The rate of the boat approaching the dock when 125 ft of rope is out is 101.6 ft/min
let x be the horizontal distance to the dock. And the rope is attached to the boat 10 feet below the pulley
Using Pythagorean theorem
x^2=R^2-10^2
where R is the rope length to the pulley.
Differentiates with respect to time t
2x dx/dt=2RdR/dt
Xdx/dt = RdR/dt ...... (1)
If the boat is approaching the dock when 125 ft of rope is out
This is R = 125ft
Using Pythagorean theorem again
X^2 = R^2 - 10^2
X^2 = 125^2 - 10^2
X^2 = 15525
X = 124.6 ft
The rate the boat approaching the dock = dx/dt
While the rope is pulled through the pulley at a rate of 20 ft/min = dR/dt
Solve for dx/dt when R is 125, x= 124.6, and dR/dt= 20ft/min
Substitute all in equation 1
124.6 dx/dt = 125 × 20
dx/dt = 2500/124.6
dx/dt = 101.6 ft/min
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certain standardized math exam have a mean of 100 and a standard deviation of 60. of a sample of 36 students who take this exam, what percent could you expect to score between 70 and 90
It is about 24% of the students could be expected to score between 70 and 90 on the exam.
To find the percentage of students who score between 70 and 90 on the exam, we need to determine what proportion of the exam scores falls within that range. We can do this by converting the scores to standard units and using a table of the standard normal distribution.
First, we need to convert the scores to standard units. We do this by subtracting the mean of 100 from each score and then dividing by the standard deviation of 60. For a score of 70, the standard units would be (70 - 100)/60 = -1.67. For a score of 90, the standard units would be (90 - 100)/60 = -0.67.
Next, we can use a table of the standard normal distribution to find the proportion of scores that fall within that range. For example, a table of the standard normal distribution might tell us that the proportion of scores between -1.67 and -0.67 standard units is about 0.24
Percentage of scores within range = 8.64/36 * 100% = 24%
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the distance between parallel lines 4y=3x-1 and 8y=6x-7
Answer: The distance between the two parallel lines is 11/12.
Step-by-step explanation:
The distance between two parallel lines can be found by calculating the difference between the y-intercepts of the two lines. In this case, the y-intercept of the first line is (-1/4,0), and the y-intercept of the second line is (-7/6,0). The difference between these y-intercepts is (-1/4 - (-7/6)) = 11/12. Therefore, the distance between the two parallel lines is 11/12.
when some of the variables represent categories, we can apply a useful summarization method called tabulation, where we simply count how many people or items are in each category or combination of categories. true false 1.25 points question 1 of 8 next question last questionunsaved change moving to another question will save this res
The given statement is true for tabulation method representing the variable different categories and summarize it in tabulation method makes the calculation simple.
As given in the question,
Let the variable 'x' , 'y' , and 'z' represent some different categories.To simplify the data represent the category in tabulation form.Each category represent the frequency of its own.Now to do the calculation simply count the number of items present in each category.This makes the calculation simple and easy to handle.Therefore, the given statement of representing the variable different categories and summarize it in tabulation method makes the calculation simple is a true statement.
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Point D, E, and F are midpoint of the ide of ΔABC. The perpendicular biector of AB i m, and the perpendicular biector of BC i n. Line m and n interect at T. If TA=5. 9, what i TC?
The value of TC = 5.9
According to the given figure of the triangle ABC, (refer to the attached figure)
The length of perpendicular bisector AC is = m
The length of perpendicular bisector BC is = n
The point at which line m and line n are intersecting = T
Given the value of TA = 5.9
According to the corner theorem.
AC = CF
So, ΔTFA ≅ ΔTFC
⇒ TA = TC = 5.9
Therefore, The value of TC = 5.9
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a wooden cuboid has an open flame base with a square surface with 1.2 m sides and a height of 0.25 m. Find the surface of the cuboid.
Answer:
2.64 square meters.
Step-by-step explanation:
To find the surface area of a cuboid, you need to find the area of each of the six faces and add them together. A wooden cuboid with an open flame base that has a square surface with 1.2 meter sides and a height of 0.25 meters would have a surface area of 1.2 * 1.2 + 4 * (1.2 * 0.25) = 1.44 + 1.2 = 2.64 square meters. This is because the base of the cuboid has an area of 1.2 * 1.2 = 1.44 square meters, and each of the four sides has an area of 1.2 * 0.25 = 0.3 square meters. The total surface area of the cuboid is therefore the sum of these areas: 1.44 + 4 * 0.3 = 2.64 square meters.
