Since the probability is less than equal to 0.8907, then the value of x is 0.9750.
Given, the random variable is from of a normal distribution with
μ = 4 and σ = 1.37
.where, μ is the mean value and σ is the standard deviation.
According to the Question:
P(X≤8.907) = P( X−μ/σ ≤ 0.8907 - 4.00/ 1.37)
= P ( Z ≤ -29196.43)
Using Z-table we get a value of x which is 0.9750
So,
P(X ≤ 0.8907) = 97.50%
According to the calculations, the required value of x is 97.50%.
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55 is 40% of what number?
Answer:
55 is 40% of 137.5.
Step-by-step explanation:
To find the number that 55 is 40% of, you can divide 55 by 40% to get 137.5. This means that 55 is 40% of 137.5.
Solve for y in this diagram. Justify your answer.
The value of y in the isosceles triangle is AC = 6 cm
What Is an Isosceles Triangle?
A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
The three types of Isosceles Triangles are :
Isosceles acute triangle
Isosceles right triangle
Isosceles obtuse triangle
Given data ,
Let the triangle be represented as ABC
Now , the angle ∠ABC = 25°
The angle ∠ACB = 25°
So , the 2 angles of a triangle is 25° so , the third angle is 130°
So , the triangle is an isosceles triangle
And , the two sides of the triangle is AB = AC
The measure of side AB = 6 cm
The measure of side AC = measure of side AB
Therefore , the measure of side AC = 6cm
Therefore , the value of AC is 6 cm
Hence , the measure of side AC of triangle is 6 cm
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John can ride his bicycle at a rate of 14 miles per hour. Convert this rate to
feet per second.
O 20.53 feet per second
O 25.03 feet per second
O205.33 feet per second
O250.33 feet per second
correct answer is a) 20.53 feet per second
John can ride his bicycle at a rate of 20.53 feet per second.
How do I calculate feet per second?
Multiplying your foot-per-minute speed by 60. This is how many seconds there are in a minute. Your speed in feet per second is the outcome. For instance, 88 feet per second is equal to 5,280 feet per minute divided by the 60 seconds in a minute.
How long is a second in feet?
One-degree of longitude equals 288,200 feet (54.6 miles), one minute equals 4,800 feet (0.91 mile), and one second equals 80 feet.
Is feet per second velocity?
A unit of velocity and speed (scalar) is the foot per second (plural feet per second) (vector quantity, which includes direction). It represents the traveled or displaced distance in feet (ft) divided by the time (in seconds) (s).
[tex]\frac{14 miles}{1 h}[/tex] × [tex]\frac{5280 ft}{1 mile}[/tex]= [tex]\frac{73920 ft}{1 hr}[/tex]
[tex]\frac{73920 ft}{1 hr}[/tex] × [tex]\frac{1 hr}{60 min}[/tex]= [tex]\frac{1232 ft}{1 min}[/tex] ×[tex]\frac{1 min}{60s}[/tex]= [tex]\frac{20.53ft}{1s}[/tex]
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Mayerlin has two summer jobs. During the week she works in the grocery store, and on the weekend she works at a nursery. She gets paid $20 per hour to work at the grocery store and $19 per hour to work at the nursery. How many total hours does she work if she does 11 hours at the grocery store and 10 hours at the nursery? How many total hours does she work if she does g hours at the grocery store and n hours at the nursery?
The total number of hours Mayerlin worked is 21 and (g + n) respectively.
What is addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. When two whole numbers are added, the sum or total of those values is obtained.
Given that, Mayerlin gets paid $20 per hour to work at the grocery store and $19 per hour to work at the nursery.
Since Mayerlin works 11 hours at the grocery store and 10 hours at the nursery, the total number of hours she worked is:
11 + 10
= 21
Now, if, Mayerline works g hours at the grocery store and n hours at the nursery, the total number of hours she worked is:
g + n
Hence, the total number of hours Mayerlin worked is 21 and (g + n) respectively.
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according to a jhu study published in the american journal of public health, widows live longer than widowers. consider the following survival data collected on 100 widows and 100 widowers following the death of spouse: years lived widow widower less than 5 25 39 5 to 10 42 40 more than 10 33 21 can we conclude at 0.05 level of significance that the proportions of widows and widowers are equal with respect to the different time periods that a spouse survives after the death of his or her mate?
To determine whether the proportions of widows and widowers living different lengths of time after the death of their spouse are equal, you can conduct a chi-squared test of independence. This test compares the observed frequencies (the number of widows and widowers living different lengths of time) to the expected frequencies, which are the frequencies that you would expect to see if the two variables (widowhood and length of time survived) were independent.
