To solve this problem, we have to find the net displacement and the net force and the multiply the dot product together and get the work done.
The work done on moving the object is 27ft*lbs
Work done in moving the object from point A to point BTo find the work done on this object, let's find the net force on the object.
Data;
force = 4lbdirection = 4, -2displacement = 7ftdirection = (0, 4) to (5,1)The unit vector of the force is
[tex]\sqrt{4^2 +(-2)^2} =\sqrt{16 + 4} = \sqrt{20}[/tex]
[tex]\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} }[/tex]
The net force acting on the object is
[tex]F = 4(\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} })\\F= (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } )[/tex]
The displacement on the object is 7ft through (0,4) to (5, -1)
The unit vector on displacement is
[tex]\sqrt{5^2 + (-1-4)^2} = \sqrt{25+25} = \sqrt{50}[/tex]
[tex]\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }[/tex]
The net displacement will be
[tex]7(\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }) = \frac{35}{\sqrt{50} }, \frac{-35}{50}[/tex]
The work done will be F.d
[tex]w = f. d \\[/tex]
[tex]w = (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } ) * \frac{35}{\sqrt{50} }, \frac{-35}{50}\\w = 17.71+ 8.854\\w = 26.567 = 27ft*lbs[/tex]
The work done on moving the object is 27ft*lbs
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Answer: the answer is B 27ft
Step-by-step explanation: its cam btw
PLEASE HELP ME ANSWER THIS AAAA
Volume of a Rectangular Prism = length x width x height
Volume = 20
Length = 2
Width = 2
Height = d
20 = 2 x 2 x d
20 = 4 x d
d = 5
Answer: d = 5 centimeters
Hope this helps!
Answer:
d = 5 cm
Step-by-step explanation:
Volume of a rectangular prism: L*W*H
L = 2 cmW = 2 cmH = d cmV = 20 cm³Substitute the values above into the formula:
V = L*W*H
20 = 2*2*d
20 = 4d
/4 /4
5 = d
Therefore, the value of d is 5 cm.
Hope this helps!
Which is not a reason an athlete uses technology to assess performance?
A. To monitor development.
B. To tailor to their training program.
C. To send to college recruiters.
D. To analyze technique.
Identify the zeros of the graphed function.
Question 8 options:
A)
x = –4, –2, 1
B)
x = –1, 0, 2, 4
C)
x = –4, –2, 0, 1
D)
x = –1, 2, 4
Answer:
A I think this is it
Step-by-step explanation:
Hope this helps :) :)
What is the approximate value of X?! Help ASAP please
Triangles are similar
x/5=12/1313x=60x=60/13x=4.615x=4.62Option E
Answer:
Both of the triangles are similar but they look like they have been rotated a bit. Sides x is similar to 12 and side 5 (the hypotenuse) is similar to 13. Therefore we can just set up an equation and cross-multiply.
[tex]\frac{x}{5} = \frac{12}{13}[/tex]
[tex](x * 13) = (5 * 12)[/tex]
[tex]13x = 60[/tex]
Divide 12 from both sides
[tex]13x/13 = 60/13[/tex]
[tex]x=4.615[/tex]
Best option would be Option E, 4.62
NEED HELP ON THIS
If z=-1-i, find z^10 in rectangular form.
The polar form of this problem is 3cis90degrees, what’s the rectangular form?
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Let [tex]z=r(\cos\theta+i\sin\theta)[/tex] be a complex number, where [tex]n[/tex] is an integer and [tex]n\geq 1[/tex]. By DeMoivre's Theorem, if [tex]z^n=r^n(\cos\theta+i\sin\theta)^n[/tex], then [tex]z^n=r^n(\cos n\theta+i\sin n\theta)[/tex].