For funsies, find what w equals to.
−4w + 2 = 14
[tex]-4w+ 2 = 14[/tex]
Subtract 2 from both sides:
[tex]-4w+2-2=14-2[/tex]
[tex]-4w=12[/tex]
Divide both sides by -4:
[tex]\dfrac{-4w}{-4} =\dfrac{12}{-4}[/tex]
[tex]= \fbox{w = -3}[/tex]
Answer:
w = -3
Step-by-step explanation:
-4w + 2 = 14
-4w + 2 - 2 = 14 - 2 (Subtract 2 from both sides)
-4w = 12
-4w/-4 = 12/-4 (Divide -4 from both sides)
w = -3
Help! I can’t seem to figure it out.
Find angle VT =
Answer:
18
Step-by-step explanation:
this seems to be an equilateral triangle so all sides are equal
5r+8=9r
-5r. -5r
8=4r
/4 /4
2=r
now fill it in
5(2)+8
10+8
18
hopes this helps
Gary bought a jewelry box for
$2.62 that was originally priced at
$5.24. What percentage is the
discount?
Answer: 50%
Step-by-step explanation:
Take 2.62 divided by 5.24, then times 100 = 50%
Then take 100% - 50% = 50%
The percentage discount is 50%
A parabola can be drawn given a focus of (6, 2) and a directrix of y = - 8 Write the equation of the parabola in any form.
The equation of the Parabola is (y - 6 )² = 28 (x + 1) of the given focus and directrix.
Given directrix x = -8
we know that x = h - a = -8
h -a = -8 ...(i)
Given Focus = ( 6,2)
we know that the Focus of the Parabola
( h + a , k ) = (6,2)
comparing h + a = 6 ...(ii)
k = 2
solving (i) and (ii) and adding
h - a + h+ a = -8 +6
2 h = -2
h = -1
Put h = 6 in equation (i)
⇒ h - a = -8
⇒ -1 + 8 = a
⇒ a = 7
The equation of the Parabola ( h,k) = (-1 , 7)
( y - k )² = 4 a ( x - h )
(y - 7 )² = 4 (7) (x -(-1))
(y - 6 )² = 28 (x + 1)
Hence, the equation of the Parabola is (y - 6 )² = 28 (x + 1) of the given focus and directrix.
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Adurey is making a scale drawing of her drawing of her rectangular bedroom. on her drawing a 10-foot wall is 8 inches. Audrey wants to add a 7-foot wall to her scale drawing. Which equation can she use to find how long she should make the wall in her drawing
The length of the wall in her drawing is given as follows:
5.6 inches.
How to obtain the length of the wall in the drawing?A scaling measurement represents the proportion of a total dimension, as it is the ratio between the length of the drawing with the actual length of the object.
On her drawing a 10-foot wall is 8 inches, hence the scale measurement for this problem is given as follows:
8 inches/10 feet = 0.8 inches per feet.
The scale means that each feet of an actual object is represented by a length of 0.8 inches on the drawing.
Audrey wants to add a 7 foot wall to the drawing, meaning that the length of the drawing is given as follows:
7 x 0.8 = 5.6 inches.
(applying the proportion found from the scale measurement).
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Which of the following is an example of the identity property of 1?
O 0+8 = 8
0 (1)=2
O-2+3=1
O 3.11(0) = 0
Answer:
3.11(0) = 0
Step-by-step explanation:
D. 3.11(0) = 0 is an example of the identity property of 1. The identity property of 1 states that any number multiplied by 1 is equal to itself. In this case, 3.11 is multiplied by 0, which is equal to 0.
What is the approximate perimeter of the triangle? use the law of sines to find the answer. 4.6 units 5.7 units 6.9 units 9.2 units
Answer:
d is the correct answer to your question
Answer:
9.2 units
Step-by-step explanation:
cause the last guy is right...
PLEASE HELP (attached image)
i didn't learn it.. so im not sure.. but i thimk 3
two fair dice are rolled. The score is the difference between the two dice.
In a dice, there is a six side
Probability of occurring a score = 1/18
= 1*2/18*2
= 2/36
= preferred outcome/ Total outcome
Only 5 is a number that has occurred twice
The score that has a probability of occurring of 1/18 is 5.
The two dice having different values 30/36 = 5/6 (because the probability of the two dice having equal values is 6/36 = 1/6.)
The probability of the second dice being less than the first dice is the same as the probability of the first dice is less than the second dice: (5/6) / 2 = 5/12.
