Jason kicked a soccer ball that was lying on the ground. It was in the air for 3 seconds before it hit the ground again. While the soccer ball was in the air it reached a maximum height of 30 ft. The height of the ball while in the air is the function of time.
Answers
Answer:
a) The domain is 0 < t < 3
The range is 0 < s < 30
b) The x-intercept are the times at the start and return of the ball to the ground
The y-intercept, is the starting height of the ball = 0
c) The axis of symmetry is the line t = 1.5, and the maximum function is the value of the height at the vertex of the parabola, they represent the turning point of the function
d) The rate of change of the function is therefore given by the derivative of function which is;
ds/dt = d(14.715×t - 1/2×9.81×t²)dt = 14.714 - 9.81×t which is the velocity of the ball at time t
∴ ds/dt = 14.714 - 9.81×t
Which is the velocity of the ball at time t
Step-by-step explanation:
The duration the soccer ball was in the air = 3 s
The maximum height reached by the soccer ball = 30 ft.
Considering the vertical motion of the ball, we have;
v = u - gt
s = u·t + 1/2·g·t²
v² = u² - 2×g×s
Where;
v = The final velocity of the ball = 0 m/s
u = The initial velocity of the ball
g = The acceleration due to gravity = 9.81 m/s²
s = The height the ball reaches = 30 ft
Given that the time to maximum height = Half the total time it was in the air, we have;
v = u - gt
v = 0 at maximum height
u = gt = 9.81 × 3/2 = 14.715 m/s
The vertical velocity = 14.715 m/s
Therefore, we have;
s ≈ 14.715×t - 1/2×9.81×t²
a) The domain is 0 < t < 3
The range is 0 < s < 30
b) The x and y-intercept are;
x-intercept, s = 0, gives;
0 ≈ 14.715×t - 1/2×9.81×t²
From which we have, t = 0 or t = 3, which are the times at the start and return of the ball to the ground
The x-intercept are the times at the start and return of the ball to the ground
The y-intercept, t = 0, gives;
s = 14.715×t - 1/2×9.81×t² = 14.715×0 - 1/2×9.81×0 = 0
Therefore, at the time t = 0 the ball is lying on the ground, height = 0
∴ The y-intercept, is the starting height of the ball = 0
c) The axis of symmetry is the line t = 1.5, and the maximum function is the value of the height at the vertex of the parabola
They represent the turning point of the function
d) The rate of change of the function is therefore given by the derivative of function which is;
ds/dt = d(14.715×t - 1/2×9.81×t²)dt = 14.714 - 9.81×t
∴ ds/dt = 14.714 - 9.81×t
Which is the velocity of the ball at time t.
Related Questions
PLEASE HELP! I'M TIMED!! 6 MINUTES LEFT!!!
Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14. Then he concluded that since the differences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is linear. What was Willis’s mistake? x: 1 2 3 4 y: 1 7 17 31 He found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14. He determined that the differences of 6, 10, and 14 are increasing by 4 each time. He concluded that the function has a constant rate of change. He reasoned that a function that has a constant rate of change is linear.
Answers
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
:)
A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and \( y \) ) is \[ \vec{V}=(u, v)=\left(a_{1}+a_{1} x+b_{1} x y\right) \vec{\imath}+\left(
Answers
A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and \( y \) ) is \[ \vec{V}=(u, v)=\left(a_{1}+a_{1} x+b_{1} x y\right) \vec{\imath}+\left(
The velocity field is given by V = (u, v), where u represents the velocity component in the x-direction and v represents the velocity component in the y-direction. The equation for u is given as a₁ + a₁x + b₁xy, and the equation for v is a₂ + a₂y + b₂xy. The terms a₁, a₂, b₁, and b₂ are constants that determine the behavior of the velocity field. The term a₁ represents a constant velocity in the x-direction, a₂ represents a constant velocity in the y-direction, b₁ represents the linear coupling between x and y in the x-direction, and b₂ represents the linear coupling between x and y in the y-direction.
The general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) can be expressed as V = (a₁ + a₁x + b₁xy) + (a₂ + a₂y + b₂xy), where a₁, a₂, b₁, and b₂ are constants.
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Triangle A’B’C’ is the image of triangle ABC. Which transformations could have been used to create A’B’C? Choose all that apply.
Answers
Transformations that may have been used to construct A'B'C include a 90° upward rotation and a 3 unit up and 3 unit right shift.
