The path of a submarine can be modeled by d=0.012t-5.29t where d is the depth the submarine reaches and t is the number of hours the submarine is submerged
a. find the vertex. Then explain the relevance of this point in the context of this problem. Round to the nearest tenth
b. Find the number of hours the submarine was submerged. round to the nearest tenths.
HELP THIS IS DUE TOMMOROW :((
ALGEBRA 2 (Quadratic equations and functions)
Answers
a) The vertex of the problem is given as follows: (220, -583), meaning that the minimum depth reached by the vertex is of 583 after 220 hours.
b) The submarine was submerged for 440.1 hours.
What is the quadratic function?The quadratic function in this problem is defined as follows:
d(t) = 0.012t² - 5.29t.
Which gives the depth of the submarine after t hours.
The coefficients of the equation are given as follows:
a = 0.012, b = -5.29.
Then the t-coordinate of the vertex is given as follows:
t = -b/2a = 5.29/(2(0.012)) = 220.
The minimum depth is then of:
d(220) = 0.012(220)² - 5.29(220) = -583.
This is a concave up parabola, which is the reason why the vertex is a minimum.
The roots of the function are given as follows:
0.012t² - 5.29t = 0
t(0.012t - 5.29) = 0.
Hence:
t = 00.012t - 5.29 = 0 -> t = 5.29/0.012 -> t = 440.1.Meaning that the submarine was submerged for 440.1 hours.
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Related Questions
Melvin paid an entrance fee of Rs 5 plus an additional Rs 1.25 per game at a local arcade. Altogether, he spent Rs 26.25. Write and solve an equation to determine how many games Melvin played.
Answers
Step-by-step explanation:
x = number of games played
c = total cost of game session
x = (c - 5)/1.25
we need to deduct the R 5 entrance fee from the total price (as this has to be paid, even if he did not pay a single game in there).
and for the remaining amount we check how often the price of 1 game fits into this renaming amount. and then we know the number of games he played.
in our specific situation c = 26.25
x = (26.25 - 5)/1.25 = 21.25/1.25 = 17
Melvin played 17 games.
Do u know this? Answer if u do
Answers
Answer:
Hi
Step-by-step explanation:
The expression was reduced to it's lowest expression or term or we say we found the common factor amongst them
Algunos estudiantes se repartieron una bolsa de galletas. Todos tomaron la misma cantidad y sobraron 5
Answers
How many solutions does this linear system have?
Y= -1/2x + 4 x + 2y=-8
Answers
Answer:
No solutions
Step-by-step explanation:
\(y=-\dfrac{1}{2}x+4 \\\\x+2y=-8\)
Substitute:
\(x+2(-\dfrac{1}{2}x+4)=-8\\\\x-x+8=-8\\\\8=-8\)
This system has no solutions.
Hope this helps!
The heights, in inches, of the 11 basketball players on a
team are shown on this stem-and-leaf plot.
Team Heights
5 3
6 99
7 3 5 6 7 8 9
8 04
Key
412 = 42 inches
Which height, in inches, is an outlier for this data?
Select one:
Answers
for height. inches. of the 11 basket
Answer:
i think is 6 99 hope this helps you
determine whether the planes are parallel, perpendicular, or neither. 15x − 3y 12z = 2, 2y = 10x 8z
Answers
The given equations of planes are: 15x - 3y + 12z = 2 & 2y = 10x - 8z
To determine whether these planes are parallel, perpendicular or neither, we need to compare the normal vectors of the planes. The normal vector of a plane is given by the coefficients of x, y and z in the equation of the plane.
The normal vector of the first plane (1) is [15, -3, 12] and the normal vector of the second plane (2) is [10, 2, -8/2] = [10, 2, -4].
Now, to check if the planes are parallel or perpendicular, we can take the dot product of the normal vectors. If the dot product is 0, then the planes are perpendicular, and if it is non-zero, then the planes are parallel.
The dot product of the normal vectors of the given planes is:
[15, -3, 12] · [10, 2, -4] = (15)(10) + (-3)(2) + (12)(-4) = 0
Since the dot product is zero, the planes are perpendicular to each other.
