Answer:
transversitile multistelular projection
Answer:
Step-by-step explanation:
The perimeter of triangle ACD that is formed by two right-angle triangles ACB and DCB, approximated to 1 decimal place is: 40.1 cm.
Now you're going to imagine that you invested $1,000 in a company one year ago, and you want to see how well your investment would be doing today.
To begin, choose a company that you're familiar with and that seems as if it might be a good investment - that is, a company that you think will have rising stock prices. Think about companies that you use or know are popular Remember, not all companies are public companies. You'll need to check the New York Stock Exchange to find out if you can actually buy shares in this company Once you've settled on a company, find its stock price from one year ago and for today Write a journal entry about your imagined investment Answer the following questions as you write
1.) What stock did you buy?
2.) Why did you think buying this stock would be a good idea?
3.) How much would you have made or lost on an investment of $1,000?
(Hint First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today Compare that to your initial investment of $1,000)
4.) Could you have made more money by selling sooner?
Answer:
Step-by-step explanation:
1. What stock did you buy?
Apple Inc.
2. Why did you think buying this stock would be a good idea?
Apple products are becoming more and more popular every day. The company is always introducing new and exciting devices. I knew it would be a safe choice to invest in.
3. How much would you have made or lost on an investment of $1,000?
I would have made $105.
Hint: First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph. Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today. Compare that to your initial investment of $1,000.
4. Could you have made more money by selling sooner?
Yes, on October 3, 2018 it was at its peak for the year.
your investment would be doing great today. you would make $115 from the given investment.
What are Stocks?A stock usually referred to as equity, is a type of investment that denotes ownership in a portion of the issuing company. Shares, also known as units of stock, entitle their owners to a share of the company's assets and income in proportion to the number of shares they possess.
Given, you're going to imagine that you invested $1,000 in a company one year ago
I will buy the stocks of amazon.The popularity of Amazon products is rising daily. The business frequently introduces cutting-edge technology. I was confident that it would be a secure investment.I would have made $115.Hint: To start, divide $1,000 by the stock's current price, one year ago, to see how many shares you might have purchased. It can be necessary to infer the stock price from the graph. The number of shares should be rounded up to the next whole number. Then, multiply the number of shares you purchased by the stock's current price to determine the share's current worth. Contrast that with your $1,000 original investment.on September 5, 2022, it was at its peak for the year.Therefore, Today, your investment would be flourishing. Your return on the stated investment would be $1,115.
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Rivika used the last four digits of her telephone number,1048, followed by its prime factorization to create her email password Determine her password
Answer: I'm pretty sure I can help, just give me like 3 minutes..
-Angie
Answer:
Her password is 1048222131.
Like Angie said, 1048 * 2* 2 * 2 * 131.
But before that you need to decompose 1048 into its prime factors.
The Prime Factorization is:
2 x 2 x 2 x 131
In Exponential Form:
23 x 1311
CSV Format:
2, 2, 2, 131
All Factors of 1048:
1, 2, 4, 8, 131, 262, 524, 1048
Prime Factors Tree
1048
/ \
2 524
/ \
2 262
/ \
2 131
There you go! If you need more help just reach out to me!
6. In the Sonoran desert, kangaroo rats (K) compete with ants (A) for food, since both eat seeds. Suppose the competition is modeled by the equations A' = 3A - 2A2 - 2AK K' = 2K - AK – 3K a) Find and classify all the equilibria for this system. b) What will happen to these species in the long run?
a) The determinant of J(1, 3/2) is positive and the trace is negative, so this equilibrium is a stable node. The determinant of J(3/2, 0) is zero and the trace is positive, so this equilibrium is a semi-stable node.
b) if the initial population of ants is zero, then the system will approach the semi-stable equilibrium (A, K) = (3/2, 0
a) To find the equilibria for this system, we need to set both A' and K' equal to 0 and solve for A and K:
1. A' = 3A - 2A² - 2AK = 0
2. K' = 2K - AK - 3K = 0
First, let's find the equilibria for equation 1:
1a. 3A - 2A² - 2AK = 0
1b. 3 - 2A - 2K = 0 (divide by A)
1c. 2A + 2K = 3
1d. A + K = 3/2
Next, let's find the equilibria for equation 2:
2a. 2K - AK - 3K = 0
2b. -A - K = -2 (divide by K)
2c. A + K = 2
Now, let's find the equilibria by solving the system of equations:
1d. A + K = 3/2
2c. A + K = 2
Since the two equations are inconsistent, there are no non-trivial equilibrium points for this system. The only equilibria are A = 0 or K = 0.
