At a model rocket competition, Mrs. Jennings launches a rocket is launched upward
from the ground with an initial velocity of 138 feet per second.
The formula for vertical motion is
h(t) = 0.5at? + vt +s, where the gravitational constant, a, is -32 feet per second squared, v
is the initial velocity, and s is the initial height. Time t is measured in seconds, velocity
v is measured in feet per second, and heights h and s are measured in feet.
Write the function that describes the height, h in feet, of the rocket l seconds into
launch
Answers
Answer:
The function that describes the height, h in feet, of the rocket, t seconds into launch is h = -16·t² + 138·t
Step-by-step explanation:
The given parameters are;
The initial velocity of the rocket, v = 138 feet per second
The vertical motion formula = h(t) = 0.5·a·t² + v·t + s
The gravitational constant, a = -32 ft./s²
s = The initial height of the rocket
Therefore, he have;
The height of the rocket, t seconds seconds into launch is given as follows;
Height = h = h(t) - s = 0.5·a·t² + v·t
Substituting the known values gives;
h(t) - s = 0.5 × (-32) × t² + 138 × t = -16·t² + 138·t
h = -16·t² + 138·t
The function that describes the height, h in feet, of the rocket, t seconds into launch is h = -16·t² + 138·t.
Related Questions
Please need the answer
Answers
Answer:
A. True
B. True
C. False
Step-by-step explanation:
Hope that helps!
PLEASE HELLPP I WILL MARK BRAINLYLIST
Answers
Answer:
3
Step-by-step explanation:
divide one side of the bigger triangle by the corresponding side of the smaller one
Answer:
3
Step-by-step explanation:
Divide the bigger triangle by the little one
3/1=3
then 12/4=3
Solve for "c."
a = b/(c-d)
Answers
Answer:
c=
ad+b
a
give me brilliant please
Step-by-step explanation:
a=
b
c−d
Step 1: Multiply both sides by c-d.
ac−ad=b
Step 2: Add ad to both sides.
ac−ad+ad=b+ad
ac=ad+b
Step 3: Divide both sides by a.
ac
a
=
ad+b
a
c=
ad+b
a
evaluate each integral by interpreting it in terms of areas. (a) 8 0 f(x) dx (b) 20 0 f(x) dx (c) 28 20 f(x) dx (d) 28 12 f(x) dx (e) 28 12 |f(x)| dx (f) 0 8 f(x) dx
Answers
To evaluate each integral in terms of areas, we need to understand that the integral represents the area under the curve of a function, f(x), between two points on the x-axis.
Let's discuss each integral:
(a) ∫₀⁸ f(x) dx: This represents the area under the curve of f(x) from x = 0 to x = 8. The integral calculates the accumulated area along this interval.
(b) ∫₀²⁰ f(x) dx: Similarly, this represents the area under the curve of f(x) from x = 0 to x = 20. It's a broader interval than (a), so it covers more area under the curve.
(c) ∫²⁰²⁸ f(x) dx: This integral represents the area under the curve of f(x) between x = 20 and x = 28. It's important to note that the interval is now shifted to the right compared to (a) and (b).
(d) ∫¹²²⁸ f(x) dx: This integral calculates the area under the curve of f(x) from x = 12 to x = 28. The interval here is larger than in (c), covering more area under the curve.
(e) ∫¹²²⁸ |f(x)| dx: This integral evaluates the area under the absolute value of f(x) from x = 12 to x = 28. The absolute value ensures that negative function values contribute positively to the area calculation, preventing any cancelation of areas.
(f) ∫₀⁸ f(x) dx: This integral is the same as (a), representing the area under the curve of f(x) from x = 0 to x = 8.
Each integral evaluates the area under the curve of f(x) for different intervals on the x-axis, providing insights into the total accumulated area in those intervals.
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I NEEED HELP PLEASEE
Answers
Answer:
D
Step-by-step explanation:
Additive Inverse Property is the idea that you are adding the same number but positives and negatives of it. So, the correct answer is D.
Hope that helps!
Write a polynomial with four terms that has a GCF of 4x^2.
Answers
This polynomial, 4x² is the GCF and (x + 2)(x - 1)(x + 3) are the remaining factors.
What is polynomial?
A polynomial is an equation made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables.
