A helicopter is lifting off from the ground and is moving vertically upward. The graph shows its vertical velocity vy versus time. How high is the helicopter after 12. 0 s have elapsed?.
Answers
After 12 seconds, the helicopter is 32.0 m below its starting position (which is the height it reached after 2.55 seconds) or 32.0 m below the ground level.
We can use the kinematic equation:
vy = u + gt
where vy = final velocity
u = initial velocity
g = acceleration due to gravity
t = time taken by the object
and set vy = 0, u = 25 m/s (since this is the initial velocity of the helicopter at t = 0) and g = -9.8 m/s² (since the object is moving upwards, the acceleration due to gravity acts downwards, hence its sign is negative).0 = 25 - 9.8tt = 2.55 s
Therefore, it takes the helicopter 2.55 s to reach its maximum height.
Now, we can use the kinematic equation:s = ut + 1/2 gt²where s = displacement (which is what we need to find)u = initial velocity (which is 25 m/s)t = time taken to reach maximum height (which is 2.55 s)g = acceleration due to gravity (which is -9.8 m/s²)
Substituting the values,s = 25(2.55) + 1/2 (-9.8)(2.55)²s = 32.0 m
Therefore, the maximum height reached by the helicopter is 32.0 m.
Now, we can find how high the helicopter is after 12 seconds have elapsed.
From the graph, we can see that after 12 seconds, the velocity of the helicopter is vy = -25 m/s (since it is moving downwards).
So, we can use the kinematic equation:vy² = u² + 2gs
where vy = final velocity (which is -25 m/s)
u = initial velocity (which is 25 m/s)
s = displacement (which is what we need to find)
g = acceleration due to gravity (which is -9.8 m/s²)
Substituting the values,
(-25)² = (25)² + 2(-9.8)s625
= 625 - 19.6ss
= -32.0 m
Therefore, after 12 seconds, the helicopter is 32.0 m below its starting position (which is the height it reached after 2.55 seconds) or 32.0 m below the ground level.
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Related Questions
Find m/TRS if m/1 = 2x + 4 and
m/2= 3x - 3.
T
P
S
1
R
Answers
If the angles are ∠1 = 2x + 4 and ∠2 = 3x - 3, then m∠TRS = 36°.
What is an angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The measure of ∠1 = 2x + 4
The measure of ∠2 = 3x - 3
The measure of ∠TRS is -
∠TRS = ∠1 + ∠2
Since, PR is a bisector then ∠1 = ∠2.
The equation is -
2x + 4 = 3x - 3
2x - 3x = - 3 - 4
-x = -7
x = 7
Substitute the value of x in the angles -
∠1 = 2(7) + 4
∠1 = 14 + 4
∠1 = 18°
∠2 = 3(7) - 3
∠2 = 21 - 3
∠2 = 18°
So, the value of ∠TRS is -
∠1 + ∠2
18° + 18°
36°
Therefore, the measure of ∠TRS is 36°.
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A flower-delivery service charges $39.95 per flower arrangement and $2.99 for delivery. The total cost y is represented by the function y=39.95x+2.99 , where x is the number of flower arrangements.
Which of the following sets of numbers would be appropriate input values for the given situation? Select all that apply.
A) Integer
B) Only Zero
C) Whole Number
D) Rational Number
E) Positive Integer
F) Negative Number
Answers
C - whole numbers
E - positive integers
Explanation
❌ A) integers include negative numbers, you can’t have negative arrangements
❌ B) only zero makes no sense, you will have some sales at some time
✅ C) whole numbers makes sense since you are selling whole flower arrangements
❌ D) rational numbers include fractions and you would not have a fraction of a flower arrangement
✅ E) positive integers are whole numbers
❌ F) negative numbers don’t make sense, your input has to be a positive number you are selling
For the numbers a,b and c listed in problem 4 , determine the number of divisors each of those numbers has.
Intro to discrete COT3100, I really need help on this question. So there is a typo on this one and its referring to question (3) Let a =2^2 3^9 5^8 11^4, b= 2^7 3^6 5^8 11^4, c= 2^5 3^5 5^10 11^3). Pretty much question four would be: For the numbers a,b, and c listed in problem 3, determine the number of divisors each of those numbers has.
Answers
The number of divisors for a, b, and c are 1350, 2520, and 1584, respectively.