b) In the long run, the species will either coexist (A ≠ 0, K ≠ 0) or one of the species will become extinct (A = 0 or K = 0). Since the system does not have a non-trivial equilibrium point, the species will most likely experience competition and one of them will eventually become extinct, depending on the initial conditions.
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"Ten more than the quotient of a number and 9 is 7
Answer:
n = 6
Step-by-step explanation:
(n - 9) + 10 = 7
(n - 9) = 7 - 10
n - 9 = -3
n = -3 +9
n = 6
If "Ten is more than the quotient of a number and 9 is 7, the obtained value will be -27.
What is the quotient?The number being divided is referred to as the dividend, and the number being divided by it is referred to as the divisor. The quotient is the outcome of the division.
Suppose the given number is n.
From the given condition, "Ten is more than the quotient of a number, and 9 is 7
We have to form the equation for the given condition,
10+ n/9= 7
We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
n/9=7-10
n/9= -3
n= -27
Thus, if "Ten is more than the quotient of a number and 9 is 7, the obtained value will be -27.
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I’m so confused, I will try to mark brainliest, sorry if I can’t figure it out.
Answer:
\(x^{\circ}+105^{\circ}=180^{\circ},\\x^{\circ}=z^{\circ},\\180^{\circ}-z^{\circ}=y^{\circ}\)
Step-by-step explanation:
Statement 1:
True - These two angles are supplementary (add up to 180 degrees) because they form one side of a line.
Statement 2:
True - These two angles are vertical angles (opposite to each other at intersection of two lines). All vertical angles are equal.
Statement 3:
False - These two angles are vertical and therefore are equal. Thus, they cannot have a difference of 105.
Statement 4:
False - Two of these angles form one side of a line which is equal to 180 degrees. Since the third angle is greater than zero, they cannot all add up to 180 degrees.
Statement 5:
True - These two angles are supplementary (add up to 180 degrees) because they form one side of a line.
Statement 6:
False - These two angles are supplementary (add up to 180 degrees) because they form one side of a line and therefore cannot be equal to 105.
Answer and Step-by-step explanation:
The answers are:
x + 105 = 180 (Supplementary angles = 180 degrees)
x = z (Vertical angles are congruent)
180 - z = y (Supplementary angles = 180 degrees)
#teamtrees #PAW (Plant And Water)
9.1.9 .wp in exercise 9.1.7, find the boundary of the critical region if the type i error probability is a. α=0.01andn=10 b. α=0.05andn=10 c. α=0.01andn=16 d. α=0.05andn=16
The specific hypothesis test, including the test statistic and the alternative hypothesis.
In exercise 9.1.7, we need to find the boundary of the critical region for different scenarios, given the type I error probability (α) and the sample size (n). Let's analyze each scenario:
a. For α = 0.01 and n = 10:
The type I error probability (α) represents the probability of rejecting the null hypothesis when it is true. In this case, with a significance level of 0.01 and a sample size of 10, we need to find the critical region boundaries. To determine the critical region, we need to consult the specific hypothesis test and the corresponding test statistic.
b. For α = 0.05 and n = 10:
Similar to the previous scenario, we have a significance level of 0.05 and a sample size of 10. Again, we need to determine the critical region boundaries based on the hypothesis test and the associated test statistic.
c. For α = 0.01 and n = 16:
In this case, the significance level is 0.01, and the sample size is 16. We need to find the boundary of the critical region by considering the hypothesis test and the relevant test statistic.
d. For α = 0.05 and n = 16:
Lastly, with a significance level of 0.05 and a sample size of 16, we must identify the critical region boundaries according to the specific hypothesis test and the corresponding test statistic.
