest earned after 45 years is approximately:
$18,000 - $5,500 = $12,500
Therefore, about $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.
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A rectangle has an area of 24 square inches. The rectangle is reduced by a scale factor of 1/2. What is the area of the new triangle?
Answer:
12
Step-by-step explanation:
i hope this is right I suggest you double check
In a crate, containing only red and green
apples, the ratio of green to red apples
is 2:1
An apple is picked at random and
removed from the crate.
A second apple is then picked at
random.
The probability of picking two green
apples is y.
Find the error interval for y.
The required error interval for y(probability of picking two green
apples) is [1/4, 1/4].
How to find the error interval?The probability of picking two green apples can be calculated by multiplying the probability of picking a green apple on the first pick by the probability of picking another green apple on the second pick, given that the first pick was a green apple.
According to data:Let's call the number of green apples in the crate G, and the number of red apples in the crate R. Based on the given information, the ratio of green to red apples is 2:1, so we have G = 2R.
The probability of picking a green apple on the first pick is G/(G + R), and the probability of picking a green apple on the second pick, given that the first pick was a green apple, is (G-1)/(G + R - 1).
Therefore, the probability of picking two green apples is:
y = (G/(G + R)) * ((G-1)/(G + R - 1)) = (G/(G + R))²
Since we know that G = 2R, we can substitute that into the equation for y to get:
y = (2R/(2R + R))² = (2/(3R + R))² = (2/4R)² = 4/16 = 1/4
So the error interval for y is [1/4, 1/4].
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If 3 yellow, 4 red and 6 blue flowers are to be planted in a line, how many different arrangements are possible?
Using permutations and combinations, we know that a total of 60,060 different arrangements of flowers can be made in a row.
What are permutations and combinations?The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations.
When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination.
Examples of permutations include arranging persons, digits, numbers, alphabets, letters, and colors.
Examples of combinations include choosing the menu, the cuisine, the clothes, the subjects, and the team.
So, we have:
3 yellow, 4 red, and 6 blue flowers.
3 + 4 + 6 = 13
Now, the number of arrangements in the row will be:
= 13!/3!4!6!
= 6,22,70,20,800/6*24*720
= 6,22,70,20,800/1,03,680
= 60,060
Therefore, using permutations and combinations, we know that total of 60,060 different arrangements of flowers can be made in the row.
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What is the slope of a line that passes through the points (0, 5) and (8, -2)
Answer:
-7/8
Step-by-step explanation:
slope = Δy/Δx = (-2 - 5) / (8 - 0) = -7/8
Travis decided to make a frame for his birthday. The frame will be cut out of a piece of steel, and the final area of the frame should be 30in². The inside of the frame has to be 11in by 6 in The area of the piece of steel before cutting out the frame is A = (11+2x)(6+2x)in²
Answer:
To make a frame with an area of 30in², Travis needs to cut out a piece of steel with an area of A = (11+2x)(6+2x)in², where x is the width of the frame. The inside of the frame must be 11in by 6in, so the width of the frame must be x = (30 - 11*6)/4 = 2.25in. The total area of the piece of steel must therefore be A = (11+2*2.25)(6+2*2.25) = 30in².
Step-by-step explanation:
To determine the value of x that will result in a final area of the frame of 30in², we can use the equation for the area of the piece of steel before cutting out the frame:
A = (11 + 2x)(6 + 2x)
We can expand this expression to get:
A = 66 + 44x + 12x^2
Since the inside of the frame has to be 11in by 6in, the area of the frame is 11 * 6 = 66in². So, we want to find the value of x that will result in the area of the piece of steel being equal to the area of the frame plus 30in². This means we want to find the value of x that will satisfy:
66 + 44x + 12x^2 = 96
Expanding the left-hand side of this equation and collecting like terms, we get:
12x^2 + 44x = 30
Dividing both sides of the equation by 12, we get:
x^2 + 3.67x = 2.5
To solve for x, we can use the quadratic formula or factoring. Once we have found the value of x, we can use it to determine the dimensions of the piece of steel before cutting out the frame.
800 people attended a football game. If 20% of the people who attended were teenagers, how many teenagers attended the game? Insert the values given in the problem then scale up or down to find the missing value. attendees percent 100 attempt 3 out of 3 Emilia Salkic Proportional Reasoning, Percents (Level 2) Feb 03, 2:20:32 PM 800 people attended a football game. If 20% of the people who attended were teenagers, how many teenagers attended the game?
Using percentages we can conclude that out of 800 people, 20% of the people who attended the football match were teenagers, 160.
What are percentages?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.
If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.
A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction.
Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.
So, we know that:
800 people attended the football game.
20% were teenagers.
Then, the number of teenagers was:
= 800/100*20
= 8*20
= 160
Therefore, using percentages we can conclude that out of 800 people 20% of the people who attended the football, match were teenagers, and 160 were.
