Answers
Solution
- The equation modeling the height of the falling object is:
\(h(t)=400-39t-157e^{-0.25t}\)Question 1:
- To find the velocity of the falling object, we simply differentiate the function with respects to time (t).
- After this, we can find when the velocity of the object is -30ft/s by substituting V = -30 and find the value of t.
- Thus, we have:
\(\begin{gathered} h(t)=400-39t-157e^{-0.25t} \\ \\ h^{\prime}(t)=\frac{d}{dt}(h(t))=\frac{d}{dt}(400-39t-157e^{-0.25t}) \\ \\ h^{\prime}(t)=-39-157(-0.25)e^{-0.25t} \\ \\ h^{\prime}(t)=V(t)=-39+39.25e^{-0.25t} \\ \\ \text{ Now that we have the expression for }V(t),\text{ we can proceed to find when the velocity is -30 by making }V(t)=-30 \\ \\ -30=-39+39.25e^{-0.25t} \\ \text{ Add 39 to both sides} \\ 39.25e^{-0.25t}=39-30=9 \\ \\ \text{ Divide both sides by 39.25} \\ \\ e^{-0.25t}=\frac{9}{39.25} \\ \\ \text{ Take the natural log of both sides} \\ \\ -0.25t=\ln(\frac{9}{39.25}) \\ \\ \text{ Divide both sides by -0.25} \\ \\ t=-\frac{1}{0.25}\ln(\frac{9}{39.25}) \\ \\ t=5.890907...\approx5.89s \end{gathered}\)- The time is 5.89s
Question 2:
- The height of the object at time t = 5.89s is gotten by substituting this value of time (t) into the equation of the height given to us.
- We have:
\(\begin{gathered} h(t)=400-39t-157e^{-0.25t} \\ \\ put\text{ }t=5.89 \\ h(t)=400-39(5.89)-157e^{-0.25(5.89)} \\ \\ h(t)=134.2818...\approx134ft\text{ }(\text{ To the nearest foot\rparen} \end{gathered}\)- the height is 134 ft
Related Questions
Meridian Community College has a total of 3,500 students. One hundred of these students are surveyed about the programs offered at the college. The 100 students surveyed in this example would be the
Answers
Using sampling concepts, it is found that the 100 students surveyed in this example would be the would be the sample.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
Hence, in this problem:
The 3,500 students represent the population.The 100 students represent the sample.More can be learned about sampling concepts at brainly.com/question/25122507
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you have a cake that is 16 inches by 18 inches.you want each piece to be exactly the same size.how many people can u serve equal sized piece of cake
Answers
The number of people are 72.
What is HCF?Highest Common Factor is the full name for HCF in mathematics.
According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.
What is LCM?Least Common Multiple is the full name for LCM in mathematics.
LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.
We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.
Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.
We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:
288 / x² = (16*18) / x² = 288 / x²
Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.
As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.
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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.
What is area?A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.
To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.
The total area of the cake is:
16 inches x 18 inches = 288 square inches
To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:
√(288 square inches) ≈ 16.97 inches
Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:
Each piece of cake will be approximately 16 inches by 16 inches.
To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:
288 square inches ÷ (16 inches x 16 inches) = 18
Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.
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Convert 79 pounds to kilograms. (1 pound = 0.454 kilogram)
17.4 kilograms
35.866 kilograms
174 kilograms
358.66 kilograms
Answers
Option B is correct answer, 79 pounds is equal to 35.866 kilograms.
What is unit conversion?
A unit conversion is used to express the same property in a different unit of measurement. Minutes can be used to measure time instead of hours, and feet, kilometers, or any other measurement can be used to measure distance in place of miles. Measurements are typically provided in one system of measurement, such as feet, but are necessary in a different system, such as chains. A mathematical formula known as a conversion factor enables an equivalent exchange of feet for chains.
As it is given in the question,
1 Pound = 0.454 Kilograms,
So, In order to convert 79 pounds into kilograms we have to multiply 0.454 by 79.
79 pounds = 79(0.454) kilograms
79 pounds = 35.866 kilograms
Therefore, option B is correct answer.
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Answer: 79 pounds = 35.866 kilograms. Option B is correct!
The Expert was correct. Can I get brainliest because it's right?
The ________ of event a is the event consisting of all simple events in the sample space s that are not in a.