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Use vertical angles to find the value of x. Use pencil and paper. Is it possible to find the value of x without using vertical angles? Explain your reasoning.
Answers
Answer:
40=(x/6)
40×6=240
x=240?
The value of x is 204 degree.
What is vertical opposite angle?The point where they meet is called a vertex. When two lines intersect, the opposite (X) angles are equal.
As line UM and FQ is intersecting at point x.
Using Vertical opposite angle,
x/6= 40
x=40*6
x=240
Hence, the vertically opposite angle is 240.
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employees in a large company are entitled to 15-minute coffee breaks. a random sample of the duration of coffee breaks for 10 employees was taken with the times shown below. assuming that the times are normally distributed, is there enough evidence at the 1% significance level to indicate that on average employees are taking longer coffee breaks than they are entitled to? the null hypothesis is?
Answers
There is enough evidence to indicate that on average employees are taking longer coffee breaks than they are entitled to.
What is the null hypothesis?
The null hypothesis is the assertion that there is no association between the two sets of data or variables being investigated in a scientific study. The term "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal relationship exists.
Here, we have
Given: Employees in a large company are entitled to 15-minute coffee breaks. a random sample of the duration of coffee breaks for 10 employees was taken with the times.
The sample mean = x = ΣX/n = 16.8000
The population mean = µ = 15
The alpha error = 0.01
The confidence coefficient = 99%
Sample Size = n = 10
Sample Variance = 3.0667
The alternative hypothesis is µ > 15
The calculated test statistics (four decimals)
t-test statistic = (16.8-15)/0.5538 = 3.2504
Hence, there is enough evidence to indicate that on average employees are taking longer coffee breaks than they are entitled to.
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A particle moves along the x-axis in such a way that its position at time t for t > 0 is given by x (t) = 1/3t^3 -3t^2 + 8t. Show that at time t - 0 the particle is moving to the right Find all values of t for which the particle is moving to the left What is the position of the particle at time t = 3? When t = 3, what is the total distance the particle has traveled?
Answers
The total distance the particle has traveled up to time t=3 is 4/3 units.
To determine whether the particle is moving to the right or left at time t=0, we can find the velocity of the particle at that time by taking the derivative of x(t) with respect to t:
x'(t) = t^2 - 6t + 8
Substituting t=0, we get:
x'(0) = 0^2 - 6(0) + 8 = 8
Since the velocity is positive at t=0, the particle is moving to the right.To find the values of t for which the particle is moving to the left, we need to find when the velocity is negative:
t^2 - 6t + 8 < 0
Solving for t using the quadratic formula, we get:
t < 2 or t > 4
Therefore, the particle is moving to the left when t is between 0 and 2, and when t is greater than 4.To find the position of the particle at time t=3, we can simply substitute t=3 into the original position equation:
x(3) = (1/3)(3^3) - 3(3^2) + 8(3) = 1
So the particle is at position x=1 when t=3.To find the total distance the particle has traveled up to time t=3, we need to integrate the absolute value of the velocity function from 0 to 3:
∫|t^2 - 6t + 8| dt from 0 to 3
This integral can be split into two parts, one from 0 to 2 and one from 2 to 3, where the integrand changes sign. Then we can integrate each part separately:
∫(6t - t^2 + 8) dt from 0 to 2 - ∫(6t - t^2 + 8) dt from 2 to 3= [(3t^2 - t^3 + 8t) / 3] from 0 to 2 - [(3t^2 - t^3 + 8t) / 3] from 2 to 3= [(12/3) - (16/3)] - [(27/3) - (26/3) + (24/3) - (8/3)]= 2/3 + 2/3 = 4/3.
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At time t = 0, the velocity of the particle is given by the derivative of x(t) with respect to t evaluated at t = 0. Differentiating x(t) with respect to t, we get:
x'(t) = t^2 - 6t + 8
Evaluating x'(t) at t = 0, we get:
x'(0) = 0^2 - 6(0) + 8 = 8
Since the velocity is positive, the particle is moving to the right at time t = 0.
