A particle moves along line segments from the origin to the points, work done is mathematically given as
W=184.5units
What is the solution of an equation that matches the model.?Considering line segments from (0,0,0)origin to (2,0,0) , (2,5,1) and (0,5,1) under the infulence of force
Generally, the equation for force is mathematically given as
F = z2i + 5xyj + 2y2k
Therefore, Considering u*v
[tex]u * v = (u_1j+u_2j+u_3k) * (v_1i+v_2j+v_3k)[/tex]
[tex]u* v = u_1v_1(i * i) + u_1v_2(i * j)+u_1v_3(i * k) + u_2v_1(j * i) + u_2v_2(j * j)+u_2_3(j* k) + u_3v_1(k * i) + u_3v_2(k * j)+u_3v_3(k * k)[/tex]
Where
[tex]i * i = j *j=k * k=0[/tex]
Hence
[tex]u* v = u_1v_2k-u_1v_3j-u_2v_1k+u_2v_3i +u_3v_1j - u_3v_2i[/tex]
[tex]u = (u_1,u_2,u_3) = (0,5,1)\\\\v = (v_1,v_2,v_3) = (-3,0,0)[/tex]
The normal equation formed
-2y + 15z = 0
z= (1/5)y
Considering the level surface and differential surface area
h(x,y,z) = -y + 5z =0
[tex]dS = |grad(h)| dA[/tex]
In terms of the x and y coordinates of (2,0,0) and (2,5,1) and (0,5,1), we can state that the ranges are 0 to 3 and 5 respectively we have
[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 5[/tex]
Using strokes theorem to evaluate
[tex]F = z2i + 5xyj + 2y2k[/tex]
[tex]curl \ F = 4yi+2zj+5yk = (4y,2z,5y)[/tex]
[tex]curl \ F * nds= \frac{1}{5}(-2z + 25y)\ dy \ dx[/tex]
In conclusion, The work done is
[tex]W=\int _CF *dr[/tex]
[tex]\int _C F * dr = \int \int curl \ F * n ds[/tex]
[tex]\int _C F *dr = \frac{123}{2}\int_0^3 \ dx[/tex]
[tex]\int _C F * dr = \frac{123*3}{2}[/tex]
W= 184.5units
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Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – 4x = 5
The solution to x^2 - 4x = 5 is x = -1 or 5
How to solve the equation?The equation is given as:
x^2 - 4x = 5
Take the coefficient of x
k = -4
Divide by 2
k/2 = -2
Square both sides
(k/2)^2 = 4
Add this value to the sides of the equation
x^2 - 4x + 4= 5 + 4
Express as a difference of two squares
(x - 2)^2 = 9
Take the square root of both sides
x - 2 = ±3
Add 2 to both sides
x = 2 ± 3
Evaluate
x = -1 or 5
Hence, the solution to x^2 - 4x = 5 is x = -1 or 5
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ƒ(x) = 4x² + 5x – 3
g(x) = 4x³ - 3x² +5
Find (ƒ + g)(x)
(f+g)(x)
= f(x) + g(x)
= 4x^2 +5x -3 + 4x^3 -3x^2 +5
= 4x^3+x^2+5x+2
f(x) is a function.
A. True
B. False
Answer:
A. true
Step-by-step explanation:
"f(x) = ... " is the classic way of writing a function.
Julian calculates the volume of a rectangular prism with the dimensions 3/4ft by 4 feet by 1/2 ft. His work is shown here.
What error did Julian make?
He multiplied the numerators incorrectly.
He multiplied the denominators incorrectly.
He simplified 12/6 incorrectly.
He wrote 4 as a fraction incorrectly.
Answer:
He multiplied the denominators incorrectly
Step-by-step explanation:
we know that
The volume of a rectangular prism is given by the formula
V=LWH
we have
L=3/4 ft
W=5/1 ft
H=1/2
substitute
V=(3/4)(5/1)(1/2)= 3x5x1= 15
₋₋₋₋₋₋₋₋ ₋₋₋₋ ft³
4x1x2= 8
therefore
He multiplied the denominators incorrectly
Find the variance of: 6 6 7 8 10 10
Step-by-step explanation:
I hope this helps!!!!!
