Answer: the rock will be at a height of 1,976 feet above the ground after approximately 8 seconds
Step-by-step explanation:
We can start by setting the height function equal to 1,976 and solving for t:
-16t² + 3000 = 1976
Subtracting 1976 from both sides, we get:
-16t² + 1024 = 0
Dividing both sides by -16, we get:
t² - 64 = 0
Factoring, we get:
(t + 8)(t - 8) = 0
So t = 8 or t = -8. We can ignore the negative solution since time cannot be negative.
Therefore, the rock will be at a height of 1,976 feet above the ground after approximately 8 seconds.
Answer: (A) 8 sec
un edificio de 5 metros proyecta una sombra de 4 metros determina la altura que tiene una casa que proyecta una sombra 2 metros
The height of a house that has a shadow projection of 2 meters is given as follows:
2.5 meters.
How to obtain the height of the house?The height of a house that has a shadow projection of 2 meters is obtained applying the proportions in the context of the problem.
The proportional relationship between the height of the building and the height of the shadow is given as follows:
5/4 = x/2
Hence we apply cross multiplication to obtain the height of the house, as follows:
4x = 10
x = 10/4
x = 2.5.
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URGENT PLEASE HELP!!!
A manager records the repair cost for 4 randomly selected stereos. A sample mean of $71.02 and standard deviation of $28.56 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the stereos. Assume the population is approximately normal.
Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The critical value to use in constructing the confidence interval is 1.645. This critical value corresponds to the 90% confidence level.
The critical value to be used in constructing the 90% confidence interval is 1.645. This is the z-score associated with a 90% confidence level. In other words, this is the value that is 1.645 standard deviations away from the mean. This value is found using the z-table, which contains the probability values for a standard normal distribution.
Therefore, the critical value to use in constructing the confidence interval is 1.645. This critical value corresponds to the 90% confidence level.
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Please do #1 and show work
The solution to the integration of the function given, ∫√(5x - 1) dx, is:
[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]
Understanding IntegrationTo solve the integral of:
√(5x - 1) dx
we can use a u-substitution.
Let u = 5x - 1, then:
du = 5 dx
dx = du/5
Now we can rewrite the integral in terms of u:
∫√(5x - 1) dx = ∫√u * (du/5)
Simplifying the integral:
(1/5) ∫√u du
Integrating √u:
(1/5) * (2/3) * u^(3/2) + C
Where C is the constant of integration
Substituting back u = 5x - 1:
(2/15) * (5x - 1)^(3/2) + C
Therefore, the solution to the integral of √(5x - 1) dx is:
[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]
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From 100 yards away, a marksman hit 27/50 of the targets last year.
The marksman hit 54% of the targets last year when expressed as a percentage, based on hitting 27 out of 50 targets from a distance of 100 yards.
From the given information, we know that a marksman hit 27 out of 50 targets last year from a distance of 100 yards.
To analyze this data, we can calculate the hit rate or success rate of the marksman. The hit rate is calculated by dividing the number of hits by the total number of attempts or trials.
Hit rate = Number of hits / Total number of attempts
In this case, the number of hits is 27, and the total number of attempts is 50.
Hit rate = 27 / 50
Simplifying the fraction, we get:
Hit rate = 0.54 or 54%
Therefore, the marksman had a hit rate of 54% last year.
This means that out of the 50 targets attempted from a distance of 100 yards, the marksman successfully hit 27 of them.
The hit rate serves as a measure of accuracy and effectiveness in target shooting. A higher hit rate indicates a higher level of skill and precision.
It's important to note that other factors such as weather conditions, visibility, and the difficulty level of the targets can influence the hit rate. Additionally, the marksman's skills may improve or vary over time, so this hit rate represents their performance specifically for the past year.
By analyzing the hit rate, we can gain insights into the marksman's accuracy and assess their proficiency in target shooting from a distance of 100 yards.
The question was incomplete. find the full content below;
Rewrite The Fraction In The Sentence Below As A Percentage.
From 100 Yards Away, A Marksman Hit 27/50 Of The Targets Last Year.
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What are the solutions for the following quadratic?
The solutions for the quadratic graph are (d) (-3, 0) and (1, 0)
How to determine the solutions for the quadratic graph?From the question, we have the following parameters that can be used in our computation:
The quadratic graph
The solutions for the quadratic graph are the points where the graph intersect the x-axis
These points are called the x-intercepts or the roots
Using the above as a guide, we have the following:
The point of intersection with the x-axis are (-3, 0) and (1, 0)
Hence, the solutions for the quadratic graph are (d) (-3, 0) and (1, 0)
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The hexagonal prism below has a base area of 36 units
2
2
and a height of 5.9 units. Find its volume.