Hence, we must first convert from rectangular to polar form:
[tex]z=-1-i\\\\r=\sqrt{a^2+b^2}\\\\r=\sqrt{(-1)^2+(-1)^2}\\\\r=\sqrt{1+1}\\\\r=\sqrt{2}[/tex]
[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)\\\\\theta=\tan^{-1}\biggr(\frac{-1}{-1}\biggr)\\ \\\theta=\tan^{-1}(1)\\\\\theta=45^\circ[/tex]
Therefore, the rectangular form for the complex number is [tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)[/tex], and now we can apply DeMoivre's Theorem to raise the complex number to the 10th power:
[tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)\\\\z^{10}=\sqrt{2}^{10}(\cos45^\circ+i\sin45^\circ)^{10}\\\\z^{10}=2^5(\cos10\cdot45^\circ+i\sin10\cdot45^\circ)\\\\z^{10}=32(\cos450^\circ+i\sin450^\circ)\\\\z^{10}=32(0+i)\\\\z^{10}=32i[/tex]
Therefore, [tex]z^{10}=32i[/tex] in rectangular form.
Problem 2
[tex]3\:\text{cis}\:90^\circ=3(\cos90^\circ+i\sin90^\circ)=3(0+i)=3i[/tex]
Therefore, [tex]3\:\text{cis}\:90^\circ=3i[/tex] in rectangular form.
Select the correct answer.
The graph of function fis shown.
Which statement correctly compares the two functions?
OA. They have the same end behavior as x approaches -
B. They have the same end behavior as x approaches -
OC. They have different end behavior as x approaches -
Composition of the functions is
commutative.
Answer:
The rule a+b=b+a, for all real numbers a,b, is the commutative law for addition. The fact that we can have g∘h≠h∘g, for some functions g,h, says that composition of functions is not commutative. Composition of functions is not the same as multiplication of functions: f=h∘gmeansf(x)=h(g(x))j=h⋅gmeansj(x)=h(x)g(x).
[tex](sinx^{2} theta)\frac{x}{y}(1+costheata)[/tex]
The result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]
How to evaluate the expression?The expression is given as:
[tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex]
Express [tex]\sin^2(\theta)[/tex] as [tex]1 - \cos^2(\theta)[/tex].
So, we have:
[tex]\sin^2(\theta) * (1 + \cos(\theta)) = (1- \cos^2(\theta)) * (1 + \cos(\theta))[/tex]
Open the bracket
[tex]\sin^2(\theta) * (1 + \cos(\theta)) = 1 + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]
Express 1 as cos°(Ф)
[tex]\sin^2(\theta) * (1 + \cos(\theta)) = cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]
Hence, the result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]
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is -0.25 rattional or irrational
a) Fill in the gaps below to describe the transformations.
clockwise/anticlockwise about (-1,0) to give
triangle A'.
Triangle A' is then reflected in the line
to give triangle A".
b) What type of single transformation maps triangle A onto triangle A"?
A"
Triangle A is rotated
O
-4
A
a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'.
Triangle A' is then reflected in the line y=0 to give triangle A''.
b) Rotation
a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'. Triangle A' is then reflected in the line y=0 to give triangle A''.
b) Rotation
Given,
Triangles A , A' , A'' .
Here,
The triangles are rotated and reflected to get different triangles .
Firstly ,
Triangle A is made to be rotated by 90° in anticlockwise direction at point (-1 , 0) .
To get A'' triangle A' is reflected from horizontal axis.
Triangle A maps into triangle A'' by rotation .
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The rule for a pattern is subtract 4. The first number of the pattern is 41. Which choice is true about this pattern?
A.The numbers in the pattern are even.
B.The numbers in the pattern are odd.
C. The numbers alternate between even and odd.
Answer:A
Step-by-step explanation:
the correct choice is: B. The numbers in the pattern are odd.
To determine if the numbers in the pattern are even, odd, or alternate between even and odd, let's examine the first few numbers in the pattern:
First number: 41
Second number: 41 - 4 = 37
Third number: 37 - 4 = 33
Fourth number: 33 - 4 = 29
As we can see, the numbers in the pattern are decreasing by 4 in each step. The first number (41) is odd, and subsequently, each number is decreasing by an even value (4). Therefore, all the numbers in the pattern will be odd.