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find the surface area of that part of the plane that lies inside the elliptic cylinder
The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder [tex]\frac{x^2}{25} +\frac{y^2}{9}[/tex] is 15π√150 and this can be determined by using the given data.
We are given the two equations are:
10x + 7y + z = 4---------(1)
[tex]\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)[/tex]
equation(1) is written as
z = 4 - 10x - 7y-----------(3)
The surface area is given by the equation:
A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)
compare equation(4) with equation(3) we get the values of ∂f/∂x and
∂f/∂y
∂f/∂x = -10
∂f/∂y = -7
substitute these values in equation(4)
A(S) = ∫∫√[(-10)² + (-7)² + 1]dA
A(S) = ∫∫√[100 + 49 + 1]dA
A(S) = ∫∫√[150]dA
A(S) = √150 ∫∫dA
Where ∫∫dA is the elliptical cylinder
From the general form of an area enclosed by an ellipse with the formula;
comparing x²/a² + y²/b² = 1 with x²/25 + y²/9 = 1, from that we get the values of a and b
a = 5 and b = 3
So, the area of the elliptical cylinder = πab
Thus;
A(S) = √150 × π(5 × 3)
A(S) = 15π√150
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ALGEBRA PLEASE HELP ASAPPPPP PLEASEEE
Belinda is thinking about buying a house for $286,000. The table below shows the projected value of two different houses for three years:
Number of years 1 2 3
House 1 (value in dollars) 294,580 303,417.40 312,519.92
House 2 (value in dollars) 295,000 304,000 313,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)
Part C: Belinda wants to purchase a house that would have the greatest value in 25 years. Will there be any significant difference in the value of either house after 25 years? Explain your answer, and show the value of each house after 25 years. (4 points)
Answer:
putting more than question is against app rules but alr
Part A: The value of each of the houses after a fixed number of years can be described by a linear function. This is because the value of each house increases at a constant rate, with the same amount added each year.
Part B: The function for House 1 could be written as f(x) = 294,580 + 8,937.6x, and the function for House 2 could be written as f(x) = 295,000 + 9,000x.
Part C: After 25 years, the value of House 1 will be approximately $750,834.40, and the value of House 2 will be approximately $753,000. The difference in value between the two houses after 25 years will be approximately $2,165.60, which is not a significant difference in the overall value of the houses. Therefore, either house would be a good choice for Belinda to purchase.
the 6-kg smooth cylinder is supported by the spring having a stiffness of kab = 120 n/m
When a spring of stiffness K = 120N/m supporting a smooth cylinder of mass 6kg is subjected to a force of 60N, the velocity it moves downward when compressed a distance of 0.2m is 1.79m/s.
Therefore, the answer is 1.79m/s.
The compression of spring, say x₀ at equilibrium position can be determined by
F = Kx₀
mg = Kx₀
6 × 9.81 = 120 × x₀
Therefore x₀ = 0.4905m
When force F = 60N is applied the spring is compressed more and let new compression of spring be x₁. Then when string compresses additional s distance
x₁ = x₀ + s
Then spring force, F₁ = Kx₁
F₁ = 120 × (0.4905 + s)
F₁ = 58.86 + 120s
Let the cylinder accelerates downward at a m/s², then
60N + mg = ma + F₁
60 + 6×9.81 = 6a + 58.86 + 120s
a = (10 - 20s) m/s²
dv/dt = 10 - 20s
We know that ds/dt = v, that is 1/dt = v/ds
Therefore, vdv/ds = 10 - 20s
vdv = (10 - 20s)ds
Integrating both sides
v²/2 = 10s - 10s²
v = √(20s - 20s²)
At s = 0.2m,
v = √(20×0.2 - 20×0.2²)
v = 1.79m/s
--The question is incomplete, answering to the question below--
"The 6kg smooth cylinder is supported by the spring having a stiffness of kAB = 120 N/m. Determine the velocity of the cylinder when it moves downward s = .2m from its equilibrium position, which is caused by the application of the force F = 60 N. (The 60 N force is not present in the equilibrium position.)"