Answers
Answer:
I think it is complement. Not so sure so sorry If i get it wrong I haven't done this in 2 or 3 years
Step-by-step explanation:
How many digits are there in the smallest sequence of repeating digits in the decimal equivalent of?
A. 4
B. 3
C. 2.
D. 1
Answers
Answer:
the answer is :B
A pitcher containing 3 ¾ gallons of punch is being poured into 3/5 gallon containers. How many containers will it take to hold all the punch ?
Answers
A system of two equal equations is shown below
3x + y = 8
4x - 2y = 3
What is the solution of the system?
Answers
Answer:
x=1.9
y=2.3
Step-by-step explanation:
I hope this helped.
We usually Round off the 79.90% to 80.
What value does 80 count?
Answers
Answer: 00.10
Step-by-step explanation: Add 00.10 to 79.90 and you get 80. Brainliest please?
The following TI-84 Plus display presents some sample statistics 1-Var Stats X-67 X-2291 IX=182,361 SX=8 OX=8.024961059 In29 Part 1 of 3 (a) Assume that a histogram of the sample is bell-shaped. Approximately what percentage of the sample values are between 43 and 917 Approximately 68% of the sample values fall between 43 and 91. Part 2 of 3 Part 2 of 3 (b) Assume that a histogram for the sample is bell-shaped. Between what two values will approximately 95% of the sample be? Approximately 95% of the sample values will fall between 4 and 5 Part: 2/3 Part 3 of 3 (c) If we do not assume that the histogram is bell-shaped, at least what percentage of the sample values will be between 51 and 837 At least (Choose one of the sample values fall between 51 and 83 X Part: 2 68% 75% Part 3 of 88.9% 95% (c) If we 93.8% all or almost all At least (Choose one) the histogram is bell-shaped, at least what percentage of the sample values will be between 51 and 837 of the sample values fall between 51 and 83. 5
Answers
For Part 2, we cannot determine the specific values between which approximately 95% of the sample will fall. And for Part 3, we cannot determine the exact percentage of sample values between 51 and 837.
From the given information, we can make the following clarifications:
Part 1: Approximately 68% of the sample values fall between 43 and 91.
Part 2: Approximately 95% of the sample values will fall between two values. However, the specific values are not provided in the given information.
Part 3: If we do not assume that the histogram is bell-shaped, it is unclear what percentage of the sample values will be between 51 and 837. The options provided are not clear and do not align with the given information.
Therefore, for Part 2, we cannot determine the specific values between which approximately 95% of the sample will fall. And for Part 3, we cannot determine the exact percentage of sample values between 51 and 837.
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A rectangular hotel room is 4 yards by 5 yards. The owner of the hotel wants to recarpet the room with carpet that costs $51.92 per square yard. How much will it cost to recarpet the room?
Answers
Answer:
it will cost him $2204 to recarpet the room.
Step-by-step explanation:
The floor of the room is rectangular. The formula for determining the area of a rectangle is expressed as
Area = length × width
The rectangular hotel room is 4 yards by 7 yards. It means that the area of the rectangular floor would be
Area = 4 × 7 = 28 square yard.
If the cost of the carpet $58.00 per square yard, the total that it will cost to recarpet the room would be
38 × 58.00 = $2204
as it reaches the point (1, 5), the y-coordinate is increasing at a rate of 4 cm/s. how fast is the x-coordinate of the point changing at that instant?
Answers
The rate of increase of the y-coordinate as it approaches the point (1, 5) is 4 cm/s.At that instant, the x-coordinate of the point is not changing; it is staying at 1.
When a point reaches a certain coordinate, it means that the point is not changing anymore. In this case, the point has reached the coordinate (1, 5), which means that the x-coordinate (1) is not changing, while the y-coordinate (5) is increasing at a rate of 4 cm/s. Therefore, the x-coordinate of the point is not changing at that instant.
x = 1
Rate of Change (x-coordinate) = 0 cm/s
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Trevor gets 10 heads when flipping a weighted coin 18 times. What is the experimental probability that the next flip will come up heads?
Write your answer as a fraction or whole number.
Answers
Answer:
5/9
i got it right
compute 4.659×10^4−2.14×10^4. round the answer appropriately.
Answers
Kepler nació 7 años más tarde que galileo y Mirko 12 años antes. Si Kepler murió con 59 años en 1630. Cuantos años vivió Galileo?