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Help……………………………………..
The value of c for which the limit of the function does not exist is given as follows:
c = -2.
When does the limit of a function not exist?The limit of a function will not exist if a function has different lateral limits, that is, if the to the right of x = c the graph has a different numeric value than to the left of x = c.
For this problem, we look at the graph at x = -2, hence:
To the left of x = -2, the function assumes a value of 4.To the right of x = -2, the function assumes a value of 6.This means that the function has different lateral limits, hence the limit of the function does not exist for c = -2.
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Find the value of cos
�
H rounded to the nearest hundredth, if necessary.
Answer:
[tex]\mbox{\large \boxed{ 0.98}}[/tex]
Step-by-step explanation:
Cos H = ratio of the base to the length of the hypotenuse
In this triangle, the base = 40, hypotenuse = 41
cos H = 40/41 = 0.9756
To the nearest hundredth this would be 0.98
There are 5,280 feet in a mile. Round answers to the nearest unit. a. How many miles does a car traveling at 42 mi/h go in one hour
The answers for questions G, H, K, and L are the same as questions C, D, K, and L, respectively, because the speed (65mi/h) remains constant.
A. 65 miles in one hour: If a car is traveling at 65 miles per hour (mi/h), then in one hour it will travel 65 miles.
B. 340,800 feet in one hour, 65 miles is equal to 5,280 x 65 = 340,800 feet.
C. 5,680 feet in one minute, 340,800 feet ÷ 60 = 5,680 feet in one minute.
D. 94.67 feet in one second, 5,680 feet ÷ 60 = 94.67 feet in one second.
E. 42 miles in one hour: If a car is traveling at 42 miles per hour, then in one hour it will travel 42 miles.
F. 221,760 feet in one hour, 42 miles is equal to 5,280 x 42 = 221,760 feet.
G. 5,680 feet in one minute.
H. 94.67 feet in one second.
I. x miles in one hour.
J. 5,280 x x feet in one hour:
K. (5,280 x x) ÷ 60 feet in one minute.
L. ((5,280 x x) ÷ 60) ÷ 60 feet in one second.
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There are 5,280 feet in a mile. Round answers to the nearest unit.
A. How many miles does a car traveling at 65mi/h go in one hour?
B. How many feet does a car traveling at 65mi/h go in one hour?
C. How many feet does a car traveling at 65mi/h go in one minute?
D. How many feet does a car traveling at 65mi/h go in one second?
E. How many miles does a car traveling at 42mi/h go in one hour?
F. How many feet does a car traveling at 42mi/h go in one hour?
G. How many feet does a car traveling at 65mi/h go in one minute?
H. How many feet does a car traveling at 65mi/h go in one second?
i. How many miles does a car traveling at x mi/h go in one hour?
J. How many feet does a car traveling at x mi/h go in one hour?
K. How many feet does a car traveling at x mi/h go in one minute?
L. How many feet does a car traveling at x mi/h go in one second?
I need some help please
Answer:
( 11 )y + ( 1 )z
Step-by-step explanation:
8y + 3y
5z - 4z
one half of three fourths of a number is 20 less than two fifths of the same number. what is the number?
We divided both sides of the equation by (3/8) to get x = (40/3), the number is 40/3.
Let the number be x.
Then one half of three fourths of x can be expressed as [tex](3/4)*(1/2)*x = (3/8)*x[/tex]
Two fifths of x can be expressed as[tex](2/5)*x[/tex]
Therefore, according to the given statement, [tex](3/8)*x = (2/5)*x - 20[/tex]
Solving for x, we get: x = (40/3)
Therefore, the number is 40/3.
To calculate this, we first wrote the given statement in terms of fractions. Then we used algebraic manipulation to solve for x. We multiplied both sides of the equation by the LCD, 40, to get [tex]40*(3/8)*x = 40*(2/5)*x - 20*40[/tex]. Then we combined like terms to get ([tex]3/8)*x + 20*(5/8)*x = 40[/tex]. Then we subtracted [tex]20*(5/8)*x[/tex] from both sides to get [tex](3/8)*x = 40 - 20*(5/8)*x[/tex]. Finally, we divided both sides of the equation by (3/8) to get x = (40/3). Therefore, the number is 40/3.
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THREE QUESTIONS 21POINTS HELP!!!
8. Six boys have heights of 1.53 m, 1.49 m, 1-60 m, 1.65 m, 1.90 m and 1.43 m. (a) Find the mean height of the six boys. (b) Find the mean height of the remaining five boys when the shortest boy leaves.
9. In a maths test the marks for the boys were 9, 7, 8, 7, 5 and the marks for the girls were 6, 3, 9, 8, 2, 2. (a) Find the mean mark for the boys. (b) Find the mean mark for the girls. (c) Find the mean mark for the whole class.