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solve the equations using elimination -8x+y=-8; 6x-y=6
Answer:
x = 1 y = 0
Step-by-step explanation:
-8x + y = -8
6x - y = 6
y have the same coefficient but one is negative and the other is positive therefore we add both the equations
we get:
-2x = -2
divide both sides by -2
x = 1
now as we have the value of x we can input this into any one of the starting equations
-8x + y =-8
-8(1) +y = -8
-8 + y = -8
add 8 to both sides
y = 0
Answer:
(1, 0 )
Step-by-step explanation:
- 8x + y = - 8 → (1)
6x - y = 6 → (2)
adding (1) and (2) term by term will eliminate y
- 2x + 0 = - 2
- 2x = - 2 ( divide both sides by - 2 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (1)
- 8(1) + y = - 8
- 8 + y = - 8 ( add 8 to both sides )
y = 0
solution is (1, 0 )
in a regression with 7 predictors and 62 observations, degrees of freedom for a t test for each coefficient would use how many degrees of freedom?
in a regression with 7 predictors and 62 observations,The degrees of freedom for a t-test for each coefficient would use 55 degrees of freedom (df = 62 - 7 = 55).
The degrees of freedom for a t-test for each coefficient is calculated by subtracting the number of predictors (7) from the number of observations (62) in a regression with 7 predictors and 62 observations,. This leaves us with 55 degrees of freedom (df = 62 - 7 = 55). Degrees of freedom measure the number of observations that are free to vary in estimating a parameter. In other words, they are the number of observations that are used to generate the estimate. In this case, there are 55 observations that can be used to estimate each coefficient.
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Write in standard notation. 4 x 10^0
Answer:
0.4 x 10^-1
Step-by-step explanation:
4 x 10^0
=> 4
=> 0.4 x 10^-1
find the area of the region enclosed by one loop of the curve. r = sin(4θ)
π/16 is the area enclosed by the curve r= sin(4θ)
The given curve is polar curve and hence the area of the polar curve is given by:
Let A be the area of the curve so,
A = [tex]\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta[/tex]
where a and b is the boundary at which r=0
so after equation r=0
sin(4θ) =0
=> sin(4θ) =0
=> 4θ = 0,π
=> θ = 0, π/4
so a=0 , b= π/4
now
A = [tex]\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta[/tex] ------(i)
so [tex]r^2[/tex] = (sin(4θ))^2
=> [tex]sin^2[/tex]( 4θ )
ans we know that
cos(2α) = 1 - [tex]2sin^2[/tex]2 α
so [tex]sin^2[/tex]= (1- cos(8θ) )/2
putting the value of r in the equation (i) we get :-
A = [tex]\int\limits^b_a {\frac{1}{4} *(1-cos8\theta) } \, d\theta[/tex]
=> 1/4* [tex]\int\limits^b_a {(1-cos8\theta) } \, d\theta[/tex]
here a=0 and b=π/4
after putting the value and solving the integral
A = π/16
so A is the area enclosed by r=sin(4θ) is π/16
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Mr. Johnson deposited $2000 in an account that earns simple interest at an annual interest rate of 6%. If
he received $360 as interest at the end of the tenure, how many years was the deposit held for?
The number of years that the deposit was held for is 3 years.
How to calculate the number of years?From the information, Mr. Johnson deposited $2000 in an account that earns simple interest at an annual interest rate of 6%. and he received $360 as interest at the end of the tenure.
It should be noted that simple interest is Illustrated as:
I = PRT
Therefore, T = Interest / Principal × Rate
Time = 360 / (2000 × 6%)
Time = 360 / 120
Time = 3 years
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3. (a) A survey on the choice of vocation for 40 students revealed that 18 liked catering, 20 liked dressmaking and 15 liked hairdressing. 2 chose catering only, 8 chose dressmaking only and 1 chose hairdressing only, 4 chose all 3 vocation. Illustrate this information on a Venn diagram. b) How many students chose dressmaking and catering only? 9)) Find the number of students who did not choose any of the 3 vocations.
The number of students who like dressmaking and catering only is 7.
The number of students who did not choose any of the 3 vocations is 12.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
Total students = 40
The Venn diagram is given below.
The number of students who like dressmaking and catering only.
= 7
Total number of students who like at least one vocation.
= 28
The number of students who did not choose any vocation.
= 40 - 28
= 12
Thus,
7 students like dressmaking and catering only.
12 students did not choose any vocation.
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which of the following is an equation of the line that is parallel to the x axis and contains (-4,2)
Answer:-2,0
Step-by-step explanation:
you have to ether multiply or divide by an easy number
Arely earned $800.00 this past summer. The graph below shows how she used her money, Arely's Summer Job Earnings How much more money did Arely save than spend on school supplies?
find the first three taylor polynomials of the function at the indicated number. f(x) = e−x; x = 0
The first three taylor polynomials of the function f(x) = e⁻ˣ at x = 0 is 1, 1 - x and 1 - x + x²/ 2.
