Answer:
u=(14/3 ,-13,23/3)
Step-by-step explanation:
Given
u=3v-2/3 w+2z
And
v=(4,-3,5)
w=(2,6,-1)
z=(3,0,4)
Putting the values of v,w and z
u=3(4,-3,5)-2/3 (2,6,-1)+2(3,0,4)
u=(12,-9,15)-(4/3,12/3,-2/3)+(6,0,8)
=(12,-9,15)-(4/3,4,-2/3)+(6,0,8)
We will perform the addition first..
=(12,-9,15)-(4/3+6 ,4+0,-2/3+8)
= (12,-9,15)-(22/3,4,22/3)
Subtraction will give us:
=(12-22/3 ,-9-4 ,15-22/3)
=(14/3 ,-13,23/3)
Final Answer:
The ordered triple for vector u is then [tex]\( u = (17\frac{2}{3}, -13, 23\frac{2}{3}) \)[/tex]
Explanation:
To find the ordered triple that represents the vector u in the equation [tex]\( u = 3v - \frac{2}{3}w + 2z \)[/tex], we need to perform the vector operations on v = (4, -3, 5), w = (2, 6, -1) , and z = (3, 0, 4).
Step 1: Multiply vector v by 3.
[tex]\[ 3v = 3 * (4, -3, 5) = (3*4, 3*(-3), 3*5) = (12, -9, 15) \][/tex]
Step 2: Multiply vector w by [tex]\( -\frac{2}{3} \)[/tex].
[tex]\[ -\frac{2}{3}w = -\frac{2}{3} * (2, 6, -1) = (-\frac{2}{3}*2, -\frac{2}{3}*6, -\frac{2}{3}*(-1)) = (-\frac{4}{3}, -\frac{12}{3}, \frac{2}{3}) \\\\\[ -\frac{2}{3}w = (-\frac{4}{3}, -4, \frac{2}{3}) \\\\\[ -\frac{2}{3}w = (-1\frac{1}{3}, -4, \frac{2}{3}) \][/tex]
Step 3: Multiply vector \( z \) by 2.
[tex]\[ 2z = 2 * (3, 0, 4) = (2*3, 2*0, 2*4) = (6, 0, 8) \][/tex]
Step 4: Add the resulting vectors from steps 1, 2, and 3.
We add the corresponding components from each vector:
[tex]\[ (12, -9, 15) + (-1\frac{1}{3}, -4, \frac{2}{3}) + (6, 0, 8) \][/tex]
To add these, perform the addition component-wise:
- For the first component:
[tex]\[ 12 + (-1\frac{1}{3}) + 6 = 12 - 1\frac{1}{3} + 6 = 11\frac{2}{3} + 6 = 17\frac{2}{3} \][/tex]
- For the second component:
[tex]\[ -9 + (-4) + 0 = -9 - 4 = -13 \][/tex]
- For the third component:
[tex]\[ 15 + \frac{2}{3} + 8 = 15 + \frac{2}{3} + 8 = 23\frac{2}{3} \][/tex]
The ordered triple for vector u is then [tex]\( u = (17\frac{2}{3}, -13, 23\frac{2}{3}) \)[/tex].
However, to express this as a proper ordered triple, we usually write the components as fractions or decimals. So, let's convert the fractions into decimals:
[tex]\[ 17\frac{2}{3} = 17 + \frac{2}{3} = 17 + 0.666\ldots \approx 17.67 \\\\\[ 23\frac{2}{3} = 23 + \frac{2}{3} = 23 + 0.666\ldots \approx 23.67 \][/tex]
So the ordered triple for vector u in decimal form is approximately u = (17.67, -13, 23.67).
Please note that the approximation is to two decimal places. If exact values are desired, it is best to leave the answer in fraction form as [tex]\( u = (17\frac{2}{3}, -13, 23\frac{2}{3}) \)[/tex].
Which statement most accurately describes Charles’s law?