To perform the chi-squared test, you will need to calculate the chi-squared statistic and the corresponding p-value. If the p-value is less than 0.05, you can conclude that there is a significant difference between the proportions of widows and widowers living different lengths of time after the death of their spouse. If the p-value is greater than 0.05, you cannot conclude that there is a significant difference between the proportions of widows and widowers.
To calculate the chi-squared statistic and p-value, you will need to follow these steps:
Calculate the expected frequencies for each group (widows and widowers) in each time period (less than 5 years, 5-10 years, more than 10 years). To do this, you will need to multiply the total number of widows (100) by the proportion of widows in each time period, and the total number of widowers (100) by the proportion of widowers in each time period.
Subtract the expected frequencies from the observed frequencies and square the result for each time period.
Divide each squared difference by the expected frequency and sum the results. This is the chi-squared statistic.
To calculate the p-value, you will need to consult a chi-squared table or use a statistical software program to determine the p-value corresponding to the chi-squared statistic and the degrees of freedom (which is equal to the number of time periods minus 1).
If the p-value is less than 0.05, you can conclude that there is a significant difference between the proportions of widows and widowers living different lengths of time after the death of their spouse. If the p-value is greater than 0.05, you cannot conclude that there is a significant difference between the proportions of widows and widowers
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22. Is the following ordered pair (-2, 9) a solution of the linear inequality y ≥ 7x+3
Answer:
x=-3/7
Step-by-step explanation:
Apples cost $1.47 per pound. Danielle buys an apple that weighs 0.62 pound. To the nearest cent, how much does Danielle's apple cost?
Answer:
x = 0.91
Step-by-step explanation:
x = 1.47 x 0.62
x = 0.9114
round x = 0.9114 to the required place
x = 0.91
a dark eyed man marries a dark eyed woman, but they have a blue eyed child. what is the probability that their second child will have blue eyes?
The probability that their second child will have blue eyes is 1/4.
Here dark eye is dominant trait and blue eyes is recessive trait.
So both man and woman is heterozygous dominant and the blue eye child is homozygous recessive.
Man and woman will produce four types of genotypes in children. One homozygous dominant (dark eye), one homozygous recessive (blue eye) and two heterozygous dominant (dark eye).
So the probability of any child to be blue eyed (homozygous recessive) will be 1/4.
Hence we get the required answer.
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Here is the graph for one equation in a system of equations:
a) Write a second equation for the system so it has infinitely many solutions.
b) Write a second equation whose graph goes through (0, 1) so the system so it has no
solutions.
The answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.What is the general form of a straight line? What is a mathematical function, equation and expression?straight line equation : The general equation of a straight line equation is given byy = mx + c
where -
[m] : slope of line
[c] : y - intercept
Given is the graph of a straight line as shown.
[A] - A second equation for the system so it has infinitely many solutions can be the one that overlaps the line given. So the second equation can be written as follows. The points are -
(0, 4) and (4, 1)
Let the line be -
y = mx + c
m = (1 - 4)/(4 - 0) = -3/4
m = -3/4
So, the equation will be -
y = (-3/4)x + 4
[B] -
For no solution, the line will be parallel to the given line. The equation of the line is → y = (-3/4)x + 4. The equation whose graph goes through (0, 1) so the system has no solutions as : y = (-3/4)x + 1.
Therefore, the answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.To solve more questions on functions, expressions and polynomials, visit the link below -
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The college graduate is hired at a law firm with a $10,000 signing bonus, that will be deposited into the savings account. The firm also agrees to immediately pay off
$25,000 in student loan debt. What is the college graduate's new net worth?
O$16,081
O $21,167
O$13,833
O $33,097
The college graduate's new net worth is given as follows:
$13,833.
How to calculate the net worth?The net worth of a company or of a person is given by the sum of the values of all assets of the person subtracted by the sum of the values of all debts of the person.
The assets if the student are given as follows:
Signing bonus: $10,000.Furniture: $14,278.Savings Account Balance: $4,337.Car Value: $14,950.Computer and Software: $11,774.The liabilities of the student are given as follows:
Car Loan: $3,250.Credit Card Balances: $5,129.Student Loans: $58,097 - $25,000 = $33,097.Thus the student's net worth is calculated as follows:
(10000 + 14278 + 4337 + 14950 + 11774) - (3250 + 5129 + 33097) = $13,863.
Which is closest to the third option among those given.