To determine the exact boundary of the critical region in each scenario, we need additional information about the hypothesis test being performed. The critical region depends on factors such as the test statistic distribution and the alternative hypothesis. With this information, we can calculate the critical values or construct confidence intervals to identify the boundaries of the critical region.
In summary, to find the boundary of the critical region for exercise 9.1.7, we need more details regarding the specific hypothesis test, including the test statistic and the alternative hypothesis.
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please helo me with both of them thank u
Answer:
13: 22 < x < 74
14: Side DF, Side DE, side EF
Step-by-step explanation:
So for the first one, you add 26 + 48 which equals 74. Then, you subtract 48 - 26 which equals 22. So the range is 22 < x < 74.
For the second one, the angle corresponds to the side across from it. The smallest side will be across from the smallest angle. So, the order is side DF, side DE , and then side EF.
Hope this helps!!! :)
Factor the following:
x² +48 - 12
2
(x) (x
Be sure to include a + sign or - sign with your number
Previous
HELPPPPPP MEEEEE
Answer:
this is a confusing one
Step-by-step explanation:
Help me to do this question plz plz plz
I will make you as brainlist plz
Answer:
1. 5
2. 12
3. a. 12
3. b. 18
Step-by-step explanation:
1. 50 - 45 = 5.
2. 26 - 18 = 8. 30 - 18 = 12. 12 + 8 = 20. 20 + 18 = 38. 50 - 38 = 12.
3. a. 24 - 12 = 12.
4. 40 - 12 = 28. 24 - 12 = 12. 28 + 12 + 12 = 52. 70 - 52 = 18.
A pancake recipe requires two and two thirds cups of milk to one cup of flour. If four and two thirds cups of milk is used, what quantity of flour will be needed, according to the recipe?
Answer:
There will need to be 2 and 1/3 cups of flour according to the recipe
Step-by-step explanation:
Given the recipe, we can say that for each 2 and 2/3s cups of milk, one cup of flour is used. We can write this as ( 2 + 2/3) cups of milk / (1) cup of flour.
We can also write 2 + 2/3 as 2*(3/3) + 2/3 = 6/3 + 2/3 = 8/3, making our ratio
(8/3) / 1
The ratio stays the same, no matter how many cups of milk or flour are used. Therefore, (8/3) /1 = (4 + 2/3) / cups of flour
Writing our final cups of flour as c, we can say
(8/3) / 1 = (4+2/3) / c
(4+2/3)/c = (12/3 + 2/3) /c = (14/3) /c
(8/3)/1 = (14/3) /c
anything divided by 1 is equal to itself
(8/3) = (14/3)/c
multiply both sides by c to make the variable not a denominator
(8/3) * c = 14/3
multiply both sides by 3 to remove the denominators
8 * c = 14
divide both sides by 8 to isolate the c
c = 14/8 = 7/3 = 6/3 + 1/3 = 2 + 1/3
There will need to be 2 and 1/3 cups of flour according to the recipe
The hypotenuse of a right triangle is 10 inches long. The longer leg is 2 inches longer than the shorter leg. Find the side lengths of the triangle.
Answer: Shorter leg = 6 inches
Longer leg = 6+2 = 8 inches
Step-by-step explanation:
Let the shorter leg bw represented by x.
Therefore, the longer leg will be x+2.
The hypothenuse is 10inches
We should note that in Pythagoras theorem, the square of the longer and shorter side equals the square of the hypothenuse. This will be:
x² + (x+2)² = 10²
x² + x² + 4x + 4 = 100
2x² + 4x = 100 - 4
2x² + 4x = 96
2x² + 4x - 96 = 0
x² + 2x - 48 = 0
x² + 8x - 6x - 48 = 0
x(x + 8) -6(x + 8) = 0
x - 6 = 0
x = 0+6.
x = 6
Shorter leg = 6 inches
Longer leg = 6+2 = 8 inches
Find the midpoint of the segment with the following endpoints.