A. The volume of a gas varies directly with its temperature at constant pressure.
B. The volume of a gas varies inversely with its temperature at constant pressure.
C. The pressure on a gas varies directly with its temperature at constant volume.
D. The pressure on a gas varies inversely with its temperature at constant volume.
Answer:
.A.The volume of a gas varies directly with its temperature at constant pressure.
Step-by-step explanation:
This law is expressed mathematically as;
V₁ /T₁ =V₂/T₂ where
V₁=initial volume
T₁=initial absolute temperature
V₂=final volume
T₂=final absolute temperature
The temperature is converted to Kelvin when doing calculations where;
0°c = 273 K
An application of this law in real world examples could be when a ball is left outside overnight it the cold, the ball shrinks a little in its volume due to decreased temperatures.
Answer:
A is the answer for sure i got it right after working it out.
Use example 4.4 on page 163 of the textbook as a guide. a set of data points and the equations of two lines are given. for each line, determine . then, determine which line fits the set of data points better, according to the least-squares criterion. line
a.y = 1 + 0.9x line
b.y = 0.8 + 1.1x
B.y i think I’m not smart
How do you determine the limit algebraically?
Answer:
0.125
Step-by-step explanation:
This is a standard calculus question. If you search out L'Hopital's Rule you will find that there are only Calculus examples present. If you use calculus, the answer comes to 1/8. The only way I can think of doing this without the use of Calculus is to let x = something very small -- say x = 0.0001 That approaches 0, but it is not quite = to 0.
So let's try it.
16 + 0.00001 = 16.00001
sqrt(16.0001) = 4.00000125
Now subtract 4
4.00000125 - 4
0.00000125
Now divide by 0.00001
0.12499998
which is close to 0.125.
If someone else can give you an answer that is "purer" than this one, take it.
Find all polar coordinates of point P where P = ordered pair 6 comma negative pi divided by 5.
Answer:
P(6,-π/6) = (6, -π/6 + 2nπ) and P(-6,-π/6) = (-6, -π/6 + (2n+1)π)
Step-by-step explanation:
We need to find all polar coordinates of
[tex]P = (6,\frac{-\pi }{6})[/tex]
The polar coordinates of any point can be reresented by (r,Ф)
where
(r,Ф) = (r, Ф+2nπ) where n is any integer and r is positive
and
(r,Ф) = (-r, Ф+(2n+1)π) where n is any integer and r is negative.
So, in the question given, r = 6 and Ф = -π/6
So, Polar coordinates will be:
P(6,-π/6) = (6, -π/6 + 2nπ) where where n is any integer and r is positive
and
P(-6,-π/6) = (-6, -π/6 + (2n+1)π) where n is any integer and r is negative.
Answer:
All polar coordinates of point P are [tex](6,-\frac{\pi}{5}+2n\pi)[/tex] and [tex](-6,-\frac{\pi}{5}+(2n+1)\pi)[/tex], where n is an integer.
Step-by-step explanation:
The given point is
[tex]P=(6,-\frac{\pi}{5})[/tex]
If a point is [tex]P=(r,\theta)[/tex], then all polar coordinates of point P are defined as
[tex](r,\theta)=(r,\theta+2n\pi)[/tex]
[tex](r,\theta)=(-r,\theta-(2n+1)\pi)[/tex]
where n is an integer.
In the given point [tex]r=6[/tex] and [tex]\theta=-\frac{\pi}{5}[/tex]. So all polar coordinates of point P are defined as
[tex](6,-\frac{\pi}{5})=(6,-\frac{\pi}{5}+2n\pi)[/tex]
[tex](6,-\frac{\pi}{5})=(-6,-\frac{\pi}{5}+(2n+1)\pi)[/tex]
Therefore all polar coordinates of point P are [tex](6,-\frac{\pi}{5}+2n\pi)[/tex] and [tex](-6,-\frac{\pi}{5}+(2n+1)\pi)[/tex], where n is an integer.
Where should you plot the ordered pair (7,5) in relation to the origin?