A polynomial with a GCF of 4x² means that 4x² is a factor common to all terms in the polynomial. One example of such a polynomial is:
4x² (x + 2)(x - 1)(x + 3) = 4x⁵ + 24x²- 36x³ - 72x²
In this polynomial, 4x² is the GCF and (x + 2)(x - 1)(x + 3) are the remaining factors.
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Help me plsssssssssssssssssssssssssss
Answers
Answer: 120
Step-by-step explanation: divide 24 by 5 to get 4.8 so its 4.8 minutes for one question
25 x 4.8 = 120
Find a third-degree polynomial equation with rational coefficients that has roots –5 and 6 + i.
Answers
The coefficients of the polynomial are rational, which means that any non-real roots occur alongside their complex conjugates. In this case, 6+i is a root, so 6-i is also a root.
So the simplest polynomial you can build with these roots is
(x - (-5)) (x - (6 + i )) (x - (6 - i )) = x ^3 - 7x ^2 - 23x + 185
(first choice)
what is the area of a trapezoid where one nase is 6 cm the second base is 4 cm and the height is eight cm
Answers
Therefore, the area of the trapezoid is 40 square centimeter.
The formula for the area of a trapezoid is Area = (1/2) * (b1 + b2) * h, where b1 and b2 are the lengths of the bases, and h is the height.
Given the measurements of the trapezoid as one base being 6 cm, the second base being 4 cm, and the height being 8 cm, we substitute these values into the formula:
Area = (1/2) * (6 + 4) * 8
Simplifying the expression within the parentheses:
Area = (1/2) * 10 * 8
Performing the multiplication:
Area = 5 * 8
Further simplifying the expression:
Area = 40
Area = (1/2) * (6 + 4) * 8
= (1/2) * 10 * 8
= 5 * 8
= 40 square cm
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the body mass of a man is xkg.thebody mass of his two children are five-sixth and four_fifths of their father5 x over 6 + 4 x over 5 5 x over 6 + 4 x over 5
Answers
56/120
Step-by-step explanation:
The body masses of the two children in terms of their father's body mass, x, are:
First child's body mass = 5x/6 kg
Second child's body mass = 4x/5 kg
To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.
Let the body mass of the man be x kg.
The first child's body mass is five-sixths of their father's body mass:
Body mass of the first child = (5/6) * x
= 5x/6 kg.
The second child's body mass is four-fifths of their father's body mass:
Body mass of the second child = (4/5) * x
= 4x/5 kg.
Therefore, the body masses of the two children in terms of their father's body mass, x, are:
First child's body mass = 5x/6 kg
Second child's body mass = 4x/5 kg
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Quiz Active
1
2
B
8
The figure shows five points. A point has been translated right and up.
D
9 10
Based on the graph, which statements about the points could be true? Check all that apply.
Answers
The point (5, 10) has not been translated in the given figure.Hence this statement is false.
The graph shows five points.
A point has been translated right and up.
Now, the statements that are true based on the graph are as follows:
The point (9, D) has been translated right and up.Answer: False
There is no information given about point (9, D).
So, we cannot say anything about the translation of point (9, D).
The point (1, 8) has been translated right and up.Answer: True
As explained above, the point (1, 8) has been translated 7 units to the right and 2 units up to get the new point (8, 10). So, this statement is true.
The point (2, 9) has been translated right and up.Answer: False
The point (2, 9) has not been translated in the given figure.
So, this statement is false.
Statement 4: The point (8, B) has been translated right and up.Answer: True
The point (8, B) has been translated 1 unit up in the given figure. So, this statement is true.
The point (5, 10) has been translated right and up.Answer: False
The point (5, 10) has not been translated in the given figure.
So, this statement is false.
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Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer. A used Car salesperson can be paid using two methods of commission. METHOD X uses straight commission 3.5% of the selling price of all vehicles sold. METHOD Y uses a fixed amount of £250 per week plus commission of 1.5% of the selling price of all vehicles sold. If the total selling price of the Cars sold in each week is on average £20,000, calculate which of the two methods of commission the salesperson would prefer.
Answers
The cost of one computer is £600 and the cost of one printer is £800.
Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, and the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer.
Let the cost of a computer be x and the cost of a printer be y.