10. Five different drinks have an average (mean) price of £1.50. When a sixth drink is added the new average price is £1.60. How much did the sixth drink cost?
I'll do problem 8 to get you started.
Part (a)
To find the mean, we first add up the values
1.53+1.49+1.60+1.65+1.90+1.43 = 9.6
Then divide over 6 since this is the number of values in the set.
9.6/6 = 1.6
Answer: 1.6 meters==================================================
Part (b)
The shortest boy is 1.43 meters tall. If he leaves the group, then we have these heights leftover
1.53, 1.49, 1.60, 1.65, 1.90
Adding them up gets us
1.53+1.49+1.60+1.65+1.90 = 8.17
Then divide by 5
8.17/5 = 1.634
Answer: 1.634 metersHow Much SAND lol
Please Help
Step-by-step explanation:
Volume.
[tex]v = lwh[/tex]
[tex]l = 20 \: w = 18 \: h = 0.5[/tex]
We just multiply these three numbers.
[tex](20)(18)(.5) = 180[/tex]
[tex]180 {ft}^{3} [/tex]
a simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations. True/False ?
True, a simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.
What does standard deviation mean ?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
What does a simple random sample mean?
A subset of participants is randomly chosen from a population by the researcher using simple random sampling, a sort of probability sampling.
The probability of being chosen is the same for every person in the population. Then, data are gathered from as much of this randomly selected subgroup as possible.
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A group of volunteers tagged and released 29 owls as part of a research project. Later, the researchers counted 902 owls, 11 of which had tags. To the nearest whole number, what is the best estimate for the owl population?
Based on the given information, the best estimate for the owl population is 891.
The team of volunteers released 29 owls, and later the researchers counted 902 owls, 11 of which had tags. This means that 891 owls were not tagged, so the total owl population is 891 + 29 = 920. However, the question is asking for an estimate to the nearest whole number, so the best estimate for the owl population is 891.
To further understand the owl population, researchers can look at several factors. These include the types of habitats that owls inhabit, the availability of food in those habitats, the presence of predators or other threats, and the overall health of the owl population.
Researchers can also use various methods to monitor the population and determine if it is increasing or decreasing over time.
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Each month, a shopkeeper spends 7x+19 dollars on rent and electricity. If she spends 2x−7 dollars on rent, how much does she spend on electricity? Use pencil and paper. For which value(s) of x is the amount the shopkeeper spends on electricity less than $100? Explain how you found the value(s).
Answer:
Step-by-step explanation:
7x + 19 = cost rent and electricity
2x - 7 = cost of rent only
cost of electricity only = (7x + 19) - (2x - 7) = 5x + 26
5x + 26 < 100
5x < 74
x < 74/5
x < $14.80
Find the value of x [6x-1] [10x+5]
Answer:
x = 6
Step-by-step explanation:
You want the value of x in the geometry where an angle bisector has divided a triangle into sides 42 and (6x-1), and corresponding sides 78 and (10x+5).
ProportionThe angle bisector divides the sides of the triangle proportionally:
(6x -1)/42 = (10x +5)/78
13(6x -1) = 7(10x +5) . . . . . . . . multiply by 546
78x -13 = 70x +35 . . . . . . . simplify
8x = 48 . . . . . . . . . . . . . . add 13-70x
x = 6 . . . . . . . . . . . . . . divide by 8
Find the size of angle x using parallel line facts. Give answer in degrees (°).
Answer:
Hi There! Here's your answer.
An automat machine make good pieces with a probability 0,96. Wich are the chances that the two piece is wrong?
The given information states that the machine produces good pieces with a probability of 0.96, which means that there is a 0.04 probability of getting a bad piece.
To calculate the probability of getting two bad pieces in a row, we multiply the probabilities of each individual bad piece:
0.04 * 0.04 = 0.0016
So the chances of getting two bad pieces are 0.0016, or 0.16%. This means that out of 100 tries, you would expect to get two bad pieces in a row 0.16 times.
It's vital to remember that independent events, like obtaining two terrible pieces, have probabilities that are determined by multiplying the individual possibilities.
This is based on the idea of the multiplication rule of probability, which states that the likelihood of two unrelated events occurring simultaneously is the sum of the probabilities of each event occurring separately.
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At what point do the graphs of the lines below intersect?
