The fire department is setting off fireworks. They notice that the casing of the firework hits the ground 78 meters from where the firework was launched. The firework exploded at a maximum height of 760. 5 meters
Answers
One possible function to model the firework scenario is h(t) = -4.9t² + 77.8t + 0.5, derived from a parabolic path due to gravity, with a maximum height of 760.5 meters and landing 78 meters away from launch.
One possible function to model this scenario could be:
h(t) = -4.9t² + 77.8t + 0.5
where h(t) is the height (in meters) of the firework above the ground at time t seconds after it was launched.
To derive this function, we first note that the path of the firework can be modeled by a parabolic function due to gravity. The vertex of this parabola corresponds to the maximum height of the firework, which occurs at t = 77.8 / (2 * 4.9) = 7.96 seconds.
At this time, the height of the firework is h(7.96) = 760.5 meters, which we can use to solve for the coefficient of the quadratic term (-4.9) in the function h(t). We also know that the firework lands 78 meters away from where it was launched, which means that it spends a total of 15.92 seconds in the air (assuming no air resistance). We can use this fact to solve for the linear term (77.8) in the function h(t).
Finally, we add a constant term of 0.5 to adjust for the initial height of the firework above the ground at t = 0.
Note that this function assumes idealized conditions and does not take into account air resistance or other factors that may affect the flight of the firework.
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Complete question:
The fire department is setting off fireworks. They notice that the casing of the firework hits the ground 78 meters from where the firework was launched. The firework exploded at a maximum height of 760. 5 meters. Write a function to model this scenario.
Related Questions
5. Set up, but don't evaluate, the integral that gives the length of the curve y = √2x + 1 from x = 0 to x = 4. Circle your final integral.
Answers
The integral that gives the length of the curve y = √(2x + 1) from x = 0 to x = 4 is ∫[0,4] √(1 + (1/√(2x + 1))²) dx.
To find the length of the curve defined by the equation y = √(2x + 1) from x = 0 to x = 4, we can use the arc length formula for a curve in Cartesian coordinates:
L = ∫ [a, b] √(1 + (dy/dx)²) dx
In this case, dy/dx represents the derivative of y with respect to x. Let's calculate dy/dx:
dy/dx = d/dx (√(2x + 1))
= (1/2)(2x + 1)^(-1/2)(2)
= (1/√(2x + 1))
Now, substitute this value into the arc length formula:
L = ∫ [0, 4] √(1 + (dy/dx)²) dx
= ∫ [0, 4] √(1 + (1/√(2x + 1))²) dx
Therefore, the integral that gives the length of the curve is:
∫ [0, 4] √(1 + (1/√(2x + 1))²) dx
Please note that this is the setup of the integral. To evaluate it, you would need to perform the integration using appropriate techniques, such as substitution or integration by parts.
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Select the correct answer.
Find the quotient of
O A.
B.
O c.
(5+21) (6-4)
(2+1)
36-38
36 +38
68-54
D. 68 +5
and express it in the simplest form.
Reset
Next
Answers
The quotient of (5+21) (6-4) and (2+1) is 13/3, expressed in its simplest form
The quotient of two numbers is a way of expressing the ratio of their values. It is the result of dividing one number by the other, and can be written as a fraction or as a decimal.
The quotient of 4 and 8 is 0.5, since 4 divided by 8 is 0.5.
The quotient of (5+21) (6-4) and (2+1) can be expressed as follows:
First, we need to solve each parenthesis separately. The first parenthesis is (5+21), which equals 26. The second parenthesis is (6-4), which equals 2. Therefore, the quotient of (5+21) (6-4) is 26/2, which can be simplified to 13/1.
Now, we need to divide 26/2 by (2+1). The result is 13/3, which is the final quotient.
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Finding the final amount in a world power problem on a compound interest
Answers
Using the compound interest formula, we have:
\(FV=2000(1+\frac{0.12}{2})^{6\cdot2}\)\(FV=2000(1.06)^{12}\)\(FV\approx4024.39\)3(2x + 4) + 2(x-2)
Match the equivalent expressions
Answers
Answer:
3(2x+4)+2(x-2)
6x+12+2x-4
6x+2x+12-4
8x+8
I am from grade 9 from which grade are you
Question in attachment
Answers
When an object is reflected, the orientation changes.
Option D.
Please help it’s an easy question for other people
Answers
Answer:
-6
Step-by-step explanation:
Hope this helped
Brainliest is appreciated.
Answer:
-6
Step-by-step explanation:
Each line is 1 unit on the number line
We are 1 unit to the left of the -5
Going to the left means it is one more unit negative than -5
-5 -1 = -6
Select the correct answer.