(8, 10) and (1,4)
Answer:
(4.5, 7)
Step-by-step explanation:
x = 1/2(x^1 + x^2)
x = 1/2(8 +1)
x = 1/2(9)
x = 4.5
y = 1/2(y^1 + y^2)
y = 1/2(10 + 4)
y = 1/2(14)
y = 7
(4.5, 7)
Assume the current spot rate is can$1.2803 and the one-year forward rate is can$1.2745. also assume the nominal risk-free rate in canada is 4.8 percent while it is 4.2 percent in the u.s. using covered interest arbitrage, you can earn a profit of ___ for every $1 invested over the next year.
Using covered interest arbitrage, you can earn a profit of approximately 0.60 cents for every $1 invested over the next year.
Calculate the interest rate differential.
The interest rate differential is the difference between the nominal risk-free rates in Canada and the U.S. In this case, the differential is 0.6% (4.8% - 4.2%). Calculate the forward premium or discount: The forward premium or discount is the difference between the one-year forward rate and the spot rate. In this case, the forward premium is 0.0058 (1.2803 - 1.2745).
Determine the profit: To calculate the profit, multiply the forward premium by the investment amount. In this case, for every $1 invested, you would earn approximately 0.60 cents (0.0058 * $1).
Please note that exchange rates and interest rates fluctuate, so the actual profit may vary.
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For every $1 invested over the next year, you can earn a profit of can$0.006 through covered interest arbitrage.
To determine the profit from covered interest arbitrage, we need to compare the returns from investing in Canada versus the returns from investing in the US. Covered interest arbitrage involves borrowing money at the lower interest rate and converting it into the currency with the higher interest rate.
First, let's calculate the profit in Canadian dollars. The one-year forward rate of can$1.2745 tells us that $1 will be worth can$1.2745 in one year. Therefore, by investing $1 in Canada at the risk-free rate of 4.8%, we will have can$1.048 after one year (can$1 * (1 + 0.048)).
Now, let's calculate the profit in US dollars. By investing $1 in the US at the risk-free rate of 4.2%, we will have $1.042 after one year ($1 * (1 + 0.042)).
The difference between the Canadian dollar profit and the US dollar profit is can$1.048 - $1.042 = can$0.006.
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B.Tech First year
MWI -0. 5. Solve the differential equation y(2x2 - xy +1}x + (x - y)dy = 0. 6.
(2x^2 - xy + 1)(x - y) = K. This is the general solution to the given differential equation.
To solve the given differential equation:
y(2x^2 - xy + 1)dx + (x - y)dy = 0
We can start by rearranging the equation:
ydx(2x^2 - xy + 1) + (x - y)dy = 0
Next, we can divide both sides by (2x^2 - xy + 1)(x - y) to separate the variables:
ydx/(2x^2 - xy + 1) + dy/(x - y) = 0
Now, we can integrate both sides of the equation with respect to their respective variables.
∫(ydx/(2x^2 - xy + 1)) + ∫(dy/(x - y)) = 0
To integrate the first term, we can use the substitution u = 2x^2 - xy + 1:
∫(ydx/u) = ∫(dy/(x - y))
Differentiating u with respect to x, we get:
du/dx = 4x - y - xy'
Rearranging, we have:
dy/dx = 4x - xy - du/dx
Substituting this into the second term, we get:
∫(dy/(x - y)) = ∫(du/dx/(4x - xy - du/dx))
Simplifying the integral, we have:
∫(dy/(x - y)) = ∫(du/(4x - y - u))
Now, we can integrate both terms:
∫(ydx/u) + ∫(dy/(x - y)) = 0
ln|u| + ln|x - y| = C
ln|u(x - y)| = C
Taking the exponential of both sides:
u(x - y) = e^C
Since C is a constant, we can write it as e^C = K:
u(x - y) = K
Substituting back the expression for u, we have:
(2x^2 - xy + 1)(x - y) = K
This is the general solution to the given differential equation.
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Help i will mark Brainliest
Answer:
149 per person
Step-by-step explanation:
the question was not understandable
Write an addition problem that has a sum of -24. Include one positive number and one negative number in the problem
-26 + 2 = -24
I hope this helps you, have a great rest of your day. :)
Answer:
-30 + 6 = -24
Step-by-step explanation:
Having -30 as the first number in the equation makes the equation negative. But by adding 6, then it will be -24, which is the answer we are trying to get to.