�
=
9
�
+
2
y=9x+2
�
=
−
3
�
+
12
y=−3x+12
(
−
5
3
,
−
13
)
(−
3
5
,−13)
(
−
7
6
,
15
1
2
)
(−
6
7
,15
2
1
)
(
5
6
,
9
1
2
)
(
6
5
,9
2
1
)
(
5
3
,
17
)
(
3
5
,17)
The solution of the equations y = 9x + 2 and y = - 3x + 12 will be (5/6, 19/2). Then the correct option is C.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equations are given below.
y = 9x + 2 ...1
y = - 3x + 12 ...2
From equations 1 and 2, then we have
9x + 2 = - 3x + 12
12x = 10
x = 5 / 6
Then the value of 'y' is given as,
y = 9(5/6) + 2
y = 15/2 + 2
y = 19 / 2
The solution of the equations y = 9x + 2 and y = - 3x + 12 will be (5/6, 19/2). Then the correct option is C.
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a random variable x is exponentially distributed with a mean of 25. what is the probability that x is between 25 and 30?
The probability that x is between 25 and 30 is 0.087.
The cumulative distribution function (CDF) of an exponential distribution with mean 25 is given by:
F(x) = 1 - exp(-x/25)
The probability that x is between 25 and 30 can be found by evaluating the CDF at x = 30 and x = 25 and subtracting the two values:
P(25 < x < 30) = F(30) - F(25) = (1 - exp(-30/25)) - (1 - exp(-25/25))
= (1 - exp(-1.2)) - (1 - exp(-1))
= 0.255 - 0.368
= 0.087
So, the probability that x is between 25 and 30 is 0.087.
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a sequence can be defined by an = an-1 + an-2 where a0 = 0 and a1 = 1. What are the first 6 terms of the sequence?
The first six terms of the sequence are 1, 1, 2, 3, 5 and 8. The solution has been obtained by using arithmetic progression.
What is arithmetic progression?
In an arithmetic progression (AP) sequence of numbers, there is always the same amount of difference between any two subsequent integers. Arithmetic Sequence is another name for it.
We are given a sequence as a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] + a[tex]_{n-2}[/tex] where a₀ = 0 and a₁ = 1.
So, the first term is a₁ = 1
The second term is
a₂ = a₂₋₁ + a₂₋₂
a₂ = a₁ + a₀
a₂ = 1
The third term is
a₃ = a₃₋₁ + a₃₋₂
a₃ = a₂ + a₁
a₃ = 1 + 1
a₃ = 2
The fourth term is
a₄ = a₄₋₁ + a₄₋₂
a₄ = a₃ + a₂
a₄ = 2 + 1
a₄ = 3
The fifth term is
a₅ = a₅₋₁ + a₅₋₂
a₅ = a₄ + a₃
a₅ = 3 + 2
a₅ = 5
The sixth term is
a₆ = a₆₋₁ + a₆₋₂
a₆ = a₅ + a₄
a₆ = 5 + 3
a₆ = 8
Hence, the first six terms of the sequence are 1, 1, 2, 3, 5 and 8.
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write a formula for a linear function f(x) that models the situation, where x is the number of years after 2007. in 2007 the average adult ate 52 pounds of chicken. this amount will increase by 0.8 pounds per year until 2012.
Step-by-step explanation:
x = number of years after 2007.
x = 0 for 2007.
PC(x) is a function that calculates how many pounds of chicken the average adult will eat every year (x) after 2007 (up to 2012).
PC(x) = 0.8x + 52
0 <= x <= 5
in 2007 (x = 0) the average adult ate 52 pounds.
in every year after 2007 until 2012 0.8 pounds get added to the amount of the previous year.
so, in 2012 (x = 5) the average adult will eat
PC(5) = 0.8×5 + 52 = 4 + 52 = 56 pounds of chicken.
what is the area of the parallelogram
Answer:
9yd^2
Step-by-step explanation:
A = bh
You are given the height of 2yd and a base of 4.5 yd.
A = (2yd)(4.5yd)
= 9yd^2
Answer:
9yd
Step-by-step explanation:
3½²-2²= √8.25=2.8
4.5-2.87=1.63
½×2.87×2=2.87
½(4.5+1.63)2=6.13
6.13+2.87=9yd
Write the equation of a circle whose center is at (-11,15) and whose radius is 9
Your answer must be in Standard Form AND simplified
Answer:
[tex]\textsf{Standard form}: \quad (x+11)^2+(y-15)^2=81[/tex]
[tex]\textsf{Simplified form}: \quad x^2+22x+y^2-30y+265=0[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Equation of a circle in standard form}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Given the center is (-11, 15) and the radius is 9:
a = -11b = 15r = 9Substitute the values of a, b and r into the equation of a circle:
[tex]\implies (x-(-11))^2+(y-15)^2=9^2[/tex]
[tex]\implies (x+11)^2+(y-15)^2=81[/tex]
To write the equation in simplified form, expand the brackets:
[tex]\implies x^2+22x+121+y^2-30y+225=81[/tex]
Collect like terms:
[tex]\implies x^2+22x+y^2-30y+225+121-81=0[/tex]
[tex]\implies x^2+22x+y^2-30y+265=0[/tex]