The volume of the hexagonal prism is 212.4 unit square
What is Prism?Prism is three-dimensional solid which has identical faces at both ends. It is a polyhedron, which means all faces are flat.
How to determine this
When an hexagonal prism has a base area = 36 units
Height = 5.9 units
Volume of Prism = Base area * Height
Volume of prism = 36 units * 5.9 units
Volume = 212.4 units square
Therefore, the volume of the hexagonal prism is 212.4 units square
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Anna built a prism in the shape of a cube out of wood
The volume of the two prisms compares that the volume of prism B will double.
We are given that side length of the cube measured 18 inches in length. She built another prism (Prism B) with the same dimensions as the cube, except she doubled its height.
When the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is same as its base, then its volume is:
V = B x h
So, the volume of the two prism A= V = B x h
V = 18 x h = 18h
the volume of the two prism B= V = B x h
V = 18 x 2h = 36h
So, the volume of prism B will double thus the correct option is B.
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The complete question is;
Anna built a prism (Prism A) out of a cube of wood. The side length of the cube measured 18 inches in length. Anna built another prism (Prism B) with the same dimensions as the cube, except she doubled its height.
How does the volume of the two prisms compare?
The volume of prism B will triple.
The volume of prism B will double.
The volume of prism B will decrease.
The volume of prism B will be cut in half.
subtract these polynomials
(3x^-2x+5)-(x+3=
2x² -2x+2 is the polynomial we obtained after subtraction
The given polynomials are (3x²-2x+5)-(x²+3)
Three times of x square minus two times of x plus five minus x square plus three
We have to subtract the polynomials
3x²-2x+5 -x² - 3
Combine the like terms
2x² -2x+2
Hence, the polynomial we obtained after subtraction is 2x² -2x+2
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Which of the following is not a condition for a geometric setting?
The trials are independent
The probability of success is the same for each trial
There are a fixed number of trials
The variable of interest is the number of trials required to reach the first success
There are only 2 outcomes for each trial
There are a fixed number of trials is not a condition for a geometric setting
In a geometric setting, we are dealing with a sequence of independent trials, where each trial can result in either a success or a failure.
The key concept in a geometric setting is the number of trials needed until the first success occurs.
The trials are independent is essential in a geometric setting.
It means that the outcome of one trial does not affect the outcome of subsequent trials.
The probability of success is the same for each trial is also crucial in a geometric setting.
It implies that the probability of achieving a success does not change from trial to trial.
There are a fixed number of trials is not specific to a geometric setting.
The variable of interest is the number of trials required to reach the first success is fundamental to a geometric setting.
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In ΔWXY, w = 320 inches, y = 740 inches and ∠Y=169°. Find all possible values of ∠W, to the nearest 10th of a degree.
Write the equation of the hyperbola
Using the center and distance between co-vertex and center, the equation of the hyperbola is written below
[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]
What is the equation of hyperbolaA hyperbola, in analytic geometry, is a conic section that is formed when a plane intersects a double right circular cone at an angle such that both halves of the cone are intersected.
The equation of hyperbola is given as;
[tex]\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1[/tex]
where (h,k) is the center of the hyperbola, a is the distance between a vertex and the center, and b is the distance between a co-vertex and the center.
In this case, the center is (10,−3), a=7, and b=12. Therefore, the equation of the hyperbola is
The equation of the hyperbola is;
[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]
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A sculpture of the Earth is 829 kg. How many hydrpgen atoms
The number of hydrogen atoms present in the sculpture of earth if the mass of earth is 829 kg is 4.145 × 10²⁹.
Given that,
Mass of the sculpture of the earth = 829 kg
We know that,
Mass of an hydrogen atom = 2 × 10⁻²⁷ kg
Number of hydrogen atoms = Mass of earth / Mass of hydrogen atom
= 829 / 2 × 10⁻²⁷
= 414.5 × 10²⁷
= 4.145 × 10²⁹
Hence the required number of atoms is 4.145 × 10²⁹.
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Sonya took out a mortgage of $65,000 at 7% for 25 years. What is the cost of the mortgage?
137,823
2.70,987
123,823
151,182
Answer:
To calculate the cost of the mortgage, we need to find the total amount that Sonya will pay back over the 25-year period.