Then, the two simultaneous equations are:5x + 4y = 6600 ---------------------- (1)
4x + 5y = 6000 ---------------------- (2)
Solving equations (1) and (2) simultaneously:x = 600y = 800
Therefore, the cost of a computer is £600 and the cost of a printer is £800..
:Therefore, the cost of one computer is £600 and the cost of one printer is £800.
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the qualified applicant pool for four management trainee positions consists of nine women and seven men. (a) how many different groups of applicants can be selected for the positions? (b) how many different groups of trainees would consist entirely of women? (c) probability extension: if the applicants are equally qualified and the trainee positions are selected by drawing the names at random so that all groups of four are equally likely, what is the probability that the trainee class will consist entirely of women? (round your answer to four decimal places.)
Answers
There are 1820 different groups of applicants for 4 management trainee positions, 126 different groups of trainees consisting entirely of women, and a 0.0692 probability that the trainee class will consist entirely of women.
The number of different groups of applicants that can be selected for the four management trainee positions can be calculated using the combination formula:
nCr = n! / (r! * (n-r)!)
where n is the total number of applicants (16 in this case) and r is the number of positions to be filled (4 in this case).
So the number of different groups of applicants that can be selected is:
16C4 = 1820
Therefore, there are 1820 different groups of applicants that can be selected for the four management trainee positions.
The number of different groups of trainees that would consist entirely of women can be calculated using the combination formula again, but this time we are selecting all 4 positions from the 9 female applicants:
9C4 = 126
Therefore, there are 126 different groups of trainees that would consist entirely of women.
Assuming that all groups of four are equally likely to be selected, the probability that the trainee class will consist entirely of women can be calculated by dividing the number of different groups of trainees that consist entirely of women (126) by the total number of different groups of applicants (1820):
Probability = 126 / 1820 = 0.0692
So the probability that the trainee class will consist entirely of women is 0.0692 (rounded to four decimal places).
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Suppose y varies inversely with x, and y = 49 when x = 17
. What is the value of x when y = 7 ?
Answers
Answer:
119 is the value of x when y = 7
Step-by-step explanation:
Since y varies inversely with x, we can use the following equation to model this:
y = k/x, where
k is the constant of proportionality.Step 1: Find k by plugging in values:
Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality. We can find k by plugging in 49 for y and 17 for x:
Plugging in the values in the inverse variation equation gives us:
49 = k/17
Solve for k by multiplying both sides by 17:
(49 = k / 17) * 17
833 = k
Thus, the constant of proportionality (k) is 833.
Step 2: Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:
Plugging in the values in the inverse variation gives us:
7 = 833/x
Multiplying both sides by x gives us:
(7 = 833/x) * x
7x = 833
Dividing both sides by 7 gives us:
(7x = 833) / 7
x = 119
Thus, 119 is the value of x when y = 7.
A company's flexible budget for 42000 units of production showed variable overhead costs of $50,400 and fixed overhead costs of $58000. THe company incurred overhead costs of $97660 while operating at a volume of 34000 units. What is the controllable cost variance
Answers
the controllable cost variance is $9,400.
To calculate the controllable cost variance, we need to compare the actual variable overhead costs with the flexible budgeted variable overhead costs based on the actual production level.
The flexible budgeted variable overhead cost per unit is:
$50,400 ÷ 42,000 = $1.20 per unit
The flexible budgeted variable overhead cost for 34,000 units is:
$1.20 × 34,000 = $40,800
The difference between the actual variable overhead costs and the flexible budgeted variable overhead costs is:
$50,200 - $40,800 = $9,400
what is variable?
In mathematics, a variable is a symbol or letter that represents a value or quantity in a mathematical expression or equation. Variables can take on different values or quantities, which can be manipulated and solved for using mathematical operations. In algebra, variables are often used to represent unknown values that need to be solved for, while in calculus, variables can represent rates of change or infinitesimally small quantities.
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The following product can be expanded into a power series with coefficients ak:
expression is given in attach file.
Find the coefficients ak in front of the individual xk terms for all k 2 N
Answers
Using coefficients ak, the following product may be extended into a power series: the expression is provided in the attached file. For each of the \(k 2 N\)phrases, determine the coefficients ak before them. The formula \(ak = (-1)k(k+1)/2\) yields the coefficients ak.