Using the GCF factor the given expression: 21xy + 14y
7(3xy + 2y)
7y(3x + 2)
3(7xy + 14y)
7xy(3 +2)
Since 7y is common to both factors, hence the GCF of the expression is 7y. The factored form will be 7y(3x + 2)
Greatest common factor of an expressionThe greatest common factor is the value that will divide an expression without leaving a remainder.
Given the expression 21xy + 14y
Find the factors
21xy = 7 * 3 * x * y
14y = 7 * 2* y
Since 7y is common to both factors, hence the GCF of the expression is 7y. The factored form will be 7y(3x + 2)
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Polygon G H I J K has 5 sides.
Which statements are true about the regular polygon? Select three options.
The sum of the measures of the interior angles is 900°.
Each interior angle measures 108°.
All of the angles are congruent.
The polygon is a regular hexagon.
The sum of the measures of the interior angles is 180(5 – 2)°.
Answer:
Each interior angle measures 108°.All of the angles are congruent.The sum of the measures of the interior angles is 180(5 – 2)°.Step-by-step explanation:
(1) The sum of the interior angles of a polygon is [tex]180(n-2)[/tex] degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.
(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.
(3) By definition, all angles of a regular polygon are congruent.
(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.
(5) This is true. (See statement (1)).
Answer:
Options B, C, E
Step-by-step explanation:
X
23 25 26 31 34 38
P(X)
0.16 0.09 0.18 0.12 0.24 0.21
What is the mean of this discrete random variable? That is, what is E(X), the
expected value of X?
A. 31.29
OB. 30.47
OC. 29.5
OD. 28.5
Using it's formula, it is found that the mean of the discrete random variable is given by:
B. 30.47.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Hence, considering the table, the mean of the discrete distribution is:
E(X) = 23 x 0.16 + 25 x 0.09 + 26 x 0.18 + 31 x 0.12 + 34 x 0.24 + 38 x 0.21 = 30.47.
Hence option B is correct.
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which number is equal to 4 half
Answer:
2
Step-by-step explanation:
4 halves=2
1 half=0.5
2 halves=1
3 halves=1.5
4 halves=2
Hope plans to run one day this week, play tennis one day, swim one day, and play soccer one day. A tree diagram would show different combinations in which she can do these.
The probability that Hope performs any of the activities each day of the week can be expressed in the tree diagram.
What is a tree diagram?A tree diagram is a term for a graphical tool that shows the possible outcomes of an experiment. To build a tree diagram, start by putting a branch for each of the possibilities.
What would the tree diagram of Hope's activities look like?The tree diagram of Hope's activities must include all the days of the week and on each day there must be three branches for each of the possible activities that she is going to do (play tennis, swim or play soccer).
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The question is in the image. I
8. Which statement is an example of a transitive relationship?
O
If all b and b ll c, then a ll c.
If m 1n and m 1 p, then m ll p.
If x = 2y and 2y = 8, then x = 4.
If I m and m ll n, then I n.
O
Answer:
Transitive
If x = 2y and 2y = 8, then x = 4.
4x-6y=17 4x+2y=21 solua
What is the value of x?
log 3x =4
A. 7 B. 27 C. 81 D. 12
Answer:
81
Step-by-step explanation:
for example log2 8=3 is the same as 2^3=8, so if you switch around the variables from your question, your able to do 3^4, which is 81
Please Answer fast
Find the value of x°.
Answer:
X=60°
Step-by-step explanation:
Because the sum of angle of all side of a triangle is 180°
and
if that goes on
the equation become
x°+75°+45°=180°
x°+120°=180°
x°=180°-120°
x°=60° hence prove
Determine a series of transformation that would map polygon ABCDE onto polygon A'B'C'D'E'
What is the sum?