Hope this helped!
brainly?...
These are my cats, idek if it worked lol, also 40x2 bc why not you don’t have to answer
Answer:
It didn't work, 40 x 2 = 80
Step-by-step explanation:
have a good day
Answer:
Hey! I don't see any cats :(
Step-by-step explanation:
40x2= 80 !
Hope this helps!
Have a nice day! ♥(>'-'<)
please help much appreciated!
The equation of the inequality graph with dashed line
y > 2x - 4The equation of the inequality graph with solid line
y ≥ -x + 4How to derive the equationsUsing the slope intercept form of the straight line which is of the form
y = mx + c
The slope, m is the ratio of the change in the output to the change in the input. This is given by the formula
m = (y₀ - y₁) / (x₀ - x₁)
Slope calculation using the points (0, -4) and (2, 0)
m = (-4 - 0) / (0 - 2)
m = 2
y intercept, c from the graph
c = -4
applying inequality representations
shading above the line is greater than and dotted lines means it does not have equal to
hence y > 2x - 4
for the solid line graph
the slope, m calculating using the points on the graph (0, 4) and (4, 0)
m = (4 - 0) / (0 - 4)
m = (4) / (-4)
m = -1
y intercept, c from the graph
c = 4
The equation of the line is y = -x + 4
Solid lines indicate an equality in the inequality, while shading over the line indicates a greater than
hence y ≥ -x + 4
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y = 1/2x + 8
What does x equal?
x= -16
substitute y=0
0=1/2x+8
multiply both sides
=0=x+16
move the variable to the left
-x = 16
change the signs
final ; x = -16
a(x+y)-a(x-y) simplifiyed
Answer:
ax + ay - ax + ay
= 2ay
answer is 2ay
Any remainders? What’s the answer?
whats the percent change of 10 gallons to 24 gallons
Answer: 140%
Step-by-step explanation:
Answer:
140%
Step-by-step explanation:
BRAINLIEST PLSSSS
Round 638638638 to the nearest hundred.
Answer:
638638600
Hope that helps!
Step-by-step explanation:
Answer:
638638600
Step-by-step explanation:
18- 12y = -22 -7y solve for y
Answer: y=8
Step-by-step explanation:
To solve for y, you want to use algebraic properties to isolate y.
18-12y = -22-7y [add both sides by 7y]
18-5y=-22 [subtract both sides by 18]
-5y=-40 [divide both sides by -5]
y=8
Now, we know that y=8.
Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by 7000p C(p) = 100-p (a) Find the domain of this function. (Enter your answer using interval notation.) (b) Find the functional value. (Round your answer to the nearest cent.) C(43) = $ Explain what it means. C(43) is the ---Select--- ---Select--- of the particulate pollution from of removing the smokestacks of the industrial plant. (c) Find the functional value. C(90) = $ Explain what it means. ---Select- of the particulate pollution from C(90) is the ---Select--- of removing the smokestacks of the industrial plant. (d) Find the functional value. C(99) = $ Explain what it means. C(99) is the ---Select--- ---Select-- of the particulate pollution from of removing the smokestacks of the industrial plant. (e) Find the functional value. C(99.8) = $ Explain what it means. of removing ---Select- of the particulate pollution from C(99.8) is the ---Select--- the smokestacks of the industrial plant.
a) The domain of the function : C(p) = 7000p/(100-p) is (0, 100). b) it costs $5271.93 to remove 43% of particulate pollution. c) It costs $63000 to remove 90% . d) it costs $693000 to remove 99% . e) it costs $698986.87 to remove 99.8%.
(a) The function's domain is the set of values that p can take such that C (p) makes sense.
For this function, the denominator 100-p must not equal zero,
so p ≠ 100, and the domain is therefore the interval (0, 100).
Therefore, the domain of the function
C(p) = 7000p/(100-p) is (0, 100).
(b) To compute C(43), substitute p = 43 into the function:
C(43) = 7000 (43) / (100-43)
= 7000 (43) / (57)
= 5271.93
= $5271.93.
Therefore, it costs $5271.93 to remove 43% of particulate pollution from the smokestacks of an industrial plant.