To get the coefficients ak, we may first simplify the above formula by factoring out a -x and rearranging terms. This results in the equation: \((1-x)/(1+x)2 = -x/(1+x) - x2/(1+x)2.\)
Now, each term in the statement may be expanded into a power series using the formula for the geometric series. This results in: Both\(-x/(1+x) and -x2/(1+x)2\) are equal to\(-x + x + x + 2 + x + 3 +...\)
By combining like terms and adding these two power series, we can determine that the coefficient in front of \(xk is (-1)k(k+1)/2.\) Hence,\(ak = (-1)k(k+1)/2\) is the formula for the coefficients ak.
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Perform the indicated operations. Write the answer in standard form, a+bi.
-4+4i / -3-6i
Answers
Answer:
\( \frac{ - 4 + 4i}{ - 3 - 6i} \\ multiply \: and \: divide \: by \: - 3 + 6i \\ \frac{ - 4 + 4i}{ - 3 - 6i} \times \frac{ - 3 + 6i}{ - 3 + 6i} \\ = \frac{ ( - 4 + 4i)( - 3 + 6i)}{ ( - 3 - 6i)( - 3 + 6i)} \\ = \frac{12 - 24i - 12i + 24 {i}^{2} }{ {( - 3)}^{2} - {(6i)}^{2} } \\ = \frac{12 - 24 - 36i}{9 + 36} \\ = \frac{ - 12 - 36i}{45} \\ \frac{ - 36i}{45} + \frac{ - 12}{45} \\ thank \: you\)
Line m passes through point (5, 8) and has a slope 3/5. What is the equation for the line
Answers
The equation for the line is y = 3/5x + 5.
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
y = mx + b
8 = 3/5(5) + b
8 = 15/5 + b
b = 5
∴ equation is y = 3/5x + 5
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Cal Italy the percentage increase of the units that went from 200units per week to 260 units per week
Answers
Answer:
Percentage increase = 30%
Step-by-step explanation:
Given:
Current units = 200 units
New unit = 260 units
Find:
Percentage increase
Computation:
Percentage increase = [(New unit-Current units)/Current units]100
Percentage increase = [(260 - 200)/200]100
Percentage increase = 30%
eddie clauer sells a wide variety of outdoor equipment and clothing. the company sells both through mail order and via the internet. random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. a random sample of 19 sales receipts for mail-order sales results in a mean sale amount of $92.80 with a standard deviation of $24.75 . a random sample of 11 sales receipts for internet sales results in a mean sale amount of $74.70 with a standard deviation of $26.75 . using this data, find the 95% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. assume that the population variances are not equal and that the two populations are normally distributed. step 1 of 3 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
Answers
Rounding to three decimal places, the critical value is ±2.109.
The critical value for a 95% confidence interval, we need to look up the t-distribution with degrees of freedom given by:
df = [(s1²/n1 + s2²/n2)²] / [((s1²/n1)²/(n1-1)) + ((s2²/n2)²/(n2-1))]
s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes.
Plugging in the values given in the problem:
df = [((24.75)²/19 + (26.75)²/11)²] / [(((24.75)²/19)²/18) + (((26.75)²/11)²/10)]
≈ 17.517
Using a t-distribution table or a calculator, we can find the critical value for a 95% confidence interval with 17 degrees of freedom:
\(t_c\) = ±2.109We must get the crucial value for a 95% confidence interval using the degrees of freedom provided by the following t-distribution:
(S12/n1 + S22/n2)2 = df ((s22/n2)2/(n2-1)) + ((s12/n1)2/(n1-1))))
The sample standard deviations are s1 and s2, and the sample sizes are n1 and n2.
Inserting the values from the problem:
df = [((24.75)²/19 + (26.75)²/11)²] / [(((24.75)²/19)²/18) + (((26.75)²/11)²/10)]
≈ 17.517
We may get the crucial value for a 95% confidence interval with 17 degrees of freedom using a t-distribution table or a calculator:
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Two angles form a linear pair. The measure of one angle is
4 times the measure of the other angle. Find the measure of each angle.