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Answer:
the correct answer is 12057
Step-by-step explanation:
in order to calculate net worth, add up the assets, and then subtract the debt. be sure to pay attention to details
heres an UNRELATED TO THE QUESTION example:
i have...
$500 in my savings
$20 in my wallet
but im $200 deep in credit card debt..
(add 500 + 20, then subtract 200)
net worth: 320
Which of the following equations has a solution different from the rest? (1 point)
¾ x+5=− ¼
½ x−3= ½
−1/7 x−34=¼
−0.35x−0.52=1.93
Answer: (-1/7)x - 34 = 1/4
Step-by-step explanation: The solution for all other equations is 7 and for the 3rd equation, the solution is 239.75 or 959/4
1) 3/4 X +5=-1/4
x=-7
2) 1/2X - 3 = 1/2
x=7
3) x = -137×7 /4
4) x= -7
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write a logarithmic equation (using only real numbers) that has no real solutions. explain why there are no real solutions.
The equation is log_2 (3x - 5) = 9 There are no real solutions to this equation because the logarithm of a negative number is undefined. The left side of the equation would require the argument to be negative, thus making the equation impossible to solve.
This equation cannot be solved because the logarithm of a negative number is undefined. The left side of the equation is of the form log_2 (N), where N is some real number.For the equation to have any real solutions, N needs to be greater than 0. However, in this equation, N is equal to 3x - 5, which can be negative for certain values of x. This means that there is no real number x that can be substituted into the equation to make it true, since the logarithm of a negative number is not defined. Therefore, this equation has no real solutions.
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Which shows the expression below in simplified form?
(6.3 × 1011) ÷ (7 × 105)
A.
9 × 105
B.
-0.7 × 105
C.
9 × 104
D.
9 × 107
Answer: It's D.
Step-by-step explanation: When you simplify you get the answer D.
Answer:
0.9 x 10^6
Step-by-step explanation:
6.3 divided by 7 is 0.9
10^11 ÷ by 10^5 is 10^6
1 point
Over one week, a snack booth at a fair sold 362 cans of soft drinks for $1.75 each and
221 hot dogs for $2.35 each. Which calculation will give the closest estimate of the sales
of soft drinks and hot dogs?
The calculation that will give the closest estimate of the sales of soft drinks and hot dogs is 360 * 2 + 220 * 2
How to determine the calculation that will give the closest estimateFrom the question, we have the following parameters that can be used in our computation:
Time = one week
Number of cans = 362
Unit price of soft drink = $1.75
Number of hot dogs = 221
Unit price of hot dogs = $2.35
The calculation that will give the closest estimate is represented as
Estimate = Number of cans * Unit price of soft drink + Number of hot dogs * Unit price of hot dogs
Substitute the known values in the above equation, so, we have the following representation
Estimate = 362 * 1.75 + 221 *2.35
Approximate
Estimate = 360 * 2 + 220 * 2
Hence, the expression is 360 * 2 + 220 * 2
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In a group of 500 people determine how many are suspects in the following scenario.
A wallet was stolen from an office in a building with 500 employees. The suspect was wearing black pants, a white button-down shirt, and a multicolored tie. In one of the offices in the building, the following data was collected.
30 people total in the office
22 wearing a white button down shirts
16 wearing black pants
7 wearing a multicolored tie
Using the data, how many suspects are there?
Using the given data, the number of suspects is; 7
How to find the intersection of mathematical sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.
However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.
Now, we are told that;
Total number of people in the office = 30 people
Number of people wearing a white button down shirts = 22
Number of people wearing black pants = 16
Number of people wearing a multicolored tie = 7
Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;
The number of suspects = A ∩ B ∩ C = 7 people
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Which ordered pair is a solution to the equation y = –23x + 9?
A (−32,10)
B (0,10)
C (−1,1023)
D (23,10)
Answer: None of these
Step-by-step explanation:
A. If [tex]x=-32[/tex], then [tex]y=745[/tex], not [tex]10[/tex].
B. If [tex]x=0[/tex], then [tex]y=9[/tex], not [tex]10[/tex].
C. If [tex]x=-1[/tex], then [tex]y=32[/tex], not [tex]1023[/tex].
D. If [tex]x=23[/tex], then [tex]y=-520[/tex], not [tex]10[/tex].
what is the probability of having x failures in the next 100 mowers tested for x from 0 to 20 mower test
The ratio of the number of mowers that fail to the overall number of mowers is known as the fraction of mowers that fail the functional performance test. Consequently, 9/500 lawnmowers fail, then the probability of having x failures in the next 100 mowers is = [tex]0.018x[/tex]
Probability of having x mower fail = 0.018x
Number of mowers that fail = 54
Total number of mowers = 3000
The probability of failure can be defined as,
= [tex]\frac{Number of mowers that fail}{Total number of mowers}[/tex]
Fraction that failed = [tex]\frac{54}{3000}[/tex]
Fraction that failed = [tex]\frac{9}{500}[/tex]
Fraction that failed = 0.018
Therefore,
The ratio of the number of mowers that fail to the overall number of mowers is known as the fraction of mowers that fail the functional performance test. Consequently, 9/500 lawnmowers fail, then the probability of having x failures in the next 100 mowers is = [tex]0.018x[/tex]
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3, 1.6, 2.8, 2.5, 1.7, 2.8
What is the mean absolute deviation of these numbers?
The mean absolute deviation of the given numbers is 0.5.
What is a mean?The mean is the sum of all values divided by the total number of values.
The mean of the given number is obtained by dividing the sum of the values by its total number of value.
i.e. (1.6+1.7+2.5+2.8+2.8+3)/6 = 2.4
Then taking the difference of each number from the mean.
i.e. (1.6-2.4), (1.7-2.4),(2.5-2.4),(2.8-2.4),(2.8-2.4),(3-2.4)
i.e. -0.8,-0.7,0.1,0.4,0.4,0.6
Take the sum of the absolute value of the above numbers
i.e. |-0.8+-0.7+0.1+0.4+0.4+0.6| = 3
Divide 3 by 6 to obtain mean absolute deviation.
i.e 3/6 = 1/2 =0.5
Hence, 0.5 is the mean absolute deviation of the given numbers.
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Davina charges $15 an hour to weed gardens. What does she charge to weed a garden for 1, 2, 3, and 4 hours?
Answer:
1 - $15
2- $30
3 - $45
4 - $60
Step-by-step explanation:
$15/hour
1 - $15 =1*15
2- $30 =2*15
3 - $45 =3*15
4 - $60=4*15
A car traveled at an average speed of 60 mph for two hours. how far did it travel? responses 30 miles 30 miles 60 miles 60 miles 120 miles 120 miles 150 miles
Answer: 120 miles
Step-by-step explanation:
If a car goes 60 miles per hour then in two hours (60×2) it will go 120
how much less is the value including 13% VAT in Rs.3200 than Rs.3820
The less value including 13% VAT in Rs. 3200 than Rs. 3820 is 340 rupees.
What is a percentage?A percentage is a ratio or number that may be expressed as a fraction of 100. Additionally, it is denoted by the sign "%."
Here, we have VAT.
A flat charge called value-added tax (VAT) is imposed on a purchase. It resembles a sales tax in some ways, with the exception that with a sales tax, the consumer pays the entire amount due to the government at the moment of sale. With a VAT, several participants to a transaction each pay a piece of the tax amount.
Value on Rs. 3200 with 13% VAT
= 3200 + 30% of 3200
= 3200 + 960
= 4160 rupees
Now, the less value,
= 4160 - 3820
= 340 rupees.
Therefore, the less value is 340 rupees.
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How many leave were longer then 7 centimeters
Answer:
You could pick as many as you like. Ideally you would use all the leaves on the tree, but that would be rather a large number to measure, and your parents might not be very happy if you stripped the tree bare!So let's try 100 leaves.How to get a random sample?Here is one way you could get a random sample:Try taking all the leaves on one branch of the tree. After you've discarded any that are broken, then see how many there are. If there are less than 100, then get the leaves from another branch until you have more than 100. Then write a different number (starting with 1) on each leaf with a marking pen.Write the same numbers on small pieces of paper.Fold the pieces of paper.Put them into a hat and mix them up.Draw 100 pieces of paper (without looking) from the hat. The first 100 pieces of paper you draw would give you the numbers of the leaves to use in the experiment.The next thing you need to decide is how to measure the leaves, andhow accurate your measurements should be:How to measure?Keeping your leaves flat, use a ruler to measure the length of each leaf from the pointy part at one end of the leaf to the point where the leaf joins the stalk at the other end. Maybe your leaves bend a bit, but don't follow the main rib of the leaf as this would make measurement too difficult.Just measure in a straight line as shown in the following diagram:leafHow accurate?You should measure the length of each leaf to the nearest millimeter.Now you're ready to begin.Measure the length of each leaf to the nearest millimeter and record you results in a table, as follows:
Step-by-step explanation:
What is transpose of matrix
Step-by-step explanation:
it is the process of changing rows to columb
7
10
1
2/5
Cedric has
3
of the pie
of the pie
of the pie
of the nie
4
of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
C
PR
The fraction of the pie left that each friend will receive is; 3/8 of the pie
How to divide fractions?Dividing two fractions is simply the same as multiplying the first fraction by the reciprocal of the second fraction.