3
5
X+3
6-zX
I AM MARKING BRAINLIEST TO CORRECT ANSWER!!! PLEASE HELP!
Answer:
135
Step-by-step explanation:
3b + B = 180
4b = 180. ÷4
b = 45
a = 135
Cool Down
Lesson 3: Reasoning about Equations with Tape Diagrams
Cool Down: Three of These Equations Belong Together
Here is a diagram.
X
1. Circle the equation that the diagram does not match.
06+3x=30
03(x+6)=30
0 3x-30-6
030-3x+6
2. Draw a diagram that matches the equation you circled.
Using the figure given, The one equation that matches with the diagram is 3x=30-6. The diagram that matches the equation circled is given in the image attached.
What is the Equations about?From the above, we can see that the equation that matches with the diagram are:
3(x+6)=3030=3x+66+3x=30Note that for 3(x+6)=30
3x + 18 = 30
3x = 30-18
3x = 12
x = 12/3
x = 4
Then fixing x into the equation =
3(x+6)=30
3(4+6)=30
Therefore , 12 + 18 will give us 30 and the answer is straight forward. The same applies for 30=3x+6 and 6+3x=30 as the answer is straight forward.
But the one equation that does not matches with the diagram is 3x=30-6 because its output is not straight forward.
3x =30-6
3x = 24
x = 24/3
x = 8
Fixing 8 into the equation
3x = 30-6
3(8) = 24
=24 is the answer and not 30
Therefore, Using the figure given, The one equation that matches with the diagram is 3x=30-6.
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Beginning in the middle of summer, the average temperature for a certain year in Phoenix could approximately be modeled by the function f(x)=31cos(0.0055πx)+88, where x represents the number of days since the middle of the summer, and f(x) represents the average temperature in degrees Fahrenheit.
What was the lowest average temperature in Phoenix that year (approximately)?
A) 57∘F
B) 31∘F
C) 55∘F
D) 88∘F
By finding the minimum of the given function, we conclude that the lowest average temperature that year is 57°F.
What was the lowest average temperature in Phoenix that year?We know that the average temperature is given by the equation:
f(x)=31cos(0.0055πx)+88
And it is in Fahrenheit degrees.
To get the lowest average temperature, we just need to find the minimum of the above function.
Remember that the minimum of the cosine function is:
cos(x) = -1
Then the lowest value of the above function is:
f(x₀) = 31*(-1) + 88 = 57
From this, we conclude that the lowest average temperature that year is 57°F, so the correct option is A.
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help me pls dont write fake answers pls
Answer:
it’s C, 5.2
hope i helped
ur wlcm :)
correct me if im wrong
What is the perimeter of this triangle?
Answer: [tex]a+b+\sqrt{a^{2}+b^{2}}[/tex]
Step-by-step explanation:
The distance from (0,b) to (0,0) is b.
The distance from (0,a) to (0,0) is a.
Using the Pythagorean theorem, the distance from (0,b) to (a,0) is [tex]\sqrt{a^{2}+b^{2}}[/tex]
So, the perimeter is [tex]\boxed{a+b+\sqrt{a^{2}+b^{2}}}[/tex]
Match each fraction on the left with an equivalent fraction on the right. Some options on the right will be used more than once.
Answer:
4/7=12/21
18/20=9/10
6/5=30/25
81/90=9/10
Step-by-step explanation:
12 / 21 will be equal to 4/7 and is denoted in the simplest form.
What is an equivalent fraction?A fraction that possesses the same value as another fraction regardless of how it's denominators and numeric components could be different is said to be equivalent.
12 / 21 can be simplified with the help of 3. This will result in 4/7.
18/20 can be simplified with the help of 2. This will result in a 9/10.
30/25 can be simplified with the help of 5. This will result in 6/5.
81/90 can be simplified with the help of 9. This will result in a 9/10.