Event Bis dependent on event A, and event A occurs before event B. Which expression is equal to the probability of event A?
OA. P(BNA)
P(B)
OB. P(BNA)
P(BA)
Oc. P(ANB)
P(AB)
OD. P(ANB)XP(B|A)
xP
OE. P(ANB)~P(B)
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Answers
The main answer is OB. P(BNA) P(BA). Since event B is dependent on event A and occurs after event A, the probability of event A can be expressed as P(A) = P(A) x P(B|A), where P(B|A) represents the conditional probability of event B given that event A has already occurred.
Therefore, the correct expression for the probability of event A is P(BNA) P(BA), where P(BNA) represents the joint probability of event B and event A occurring together.
The correct answer is:
OD. P(A∩B) x P(B|A)
Since event B is dependent on event A, and event A occurs before event B, the probability of event A occurring is equal to the joint probability of both events occurring (P(A∩B)) multiplied by the conditional probability of event B occurring given that event A has occurred (P(B|A)).
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Takyra has n nail polish colors. Samantha has 4 more than twice the number of nail polish colors. In terms of n,
how many nail polish colors does Samantha have?
3n - 4
3n +4
2n +4
2n x 4
Answers
Answer: 2n+4
Step-by-step explanation:
"(4 more than) twice the number" is 2x
"4 more (than twice the number)" is +4
Put them together: 2n + 4
Please help me solve the question from below. It is from IM3 Algebra
Answers
The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.
To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:
log₂(x - 1) = x³ - 4x
Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.
For the point (2, 0):
log₂(2 - 1) = 2³ - 4(2)
log₂(1) = 8 - 8
0 = 0
The equation holds true for the point (2, 0), so (2, 0) is one solution.
For the point (1.1187, -3.075):
log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)
log₂(0.1187) = 1.4013 - 4.4748
-3.075 = -3.0735 (approx.)
The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.
Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.
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Please help me complete this chart of math, pleaseee help thank youuu
Answers
The chart has been completed and the information has been given below:
Compound Principal Interest rate No.of compounding periods Compound Interest Final amountAnnually $9200 6% 15 9200(1+0.06)15 $22084.34
Semi-Annually $9200 6/2 = 3% 15*2 = 30 9200(1+0.03)30 $22330.81
Quaterly $9200 6/4 = 1.5% 15*4 = 60 9200(1+0.015)60 $22477.62
Monthly $9200 6/(12*15) = 1/30 %
15*12*15 = 2700
9200(1+1/(30*100))2700
$22624.96
Weekly $9200 6/(15*52) = 1/130 15*52*15 = 11700
9200(1+1/(130*100))11700
$22627.57
Daily $9200 6/(15*365) = 2/1825
15*365*15 = 82125
9200(1+2/(1825*100))82125
$22628.24
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on the interval [ 0 , 2 π ) determine which angles are not in the domain of the tangent function, f ( θ ) = tan ( θ ). What angles are NOT in the domain of the tangent function on the given interval?
Answers
The angles π/2 and 3π/2 are not in the domain of the tangent function on the given interval.
The tangent function is defined as the ratio of sine to cosine:
tan(θ) = sin(θ)/cos(θ)
Since the cosine function is in the denominator, it cannot be zero because division by zero is undefined. Therefore, the values of θ that make the cosine function zero are not in the domain of the tangent function.
In the interval [0, 2π), the cosine function has zeros at θ = π/2 and θ = 3π/2. At these points, the denominator of the tangent function becomes zero, making the tangent function undefined.
Therefore, the angles that are not in the domain of the tangent function on the given interval are π/2 and 3π/2.
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44. Each child born to a particular set of parents has a probability of 0.25 of having blood type O. If these parents have 5 children.
What is the probability that
a. Exactly two of them have blood type O
b. At most 2 have blood type O
c. At least 4 have blood type O
Answers
Using the binomial distribution, the probabilities are given as follows:
a. 0.2637 = 26.37%.
b. 0.8965 = 89.65%.
c. 0.0148 = 1.48%.
What is the binomial distribution formula?The formula is:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters for this problem are:
n = 5, p = 0.25.