One way to do this is to use the formula for the future value of an annuity, which is:
FV = Pmt x ((1 + r)^n - 1) / r
where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods. In this case, we want to find the total future value of the mortgage payments over 25 years, so we can set Pmt equal to the monthly mortgage payment, r equal to the monthly interest rate, and n equal to the total number of months in 25 years.
First, let's convert the annual interest rate to a monthly interest rate by dividing by 12:
r = 7% / 12 = 0.00583
Next, we can use an online mortgage calculator or a spreadsheet to find the monthly mortgage payment based on the loan amount, interest rate, and term. For a $65,000 mortgage at 7% for 25 years, the monthly payment is approximately $471.78.
Finally, we can plug in the values into the formula for the future value of an annuity:
FV = $471.78 x ((1 + 0.00583)^300 - 1) / 0.00583
FV ≈ $141,535.15
Therefore, the total cost of the mortgage over 25 years is approximately $141,535.15. This includes the original loan amount of $65,000 plus the interest that accumulates over the 25-year period.
Step-by-step explanation:
To calculate the cost of the mortgage, we need to find the total amount that Sonya will pay back over the 25-year period.
One way to do this is to use the formula for the future value of an annuity, which is:
FV = Pmt x ((1 + r)^n - 1) / r
where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods. In this case, we want to find the total future value of the mortgage payments over 25 years, so we can set Pmt equal to the monthly mortgage payment, r equal to the monthly interest rate, and n equal to the total number of months in 25 years.
First, let's convert the annual interest rate to a monthly interest rate by dividing by 12:
r = 7% / 12 = 0.00583
Next, we can use an online mortgage calculator or a spreadsheet to find the monthly mortgage payment based on the loan amount, interest rate, and term. For a $65,000 mortgage at 7% for 25 years, the monthly payment is approximately $471.78.
Finally, we can plug in the values into the formula for the future value of an annuity:
FV = $471.78 x ((1 + 0.00583)^300 - 1) / 0.00583
FV ≈ $141,535.15
Therefore, the total cost of the mortgage over 25 years is approximately $141,535.15. This includes the original loan amount of $65,000 plus the interest that accumulates over the 25-year period.
What is half of 11 5 and 5/8
The half of 11 5/8 inches is; 5 13/16
Half of a fraction
The number given is; 11 5/8 inches
This can be written as an improper fraction;
= ((8×11)+5)/8 = 93/8
Hence, half of 93/8 is;
= 93/8 ÷ 2
= 93/8 × 1/2
= 93/16
= 5 13/16
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An American traveling in Japan wishes to exchange American money (dollars, symbol $) for Japanese money (yen, symbol ). If the exchange rate is , then how many dollars will the traveler need to purchase ?
The traveler will need (y / x) dollars to purchase y yen.
To determine the number of dollars the traveler will need to purchase a certain amount of yen, we need to divide the desired amount of yen by the exchange rate.
Let's assume the traveler wants to purchase y yen.
and, the exchange rate is 1 dollar = x yen.
To find the number of dollars, we can set up the following equation:
y yen × (1 dollar / x yen) = (y / x) dollars
Therefore, the traveler will need (y / x) dollars to purchase y yen.
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To calculate the number of dollars needed to purchase a specific amount of Japanese yen, we'll need the exchange rate between the two currencies. However, the exchange rate provided in your question is missing. Please provide the exchange rate between the US dollar (USD) and the Japanese yen (JPY) so that I can help you calculate accurately.
If tanA = 60/11 and sinB = 45/53 and angles A and B are in Quadrant I, find the value of tan(A-B)
Based on the information, it should be noted that the value of tan(A-B) is 234/583.
How to calculate the valueGiven:
tanA = 60/11
sinB = 45/53
A and B are in Quadrant I
We can use the following identity to find tan(A-B):
tan(A-B) = (tanA - tanB)/(1 + tanA*tanB)
Substituting the given values, we get:
tan(A-B) = (60/11 - 45/53)/(1 + (60/11)*(45/53))
= (15/53)/(295/583)
= 234/583
Therefore, the value of tan(A-B) is 234/583.
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Please help. Any unnecessary answers will be reported.
If n! = (2^8)(3^4)(5^2)(7), then what is n? Note that n! = n × (n - 1) × (n - 2) × ... × 1.
Answer:
n = 10
Step-by-step explanation:
Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.
