(a) The height of the ladder is 5.2 m.
(b) The horizontal distance of the ladder from the wall is 3 m.
What is the height of the ladder?(a) The height of the ladder is calculated by applying the following formula.
sin θ = opposite side / hypotenuse side
where;
opposite side = height = h hypotenuse side = length of the ladder = LSin 60 = h/6
h = 6m x sin (60)
h = 5.2 m
(b) The horizontal distance of the ladder from the wall is calculated as;
cos 60 = x / 6 m
x = 6 m cos (60)
x = 3 m
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PLEASE HELP WILL MARK BRAINLIEST
Answer:
I believe the answer is (A)
*Substituting the x and y values from the table into the equation(A) will balance the right side of the equation to the left side of the equation.
A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it.
If there’s a red mark on the bottom of the duck, the person wins a small prize.
If there’s a blue mark on the bottom of the duck, the person wins a large prize.
Many ducks do not have a mark.
After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize.
Estimate the number of the 160 ducks that you think have red marks on the bottom
Answer:
Here is the answer
Step-by-step explanation:
That will show you.
NEED HELP WHAT ARE THSES TWOO!!
Can i have some help please!!
Answer: $93649
Step-by-step explanation:
Since this is an exponential growth problem, then we can use the equation 50,000(1.04)^16. Solve it and you get 93649.06228. Round to the nearest dollar, which is probably whole number, so it is 93649.
A bag of Skittle contains 16 red, 4 orange, 10 yellow, and 12 green Skittles. What is the ratio of yellow to red Skittles?
Answer:
5:8
Step-by-step explanation:
yellow:red
10:16
simplified would be 5:8
***important note, when doing ratio, make sure to list the term that is asked for first. example: it's yellow to red skittles and not red to yellow. red to yellow would be 8:5 and that would be a wrong answer, so read carefully:)
Answer:
5:8
Step-by-step explanation: you can divide 10:16 by 2 to make 5:8, and that is the simplest form.
11. A bag contains 2 blue marbles and 2 green marbles. What is the probability of drawing a blue marble followed by a green marble, without replacing the first marble before drawing the second marble?
Please show work ty
Answer: your answer should be 50%
Step-by-step explanation: This is because there are only four marbles in the bag total and only 2 are blue and only 2 are green so your chances of pulling out either is 50%
Answer:
33%
Step-by-step explanation:
2 blue marbles + 2 green marbles = 4 marbles
1st draw for blue: 2/4 (2 blue marbles out of 4 marbles)
2nd draw for green: 2/3 (1 less marble from 4, marble not put back in)
2/4 x 2/3 = 4/12 = 1/3 = 0.33 or 33%
"
4. Find the inverse Laplace transform of: (s^2 - 26s – 47 )/{(s - 1)(s + 2)(s +5)} 5. Find the inverse Laplace transform of: (-2s^2 – 3s - 2)/ {s(s + 1)^2} 6. Find the inverse Laplace transform of: (-5s - 36)/ {(s+2)(s^2+9)}.
The inverse Laplace transform of (-5s - 36) / ((s + 2)(s²+ 9)) is [tex]-4e^{-2t}[/tex]+ (-cos(3t) + 8sin(3t))/3.
To find the inverse Laplace transforms of the given expressions, we can use partial fraction decomposition and known Laplace transform pairs. Let's solve each one step by step:
To find the inverse Laplace transform of (-2s² - 3s - 2) / (s(s + 1)²):
Step 1: Factorize the denominator:
s(s + 1)² = s(s + 1)(s + 1)
Step 2: Perform partial fraction decomposition:
(-2s² - 3s - 2) / (s(s + 1)²) = A/s + (B/(s + 1)) + (C/(s + 1)²)
Multiplying through by the common denominator, we get:
-2s² - 3s - 2 = A(s + 1)² + B(s)(s + 1) + C(s)
Expanding and equating coefficients, we find:
-2 = A
-3 = A + B
-2 = A + B + C
Solving these equations, we find: A = -2, B = 1, C = 0.