To find the values of t for which the particle is moving to the left, we need to find the values of t for which the velocity is negative. Solving the inequality x'(t) < 0, we get:
(t - 2)(t - 4) < 0
This inequality is satisfied when 2 < t < 4. Therefore, the particle is moving to the left when 2 < t < 4.
To find the position of the particle at time t = 3, we simply evaluate x(3):
x(3) = (1/3)3^3 - 3(3^2) + 8(3) = 1
When t = 3, the particle has traveled a total distance equal to the absolute value of the change in its position over the interval [0,3], which is:
|x(3) - x(0)| = |1 - 0| = 1
Supporting Answer:
To determine whether the particle is moving to the right or left at time t = 0, we need to find the velocity of the particle at that time. The velocity of the particle is given by the derivative of its position with respect to time. So, we differentiate x(t) with respect to t and evaluate the result at t = 0 to find the velocity at that time. If the velocity is positive, the particle is moving to the right, and if it is negative, the particle is moving to the left.
To find the values of t for which the particle is moving to the left, we need to solve the inequality x'(t) < 0, where x'(t) is the velocity of the particle. Since x'(t) is a quadratic function of t, we can factor it to find its roots, which are the values of t at which the velocity is zero. Then, we can test the sign of x'(t) in the intervals between the roots to find when the velocity is negative and hence, the particle is moving to the left.
To find the position of the particle at time t = 3, we simply evaluate x(t) at t = 3. This gives us the position of the particle at that time.
To find the total distance traveled by the particle when t = 3, we need to find the absolute value of the change in its position over the interval [0,3]. Since the particle is moving to the right at time t = 0, its position is increasing, so we subtract its initial position from its position at t = 3 to find the distance traveled. If the particle were moving to the left at time t = 0, we would add the initial position to the position at t = 3 instead.
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Antony borrowed 20,000,000 for 7 years his interest rate is 5% how much interest will he pay in all
Answers
Answer:
7,000,000
Step-by-step explanation:
\(Principal = 20,000,000\\Time =7\:years\\Rate = 5\%\\Simple\:interest =?\\\\Simple\:interest = \frac{Principal\times Rate\times Time}{100} \\\\S.I= \frac{20000000\times 5 \times 7}{100} \\\\S.I==\frac{700000000}{100}\\\\Simple\: interest=7000000\)
The solution is, he will pay 7000000 interest in all.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
Here, we have,
formula: I = Prt.
here, we have,
given that,
Antony borrowed 20,000,000 for 7 years his interest rate is 5%
i.e. we get,
P= 20,000,000
t = 7
r= 5%
and, we have to find I
so, we have,
I = P r t
=20,000,000*5*7/100
=7000000
Hence, he will pay 7000000 interest in all.
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what is the equation of the line?
Answers
Answer:
x=3
Step-by-step explanation:
the x axis is going across by 2 and the number in between 2 and 4 is 3 and the line is going through the x axis hence the equation of the line is x=3
Answer:
\(x=3\)
Step-by-step explanation:
Normally, linear equations would be written in slope-intercept form, \(y=mx+b\), where \(m\) is the slope and \(b\) is the y-intercept (the value of y when the line crosses the y-axis). However, linear equations for horizontal or vertical lines are organized differently.
Here, we're given a vertical line. Vertical lines are written like \(x=d\), where \(d\) is the x-intercept, or the value of x when the line crosses the x-axis.
From the graph, we can tell that the x-intercept is 3. Therefore, our equation would be \(x=3\).
I hope this helps!
One number is 16 more than another number. The two numbers have a sum of 120. Which system of equations could you use to find the two numbers?