What is transformations?Transformation in mathematics refers to the process of changing the position, size, or shape of a geometric object. The following are the most common types of transformations: Translation: It involves moving an object from one location to another without changing its size or orientation. Reflection: It involves flipping an object over a line of reflection, so that the object and its image are mirror images of each other. Rotation: It involves rotating an object around a fixed point, called the center of rotation. Dilation: It involves changing the size of an object, either making it larger or smaller, while preserving the shape of the object. Shear: It involves skewing an object in a given direction, causing its shape to be distorted. Similarity Transformation: It is a combination of transformations that preserve the shape of an object, but changes its size and orientation.
Here,
Triangle A’B’C’ is the image of triangle ABC. Transformations could have been used to create A’B’C,
Rotation of 90° upwards.
Shift of 3 units up and 3 units to the right.
Transformations could have been used to create A’B’C is Rotation of 90° upwards and Shift of 3 units up and 3 units to the right.
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the assumptions going into the model are that: a. the mean value of the number of disasters at a given temperature rise is linear in temperature rise b. the actual number of disasters is approximately normally distributed around its mean with a constant variance. the true value that was left out was 16, use the standard error of prediction (the stuff in the square root in the prediction interval) and the prediction from the regression line to calculate a t statistic. what is the pvalue for the null hypothesis that the point belongs to this line under these
Answers
Based on the given assumptions, we can assume that the model predicts the number of disasters at a given temperature rise linearly. However, it is important to note that this model is based on certain assumptions that may or may not be accurate.
These assumptions include the mean value being linear in temperature rise and the actual number of disasters being normally distributed with constant variance.
Given the true value of 16 that was left out, we can use the standard error of prediction and the prediction from the regression line to calculate a t statistic. The null hypothesis is that the point belongs to this line under these assumptions.
To calculate the t statistic, we can use the formula:
t = (observed value - predicted value) / standard error of prediction
Using the given information, we can calculate the t statistic as:
t = (16 - predicted value) / standard error of prediction
Once we have the t statistic, we can calculate the p-value using a t-distribution table or a statistical software. The p-value represents the probability of getting a t statistic as extreme or more extreme than the one we calculated under the null hypothesis.
Based on the p-value, we can determine if we reject or fail to reject the null hypothesis. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that the point does not belong to the line. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that the point belongs to the line.
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Can somebody help me please
Answers
Answer: The answer is AC.
Step-by-step explanation:
Think of only the end points. Imagine that the B is not there. If the B is not there, you are left with AC. I hope this helps!! :)
1. determine if the following are probability distributions (if no, state why). a. x 3 6 9 12 15 p(x) 4/9 2/9 4/9 1/9 1/9a. yes, the values of X are all positiveb. yes, the probbabilities associated with each X are all positive and they all add up to 1c. no, the values of X do not start at 1 and the probabilities do not add up to 1d. no, the probabilities do not add uo to 1
Answers
yes, the probabilities associated with each X are all positive and they all add up to 1.
What is probability?
The probability of an event can be calculated using the probability formula by simply dividing the favourable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anywhere between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes.
For the given probability distribution, we have
A) The sum for all probabilities in the second column is 1. So, this is a probability distribution.
b) yes, the probabilities associated with each X are all positive and they all add up to 1 in the given table.
Hence, the probabilities associated with each X are all positive and they all add up to 1
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Recall from lecture the de-coupled RL-RC circuit (R
21
=[infinity]), where
x
˙
=Ax, and A is a 2×2 diagonal matrix with values A
11
and A
22
. What is the solution x
1
(t) if starting at t=0 ? Use "x10" for x
1
(0), "X20" for x
2
(0), and "A11" for A
11
etc. To denote e
x
, use "exp (x) ". Hint: for those in need of a refresher on ODEs, you might find this helpful.
Answers
The solution x1(t) for the de-coupled RL-RC circuit can be found by solving the differential equation x1'(t) = A11 * x1(t), where A11 is a constant value.
To solve this differential equation, we can use separation of variables.
1. Begin by separating the variables by moving all terms involving x1(t) to one side of the equation and all terms involving t to the other side. This gives us:
x1'(t) / x1(t) = A11
2. Integrate both sides of the equation with respect to t:
∫ (x1'(t) / x1(t)) dt = ∫ A11 dt
3. On the left side, we have the integral of the derivative of x1(t) with respect to t, which is ln|x1(t)|. On the right side, we have A11 * t + C, where C is the constant of integration.