Given a = 2² × 3⁹ × 5⁸ × 11⁴, b = 2⁷ × 3⁶ × 5⁸ × 11⁴ and c = 2⁵ × 3⁵ × 5¹⁰ × 11³. The task is to find the number of divisors each of those numbers has. The number of divisors of a number is the count of numbers that divide that number without leaving a remainder. The formula to find the total number of divisors for a given number N is as follows: Total divisors = (a + 1) (b + 1) (c + 1) …Here, a, b, c, etc., are the powers of prime factors of N. Let's calculate the number of divisors for each of these numbers:
a = 2² × 3⁹ × 5⁸ × 11⁴. Prime factorization of a: 2² × 3⁹ × 5⁸ × 11⁴. Number of factors = (2 + 1) (9 + 1) (8 + 1) (4 + 1) = 3 × 10 × 9 × 5 = 1350. Number of divisors of a = 1350
b = 2⁷ × 3⁶ × 5⁸ × 11⁴. Prime factorization of b: 2⁷ × 3⁶ × 5⁸ × 11⁴. Number of factors = (7 + 1) (6 + 1) (8 + 1) (4 + 1) = 8 × 7 × 9 × 5= 2520. Number of divisors of b = 2520
c = 2⁵ × 3⁵ × 5¹⁰ × 11³. Prime factorization of c: 2⁵ × 3⁵ × 5¹⁰ × 11³. Number of factors = (5 + 1) (5 + 1) (10 + 1) (3 + 1)= 6 × 6 × 11 × 4= 1584. The number of divisors of c = 1584. Therefore, the number of divisors for a, b, and c are 1350, 2520, and 1584, respectively.
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Ashton is looking for new soccer cleats for the new season. He found the perfect pair, Nike vapor edge pro 360, But the cost is $140 without taxes. Ashton only his $150. If he has to pay the full price and an 8% tax fee, would he be able to buy his cleats? Why or why not.
Answers
140•0.08=11.2
To then find the total cost of the shoes with tax you add 140 + 11.2 = 151.2
So no ashton will not be able to afford the shoes because he is 1.2 dollars over budget.
The temperature was 23° F at 8 A.M. By 1 P.M. the temperature was 13° F. Which of the following best represents the change in the temperature from 8 A.M. to 1 P.M.?
Answers
Answer:
G: -10 F
Step-by-step explanation: The temparature went down by 10 which means it subtracted 10 so it's -10
A Complete the table. What pattern(s) do you see in the Total bacteria column?
don't answer the blank inside the chart
Answers
Answer:
4 then 6 then 8
Step-by-step explanation:
2×2=4
2×3=6
2×4=8
a continuous random variable x has a uniform distribution between 5 and 25 (inclusive), then p(x = 15) = 0.05. a. true b. false
Answers
Answer:
Step-by-step explanation:
The probability of a continuous random variable taking any specific value is always zero, so the statement p(x = 15) = 0.05 is false.
for breakfast you eat a bowl of oatmeal and 1/4 cup of added raisins, for lunch, a turkey sandwich and a glass of fresh orange juice. how many servings of fruit and cereal have you had?
Answers
For breakfast, you have had 1/2 a serving of cereal and 1/4 cup of raisins, which count as one serving of fruit.
For breakfast, you have had one serving of cereal and one serving of fruit. In general, one serving of cereal is considered to be one cup, while one serving of fruit is considered to be one half cup. Therefore, in your bowl of oatmeal, you would have had two servings of cereal, and in your quarter cup of raisins, you would have had one serving of fruit. For lunch, you have had one serving of fruit in your glass of orange juice.
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If 3loga +5loga=log64.what is a?
Answers
Next, we can use the property that says loga(b) = c if and only if a^c = b to solve for a. Since we are given that 3loga(a) + 5loga(a) = log64, we can set a^8 = 64 and solve for a: a^8 = 64, so a = 2^(1/8). Therefore, the value of a is approximately 1.19.
I will give brainiest
Answers
Jack rides his bicycle 4 miles in 30 minutes. If he maintains this rate, how far will he ride in 3 hours?
A 12 miles12 miles
B 24 miles24 miles
C 34 miles34 miles
D 240 miles
Answers
Answer:B
Step-by-step explanation:
4 miles = 30 minutes
8 miles = 1 hour
24 miles = 3 hours
TRUE/FALSE. if x=ye^y then the explicit differentiation to find dx/dy, and the implicit differentiation to find dy/dx yield consistent results.