A)y=x – 16
y=x + 120
B)y=x + 16
y = x + 120
C)y=x - 16
y=x – 120
D)y= x - 16
y = -x + 120
Answers
Answer: D)y= x - 16
y = -x + 120
Step-by-step explanation:
Let the two numbers be x and y
such that if one number is x , the other number y
Let x be the number which is 16 more than another number , so that it can be expressed as
x= y+16 which can also be written as
y= x - 16
Also, if the two numbers have a sum of 120, then it can be represented as
x+y=120 or
y = -x + 120
Therefore system of equations to find the two numbers are
D)y= x - 16
y = -x + 120
Carlo and his brother, agreed to buy a bicycle by sharing out the cost. The ratio of the amount of money paid by Carlo to that paid by his brother was 5: 2. The bicycle cost P3500. Find the amount paid by each of them.
Answers
Answer:
Carlo paid 2500 dollars and his brother paid 1000 dollars
Step-by-step explanation:
Given -
The ratio of cost shared by Carlo and his brother is 5:2
Which means Carlo paid 5/7th part of the total cost of bicycle
5/7 * 3500 = 2500 dollars
The amount paid by his brother is 3500 - 2500 = 1000 dollars
When parking a car in a downtown parking lot, drivers pay according to the number of hours or fraction thereof. the probability distribution of the number of hours cars are parked has been estimated as follows:
a. mean=
b. standard deviation=
the cost of parking is 5 dollars per hour. calculate the mean and standard deviation of the amount of revenue each car generates.
a. mean=
b. standard deviation
col1 x 1 2 3 4 5 6 7 8
col2 p(x) 0.229 0.113 0.114 0.076 0.052 0.027 0.031
0.358
Answers
1) a. mean = 4.164 b. standard deviation = 0.7792
2) a. mean = $20.82 b. standard deviation = $3.896
To calculate the mean of the number of hours, we multiply each possible value by its probability and then add them up,
Mean = (1)(0.229) + (2)(0.113) + (3)(0.114) + (4)(0.076) + (5)(0.052) + (6)(0.027) + (7)(0.031) + (8)(0.358) = 4.164
Therefore, the mean number of hours that cars are parked is approximately 4.164.
To calculate the standard deviation of the number of hours, we use the formula,
SD = sqrt[(1/n) * sum(p(x)*(x - mean)^2)]
where n is the sample size, p(x) is the probability of each possible value, mean is the mean of the distribution, and x is each possible value.
Plugging in the values,
SD = sqrt[(1/8) * ((1-4.164)^20.229 + (2-4.164)^20.113 + (3-4.164)^20.114 + (4-4.164)^20.076 + (5-4.164)^20.052 + (6-4.164)^20.027 + (7-4.164)^20.031 + (8-4.164)^20.358)]
SD = sqrt[(1/8) * (2.4212)]
SD = 0.7792
To calculate the mean and standard deviation of the revenue generated per car, we simply multiply the mean and standard deviation of the number of hours by the cost per hour:
Mean revenue per car = 4.164 * $5 = $20.82
Standard deviation of revenue per car = 0.7792 * $5 = $3.896
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The expression -370+13m represents a submarine that began at a depth of 370 feet below sea level and ascended at a rate of 13 feet per minute. What was the depth of the submarine after 9 minutes?
Answers
Answer:
Depth after 9 minutes is -253 feet
Step-by-step explanation:
Since we can find the submarine's depth as a function of time, m (in minutes), lets use the function to calculate the answer.
We are given the equation for depth: Depth(m) = -370+13m
Depth(x) means that the equation will tell us the submarine's depth after m minutes. The equation is missing the units, but we know from the statement that the initial depth is -370 feet and the rate of ascention is +13 feet/min. So we can enhance the equation by rewriting it with the units.
Depth(m) = -370ft+13(feet/minute)*m [m is minutes]
The sub's depth after 9 minutes is:
Depth(9) = -370ft+13(feet/minute)*(9 minutes)
Depth(9) = -370ft + 13*(9)
Depth(9) = -370+117
Depth(9) = -253 feet
Please help me I am really confused and need help with this.
Answers
Answer:
Step-by-step explanation:
y=10
Evaluate the expression when x=-3.
x^2+5x=-4
Answers
\((-3)^{2} + 5(-3) = - 4\\9 - 15 = - 4\\-6 \neq -4\)
This is not possible, as -6 is not equal to -4.