C(43) is the cost of removing 43% of the particulate pollution from the smokestacks of the industrial plant.
(c) To compute C(90),
substitute p = 90 into the function:
C(90) = 7000 (90) / (100-90)
= 63000
= $63000.
Therefore, it costs $63000 to remove 90% of particulate pollution from the smokestacks of an industrial plant.C(90) is the cost of removing 90% of the particulate pollution from the smokestacks of the industrial plant.
(d) To compute C(99), substitute p = 99 into the function:
C(99) = 7000 (99) / (100-99)
= 693000
= $693000.
Therefore, it costs $693000 to remove 99% of particulate pollution from the smokestacks of an industrial plant.
C(99) is the cost of removing 99% of the particulate pollution from the smokestacks of the industrial plant.
(e) To compute C(99.8), substitute p = 99.8 into the function:
C(99.8) = 7000 (99.8) / (100-99.8)
= 698986.87
= $698986.87.
Therefore, it costs $698986.87 to remove 99.8% of particulate pollution from the smokestacks of an industrial plant.
C(99.8) is the cost of removing 99.8% of the particulate pollution from the smokestacks of the industrial plant.
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Which of the following situations are equal to 60%? Select all that apply.
A) 6 out of 12
B) 9 out of 15
C) 15 out of 25
D) 24 out of 40
E) 33 out of 55
Segment JK has endpoints J(2,4) and K(6,2). You dilate the segment using a dilation centered at the origin with a scale factor of 1/2 and then reflect the image over the x-axis. Where is the final image of K?
The final image of K would be at (3,-1) after the given sequence of transformation Segment JK.
What is Dilation?Dilation is a process for creating similar figures by changing the size.
Segment JK has endpoints J(2,4) and K(6,2).
A dilation by a factor of 1/2 means that each coordinate value will be multiplied by 1/2.
The dilation of segment JK with a scale factor of 1/2 would shrink the segment by half, so the coordinates of K would be (3,1).
Reflecting over the x-axis would change the sign of the y-coordinate, so the final image of K would be at (3,-1).
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in the formula, =1+(2-3)+5/6-6^2, what will access evaluate first?
in the formula, =1+(2-3)+5/6-6^2, The final result of the formula is -35.1667.
In the formula =1+(2-3)+5/6-6^2, the order of operations dictates that the exponentiation operator (^) is evaluated first, followed by multiplication and division from left to right, and then addition and subtraction from left to right.
So, access will evaluate 6^2 first, which equals 36. Then, it will evaluate the division 5/6, which equals 0.8333 (rounded to four decimal places).
Next, it will evaluate the subtraction (2-3), which equals -1. Then, it will evaluate the addition (1+(-1)), which equals 0. Finally, it will evaluate the multiplication (-6 * 6), which equals -36.
Putting it all together, we get:
=1 + (2-3) + 5/6 - 6^2
= 1 + (-1) + 0.8333 - 36
= -35.1667
Therefore, the final result of the formula is -35.1667.
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Round to the nearest hundredth
Answer:
hope this is correct
Answer:
AC ≈ 2.87
Step-by-step explanation:
Using the sine ratio in the right triangle
sin35° = \(\frac{opposite}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{AC}{5}\)
Multiply both sides by 5
5 × sin35° = AC , thus
AC ≈ 2.87 ( to the nearest hundredth )
Al released his balloon from the 10-yard line, and it landed at the 16-yard line. If the ball reached a height of 27 yards, what equation represents the path of his toss?
The equation of the path of the parabola is y = a(x - 13)² + 27
Given data ,
To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.
The equation of a parabola in vertex form is given by:
y = a(x - h)² + k
where (h, k) represents the vertex of the parabola
Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.
The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:
h = (10 + 16) / 2 = 13
Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)
Now, let's substitute the vertex coordinates (h, k) into the general equation:
y = a(x - 13)² + k
Substituting the vertex coordinates (13, 27)
y = a(x - 13)² + 27
To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).
This means that the highest point (13, 27) lies on the parabola
Substituting the vertex coordinates (13, 27) into the equation
27 = a(13 - 13)² + 27
27 = a(0) + 27
27 = 27
Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number
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