Taylor polynomial of degree n for a function f(x) which is infinitely differentiable at a is
f(a) + f'(a)×(x - a)/ 1! + f''(a)×(x - a)²/ 2! + ... + (f⁽ⁿ⁾(a)×(x - a)ⁿ/ n! = ∑(i = 1 to n)(f⁽i⁾(a)×(x - a)^{i}/ i!)
where f⁽i⁾(a) denotes the ith derivative of f(x) at a
The first, second and nth derivative of the function f(x) = e⁻ˣ is
f'(x) = -e⁻ˣ
f''(x) = e⁻ˣ
f⁽ⁿ⁾x = (-1)ⁿe⁻ˣ
First Taylor polynomial, n = 1, here f(x) = e⁻ˣ and a = 0.
P₁(x) = f(0) = e⁻⁰ = 1
Similarly
P₂(x) = f(0) + f'(0)(x - 0)/ 1!
P₂(x) = 1 + -1×e⁻⁰×(x - 0)
P₂(x) = 1 - x
P₃(x) = f(0) + f'(0)(x - 0)/ 1! + f''(0)(x - 0)²/ 2!
P₃(x) = 1 - x + e⁻⁰×(x - 0)²/ 2
P₃(x) = 1 - x + x²/ 2
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What are the vertex and range of y = |2x 6| 2? (0, 2); 2 < y < [infinity] (0, 2); −[infinity] ≤ y < [infinity] (−3, 2); 2 < y < [infinity] (−3, 2); −[infinity] ≤ y < [infinity]
Although part of your question is missing, you might be referring to this full question: What are the vertex and range of y = |2x + 6| + 2?
(0, 2); 2 < y < ∞
(0, 2); −∞ ≤ y < ∞
(−3, 2); 2 < y < ∞
(−3, 2); −∞ ≤ y < ∞
The vertex of the function is (–3, 2) and the range of the function is 2 < y < ∞.
The given modulus function:
y = |2x + 6| + 2
Now, we get two equations out of the absolute value function:
y = 2x + 6 + 2
y = 2x + 8
and
y = –2x – 6 + 2
y = –2x – 4
The vertex of the function will be at a point where these two equations are equal. So, we can calculate the vertex as follows:
2x + 8 = –2x – 4
2x + 2x = –4 – 8
4x = –12
x = –3
If x = –3, then y = 2(–3) + 8 = –6 + 8 = 2
Thus, the vertex of the function is (–3, 2).
Now, the values that y can take will range from 2 to infinity as y cannot take values below the vertex.
Thus, the range of the function is 2 < y < ∞.
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help will give brainliest
Answer:
Square, rhombus, parralelogram
Step-by-step explanation:
Bro too much to type trust
Is the line perpendicular?
The situation is based on football. One player starts a couple of yards in the endzone while the other starts at the 8-9 yard line. The player in the endzone almost scores when he is tracked down by the guy on the 8-9 yard line. So does the starting position of these players form a perpendicular line?
Yes, the starting position of these players form a perpendicular line.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
Using Trigonometry
sin [tex]\theta[/tex] = 33.33/100
sin [tex]\theta[/tex] = 0.3333
[tex]\theta[/tex] = [tex]sin^{-1}[/tex] (0.3333)
[tex]\theta[/tex] = 19.469
cos 19.469 = B/ 100
0.9428 = B/ 100
B= 94.28
tan [tex]\theta[/tex] = P/B
tan [tex]\theta[/tex] = 94.28/ 33.33
[tex]\theta[/tex] = 70.5
Using Angle Sum property
< 3= 180 - (70.5 + 19.5)
<3 = 180 - 90
<3 = 90
Hence, they form perpendicular line.
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When ordering the Kid' Lunch at Burger Univere, the cutomer mut chooe a ize, whether or not to have cheee, a ide order, and a type of fruit drink. Here are the poibilitie for each choice. Choice Poibilitie Size Small, Large Cheee? With cheee, Without cheee Side order Frie, Onion ring Fruit drink Orange, Grape, Cherry, Lemonade How many Kid' Lunche are poible?
The fundamental counting principal there will be 2*2*2*4*2 = 64 possible lunches.
What is fundamental counting principal ?
According to this concept, the sum of the outcomes of two or more independent events is equal to the product of the outcomes of each individual event. For instance, a youngster picking from a menu of six ice cream flavors and three types of cones will have a total of 6 x 3 = 18 options.
Here size has two types say 2
Here cheese has two types say 2
Here type of bun has two types say 2
Here side order has four types say 4
Here fruit drink has two types say 2
So, according to the fundamental counting principal there will be 2*2*2*4*2 = 64 possible lunches.
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