So the equation becomes:
ln|x1(t)| = A11 * t + C
4. To solve for x1(t), we can exponentiate both sides of the equation:
|x1(t)| = exp(A11 * t + C)
5. Taking the absolute value of x1(t) allows for both positive and negative solutions. To remove the absolute value, we consider two cases:
- If x1(0) > 0, then x1(t) = exp(A11 * t + C)
- If x1(0) < 0, then x1(t) = -exp(A11 * t + C)
Here, x1(0) is denoted as x10.
Therefore, the solution x1(t) for the de-coupled RL-RC circuit, starting at t=0, is given by either x1(t) = exp(A11 * t + C) or x1(t) = -exp(A11 * t + C), depending on the initial condition x10.
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Amelie is making a recipe that uses 134 cups flour. She is making 212 times the original recipe. Amelie draws this model to represent the number of cups of flour she needs. How many cups of flour does Amelie need
Answers
Amelie needed 335 cups of flour for the recipe.
How is quantity calculated?The whole centre line length, as well as the construction's breadth and depth, must be multiplied in order to determine the required amount of quantity. Every time the main wall is attached to a cross wall, a partition, or a verandah, the centre line length will be halved at that intersection.Any number, variable, or algebraic combination of other numbers can be a quantity in a mathematical equation. Seven, ten, x, and the product of x and seven, or x + seven, are the four numbers in the equation x + 7 = 10.The unit price is the cost per unit of the product you are purchasing. The amount might be given per thing or per measurement type, such ounces, grammes, gallons, or litres.Given data :
She is making 2 1/2 or 2.5 times the original recipe.
Cups in original recipe= 134 cups
cups Amelie will need= 2.5 × 134
= 335 cups
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Is the line x=5−3t,y=5+4t,z=−7t parallel to the plane 3x+y+z=10 ? Give reasons for your answer. Since the product of the vector parallel to the given line and the normal vector of the given plane is , the line parallel to the plane.
Answers
The line given by the parametric equations x = 5 - 3t, y = 5 + 4t, z = -7t is parallel to the plane 3x + y + z = 10.
To determine if the line is parallel to the plane, we can compare the direction vector of the line with the normal vector of the plane. The direction vector of the line is given by the coefficients of t in the parametric equations, which is (-3, 4, -7).
The normal vector of the plane is the coefficients of x, y, and z in the plane equation, which is (3, 1, 1).
To check if the line is parallel to the plane, we calculate the dot product of the direction vector and the normal vector. If the dot product is zero, then the line is parallel to the plane.
Taking the dot product, (-3, 4, -7) · (3, 1, 1) = (-9) + (4) + (-7) = -12. Since the dot product is not zero, the line is not parallel to the plane.
Therefore, the line x = 5 - 3t, y = 5 + 4t, z = -7t is not parallel to the plane 3x + y + z = 10.
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PLSSSSS HELP! WILL GIVE BRAINLIEST!
If 3 < a < 4 and 6 < b < 7 , find a/b
Answers
Answer:
a:c=3:4 b:c=6:7 Multiply the first equation by 3, a:c=9:12 multiply 2nd equation by 2 we get 12:14 a:b:c=9:12:14 a:c=9:14 note:The LCM of 4 and 6 is 12 .
Step-by-step explanation:
Answer:
a = 3.1 - 3.9 | b = 6.1 - 6.9
Step-by-step explanation:
If 'a' is greater than 3 but less than 4, then 'a' must be in between 3 & 4. so, 'a' is any number between 3.1 - 3.9.
If 'b' is greater than 6 but less than 7, then 'b' must be in between 6 & 7. so, 'b' is any number between 6.1 - 6.9.
Hope this helps!
Find the number of all the 2-digit numbers satisfying the
following congruences x = 3(mod7), x = 2(mod5).
OLEASE HELP
Answers
Use the Chinese remainder theorem.
Start with x = 3×5 + 2×7 = 15 + 14 = 29. Now,
• 29 ≡ 15 ≡ 1 (mod7)
• 29 ≡ 14 ≡ 4 (mod5)
Adjust for this by multiplying the first term in x by 3, and the second term by 3 (because 4×3 ≡ 12 ≡ 2 (mod5)).
So now x = 3×5×3 + 2×7×3 = 45 + 42 = 87, and
• 87 ≡ 45 ≡ 3 (mod7)
• 87 ≡ 42 ≡ 2 (mod5)
The CRT then says that x ≡ 87 (mod(7×5)) ≡ 87 (mod35), which is to say any number x = 87 + 35n satisfies both congruences (where n is any integer).