Answers
The explicit differentiation and implicit differentiation both yield consistent results so that the statement is true.
If we have an equation x = ye^y, we can find dx/dy using explicit differentiation as follows:
x = ye^y
Differentiating both sides with respect to y:
dx/dy = (d/dy) (ye^y) = e^y + ye^y
On the other hand, to find dy/dx using implicit differentiation, we differentiate both sides of the equation x = ye^y with respect to x:
d/dx (x) = d/dx (ye^y)
1 = (dy/dx) e^y + y (d/dx) (e^y)
1 = (dy/dx) e^y + y e^y (dy/dx)
(dy/dx) (e^y + y e^y) = 1
dy/dx = 1 / (e^y + y e^y)
We can see that these two expressions for the derivatives, dx/dy and dy/dx, are consistent. We can substitute y = ln(x) in the expression for dy/dx to get:
dy/dx = 1 / (e^(ln(x)) + ln(x) e^(ln(x))) = 1 / (x + ln(x))
We can verify that this is equal to dx/dy by substituting y = ln(x) in the expression for dx/dy:
dx/dy = e^y + ye^y = e^(ln(x)) + ln(x) e^(ln(x)) = x + ln(x)
Therefore, we can conclude that the explicit differentiation and implicit differentiation both yield consistent results.
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The two top concert tour in 2016 were concert A and concert B. Based on average ticket prices, it cost a total of $1262 to purchase six tickets for concert A and six tickets for concert B. three tickets for concert B cost a total of $687. how much did an average ticket coast for each tour
Answers
Given:
The total cost of 6 tickets for concerts A and 6 tickets for concert B is $1262
The cost of three tickets for concert B is $687.
Required:
To find an average ticket cost for each tour.
Explanation:
Let the cost of tickets for concert A is x and for concert B be y.
Now by using the given information we will make the linear equation.
Then the equations become:
\(\begin{gathered} 6x+6y=1262.....(1) \\ 3y=687......(2) \end{gathered}\)We will solve equation (2) for y.
\(\begin{gathered} 3y=687 \\ y=\frac{687}{3} \\ y=229 \end{gathered}\)Now substitute the value of y in equation (1) and get the value of x.
\(undefined\).s
we are interested in testing to see if the variance of a population is less than 5. the correct null hypothesis is σ< 5. σ< 25. σ^2 ≥ 5. σ^2 ≥ 25.
Answers
The variance of a population is less than 5. Null hypothesis reflects the initial presumption or claim that something is true in this case and true option is : σ^2 ≥ 5.
In hypothesis testing, the null hypothesis (H0) represents the assumption or claim that is initially presumed to be true. In this scenario, we are interested in testing whether the variance of the population is less than 5.
The notation σ^2 represents the population variance, and the symbol ≥ denotes "greater than or equal to." Therefore, the correct null hypothesis is that the population variance is greater than or equal to 5 (σ^2 ≥ 5).
The other options listed are not correct for this scenario:
- σ < 5: This alternative hypothesis suggests that the population variance is strictly less than 5, which is not the hypothesis we want to test.
- σ < 25: This alternative hypothesis suggests a different value for the population variance, which is not what we are interested in.
- σ^2 ≥ 25: This alternative hypothesis sets a higher threshold for the population variance, which is not the hypothesis we want to test.
Therefore, the correct null hypothesis is σ^2 ≥ 5, indicating that the population variance is greater than or equal to 5.
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Solve for x in the diagram below.
Answers
Answer: 5x + (x + 54) = 6x + 54
So now 6x + 54 = 90 because u are solving a right angle.
90 - 54 is 36. So 6x = 36 and 36 divided by 6 is 6. Your answer for X = 6 Hope this helps you please mark brainliest
Step-by-step explanation:
7 grade math please help
Answers
Answer:
Step-by-step explanation:
-3.4 is the lowest temperature.
Coldest temperature is -3.4 is recorded at 3:00 pm
The temperature closest to freezing point of water is -0.15
Answer:
Step-by-step explanation:
3:00pm is the coldest
12:00pm is the closest to freezing
Box Plots Sixty-five randomily selected car salespersons were asked the number of cars they senerally sell in one wrek. Foutres people answered that they generally sell three cars; tineteea generally sell four cars; hivive grnerally sell five cars; nine genetally sell six cars; eleven generally sell seven cais. Construct a box plot below, U'se a ruler to measure and scale accurately. Loolding at your box plot, does it appear that the data are concentrated together, siead out evealy, of concentrated ia some areas, but not in others? How can you tell?