Answers
Answer:
what
Step-by-step explanation:
Required information Sheena can row a boat at 2.30mi/h in still water. She needs to cross a river that is 1.20mi wide with a current flowing at 1.60mi/h. Not having her calculator ready, she guesses that to go straight across, she should head upstream at an angle of 25.0 ∘from the direction straight across the river. How far upstream or downstream from her starting point will she reach the opposite bank? If upstream, enter a positive value and if downstream, enter a negative value. mi Required information Sheena can row a boat at 2.30mi/h in still water. She needs to cross a river that is 1.20mi wide with a current flowing at 1.60mi/h. Not having her calculator ready, she guesses that to go straight across, she should head upstream at an angle of 25.0 ∘from the direction straight across the river. In order to go straight across, what angle upstream should she have headed?
Answers
Sheena will reach the opposite bank approximately 11.269 miles downstream from her starting point.
To determine how far upstream or downstream Sheena will reach the opposite bank, we can use the concept of vector addition.
Let's analyze the situation:
Sheena's boat speed in still water is 2.30 mi/h.
The river width is 1.20 mi.
The current is flowing at a speed of 1.60 mi/h.
To go straight across the river, Sheena needs to balance the current by heading upstream at an angle that compensates for the downstream drift caused by the current.
Let's calculate the time it takes for Sheena to cross the river at an angle of 25.0 degrees upstream:
First, we calculate the effective downstream speed caused by the current:
Effective downstream speed = Current speed = 1.60 mi/h.
Then, we calculate the effective upstream speed required to counteract the current:
Effective upstream speed = Boat speed in still water * sin(angle)
= 2.30 mi/h * sin(25.0 degrees)
≈ 0.976 mi/h.
Now, we can calculate the time it takes to cross the river:
Time = River width / (Effective upstream speed - Effective downstream speed)
= 1.20 mi / (0.976 mi/h - 1.60 mi/h)
≈ 7.043 hours.
Since Sheena's boat speed is slower than the current speed, she will not be able to reach the opposite bank directly. She will be carried downstream by the current, and the distance downstream can be calculated as:
Distance downstream = Effective downstream speed * Time
= 1.60 mi/h * 7.043 hours
≈ 11.269 mi.
Therefore, Sheena will reach the opposite bank approximately 11.269 miles downstream from her starting point.
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The diameter of a circle is 12 centimeters. What is the circle's area?
Answers
BEST ANSWER :
CIRCLE
solve for area
A = 113.1 cm^2
d diameter = 12 cm.
Answer:
Area of circle = π r^2
Step-by-step explanation:
Diameter = 12
Radius = 12/2
= 6
Area = π x 6^2
= π x 36
= 113.04
therefore the area of the circle is 113.04
Answer this question correctly, please give the correct answer.
Answers
set equations equal and solve
2x+7 = -x+1
collect like terms
3x = -6
divide
x=-2
1. 3/5 divided by 7/12
Answers
\( \frac{3}{5} \div \frac{7}{12 } \)
\( = \frac{3}{5} \times \frac{12}{7} \)
\( = \frac{36}{35} \)
\( = 1 \frac{1}{35} \)
Given f(x) = -3x + 5, solve for x when f(x) = -4
Answers
Answer:
3
Step-by-step explanation:
Given
f(x) = - 3x + 5
f(x) = - 4
-3x + 5 = - 4
- 3x = - 4 - 5
- 3x = - 9
x = 3
Hope it will help :)
Answer:
x=3
Step-by-step explanation:
i believe it's like this, i am not sure
Y= -3x +5
-4= -3x+5
subtract 5 on both sides
-9= -3x
divide -3 on both sides
x=3
A virtual reality headset lists for $719. Find the net cost after trade discounts if the series discount is 10/30.
Answers
Answer:
479.33
Step-by-step explanation:
10/30 is the same as 1/3 or 33.34%.
Multiply the fraction to the original price then subtract.
719 * 1/3 = 239.67
719 - 239.67 = 479.33
Best of Luck!
core-s-up is a company that helps students improve their test scores on college entrance exams. they advertise that the study program increases a person's score on the gmat by an average of 30 points. a consumer group wishes to test if the average score increase differs from 30 points. assume the population distribution of increase in gmat scores is approximately normal. true or false--the consumer group could have made a type ii error.
Answers
True. The consumer group could have made a type II error. A type II error occurs when the consumer group fails to reject the null hypothesis, which states that the average score increase is equal to 30 points, even though it is actually false.