PLLKEEASE HELPPPPPPP ASAPP
Answers
Answer:
x = 19
Step-by-step explanation:
(5x + 4)° + (x - 2)° + (3x + 7)° = 180°
(5x + x + 3x)° + (4 - 2 + 7)° = 180°
9x° + 9° = 180° → ÷9
x + 1 = 20
x = 20 - 1
x = 19
-(-2)+(-2)2-4(1)(-3) 2. Simplify the expression 2(1) a. 1 c. 3 b. 2 d. 4
Answers
Answer:
2(1) is 2
Is this wht you were asking, or...
Put the following equation of a line into slope-intercept form, simplifying, all
fyachong
5x+6y=-24
Answers
Answer:
y=-5/6x-4
Step-by-step explanation:
Nick climbed a hill with an elevation of feet. Later that day, he returned home descending 700 feet. Jacob deposited his paycheck of $ . Later that week, he withdrew the same amount of $225 to buy a new TV. Janine was scuba diving and dove 25 feet to look at the fish on the coral reef. She then swam feet to the surface. The temperature started at -25 degrees. During the day, the temperature rose 5 degrees and then dropped 5 degrees. At the end of the day, the temperature was degrees.
Answers
Answer:
700, 225, 25, -25
Step-by-step explanation:
In the question given, we have to fill the blanks in the situations to describe an opposite quantities which combines to make zero.
1. Nick returned home descending 700 feet later at the day because he climbed a hill that was 700 feet high.
2. Jack deposited an amount of $225 in his account but later that week, he bought a new TV by withdrawing the amount of $225 from his account.
3. Janine dove into the sea to look at the coral reefs to a depth of 25 feet, and then she swam back to the sea surface by swimming 25 feet upwards.
4. The final temperature at the end of the day was -25 degrees, as the morning temperature was -25 degrees and then at daytime, it rose for 5 degrees and then again dropped by 5 degrees.
What is the solution for the system of equations {4x−3y=36x−2y=4?
Answers
Answer:
x = 1/25
y = 32/25
Step-by-step explanation:
a large mixing tank currently contains 100 gallons of water into which 5 pounds of sugar have been mixed . A tap will open pouring 10 gallons per minute of water into the tank at the same time sugar is poured into the tank at a rate of 1 pound per minute. Find the concentration ( pounds per gallon) of sugar in the tank after 12 minutes
Answers
After 12 minutes, the concentration of sugar in the tank is approximately 0.0773 pounds per gallon.
To find the concentration of sugar in the tank after 12 minutes, we need to consider the amount of sugar and water added during that time period.
The tank initially contains 100 gallons of water with 5 pounds of sugar mixed in. Over the course of 12 minutes, the tap pours in 10 gallons per minute of water and 1 pound per minute of sugar.
After 12 minutes, the total amount of water added is 10 gallons/minute * 12 minutes = 120 gallons. The total amount of sugar added is 1 pound/minute * 12 minutes = 12 pounds.
Therefore, the final volume of water in the tank is 100 gallons (initial) + 120 gallons (added) = 220 gallons.
To find the concentration of sugar in the tank after 12 minutes, we divide the total amount of sugar (5 pounds initial + 12 pounds added) by the final volume of water (220 gallons):
Concentration of sugar = (Total amount of sugar) / (Final volume of water)
= (5 pounds + 12 pounds) / 220 gallons
= 17 pounds / 220 gallons
Simplifying the expression, we get:
Concentration of sugar = 0.0773 pounds/gallon
Therefore, after 12 minutes, the concentration of sugar in the tank is approximately 0.0773 pounds per gallon.
It's important to note that in this scenario, we assume perfect mixing of the sugar and water in the tank. Also, the concentration of sugar may vary over time as more water and sugar are added.
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What does the things down below mean?
2(x + 3)
Answers
Answer:
2x+6
Step-by-step explanation:
You would have to work it out like this:
2(x+3)
2 times x and 2 times 3
*This is kinda like a rainbow!*
2 times x is 2x
2 times 3 is 6
so it would be 2x+6
Answer:
2x + 6
Step-by-step explanation:
You can simplify it by distributing the 2 outside the parthenthesis using the distributive property. Distribute the 2 with the x to get 2x, and distribute the 2 with the 3 to get 6. Together you get 2x + 6.