Step 3: Express the inverse Laplace transform in terms of known Laplace transform pairs:
[tex]L^{-1(-2s^{2} - 3s - 2) }[/tex]/ (s(s + 1)²) = [tex]L^{-1(-2/s)}[/tex] + [tex]L^{-1(1/(s + 1)) }[/tex]+ [tex]L^{-1(0/(s+1)^{2} }[/tex]
= -2 + [tex]e^{-t}[/tex]+ 0t[tex]e^{-t}[/tex]
Therefore, the inverse Laplace transform of (-2s² - 3s - 2) / (s(s + 1)²) is -2 + [tex]e^{-t}[/tex].
To find the inverse Laplace transform of (-5s - 36) / ((s + 2)(s² + 9)):
Step 1: Factorize the denominator:
(s + 2)(s² + 9) = (s + 2)(s + 3i)(s - 3i)
Step 2: Perform partial fraction decomposition:
(-5s - 36) / ((s + 2)(s² + 9)) = A/(s + 2) + (Bs + C)/(s² + 9)
Multiplying through by the common denominator, we get:
-5s - 36 = A(s² + 9) + (Bs + C)(s + 2)
Expanding and equating coefficients, we find:
-5 = A + B
0 = 2A + C
-36 = 9A + 2B
Solving these equations, we find: A = -4, B = -1, C = 8.
Step 3: Express the inverse Laplace transform in terms of known Laplace transform pairs:
[tex]L^{-1(-5s - 36)}[/tex] / ((s + 2)(s² + 9)) = [tex]L^{-1(-4/(s + 2))}[/tex] + [tex]L^{-1((-s + 8)/(s^2 + 9)}[/tex])
= [tex]-4e^{-2t}[/tex] + (-cos(3t) + 8sin(3t))/3
Therefore, the inverse Laplace transform of (-5s - 36) / ((s + 2)(s²+ 9)) is [tex]-4e^{-2t}[/tex]+ (-cos(3t) + 8sin(3t))/3.
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Different weights are suspended from a spring and the length of the spring is measured. The results are shown in the table below.
(b) Find the correlation coefficient, r.
The correlation coefficient for the data-set in this problem is given as follows:
r = 0.9553.
How to obtain the correlation coefficient for the data-set?The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.
The input and the output of the data set are given as follows:
Input: weight.Output: length of spring.From the table, the points are given as follows:
(100, 25), (150, 35), (200, 32), (250, 37), (300, 48), (350, 49), (400, 52).
Inserting these points into the calculator, the correlation coefficient is given as follows:
r = 0.9553.
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Solve the following problem using Simplex Method: MAX Z=6X1 + 10X2 + 5 X3 ST X1 + 2X2 + 4X3 <=8 6X1 + 4X2 <=24 6X1 + 5X3 <=30 X1,X2,X3 >=0
The maximum value of the objective function Z is 120. The optimal values for the decision variables are X1 = 8, X2 = 0, and X3 = 0. The constraints are satisfied, and the optimal solution has been reached using the Simplex Method.
To compute the problem using the Simplex Method, let's convert it into standard form.