So there are 3 possible 2-digit numbers that work: {17, 52, 87}.
To confirm:
• 17 ≡ 15 + 2 ≡ 2 (mod5) and 17 ≡ 14 + 3 ≡ 3 (mod7)
• 52 ≡ 50 + 2 ≡ 2 (mod5) and 52 ≡ 49 + 3 ≡ 3 (mod7)
• 87 ≡ 85 + 2 ≡ 2 (mod5) and 87 ≡ 84 + 3 ≡ 3 (mod7)
Yoo how yall doinnnnn
Answers
Answer:
pretty good tired of the virus stuff but good
Step-by-step explanation:
Answer:
Im great... how bout you?
Step-by-step explanation:
The heights of two similar Cylinder are 4cm and 6cm. If the volume of the smaller Cylinder 48cm³, find the volume of the larger Cylinder
Answers
H₁ = 4 cm {Height of the smaller cylinder}
H₂ = 6 cm {Height of the larger cylinder}
Therefore the ratio of corresponding dimensions of these cylinders is:
6:4 = 1.5
If the ratio of corresponding dimensions of similar solids is k then the ratio of their volumes is k³.
So:
\(V_2=(1.5)^3V_1\\\\V_2 = 3.375\cdot48\,cm^3=162\,cm^3\)
The volume of the larger Cylinder is 162 cm³Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table. Monthly Charge for Plan A Minutes used, x Monthly charge ($), y 0 14.45 3 14.84 6 15.23 9 15.62 12 16.01 Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B? 0.13 0.17 0.39 0.45
Answers
Answer:
.13
Step-by-step explanation:
did the test
Answer:
.17
Step-by-step explanation:
EDG 2020-2021
A sample of bacteria taken from a river has an initial concentration of 2.1 million bacteria per milliliter and its concentration triples each week. (a) Find an exponential model that calculates the concentration after x weeks. (b) Estimate the concentration after 1.6 weeks. (a) B(x) = (Type an equation usingx as the variable.)
Answers
The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.
This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.
To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.
The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.
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A square has sides of length 6/12 inches. Area of length times width.
What is the area of the square in square inches?
Answers
The area of the square is 1/4inches² in square inches
What is area of squareThe area of a square is calculated by multiplying its two sides, that is area = s × s, where, 's' is one side of the square.
The square has side of length = 6/12
this can be simplified as 1/2
so
area of the square = (1/2 × 1/2) inches ²
area of the square = 1/4inches²
Thus, the area of the square is calculated using area = s × s, as 1/4inches²
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Let f: R+R be defined by f(x) = 4x3 – 2. (a) Show that f is injective and surjective. (b) Find f-(x).
Answers
(a) The function f(x) = 4x³ - 2 is injective (one-to-one) and surjective (onto).
(b) The inverse function of f is f⁻¹(x) = ∛((x + 2)/4).
(a) To show that the function f: R → R defined by f(x) = 4x³ - 2 is injective (one-to-one) and surjective (onto):
Injectivity: Suppose we have two values x₁ and x₂ in the domain such that f(x₁) = f(x₂). We need to prove that x₁ = x₂. So, let's assume 4x₁³ - 2 = 4x₂³ - 2. By simplifying, we get 4x₁³ = 4x₂³.
Dividing both sides by 4 gives us x₁³ = x₂³.
Taking the cube root of both sides gives x₁ = x₂. Therefore, the function f is injective.
Surjectivity: For surjectivity, we need to show that for every y in the codomain (R), there exists at least one x in the domain (R) such that f(x) = y. Let's take an arbitrary y ∈ R.
We need to find an x such that f(x) = y. Solving the equation 4x³ - 2 = y for x, we have x = ∛((y + 2)/4). Thus, for any y in the codomain, there exists an x in the domain such that f(x) = y. Therefore, the function f is surjective.
(b) To find f⁻¹(x) (the inverse function of f), we interchange the roles of x and f(x) in the original function equation and solve for x.
Start with y = 4x³ - 2 and solve for x:
y + 2 = 4x³
x³ = (y + 2)/4
x = ∛((y + 2)/4)
Thus, the inverse function of f is f⁻¹(x) = ∛((x + 2)/4).