Therefore, n! represents the product of all positive integers from 1 to n.
[tex]\boxed{n!=n \times(n-1) \times(n-2) \times ... \times 1}[/tex]
Given expression:
[tex]n! = (2^8)(3^4)(5^2)(7)[/tex]
The expression for n! has been given as the product of prime factors.
As n! represents the product of all positive integers from 1 to n, begin by writing out the positive integers from 1 in ascending order as the product of primes (using exponents where possible):
[tex]\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-14}\vphantom{\dfrac12}n&1&2&3&4&5&6&7&8&9&10&11&12&13\\\cline{1-14}\vphantom{\dfrac12}\sf Product\;of\;primes&1&2&3&2^2&5&3\cdot 2&7&2^3&3^2&5 \cdot 2&11&2^2\cdot 3&13\\\cline{1-14}\end{aligned}\;\;\sf etc.[/tex]
If we examine the prime products of the given expression, we can see that largest prime number 7 appears only once. Therefore, n must be less than 14, since the next time 7 appears as a prime factor is when 2 · 7 = 14.
The prime number 5 appears twice in the given expression.
From the above table, we can see that the first two times the number 5 is present is (1) on its own, and (2) as a factor of 10. Therefore, n must be equal to or more than 10.
The prime number 3 appears four times in the given expression.
From the above table, we can see that the first four times the number 3 is present is (1) on its own, (2) as a factor of 6, (3) & (4) as both factors of 9.
The 5th time prime number 3 is present is as a prime factor of 12. Therefore, n must be less than 12, else 2⁵ would be a factor of n!.
Therefore, we have determined that 10 ≤ n < 12.
As 11 is a prime number and does not appear in the given expression for n!, we can conclude that n = 10.
We can check this by calculating the given expression and 10!:
[tex]\begin{aligned}n! &= (2^8)(3^4)(5^2)(7)\\&=256 \cdot 81\cdot25\cdot7\\&=20738\cdot25\cdot7\\&=518400\cdot7\\&=3628800\end{aligned}[/tex]
[tex]\begin{aligned}10!&=10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=90 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=720 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=5040 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=30240 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=151200 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=604800 \cdot 3 \cdot 2 \cdot 1\\&=1814400 \cdot 2 \cdot 1\\&=3628800 \cdot 1\\&=3628800\end{aligned}[/tex]
Therefore, this proves that n = 10.
37 and 1/2 % of 104?
37 and 1/2 % of 104 is 39 .
Given,
37 and 1/2 % of 104
Simplifying further,
Convert mixed fraction into simple fraction,
37 and 1/2 % = 75/2%
Now,
75/2% of 104
= 75/2 ×1/100×104
=39 .
Hence 39 is the required answer.
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What kind of slope is this
In the given graph there is zero slope of the line.
As shown the points on the line
The coordinates of points be,
(4, 2) and (4, -2)
Since we know that slope of line passing through the points,
(x₁ , y₁) and (x₂, y₂) is, m = (y₂ - y₁)/(x₂ - x₁)
Here,
(x₁ , y₁) = (4, 2)
(x₂, y₂) = (4, -2)
Now the slope be = (-2 - 2)/(4 - 4)
= -4/∞
= 0
Therefore,
There is zero slope.
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I need help can someone help me
The two figures are congruent because a reflection and a translation are used to map Figure 1 onto Figure 2.
The angle corresponding to angle M is given as follows: <S.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Lateral or vertical movements.Reflections: A reflection is either over one of the axis on the graph or over a line.Rotations: A rotation is over a degree measure, either clockwise or counterclockwise.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.For this problem, the two transformations are:
Reflection, as the orientation changed.Translation, as the position changed.These two are rigid motions, keeping the side lengths constant, hence the figures are congruent.
Angle S is corresponding to angle M, as they are the angles at the "pointed" vertex of the figure.
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In an ice cream shop, the probability that customers order chocolate flavor is 0.6, vanilla flavor is 0.5. Determine the probability of ordering chocolate or vanilla.
(Which probability formula(s) to be used? Why?
Using the formula for two events not mutually exclusive, the probability of ordering either one is given as 0.8.
What is the probability of independent events?Since we assume that the events are not mutually exclusive, this implies that the occurrence of event B is not affected by the probability of occurrence of event A.
Then, the probability of ordering either one is the sum of their individual probabilities minus the probability of ordering both.