Hope this helps! :)
Suppose a jar contains r red balls and b blue balls, each with a unique identifier on it. How many ways are there to choose a set of two balls of the same color? Of different colors? Show that the sum of these two numbers is the number of ways of choosing two balls from the total, ignoring color.
Answers
Answer:
Ways to choose a set two balls of the same color:
[0.5 * (b) * (b - 1)] + [0.5* (r) * (r - 1)]
Different colors:
0.5 * [(b) * (r) + (r) * (b)] = 0.5 * (2 * b * r)
= b * r
Any two balls
0.5 * (b + r) * (b + r - 1)
= 0.5 * [b * (b + r - 1) + r * (b + r - 1)]
= 0.5 * [b^2 + b * r - b + b * r + r^2 - r]
= 0.5 * [b^2 - b + r^2 - r + b * r + b * r]
= 0.5 * [b * (b - 1) + r * (r - 1) + 2 * b * r]
= 0.5 * (b * (b - 1)) + 0.5 * (r * (r - 1)) + 0.5 * (2 * b * r)
= [0.5 * (b * (b - 1)) + 0.5 * (r * (r - 1))] + [b * r]
= Number of ways of choosing two balls of the same color + number of ways of choosing two balls with different colors
Step-by-step explanation:
A car is traveling at a rate of 80 kilometers per hour. What is the car's rate in miles per hour? How many miles will the car travel in 3 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answers
Answer:
The car's rate is 50 miles per hour, and it will travel 150 miles in 3 hours
Step-by-step explanation:
There are about 1.6 kilometres in a mile, meaning that in 80 miles there are about 50 miles. This means that the car's rate in miles per hour is about 50. This means that in 3 hours, it will travel about 50*3=150 miles. Hope this helps!
A certain bakery sells two sizes of round cakes. The radius of the large cake is 3 times the radius of the small cake. If the top of the large cake has an area of 261 in?, what is the area of the top of the small cake?
Answers
R x R x π = 261
R² = 83.078
R = 9.11
Small cake radius = 9.11/3
small cake radius = 3.038
Area of small cake = 3.038 x 3.038 x π
Area of small cake = 29 in²
Mandissa and Katelynn each make a pitcher of strawberry lemonade. Mandissa wants her drink to be more strawberry flavored 2 1/4 with less lemon. She uses times as many strawberries as Katelynn uses, and 2/3 the amount of lemons. If Katelynn 3/4 uses cup of strawberries and 6 lemons to make her pitcher of lemonade, how many strawberries and lemons will Mandissa use?
Answers
The quantity of strawberries and lemons Mandissa will use is 1 ⅛ cups and 4 cups respectively.
How many strawberries and lemons will Mandissa use?If Katelynn uses 3/4 cup of strawberries, Mandissa will use times as many strawberries, which is 2 1/4 times as much. To find out how much that is, we multiply:
Mandissa:
lemons = 2/3 of 6= 2/3 × 6= 12/3= 4
Strawberry = 1.5 × 3/4= 4.5/4= 1 1/8
Katelyn: 3/4 uses cup of strawberries6 lemons
Ultimately, Mandissa used is 1 ⅛ cups of strawberries and 4 cups of lemons.
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Solve 210 ÷ 30 = ___ using mental math.
7
70
700
7,000
Answers
Answer:
7
-by-step explanation:
none needed just do it in your head like 21 devided by 3=7
Write the equation for g(x)
Answers
The equation of the function, g(x) from the task content is; g(x) = -x/25 + 203/25.
What is the equation of the function g(x)?From observation of the function, f(x), it follows that the slope of f(x) is 25. Hence, it follows that the slope of g(x) is; -1/25 since both functions are perpendicular to each other.
Therefore, the equation for g(x) is;
-1/25 = (y-8)/(x-3)
25y -200 = -x +3
Hence, y = -x/25 + 203/25.
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