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Find the area of the shaded region, Enter your answer as a reduced fraction. -(x)=(x - 2)² -g(x) = x m Ci H O m A = 0 squared units 3
Answers
To find the area of the shaded region, we need to determine the limits of integration and evaluate the definite integral of the difference between the functions f(x) = (x - 2)² and g(x) = x. The result will give us the area in square units.
The shaded region is bounded by the curves of the functions
f(x) = (x - 2)² and g(x) = x.
To find the area of the region, we need to calculate the definite integral of the difference between the two functions over the appropriate interval.
To determine the limits of integration, we need to find the x-values where the two functions intersect.
Setting the two functions equal to each other, we have (x - 2)² = x. Expanding and simplifying this equation, we get x² - 4x + 4 = x. Rearranging, we have x² - 5x + 4 = 0.
Factoring this quadratic equation, we get (x - 1)(x - 4) = 0, which gives us two solutions: x = 1 and x = 4.
Therefore, the limits of integration for finding the area of the shaded region are from x = 1 to x = 4. The area can be calculated by evaluating the definite integral ∫[1 to 4] [(x - 2)² - x] dx.
Simplifying and integrating, we have ∫[1 to 4] [x² - 4x + 4 - x] dx = ∫[1 to 4] [x² - 5x + 4] dx. Evaluating this integral, we find the area of the shaded region is 3 square units.
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The perimeter of a rhombus is 20. If the length of its longer downhill measures 8, what is the length of the shorter diagonal?
Answers
Answer:
2
Step-by-step explanation:
rhombus = a parallelogram
so 20 = 2*(8+x)
so x =2
Given f(x)=x*-x³-6x², for what values of x will f(x) > 0?
Answers
The values of x will f(x) > 0 for x < 0, and f(x) < 0 for -6 < x < 0 and x > -6.
To determine the values of x for which f(x) > 0, we need to find the intervals where the function is positive. Let's analyze the function f(x) = x*-x³-6x².
First, let's factor out an x from the expression to simplify it: f(x) = x(-x² - 6x).
Now, we can observe that if x = 0, the entire expression becomes 0, so f(x) = 0.
Next, we analyze the signs of the factors:
1. For x < 0, both x and (-x² - 6x) are negative, resulting in a positive product. Hence, f(x) > 0 in this range.
2. For -6 < x < 0, x is negative, but (-x² - 6x) is positive, resulting in a negative product. Therefore, f(x) < 0 in this range.
3. For x > -6, both x and (-x² - 6x) are positive, resulting in a negative product. Thus, f(x) < 0 in this range.
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14 + 18 ÷ (2 x 18) - 7 using order of operations
Answers
Answer:
1/2x+7
Step-by-step explanation:
Answer: 11
Step-by-step explanation:
First use a step by step process called BODMAS which stands for brackets of(x) division multiplication additon and subtraction
A baseball team played 32 question games and lost eight can use the catcher in 5/8 of the winning games in 1/4 of the losing games what fraction of the games did the team win
Answers
Answer:
3/4
Step-by-step explanation:
From this question we have that this team played 32 games.
They lost 8 out of these 32 games
So their total wins = 32 - 8 = 24
Therefore the fraction of their win would be = win / total number of games played
= 24/32
When reduced further
24/32 = 3/4
Therefore the fraction of games which the team won = 3/4
Thank you!
5. There are 29 students available to represent the upperclassmen at a fair.
13 are juniors and 16 are seniors. What is the probability, as a percent that
a senior and junior will be chosen?
Answers
Answer:
The probability that a senior will be chosen is 55.2% or 16/29. And The probability a Junior will be chosen is 44.8% or 13/29.
Explanation:
Since the total students are 29. I put the 29 as the denominator and converted these fractions into percentages to find my answer.
The required probability that a senior and a junior will be chosen is 51.2%.
Given that,
There are 29 students available to represent the upperclassmen at a fair. 13 are juniors and 16 are seniors. The probability, as a percentage that a senior and junior will be chosen, is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
The probability that a senior and a junior will be chosen
= {13C1 × 16C1}/[29C2]
= 208/[14×29]
= 0.512
= 51.2%
Thus, the required probability that a senior and a junior will be chosen is 51.2%.
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in how many ways can you create a two-element set where each element in the set is an positive integer less than 95?
Answers
In order to establish a two-element set with each element being a positive integer smaller than 95, there are thus 4371 possible combinations.
Combinations are defined by the following formula: C(n, r) = n! / (r! * (n-r)!)