So, the correct choice is:
B. The numbers in the pattern are odd.
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Rewrite the equation below so that it does not have fractions:
3/4x - 2 = 5/12
Do not use decimals in your answer.
Answer:
Equation = [tex]\frac{3}{4}[/tex] x - 2 = [tex]\frac{5}{12}[/tex]
First: [tex]\frac{3}{4}[/tex] x = [tex]\frac{5}{12}[/tex] + 2
Then: [tex]\frac{3}{4}[/tex] x = [tex]\frac{29}{12}[/tex]
Answer: x = [tex]\frac{29}{9}[/tex] —> 9x = 29
—-
Have a nice day!!
when A complete 1/3 part of any work B can complete 1/4 part of that same work. Similarly when B complete 1/5 part of that work C can complete 1/2 part of that same work. if A can complete that work in 20 hours, then in how many hours can C complete that work.
Answer:
10.672hrs ( maybe)
Step-by-step explanation:
A can complete the work in 20 hrs then 1/3 part can be completed in 20*1/3=6.67hrs
B can complete the 1/4 part of the work in same time then B can complete hole work in 6.67*4=26.68 hrs
B can complete the 1/5 part of work in 26.67/5=5.336hrs
according to question C can complete 1/2part of work in same time then the whole work can complete in
2*5.336=10.672hrs
how do i do this?? thanks in advance!
Select the reason that best supports statement 5 in the given proof. (See Image)
A distributive property
B substitution
C reflective property
D subtraction property of equality
Answer:
Substitution
Step-by-step explanation:
In your premises, the state AB = BC is given to be true. In math, substitution is taking one value in an equation and "subbing it out for" one that we know has the same value. This means anywhere we see AB, we can substitute BC and the equation will still be true, because AB = BC.
In the example given, that changes AB + BC = AC to AB + AB = AC.
We substituted the AB with BC, because we know that they are of the same value.
A pot of soup, currently 16°C above room temperature, is left out to cool. If that temperature
difference decreases by 6% per minute, then what will the difference be in 16 minutes?
If necessary, round your answer to the nearest tenth.
°C
Answer:
5.9 C
Step-by-step explanation:
Plug in 16°C for the initial amount, 0.06 for the rate of decrease, and 16 minutes for the time elapsed.
y= a(1–r)t
y= 16(1–0.06)16 Plug in values
y= 16(0.94)16 Subtract
y= 16(0.37157…) Simplify
y= 5.94518… Multiply
Round to the nearest tenth.
5.94518… → 5.9
To the nearest tenth, the difference in temperature will be 5.9°C.
Respond
1. Describe a real-life situation that can be modeled by a function (a relation in which every input
value corresponds to only one output value). The situation must be different from the examples
provided in the reading and in the homework. Identify the input value and the output value of the function, and provide justification that your
relation does, in fact, represent a function.
2. Create a function in the form y = f(x) that models the relation described. You may choose variables in place of y or x that better represent the relation, as seen in the provided example.
3. Identify the domain and range of your function, using proper mathematical notation.
4. Cite any sources you may have used in
formulating your response.
A real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.
What is a function?It should be noted that a function simply means an expression that shows the relationship between the variables.
In this case, a real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.
The function will be:
= 20 + 5w
where w represents the number of weeks.
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Please help with this question.
Answer: 3
Step-by-step explanation:
The price of a tv was decreased by 20% to £1440. What was the price before the decrease?
Answer:
€ 1800
Step-by-step explanation:
x - 20% of x = 1440
x - 20x/100 = 1440
x - x/5 = 1440
(5x - x)/5 = 1440
4x/5 = 1440
therefore x = 1440 × 5/4 [ transpose 4/5 to right hand side ]
x = 360 × 5
= € 1800
SOMEONE PLEASE HELP WILL MARK BRAINLIEST
Answer:
75.96°
Step-by-step explanation:
[tex] \angle A = \tan^{-1}\bigg(\frac{8}{2}\bigg)[/tex][tex] \angle A = \tan^{-1}(4)[/tex][tex] \angle A =75.963756532\degree[/tex][tex] \angle A \approx 75.96\degree[/tex]Find the next two terms in this
sequence.