Maximize:
Z = 6X1 + 10X2 + 5X3
Subject to the constraints:
X1 + 2X2 + 4X3 <= 8
6X1 + 4X2 <= 24
6X1 + 5X3 <= 30
X1, X2, X3 >= 0
Introducing slack variables S1, S2, and S3 for each constraint, the constraints can be rewritten as equalities:
X1 + 2X2 + 4X3 + S1 = 8
6X1 + 4X2 + S2 = 24
6X1 + 5X3 + S3 = 30
Now, we have the following equations:
Objective function:
Z = 6X1 + 10X2 + 5X3 + 0S1 + 0S2 + 0S3
Constraints:
X1 + 2X2 + 4X3 + S1 = 8
6X1 + 4X2 + S2 = 24
6X1 + 5X3 + S3 = 30
X1, X2, X3, S1, S2, S3 >= 0
Next, we will create the initial simplex tableau:
| X1 | X2 | X3 | S1 | S2 | S3 | RHS |
---------------------------------------
Z | 6 | 10 | 5 | 0 | 0 | 0 | 0 |
---------------------------------------
S1 | 1 | 2 | 4 | 1 | 0 | 0 | 8 |
---------------------------------------
S2 | 6 | 4 | 0 | 0 | 1 | 0 | 24 |
---------------------------------------
S3 | 6 | 0 | 5 | 0 | 0 | 1 | 30 |
---------------------------------------
By performing the simplex pivot operations and iterating through the simplex method steps, we find the following tableau:
| X1 | X2 | X3 | S1 | S2 | S3 | RHS |
---------------------------------------
Z | 0 | 0 | 5 | -6 | 0 | -60| 120 |
---------------------------------------
X1 | 1 | 2 | 4 | 1 | 0 | 0 | 8 |
---------------------------------------
S2 | 0 | -8 | -24| -6 | 1 | 0 | 0 |
---------------------------------------
S3 | 0 | 0 | -1 | -6 | 0 | 1 | 0 |
---------------------------------------
The optimal solution is Z = 120, X1 = 8, X2 = 0, X3 = 0, S1 = 0, S2 = 0, S3 = 0.
Therefore, the maximum value of Z is 120, and the values of X1, X2, and X3 that maximize Z are 8, 0, and 0, respectively.
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Kelly received two gift cards to her favorite store. One card was worth $25 and the other was
worth $40. She went shopping and used the cards to buy 3 shirts for $9 each and 2 skirts for
$17 each. How much gift card money did she have left?
Bella withdrew $80 from her checking account over a period of 4 weeks. Which equation can be used to represent the average weekly change in her bank account?
A.+$800÷−4=−$200
B.−$800÷−4=$200
C.+$800÷4=−$200
D.−$800÷4=−$200
Answer:
D is the answer
Step-by-step explanation:
In a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. If students participated in the poll, how many chose Orange?
Answer:
1666.70
Step-by-step explanation: 10,000/6=1666.70
Determine the area and circumference of a circle with diameter 20 inches.
The area of the circle with a diameter of 20 inches is 100π square inches, and the circumference of the circle is 20π inches.
To determine the area and circumference of a circle with a diameter of 20 inches, you need to use the formulas for these measures.
A circle is a set of points that are equidistant from the center point, and the diameter of a circle is the longest line that can be drawn from one point on the circle to another while passing through the center point. The formulas for the area and circumference of a circle are as follows:
A = πr²C = πd
where A is the area of the circle, C is the circumference of the circle, r is the radius of the circle, d is the diameter of the circle, and π (pi) is a mathematical constant that approximates to 3.14.
To find the area of a circle with a diameter of 20 inches, you need to find the radius of the circle first. The radius is half of the diameter, so r = d/2 = 20/2 = 10 inches. Therefore, the area of the circle is:A = πr² = π(10)² = 100π square inches (rounded to two decimal places).
To find the circumference of a circle with a diameter of 20 inches, you can either use the formula C = πd or you can use the formula C = 2πr. Since you already know the diameter, let's use the first formula. C = πd = π(20) = 20π inches (rounded to two decimal places).
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Please help. No files allowed or you will be reported
Solve the initial value problem below using the method of Laplace transforms.
y'' + 2y' - 3y = 0, y(0) = 2, y' (0) = 18
To solve the initial value problem using the method of Laplace transforms, we'll first take the Laplace transform of both sides of the differential equation.