The probability formula is:
p (chocolate or vanilla) = p (chocolate) + p (vanilla) - p (chocolate and vanilla)
p (chocolate) = 0.6
p (vanilla) = 0.5
p (chocolate or vanilla) = 0.6 + 0.5 - 0.6 * 0.5
= 1.1 - 0.3
= 0.8
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I really need help doing this. please help me.
The bisector angle is angle PQT which is equal to angle RQT.
What is angle bisector?Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.
The bisected angle can be obtained using a pair of compass and a pencil attached to it.
To bisect the given angle RQP; we will take the following steps;
place the compass on exactly point Qexpand the radius of the compass such that the pencil attached to the compass will be in between R and P.strike an arc with the pencil clock wisestrike another arc with the pencil anti clock wise such that the two arc intersects.draw a line from point Q to intersect the two arcs.label the point of intersection of the two arcs Tangle PQT is equal to angle RQTLearn more about bisector angles here: https://brainly.com/question/24334771
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please help! thank uu ~ :)
Answer:
Unlikely.
Step-by-step explanation:
Possibility Formula: [tex]\frac{Desired Outcome}{Total Possible Outcoes}[/tex]
We want to roll a 5. On a standard six-sided die, then the odds of that happening is [tex]\frac{1}{6}[/tex]
[tex]\frac{1}{6}[/tex] is unlikely.
equal fractions for 2/3 and 3/5 using 15 as the common denominator
Answer:
2/3=10/15
3/5=9/15
Step-by-step explanation:
In order to turn 2/3 and 3/5 using 15 as the common denominator, we must first find out how much we need to multiply the denominator by to get 15 and use that amount to also multiply the numerator. In 2/3 the 3 needs to be multiplied by 5, therefore we also multiply the 2 by 5 giving us the result of 10/15 for the 2/3 problem. For the 3/5 we use the same tactic. The 5 in 3/5 needs to be multiplied by 3 to get to 15, therefore we multiply the 3 by 3 as well to get 9/15.
PLEASE HELP
Which of the following graphs shows an angle that would have an equivalent cosine ratio to the graph shown?
Answer: 150 deg
Step-by-step explanation:
cosine is negative in quadrants 2 and 3. the current angle, 210, is in quad 3. It will have an equal cosine value in quad 2.
that angle will be -210 degrees. in positive terms that is 360-210 = 150 degrees.
thus the answer which shows 150 degrees is correct.
in general:
[tex]cos(x) = cos(-x)[/tex]
help please quickly and give explanation
Answer:
Because y is a common variable, we can assume that they are equal to each other.
NO LINKS!!!
answer all 4!!!
WILL GIVE BRAINLIEST!!
Answer:
tan T = 12/5
sin A = 12/13
sec Z = 97/65
m<H = 54.5°
Step-by-step explanation:
In general:
sin A = opp/hyp
cos A = adj/hyp
tan A = opp/adj
sec A = 1/cos A = hyp/adj
tan T = 48/20
tan T = 12/5
AB = √(100 + 576)
AB = 26
sin A = 24/26
sin A = 12/13
XZ = √(72² + 65²)
XZ = 97
sec Z = 97/65
tan H = 7/5
H = tan^-1 7/5
m<H = 54.5°
100 Points! State whether the graph has line symmetry or point symmetry. If so, identify any lines of symmetry or points of symmetry. Photo attached. Thank you!
The line of symmetry from the graph of the absolute value function is given as follows:
x = 1.
How to define the absolute value function?An absolute value function of vertex (h,k) is defined as follows:
y = a|x - h| + k.
The line of symmetry for the absolute value function modeled above is given as follows:
x = h.
The coordinates of the vertex of the graphed linear function are given as follows:
(1, -1).
Hence the line of symmetry for the function graphed is given as follows:
x = 1.
This is because the x-coordinate of the vertex of the function is of x = 1.
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Any help on solving this?
A point on circle B with integer coordinates when r = 1 would be (5, 6).
We have, the radius of Circle A is 6 unit.
and, Radius of Circle B= 6/2= 3 unit
Using the center (2, 3) and the radius 3, we can calculate the coordinates of a point on circle B as follows:
x-coordinate = center x-coordinate + radius = 2 + 3 = 5
y-coordinate = center y-coordinate + radius = 3 + 3 = 6
So, a point on circle B with integer coordinates when r = 1 would be (5, 6).
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f+90+42=180 what is the answer of this
Answer:
hello
the answer is:
f = 180 - 42 - 90 = 48