20, 32, 42, 50, 56, [?
Answer:
so the next 2 sequences would be 60 and 62
Step-by-step explanation:
The next two terms in the given arithmetic sequence are 60 and 62.
The arithmetic sequence is given as follows:
20, 32, 42, 50, 56, ?
To find the next two terms in the sequence, let's analyze the pattern:
The sequence increases by the following increments:
12, 10, 8, 6
We can observe that the increments are decreasing by 2 each time.
To find the next two terms, we can continue this pattern:
Increment: 4 (6 - 2)
Increment: 2 (4 - 2)
Adding the increments to the previous terms:
56 + 4 = 60
60 + 2 = 62
Therefore, the next two terms in the arithmetic sequence are 60 and 62.
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PLEASE HELP For what value of x is the parallelogram a rectangle. The arrows point to the entire diagonal, not just a segment.
A box contains 14 books & 7 pieces of dusters. Each piece of duster weighs 0.2 pounds each book weighs 1.1 pounds. The box & its contents together weigh 18.25 pounds. How much does the empty box weigh?
Answer:
1.45
Step-by-step explanation:
weight of all books= 14×1.1= 15.4
weight of all duster=7×0.2= 1.4
weight of books and duster= 15.4+1.4=16.8
weight of the empty box = 18.25-16.8=1.45
Julia has 42 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 180 square meters. List each set of possible dimensions (length and width) of the field.
The list of the set of dimension for fencing the building around a rectangular plot of land is 10.5 meters and 21 meters.
Area of a rectanglearea of rectangle = lw
where
l = lengthw = widthTherefore,
perimeter = 2w+ l
42 = 2w + l
l = 42 - 2w
Hence,
area = w(42 - 2w)
180 = 42w - 2w²
-2w² + 42w - 180 = 0
-w² + 21w - 90 = 0
The dimension w can be found as follows;
w = - b / 2a
where
a = -1b = 21w = - 21 / 2 × -1
w = 10.5 meters
Then,
l = 42 - 2w
l = 42 - 2(10.5)
l = 21 meters
Therefore, the dimensions are 10.5 meters and 21 meters.
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Solve this pls explain all steps for 22.5 = 1.5x
22.5 = 1.5x
x = 22.5/1.5
x = 15
hope it helps...!!!
Answer:
x = 15
Step-by-step explanation:
1.5x = 22.5
x = 22.5/1.5
assuming your finding x
I need help with number 35
Answer:
144
Explanation:
In a regular polygon all angles and sides are equal. to find out to what all the angles add up to you take the number of sides subtract 1 and multiply by 180.
(10-2)*180=1440
1440/10=144
help will mark Brainliest
Answer:
4.03 < 16.5
Step-by-step explanation:
Four and three hundreths = 4.03
sixteen and five-tenths = 16.5
4.03 < 16.5
Help me out with this math problem for 50 points!!!
Answer:
see attached for a graph-1, -2.6, -497Step-by-step explanation:
The solution to a one-variable inequality can be graphed on a number line. The number line is shaded where the values satisfy the inequality. Boundaries of shaded regions are marked by points that are either a solid dot, or an open circle, depending on whether the point is included in the solution or not.
__
Here, the inequality tells us any value of x that is less than or equal to -1 will satisfy the inequality. Since -1 is part of the solution set, that boundary point will be marked with a solid dot. Values less than -1 are shown on a number line to the left of the point marked -1.
The graph will be a solid dot at x=-1, and shading to its left.
__
Possible solutions are any values less than or equal to -1. Some are ...
-1
-1.073
-429
giving bralinest to correct answer.
Answer:
A, 3
Step-by-step explanation:
Just look at x axis, find 6, and then start going up until you hit the line. Then record the point you hit.
1.156÷106
Please help
Will give 20 points whoever gets this right
Thank you :)
Answer:
0.0109056604
that is the answer, I used a calculator