Answers
Answer:
One angle is 144° and the other is 36°Step-by-step explanation:
Two angles of a linear pair create a straight angle therefore they add to 180°
x° - the other angle
(4x)° - one angle
x + 4x = 180
5x = 180
÷5 ÷5
x = 36
4x = 4•36 = 144
Checking: 36+144 = 180
How to solve linear equation
Answers
You can use elimination and substitution method
EXAMPLE :
Given :
2x + y = 5
3x - 5y = 1
2x + y = 5 (× -5)
3x - 5y = 1
__________
-10x - 5y = - 25
3x - 5y = 1
____________ _ (elimination)
-13x = - 26
x = - 26/-13
x = 2
Substitution x = 2 to 2x + y = 5 :
2x + y = 5
2(2) + y = 5
4 + y = 5
y = 5 - 4
y = 1
A pool was being emptied at a rate of 5 gallons per hour. The equation
Y - 60-5(x - 5) models the amount of water remaining, where s is
time (in hours) and y is the amount of water left (in gallons), Write the
corresponding equation in slope-intercept form
Answers
Answer: -5x-35
Step-by-step explanation:
Edgar records the time that it takes his school bus to take him from the bus stop to school each day. this is a ___________ random variable.
Answers
Since it involves decimal values, this is a continuous random variable.
What are continuous and discrete variables?Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, …In this problem, the time assumes decimal values, hence it is a continuous random variable.
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PLease Help Will Mrk Brainliest
Answers
Answer:
x=81°
Step-by-step explanation:
The sum of all angles in a triangle is 180°
57+42=99
180-99=81
Jorge compro en la papeleria 3 Borradores y 2 lápices, por ellos pago $47.50. si la suma de lo que cuesta un borrador y un lápizes $20 ¿cuanto vale cada borrador y cada lápiz?
Por favor es urgente
Answers
Answer:
Cost of each pencil = $12.5
Cost of each eraser = $7.5
Step-by-step explanation:
Given:
Number of eraser bought = 3
Number of pencil bought = 2
Total amount paid = $47.50
Cost of one pencil and one eraser = $20
Find:
Each cost
Computation:
Let;
Cost of each eraser = e
Cost of each pencil = p
So,
e + p = 20
e = 20 - p .................................... eq1
3e + 2p = 47.50
3(20 - p) + 2p = 47.50
60 - 3p + 2p = 47.50
-p = -12.5
Cost of each pencil = $12.5
e = 20 - p
e = 20 - 12.5
e = 7.5
Cost of each eraser = $7.5
Jada's cat weighs 3.45 kg. Andre's cat weighs 1.2 kg more than Jada's cat.
Which equation represents this situation where x is the weight of Andre's cat? [Select]
x = 3.45 - 1.2
x = 3.45 + 1.2
x + 3.45 = 1.2
x + 1.2 = 3.45
How much does Andre's cat weigh? [Select] kg
3.25
4.65
1.2
3.45
Answers
Andre's cat weighs 4.65 kg. This is because we are told that Andre's cat weighs 1.2 kg more than Jada's cat, which weighs 3.45 kg. To find the weight of Andre's cat, we simply add 1.2 kg to Jada's cat's weight.
We know that, Jada's cat weighs 3.45 kg and Andre's cat weighs 1.2 kg more than Jada's cat.
So, the weight of Andre's cat can be represented by:
x = 3.45 + 1.2
Simplifying, we get:
x = 4.65
Therefore, Andre's cat weighs 4.65 kg.
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Help me plzzzzzzz need and answer as fast as you can plzz
Answers
Answer:
9
Step-by-step explanation:
count the places (vote me brainiest)
Select the property that allows the statement 3 = x to be written x = 3.
Answers
The property that allows the statement, 3 = x, to be written as x = 3, is: symmetric property of equality.
What is The Symmetric Property of Equality?The symmetric property of equality states that for any real numbers, for example, a and b, if a = b, then, b = a. This means that, if the value of a equals b, then symmetrically, the value of b will also be equal to the value of a.
Thus, given the statement that, 3 = x, based on the symmetric property of equality, we can also state that the value of x, also equals 3. Mathematically, we can state that x = 3.
therefore, the property that allows the statement, 3 = x, to be written as x = 3, is: symmetric property of equality.
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3^-1____ 1/4
A. =
B. <
C. >
Answers
Answer:
>
Step-by-step explanation:
\(3^{-1} = \frac{1}{3}\)
\(\frac{1}{3} > \frac{1}{4}\)