Where n is the overall number of things and r denotes the number of items to be picked at random.
Without respect to order, we must select 2 elements from a possible total of 94. As a result, we can use the following formula to apply the rule: C(94, 2) = 94! / (2! * (94-2)!) = (94 * 93 * 92 *... * 3 * 2 * 1) / [(2 * 1) * (92 * 91 *... * 3 * 2 * 1)]
= (94 * 93) / (2 * 1) = 4371
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6) the circular base of a hemisphere of radius 2 rests on the base of a square pyramid of height 6. the hemisphere is tangent to the other four faces of the pyram
Answers
The length of the square base is thus \(2 x 3\sqrt{2}/2 = 3\sqrt{2}\) = A
What is hemisphere?
Consequently, a hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape. It is created by precisely cutting a spherical along its diameter, leaving behind two identical hemispheres.
EXPLANATION; Let ABCDE be the pyramid with ABCD as the square base. Let O and M be the center of square ABCD and the midpoint of side AB respectively. Lastly, let the hemisphere be tangent to the triangular face ABE at P.
Notice that triangle EOM has a right angle at O. Since the hemisphere is tangent to the triangular face ABE at P, angle EPO is also 90 degree. Hence, triangle EOM is similar to triangle EPO.
OM/2 = 6/EP
OM = 6/EP x 2
OM = \(6\sqrt{6^2 - 2^2} x 2 = 3\sqrt{2}/2}\)
The length of the square base is thus \(2 x 3\sqrt{2}/2 = 3\sqrt{2}\) = A
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solve for the variable. if necessary round to the nearest tenth.a) 6b) 30c) 14.7d) 27
Answers
Allura, this is the solution:
As you can see we have two right triangles in the figure:
Therefore,
Step 1: Let's calculate the hypotenuse of the left triangle, as follows:
c² = a² + b²
c² = 12² + 18²
c²= 144 + 324
c² = 468
c = 21.63
Step 2: Let's calculate the sides of the right triangle on the right, this way:
Leg 1 = 21.63
Leg 2 = x
Hypotenuse = 12 + y
Height of the right triangle = 18
In consequence, to find the value of the hypotenuse and y, we have:
c = 21.63²/√21.63² - 18²
c = 468/√468 - 324
c = 468/12
c = 39
Step 3: Now, we can solve for y, this way:
39 = 12 + y
y = 39 - 12
y = 27
The correct answer is D. 27
True
False
The cube can be dissected into two congruent triangular prisms that each have half the base area of the cube, so the volume of a triangular prism is V = Bh, where B is the
area of its base and h is its height
Answers
Answer:
this is true, I think so...
Compute the surface area of revolution about the -x- axis over the interval [0,1][0,1] for =−3
Answers
To compute the surface area of revolution about the -x- axis over the interval [0,1] for y=−3, we can use the formula:
SA = 2π ∫[a,b] y√(1+(dy/dx)²) dx
where a=0, b=1, and dy/dx is the derivative of y with respect to x. In this case, y=−3, so dy/dx=0.
Plugging in these values, we get:
SA = 2π ∫[0,1] -3√(1+0²) dx
SA = -6π ∫[0,1] dx
SA = -6π[x]₀¹
SA = -6π(1-0)
SA = -6π
Since surface area cannot be negative, we take the absolute value of the result, which gives us:
SA = 6π
Therefore, the surface area of revolution about the -x- axis over the interval [0,1] for y=−3 is 6π.
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Determine whether the sequence converges or diverges. If it converges, find (a). an = 5n/4n , (b). bn = cos (n) '
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a) The sequence an = 5n/4n converges to 5/4.
b) The sequence bn = cos(n) diverges because the cosine function oscillates between -1 and 1.
a) To determine if the sequence an = 5n/4n converges or diverges, we can simplify the expression. Dividing the numerator and denominator by 4n, we get an = 5/4. Since the sequence is a constant value of 5/4 for all n, it converges to the limit of 5/4.
b) The sequence bn = cos(n) involves the cosine function, which oscillates between -1 and 1 as the input value n increases. Since the cosine function does not approach a specific value and keeps oscillating, the sequence diverges. There is no single limit or value that the sequence approaches.
In summary, the sequence an = 5n/4n converges to 5/4, while the sequence bn = cos(n) diverges due to the oscillating nature of the cosine function.
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use intercepts to graph the linear equation 3x-y=-5
x intercept (_,0)
y intercept (0,5)