In this case, if the study program does increase the average score by a different amount, the consumer group may fail to detect this difference and incorrectly conclude that the average score increase is 30 points. This error is possible because no statistical test is perfect, and there is always some level of uncertainty involved in hypothesis testing.
To minimize the risk of a type II error, the consumer group should use an appropriate sample size and consider conducting a power analysis before conducting the study.
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pls help me with this. this assignment is due tomorrow morning
Answers
Answer:
64
Step-by-step explanation:
I just know
Sierra wants to know how long it will take to bike 12 km at different speeds. If she keeps a steady pace,
she can use a function to find the time for each speed.
Use the table and graph to help with your answer.
Input: x Output: y, 12 divided by x
Answers
Answer: B
Step-by-step explanation: There is a constant rate of changes because sierra wanted to test how much different speeds she can test.
The function is linear because it has constant rate of change.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which m is the slope, which is the rate of change, that is, the change in y divided by the change in x.
b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.
Given that Sierra wants to know how long it will take to bike 12 km at different speeds. If she keeps a steady pace,
Here she can use a function to find the time for each speed.
Thererefore, there is a constant rate of changes because sierra wanted to test how much different speeds she can test.
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HELP DUE IN 20 MINUTES AND I HAVE MORE TO DO!!!!
Answers
Answer:
12 5/8 ft
Step-by-step explanation:
13 - 1 = 12
7/8 - 1/4 = 5/8
=12 5/8
Lamps are made in a factory.
A random sample of 50 of the lamps is tested and 4 of them are found to be faulty.
A total of 4000 lamps is made in one day.
Calculate the number of these 4000 lamps you would expect to be faulty.
Answers
Answer:
To solve this problem, we will use the concept of proportion. We can assume that the proportion of faulty lamps in the sample of 50 is the same as the proportion of faulty lamps in the total production of 4000 lamps.
The proportion of faulty lamps in the sample of 50 is:
4/50 = 0.08
So, we can assume that 8% of the total production of 4000 lamps will be faulty.
To calculate the number of faulty lamps in the total production, we can multiply 8% by the total number of lamps:
0.08 x 4000 = 320
Therefore, we would expect 320 lamps out of the total production of 4000 lamps to be faulty.
Step-by-step explanation:
Please help im having problem
Answers
Answer:
24
Step-by-step explanation:
Do i need to explain ??????
Jason creates a scaled map of his hometown on a standard (x,y) coordinate plane. Each unit on the map represents 1 mile. He graphs his house at the point (-4,-5) andhis school at the point (-10,-11). Which of the following is closest to the distance, in miles, between Jason's school and his house?
Answers
The distance between Jason's school and his house is 8 miles.
What is the Cartesian system?
Any point can be located using a Cartesian coordinate system or coordinate system, and that point can be plotted as an ordered pair (x, y) known as Coordinates. The origin, symbolized by the letter "O," is the point where the two number lines intersect. The horizontal number line is known as the X-axis, and the vertical number line is known as the Y-axis.
Given that the coordinates of Jason's house is (-4,-5). The coordinates of his school is (-10,-11).
The formula distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].
Here, x₁ = -4, y₁ = -5,x₂= -10, y₂ = -11
The distance between points is
√[(-10-(-4))² + (-11 - (-5))²]
=√(6² + 6²)
= √(36+36)
= √72
= 6√2
= 8.48
≈ 8 miles
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can anybody help me with this?
Answers
Answer:
a) 3.6 × 10²
Time = distance / speed
So time = 1.08 × 10⁸ / 3 × 10⁸
= 1.08 × 10¹¹ / 3 × 10⁸ ( converted 10⁸ km to meter )
= 1.08 × 10³ / 3
= 0.36 × 10³
. = 3.6 × 10²
Time = 3.6 × 10²
Find the value of k and yz if y is between x and z. x y = 3 k − 2 , y z = 7 k 4 , x z = 4 k 38
Answers
Considering that y is between x and z, we have that:
The value of k is of k = 6.The length of yz is 46 units.How to find the value of k and of yz?We consider that y is between x and z, hence the length of the segment is given by:
xz = xy + yz
The separate lengths are given as follows:
xz = 4k + 38.xy = 3k - 2.yz = 7k + 4.Hence:
4k + 38 = 3k - 2 + 7k + 4.
4k + 38 = 10k + 2
6k = 36
k = 6.
Hence the length of yz is given by:
yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.
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Factorize
4a^2-24a^2b^2+9b^2
Answers