The first step in trying to divide fractions is to find the reciprocal of the second fraction. The second step is to multiply the two numerators. Thereafter, multiply the two denominators.
For example, 3/8 divided by 3/4 would be;
3/8 divided by 3/4 = 3/8 * 4/3
Now, we are told that cedric has 3/4 of a pie left.
Now, he wants to share equally among two of his friends, it means that;
Quantity received by each friend = 3/4 ÷ 2 = 3/4 * 1/2 = 3/8
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Complete question is;
Cedric has 3/4 of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
What is the simplest form of (x^2+5x-6) / (x^2+9x+18)?
a) (x+2) / (x+6)
b) 1/3
c) (x-1) / (x+3)
d) -1/3
Answer:
a. [tex]\frac{x+2}{x+6}[/tex]
Step-by-step explanation:
[tex]\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}[/tex]
What is the approximate value of y − x? 4.9° 6.2° 11.1° 17.2°
Answer:
Step-by-step explanation:
11.1
The approximate value of y - x is 17.2°.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Given a right triangle LMN.
Using the tangent function,
tan (y) = 19.1 / 14.1
= 1.3546
y = tan⁻¹ (1.3546) = 53.56°
We know that,
x + y = 90°, since the other angle is 90°.
x = 90 - 53.56° = 36.44°
y - x = 53.56° - 36.44° = 17.12° ≈ 17.2°
Hence the value of y - x is 17.2°.
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Rewrite one eighteenthx3y + seven eighteenthsxy2 using a common factor.
one thirdxy(6x2 + 7y)
one thirdx2y(6x2 + 9y)
one eighteenthxy(x2 + 7y)
one eighteenthx3y2(y + 7)
Answer:
C
Step-by-step explanation:
1/18 x³y + 7/18 xy²
1/18 xy (x² + 7y)
The area of the caribbean sea is 2.7182 × 106 km2. the area of the south atlantic ocean is 4.027 × 107 km2. find the total area. write the final answer in scientific notation with the correct number of significant digits. 4.29882 × 108 km2 4.299 × 107 km2 3.75518 × 1013 km2 3.755 × 1013 km2
The total area of the Caribbean sea and the South Atlantic ocean is 4.299 × 10⁷ km². The correct option is the second option 4.299 × 10⁷ km²
Calculating total areaFrom the question, we are to determine the total area of the water bodies.
From the given information
"The area of the Caribbean sea is 2.7182 × 10⁶ km²"
and
"The area of the South Atlantic ocean is 4.027 × 10⁷ km²"
To determine the total area, we will add up the two areas
Total area = 2.7182 × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10¹ × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10⁷ km² + 4.027 × 10⁷ km²
Total area = 4.29882 × 10⁷ km²
Total area ≈ 4.299 × 10⁷ km²
Hence, the total area is 4.299 × 10⁷ km²
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Answer:
Hence, the total area is 4.299 × 10⁷ km²
Step-by-step explanation:
the average iq test scores of an srs of 31 seventh-grade girls in a midwest school district is 105.84. suppose that the standard deviation of iq scores in this population is known to be 15. iq scores in a broad population are supposed to have mean of 100. is there evidence that the mean in this district di ers from 100? use signi cance level
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
X = 89 represent the mean of seventh-grade girls in Midwest school district
s = 15 represent the standard deviation for the sample
n = 31 sample size
μ = 100 represent the value that we want to test
'a' represent the significance level for the hypothesis test.
't' would represent the statistic (variable of interest)
[tex]p_{v}[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses,
We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:
Null hypothesis: μ = 100
Alternative hypothesis: μ ≠ 100
We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
t = (X-μ) / ([tex]\frac{s}{\sqrt{n} }[/tex] ) (Equation-1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
t = [tex]\frac{89-100}{\frac{15}{\sqrt{31} } }[/tex]
t = -4.08
Calculate the P-value
First we need to calculate the degrees of freedom given by:
[tex]df = n-1[/tex]
[tex]df = 31 -1[/tex]
[tex]df = 30[/tex]
Since is a two tailed test the p value would be:
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 )
[tex]p_{v}[/tex] = 0.00031
Therefore,
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
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7. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the
rocket's height after 3 seconds?
h(t) = -5t² +42t + 54
The rocket's height after 3 seconds is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
[tex]xvertex = -b / 2a[/tex]
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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