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apples cost $3.99 for 3 lbs. Susan wants to buy 5 lbs. How much will it cost her?
Answer: $5.99 is the answer hope this helps!
F. In what order should items weighing
51 pounds, 40 pounds, 48 pounds,
and 44 pounds be stacked if you want
them in order from heaviest to lightest?
Answer:
51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.
PLEASE HELP BRAINLIEST how many small blocks of wood each of length 6cm, breath 4cm, and height 2cm can i cut out from a block of wood of length 2m, breadth 4cm and height 2cm WITH STEP BY STEP EXPLANATION
Answer:
33 blocks
Step-by-step explanation:
Given the length , breath and height for small block 6cm, 4cm, and 2cm an d for large 2m = 200cm, 4cm and 2cm.
volume is given by
V = Length x breath x height
Volume of small block = 6 x 4 x 2 = 48 cm^3
Volume of big block = 200 x 4 x 2 = 1600 cm^
No of blocks = Volume of big block/ volume of small block
= 1600/48
= 33.33
Therefore no of blocks formed = 33
One of the roots of the equation x^2-13x+q=0 is 12. Find the other root and the value of the coefficient q.
The other root is 1 and the value of the coefficient q is 12.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x. ax²+bx+c=0. with a ≠ 0 .
Given:
x²-13x+q=0
when x= 12
So, 12²-13*12+q=0
144-156+q=0
-12+q=0
q=12
Now, x²-13x+12=0
x²-12x-x+12=0
x(x-12) - 1(x-12)=0
(x-1)(x-12)=0
x=1, 12
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Solve the Application.
In one week Tommy earns $476 in regular pay and $144 in overtime pay. A total of $197 is deducted from his paycheck for taxes and a company loan. What is his take-home pay?
$423
$413
$433
$533
Find the slope between :
(0,6
(8,-6)
This is for my hw.
Answer:
Exact form: -3/2
Decimal Form: -1.5
Step-by-step explanation:
Hello there!
We need to find out the slope of the given two coordinates/points, that are:
(0,6(8,-6)Solution:
We'll need to use the formulae that is used to find out the slope,that is:
[tex] \pink{\star}\boxed{\rm \: Slope = \cfrac{y_2 -y_1}{x_2 - x_1}} \pink{\star}[/tex]
According to this question,here:
[tex]\rm \blue{\star} (y_2 , y_1) = (-6 , 6) \blue{\star}[/tex][tex]\rm \blue{\star}(x_2 , x_1)= (8 , 0) \blue{\star}[/tex]So substitute them accordingly:
[Slope is denoted as m][tex] \rm \: m = \cfrac{ - 6 -( 6)}{8 - 0} [/tex]
Simplify using PEMDAS rule.
[tex] \rm \: m = \cfrac{ - 12}{8} [/tex]
-12/8 could be canceled.
[tex] \rm \: m = \cfrac{ - 6}{4} [/tex]
-6/4 could also be canceled.
[tex] \boxed{ \rm \: m = \cfrac{ - 3}{2} \: or \: - \cfrac{3}{2} }[/tex]
Or it could be represented as decimal:
[tex] \boxed{ \rm \: m = - 1.5}[/tex]
Hence , the slope m will be -3/2 or -1.5
[tex] \rule{225pt}{2pt}[/tex]
If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days, what is the amountof her deposit to the
nearest dollar (zero decimal place). Use a 360-day year. Enter only the number without $ sign
Answer: 2556
Step-by-step explanation:
Let the amount of the deposit be x dollars
The amount of simple interest earned can be represented by the formula PRT/100
Where,
P is the amount of deposit
R is the annual rate of interest
T is the time in years
Therefore,
P=x
R=6
T=150/360 = 15/36 = 5/12
So,
Simple interest = x(6)(5)/1200
63.90 = 30x/1200
63.90= x/40
x= 63.90×40
x=2556
Therefore, amount deposited = 2556