Taking the Laplace transform of each term, we get:
Ly'' + 2Ly' - 3Ly = 0
Using the properties of Laplace transforms and the initial value theorem, we can write the transformed equation as:
[tex]s^2Y(s) - sy(0) - y'(0) + 2sY(s) - 2y(0) - 3Y(s) = 0[/tex]
Substituting the initial conditions y(0) = 2 and y'(0) = 18, we have:
[tex]s^2Y(s) - 2s - 18 + 2sY(s) - 4 - 3Y(s) = 0[/tex]
Grouping similar terms, we obtain:
[tex](s^2 + 2s - 3)[/tex]Y(s) = 24 + 2s
Now, we can solve for Y(s) by dividing both sides by ([tex]s^2 + 2s - 3)[/tex]
Y(s) = (24 + 2s) /[tex](s^2 + 2s - 3)[/tex]
To find the inverse Laplace transform and obtain the solution y(t), we need to factor the denominator of the expression on the right-hand side:
s^2 + 2s - 3 = (s + 3)(s - 1)
We can rewrite the expression for Y(s) as:
Y(s) = (24 + 2s) / [(s + 3)(s - 1)]
Now, we need to perform partial fraction decomposition to simplify the expression. We write:
Y(s) = A / (s + 3) + B / (s - 1)
Multiplying both sides by (s + 3)(s - 1) to clear the denominators, we get:
24 + 2s = A(s - 1) + B(s + 3)
Expanding and collecting like terms, we have:
24 + 2s = (A + B)s + (3B - A)
To match the coefficients on both sides of the equation, we equate the coefficients of s and the constants:
A + B = 2 (coefficient of s)
3B - A = 24 (constant term)
Solving this system of equations, we find A = 5 and B = -3.
Now, we can rewrite Y(s) as:
Y(s) = 5 / (s + 3) - 3 / (s - 1)
Taking the inverse Laplace transform of Y(s), we can use the table of Laplace transforms or known formulas to find the solution y(t):
y(t) = 5e^(-3t) - 3e^t
Therefore, the solution to the initial value problem is:
[tex]y(t) = 5e^(-3t) - 3e^t[/tex]
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I need help imm struggling
Answer:
180in3 (180 inch cubed)
Step-by-step explanation:
12 x 5 x 3
Answer: I would assume the answer would be 180
Step-by-step explanation: The formula for volume is Length x Width x Height. So multiply all the number above and the answer will be 180
how can I solve a standard form of a linear equation?
Answer:
A standard form of a linear equation is Ax + By = C
Step-by-step explanation:
For example, 3x + 4y = 7 is a linear equation in standard form. When an equation is given the form it ia pretty easy to find the both intercepts of (x and y). It can be useful when solving a two linear equation.
Verify that f_xy = f_yx, for the function f(x,y) = 3x^7 + 4y^7 + 12.
For the function f(x,y) = 3x^7 + 4y^7 + 12, f_xy = f_yx since fx = ______ and fy = ____
Therefore, fxy= _______ and fyx = _______
Given the function: f(x,y) = 3x^7 + 4y^7 + 12To verify that f_xy = f_yx, we need to find the partial derivatives of the given function with respect to x and y. We can find them as follows: ∂f/∂x = 21x^6 ∂f/∂y = 28y^6
Now, to verify that f_xy = f_yx, we need to find f_xy and f_yx. We can find them as follows: f_xy = ∂^2f/∂y∂x = ∂/∂y(∂f/∂x) = ∂/∂y(21x^6) = 0 (since we have no y terms in the derivative of ∂f/∂x) f_yx = ∂^2f/∂x∂y = ∂/∂x(∂f/∂y) = ∂/∂x(28y^6) = 0 (since we have no x terms in the derivative of ∂f/∂y)Since f_xy = f_yx = 0, we can say that f_xy = f_yx.
Therefore, the value of fx is 21x^6 and the value of fy is 28y^6. Hence, the value of fxy is 0 and fyx is also 0.
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How many solutions does this equation have? –7q + 7 = 4 − 4q
- no solution
-one solution
-infinitely many solutions
Answer: One answer
Step-by-step explanation:
The diameter of a circle is 63 centimetres find its circumference use pie = 3.14
Answer:
197.9
Step-by-step explanation:
The formula for circumference is 2(pi)r and r is the radius
The diameter is two times the size of the radius, so by dividing the diameter by two, you can get the radius
So, r=63/2
r= 31.5
That means that 2(pi)(31.5) is the circumference
2(pi)(31.5) = 197.9 (rounded to the nearest tenth)
39 POINT BRAIN.LY QUESTION WHAAA
Answer:
thx for the points
Step-by-step explanation:
Answer:
Where is the question tho whaaAAaaaa
Suppose () = 1/8 for 0 ≤ ≤ 4 for x being a continuous random variable Is () a probability density function? Prove or disprove.