Item a:
The probability is P(X = 2), hence:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637\)
Item b:
The probability is:
\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)
In which:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373\)
\(P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955\)
\(P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637\)
Then:
\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965\)
Item c:
The probability is:
\(P(X \geq 4) = P(X = 4) + P(X = 5)\)
In which:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0147\)
\(P(X = 5) = C_{5,1}.(0.25)^{5}.(0.75)^{0} = 0.0001\)
Then:
\(P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0147 + 0.0001 = 0.0148\)
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Find the area of the trapezoid, I will give brainlist. If you can please explain how you got the answer
Answers
Answer:
36 sq inches
Step-by-step explanation:
bases are the two parallel sides -- 8" and 4"
height is perpendicular to the base -- 6"
formula for area of a trapezoid: A = 1/2h·(sum of bases)
A = 1/2(6)(8 + 4)
A = 3(12)
A = 36 sq inches
a line passes through points p(-6,8,1) and q (-4,1,3). find the standard parametric equations for the line
Answers
The standard parametric equations for the line passing through points P and Q is \($\begin{cases} x = -6 + 2t \ y = 8 - 7t \ z = 1 + 2t \end{cases}$\) .
To find the standard parametric equations for the line passing through points P(-6, 8, 1) and Q(-4, 1, 3), we first need to find the direction vector of the line. This can be done by subtracting the coordinates of point P from the coordinates of point Q:
\($\vec{PQ} = \begin{pmatrix}-4 \ 1 \ 3\end{pmatrix} - \begin{pmatrix}-6 \ 8 \ 1\end{pmatrix} = \begin{pmatrix}2 \ -7 \ 2\end{pmatrix}$\)
Now we can write the parametric equations in the form:
\($\begin{cases} x = x_0 + at \ y = y_0 + bt \ z = z_0 + ct \end{cases}$\)
where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector.
We can choose either point P or Q as the point on the line. Let's use point P. So we have:
\($\begin{cases} x = -6 + 2t \ y = 8 - 7t \ z = 1 + 2t \end{cases}$\)
These are the standard parametric equations for the line passing through points P and Q.
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AB = 6cm , AC = 12cm. Calculate the length of CD
Give your answers to 3 significant figures
Answers
Answer:
6cm , 12cm
Step-by-step explanation:
How many solutions does this system have?
Y= -7x + 8
Y= -7x - 8
Answers
Answer:
zero solutions, meaning there is no solution
Step-by-step explanation:
The two equations have the same slope, -7, and different y-intercepts, so they represent parallel lines. Since the lines never intersect, there is no solution.
Answer: zero
Answer:
B. No solutions.
Step-by-step explanation:
Look at attachment:
Hope this helps! :)
Calculate the perimeter of the figure
Answers
Answer:
76
Step-by-step explanation:
4+4+4+4+4+4+8+8+18+18 = 76
10. A box contains five and two-thirds cups of rice. If three fourths of the rice will
be used, how many cups of rice remained in the box?
14
D.
Answers
Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.
To find the number of cups of rice that remained in the box, we need to calculate three-fourths (3/4) of the total amount of rice in the box.
The total amount of rice in the box is given as five and two-thirds cups. To work with a fraction, we can convert the mixed number to an improper fraction:
5 and 2/3 = (5 * 3 + 2) / 3 = 17/3 cups
Now, we can find three-fourths (3/4) of 17/3:
(3/4) * (17/3) = (3 * 17) / (4 * 3) = 51/12 = 4 and 3/12 = 4 and 1/4 cups
Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.
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solve square root of x+1 =4
Answers
Answer:
3
Step-by-step explanation:
4 - 1 = 3
can someone help me on this plz
Answers
Dilate this shape with a scale factor of 2/3 around the origin write the coordinates of the image
Answers
A' (4/3, 4)
B' (16/3, -4)
C' (-8/3, 0)
1) Firstly, we need to locate the coordinates of that triangle:
A (2,6)
B (8,-6)
C (-4,0)
2) Since it is going to be dilated around the origin, then we need to apply the scale factor (2/3) to that pre-image, to get a smaller triangle since 2/3 < 1
2.2) So we can write out the following
Pre-image Dilation k = 2/3 Image
A (2,6) A' (4/3, 4)
B (8,-6) B' (16/3, -4)
C (-4,0) C' (-8/3, 0)
And that is the answer
help plz urgent ! “which ratio completes the probability distribution table”
1/48
3/48
28/48
16/48
Answers
Answer:
16/48
Step-by-step explanation:
NEED HELP ASAP!!!!!
What is the probability that both events will occur?
A coin and a die are tossed.
Event A: The coin lands on heads
Event B: The die is 5 or greater
P(A and B)= ?
Answers
The probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.
To find the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur, we need to determine the individual probabilities of each event and then multiply them together since the events are independent.
Event A: The coin lands on heads
A fair coin has two equally likely outcomes, heads or tails. Since we are interested in the probability of heads, there is only one favorable outcome out of two possible outcomes.