Answers
The data are concentrated in some areas but not evenly spread out. There are different frequencies for each number of cars sold per week. There are four people who generally sell three cars, ten people who generally sell four cars, five people who generally sell five cars, nine people who generally sell six cars, and eleven people who generally sell seven cars.
1. In the box plot, the box represents the interquartile range (IQR), which contains the middle 50% of the data. In this case, the IQR spans from four cars to six cars, indicating that the majority of the car salespersons fall within this range. The median, which is represented by the line within the box, is closer to six cars, suggesting that the data are skewed towards higher values.
2. The whiskers of the box plot extend to the minimum and maximum values within a certain range. In this case, the whiskers likely extend from three cars to seven cars, covering the entire range of values provided. However, without specific values for the minimum and maximum, the exact length of the whiskers cannot be determined.
3. Overall, the box plot shows that the data are concentrated around the middle values (four to six cars), indicating that there is a cluster of salespersons who generally sell within this range. However, the presence of outliers beyond the whiskers could suggest some dispersion in the data.
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Please assist me in this question and show working out. 25 points.
Answers
Answer:
400 m
Step-by-step explanation:
According to Pythagorean theorem, c^2 = a^2 + b^2
c^2 = 600^2 + 800^2 = 360000 + 640000 = 1000000
c = √1000000 = 1000 mm
(600 + 800) - 1000 = 1400 - 1000 = 400
Score 2. Given the quadratic form 4x + 4x + 4x + 2x₁x₂ + 2x₁x₂ + 2x₂x₂ Give an orthogonal transformation of the quadratic form. (Each question Score 20, Total Score 20)
Answers
An orthogonal transformation of the given quadratic form is 2(x + y)² - 2z².
Orthogonal transformation is a linear transformation that preserves the length of a vector in an inner product space. A quadratic form is a homogeneous polynomial of degree 2 in n variables, and the quadratic forms that can be reduced by an orthogonal transformation to the diagonal form are said to be orthogonal diagonalizable.
Let's consider the quadratic form 4x + 4x + 4x + 2x₁x₂ + 2x₁x₂ + 2x₂x₂:
Q(x) = 4x² + 4x² + 4x² + 2x₁x₂ + 2x₁x₂ + 2x₂x₂
= (2x + 2x + 2x)² - 2(x - x)² - 2(x - x)²
By completing the square, we can see that the given quadratic form is equivalent to Q(x) = 2(x + y)² - 2z², where x + y = a, and x - y = b. Therefore, an orthogonal transformation of the given quadratic form is 2(x + y)² - 2z².
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The probability of randomly hitting a bullseye on a dartboard with radius 12 inches depends on the size of the bullseye Thus the probability is a function of the size If this function is called PS?
Answers
If we denote the probability of hitting a bullseye on a dartboard with radius 12 inches as a function of the size of the bullseye, we can refer to this function as PS.
The function PS represents the probability of hitting the bullseye and is dependent on the size of the bullseye. The larger the bullseye, the higher the probability of hitting it, and vice versa. By adjusting the size of the bullseye, we can determine the corresponding probability of hitting it using the function PS.
It's important to note that without specific information about the relationship between the bullseye size and the probability, it's not possible to provide a specific mathematical expression or further details about the PS function. The function would need to be defined or provided to calculate the probability accurately.
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IF u answer first i will give brainles
Answers
Answer:
16
Step-by-step explanation:
5+3+5+3=16
Answer:
C) 16
Step-by-step explanation:
I hope this helps! I meant to put 16 NOT 15 earlier... SORRY. May I have brainliest?
5 1/2 - 1 1/3= _______________
Answers
Answer: 4 1/6
Step-by-step explanation: I BELIEVE the answer is
(a) select one of the pairs of systems and write down its number. (b) for the pair selected, identify each system and state one function of that system. (c) explain how the two systems work together to help maintain homeostasis in an individual.
Answers
a. Pair 2 is selected.
b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.
c. The two systems work together by sharing the region of the mouth and upper throat.
First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.
How does the respiratory system and the digestive system work together?The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.
The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.
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What is the value of z?
N
11
z+25°
Z-27°
Z-11°
Answers
Check the picture below.