Answer:
The expected value of x ; E(x) = 1
Step-by-step explanation:
F(x) = 1/8 for 0 ≤ x ≤ 4
To prove that it is a probability density function we will find E(x )
attached below is the required prove
It is proven that F(x) = 1/8 for 0 ≤ x ≤ 4 is probability density function
The expected value of X = 1
PLEASE HELPPPPPPPPPPPP
Answer:
Half of 7 is 3.5
That would be your radius.
3.5^2 x 3.14
12.25 x 3.14 = 38.465 yd2 <--------- area
3.14 x 3.5 x 2 = 21.98yd <------- perimeter
The ____ sequence begins with two ones, and then each new term is formed by adding the two terms before it: 1, 1, 2, 3, 5, 8, 13, 21,...
Answer:
Fibonacci
Step-by-step explanation:
the Fibonacci sequence
Find a1 for the arithmetic sequence's 21st term is 400 is 400 and it's common difference is 5
Answer:
8,395
Step-by-step explanation:
21 x 400 = 8,400
is = x
8, 400 - 5 = 8,395
difference = -
Brainlist Pls!
how do I solve this equation in picture
The total number of people surveyed is 75.
How many people were surveyed?The first step is to determine the number of people who had 4 or more rides that preferred a window seat.
= Total number of people that had four or more rides - total number of people who had 4 or more rides that prefer aisle
= 40 - 25 = 15
Total number of people that prefer the window seats= 15 + 20 = 35
Total number of people = total number of people that prefer the window seat + total number of people who prefer the aisle
= 35 + 40 = 75
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plsssssd help me find the anwser
Find the surface area.
24 in.
40 in.
10 in.
26 in.
Answer:
100 i think
Step-by-step explanation:
What is the biggest difference between exponential functions and other functions you have learned about up to this point?
Answer:
No no don't click the link
Answer:
The biggest difference between exponential and linear functions is that linear functions change at a constant rate, while exponential functions change at a rate proportional to it's value, or exponent.
Basically, that's also what separates exponential functions from all others. It's the only function that changes at a rate proportional to its exponent.
Step-by-step explanation:
a
& b
5. Find the following limits. (a) lim40 12 (b) limz+1+1 +22-22+2 i 2-iz-1-1
The limits are,
(a) lim(x→0) 4x/(x² + 1) = 0
(b) lim(z→-1) (1 + √(2 - 2z + z²))/(2 - iz - 1) = ((1 + √(5))(3 - i))/10
(a) To find the limit of lim(x→0) 4x/(x² + 1), we can directly substitute 0 for x in the expression:
lim(x→0) 4x/(x² + 1) = (4 × 0)/(0² + 1) = 0/1 = 0
Therefore, the limit is 0.
(b) To find the limit of lim(z→-1) (1 + √(2 - 2z + z²))/(2 - iz - 1), we can again substitute -1 for z in the expression:
lim(z→-1) (1 + √(2 - 2z + z²))/(2 - iz - 1) = (1 + sqrt(2 - 2(-1) + (-1)^2))/(2 - i(-1) - 1)
= (1 + √(2 + 2 + 1))/(2 + i + 1)
= (1 + √(5))/(3 + i)
To simplify this expression further, we need to rationalize the denominator. We can multiply the numerator and denominator by the conjugate of the denominator, which is (3 - i):
lim(z→-1) (1 + √(5))/(3 + i) × (3 - i)/(3 - i)
= ((1 + √(5))(3 - i))/(9 - i²)
= ((1 + √(5))(3 - i))/(9 + 1)
= ((1 + √(5))(3 - i))/10
Therefore, the limit is ((1 + √(5))(3 - i))/10.
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The question is -
Find the following limits:
(a) lim(x->0) 4x/(x^2 + 1)
(b) lim(z->-1) (1 + sqrt(2 - 2z + z^2))/(2 - iz - 1)