P(A) = 1/2
Event B: The die is 5 or greater
A fair six-sided die has six equally likely outcomes, numbers 1 through 6. Out of these six outcomes, there are two favorable outcomes (5 and 6) for Event B.
P(B) = 2/6 = 1/3
To find the probability of both events occurring (A and B), we multiply the individual probabilities:
P(A and B) = P(A) * P(B) = (1/2) * (1/3) = 1/6
Therefore, the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.
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I need help right now I’m in my class plz help
Answers
Answer:
1/3x + 1/2
Step-by-step explanation:
combine like terms 1/3x plus 2/3x equals 3/3x - 2/3x = 1/3x
and 3/4-1/4 = 2/4.
Answer:
1/3x+1/2
Step-by-step explanation:
1/3x+2/3x-2/3x+3/4-1/4 eliminated +2/3x-2/3x
1/3x+3/4-1/4
1/3x+2/4 simplify 2/4 to 1/2
1/3x+1/2
Mr. Gonzales started 16 yards away from the motion detector, and 2 seconds later he was 8 yards away from the motion detector. The graph shows Mr. Smith's motion. What is the rate if change over the interval [1,2] and [2,8]
Answers
Answer:
im almost 100% sure its 2
Step-by-step explanation:
if you simplify them, the difference is 2
Number 4 5 6 7 pls help!!!!!
Answers
Answer:
Here ya go!
Step-by-step explanation:
(look at picture below
A company wants to identify which of two production methods has the smaller completion time. One sample of workers is randomly selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on _____ samples.
Answers
The sampling procedure being used to collect completion time data in this scenario is based on paired samples or dependent samples.
In paired samples, each observation in one sample is uniquely linked or paired with an observation in the other sample. In this case, the workers are randomly selected, and each worker is assigned to use both production methods, one after the other. The completion time for each worker is measured under both methods, creating paired or dependent observations.
By using paired samples, the company can compare the completion times of the same workers using different production methods. This approach helps eliminate individual differences and other sources of variability among workers, focusing solely on the comparison between the two methods.
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What would the median of the following distribution be 12, 20, 13, 33, 26, 34, 25, 16, 17, 28, 36? O 25 25.5 O26 O None of these
Answers
The median is the middle value of a data set when it is arranged in ascending or descending order. To find the median, we need to arrange the given numbers in ascending order: 12, 13, 16, 17, 20, 25, 26, 28, 33, 34, 36.
Since there are 11 numbers in the data set, the median will be the value in the middle position. In this case, the middle position is the 6th position, which corresponds to the number 25.
Therefore, the median of the given distribution is 25.
The correct option is O 25.
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a motorboat travels 190 miles in 5 hours going upstream. It travels 270 miles going Downstream in the same amount of time what is the rate of the boat in still water and what is the rate of the current
Answers
To find the rate of the boat you divide the distance by the time:
\(r=\frac{d}{t}\)Going upstream is s
A product's quality characteristic has a specification (in inches) of $0.200 \pm 0.020$. If the value of the quality characteristic exceeds 0.200 by the tolerance of 0.020 on either side, the product will require a repair of $\$ 150$. The Taguchi loss function for this example is given by:
$L(x)=60(x-T)^2$
b. $L(x)=150(x-T)$
c. $L(x)=375,000(x-T)^2$
d. $L(x)=30(x-T)^2$
Answers
If the value exceeds\($0.200$\) by the tolerance of \($0.020$\) on either side, a repair cost of \($\$150$\)is incurred.
\($L(x) = 150(x - T)$\) option b.
The Taguchi loss function measures the cost or loss associated with deviations from a target value in a quality characteristic.
In this case, the specification for the quality characteristic is \($0.200 \pm 0.020$\).
If the value exceeds \($0.200$\) by the tolerance of \($0.020$\)on either side, a repair cost of $\$150$ is incurred.
Based on this information, the Taguchi loss function for this example is given by:
b.\($L(x) = 150(x - T)$\)
In the given options, option b represents the correct Taguchi loss function. The loss function is a linear function where the loss increases linearly with the deviation from the target value.
The coefficient of \($150$\) represents the cost of repair per unit deviation.
This loss function is appropriate for the given scenario as it accurately captures the cost associated with deviations from the target value.
The Taguchi loss function provides a quantitative measure to assess the impact of variations in the quality characteristic and helps in making decisions regarding process improvement and optimization.
In this case, it allows for evaluating the cost implications of exceeding the specified tolerance and guides decision-making on whether repairs are necessary based on the associated costs.
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