\(z+25=(z-27) + (z-11)\implies z+25=2z-38 \\\\\\ 25=z-38\implies \boxed{63=z}\)
Please help test corrections and worth many points
Answers
X-intercepts: x = -4, 5
Y-intercept: y = -80
End Behavior:
lim(x->∞) y = ∞
lim(x->-∞) y = -∞
X-intercepts:
To find the x-intercepts, we set y = 0 and solve for x.
0 = (x+4)²(x-5)
So, we set each factor equal to zero and solve for x:
x + 4 = 0 --> x = -4
x - 5 = 0 --> x = 5
The x-intercepts of the graph are x = -4 and x = 5.
Y-intercept:
To find the y-intercept, we set x = 0 and solve for y.
y = (0+4)² (0-5)
y = 16 × -5
y = -80
The y-intercept of the graph is y = -80.
End Behavior:
As x approaches positive infinity, y approaches positive infinity:
lim(x->∞) y = ∞
As x approaches negative infinity, y approaches negative infinity:
lim(x->-∞) y = -∞.
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I need help simplifying an expression:
(13x + 21) - (5x - 9)
______________
2
If you could walk me through the problem that would be very appreciated!
Answers
open the brackets then solve.
remember the flip the signs is needed.
\( \frac{(13x + 21) - (5x - 9)}{2} \)
\( \frac{13x + 21 - 5x + 9}{2} \)
\( \frac{8x + 30}{2} \)
= 4x + 15
Therefore the ans is 4x+15.
find x
please solve this
Answers
Answer:
120°
Step-by-step explanation:
ABCD is a cyclic Quadrilateral.
\( \angle CBE \) is the exterior angle of cyclic quadrilateral ABCD.
Since, the exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
\( \therefore x = m\angle ADC\\\\
\therefore x = 120\degree \)
It took the race car 22 minutes to travel 114. 4 kilometers. At what rate did the car travel? Use the formula r = StartFraction d Over t EndFraction, where r is the rate, d is the distance, and t is the time. Round your answer to the nearest tenth. 0. 2 kilometers per minute 5. 2 kilometers per minute 92. 4 kilometers per minute 2,516. 8 kilometers per minute.
Answers
Please Help Me with this one too
Answers
Answer:
The second one
Step-by-step explanation:
0.5 times 5 is 2.5
2.5 plus 14 is 16.5
0.5 times 10 is 5
5 plus 14 is 19
And so on
A hat company wants to create a cylindrical travel case to protect its beach sun hats using the following pattern.
net drawing of a cylinder is shown as two circles with diameters labeled 17 inches and a rectangle with a height labeled 5 inches
How many square inches of leather will be necessary to create the travel case? Approximate using π = 3.14.
2,081.82 square inches
1,174.36 square inches
720.63 square inches
493.77 square inches
Answers
Answer:
720.33 square inches.
Step-by-step explanation:
To find the amount of leather needed to create the travel case, you need to find the surface area of the cylinder. The surface area of a cylinder is given by the formula:
SA=2πr2+2πrh
where r is the radius of the base and h is the height of the cylinder. In this case, the radius is half of the diameter, so r = 17/2 = 8.5 inches. The height is given as 5 inches. Using π = 3.14, we can plug in these values and get:
SA=2×3.14×8.52+2×3.14×8.5×5
SA=452.38+267.95
SA=720.33
Therefore, the amount of leather needed is approximately 720.33 square inches. The closest answer is C. 720.63 square inches.
Answer:
720.63 square inches
To find the surface area of the cylindrical travel case, we need to add the areas of the two circular bases and the lateral surface area.
The diameter of the circular bases is given as 17 inches, so the radius is 17/2 = 8.5 inches. Using the formula for the area of a circle, we can find the area of one base:
Area of one base = πr^2 = 3.14 x 8.5^2 = 226.96 square inches
Since there are two circular bases, the total area of both bases is:
Total area of both bases = 2 x 226.96 = 453.92 square inches
The lateral surface area is a rectangle with height 5 inches and length equal to the circumference of the circular base. We can find the circumference using the formula:
Circumference = 2πr = 2 x 3.14 x 8.5 = 53.38 inches
So, the lateral surface area is:
Lateral surface area = height x circumference = 5 x 53.38 = 266.9 square inches
Therefore, the total surface area of the cylindrical travel case is:
Total surface area = 453.92 + 266.9 = 720.82 square inches (rounded to two decimal places)
So, the answer is approximately 720.63 square inches (rounded to two decimal places).