A. 7 spaces to the right, 5 times
B. 7 spaces up and 5 spaces to the right
C. 7 spaces to the right and 5 spaces up
D. 5 spaces to the right and 7 spaces up
Answer:
C
Step-by-step explanation:
C: 7 spaces to the right and 5 spaces up
this point is in Quadrant I.
Answer:
7 spaces to the right and 5 spaces up
Step-by-step explanation:
Find the volume of the solid figure.
A. 96 pi cu in
B. 120 pi cu in
C.192 pi cu in
Answer:
A. 96π in³
Step-by-step explanation:
The formula you can use to find the volume of a cone is ...
V = (π/3)r²·h . . . . where r is the radius and h is the height
Put the given numbers into the formula and do the arithmetic.
V = (π/3)(6 in)²(8 in) = 96π in³
Answer:
The answer is 96 pi cu in
Step-by-step explanation:
What is the area of the shaded region below? Will mark the brainiest if work is shown.
Answer:
Step-by-step explanation:
a touchdown in football counts for 6 points if n stands for the number of touchdowns, which equation represents how many points n touchdowns are worth
Answer:
6n
Step-by-step explanation:
Your response you have been asked to build a scale model of your school out of toothpicks. imagine your school is 30 feet tall. your scale is 1 ft:1.47 cm. if a toothpick is 6.3 cm tall, how many toothpicks tall will your model be
Answer:
563673773837737477377374
Step-by-step explanation:
JK
Answer:
im not too sure
Step-by-step explanation:
sorry
question 71 true or false
Answer:
False
Step-by-step explanation:
we know that
Applying the law of sines
24/sin(92°)=7/sin(Z°)
sin(Z)=7*sin(92°)/24
sin(Z)=0.291489
Z=arcsin(0.291489)=16.9°
How much is a tax of 5% on a purchase of $27.50? Show work
You multiply 27.50 with 5 and then divise by 100 (5%).It is around $1.37 to &1.38
To calculate the sales tax on a $27.50 purchase at 5%, convert 5% to decimal form (0.05) and multiply by the purchase amount. This results in a tax of $1.38, and the total cost with tax is $28.88.
To find the amount of sales tax due on a purchase of $27.50 with a 5% tax rate, you should first convert the percentage to a decimal. To do this, you divide by 100 or simply move the decimal point two places to the left. Thus, 5% becomes 0.05 as a decimal. Then, multiply this decimal by the total cost of the purchase to calculate the sales tax.
This calculation is as follows: $27.50 \ imes 0.05 = $1.375.
Since you generally do not pay fractions of a cent, you would round this number to the nearest cent, making the sales tax $1.38. The total cost with tax would then be the sum of the original cost plus the sales tax: $27.50 + $1.38 = $28.88.
As of May 4th, 185 people had signed up for a 5k. Of those signed up, 42 requested a short sleeve medium shirt. If we are putting in an order of 300 shirts, how many short sleeve medium shirts should we order?
Answer:
You should order 66 short sleeve mediums.
hope this helps
what is the equation of the line shown below? Give your answer in slope-intercept form. (5,4) (-4,-5)
Answer:
y = x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (- 4, - 5)
m = [tex]\frac{-5-4}{-4-5}[/tex] = [tex]\frac{-9}{-9}[/tex] = 1, thus
y = x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (5, 4), then
4 = 5 + c ⇒ c = 4 - 5 = - 1
y = x - 1 ← equation in slope- intercept form
The final equation is y = x - 1.
To find the equation of the line in slope-intercept form, which is y = mx + b, we need two pieces of information: the slope (m) and the y-intercept (b). First, let's calculate the slope using the two given points (5,4) and (-4,-5).
The formula for slope is:
m = (y2 - y1) / (x2 - x1)
Therefore:
m = (-5 - 4) / (-4 - 5) = (-9) / (-9) = 1
Now that we have the slope, we use one of the points to solve for the y-intercept. By substituting the slope and the coordinates of one of the points into the equation, we get:
4 = (1)(5) + b
4 = 5 + b
b = 4 - 5 = -1
Finally, the equation of the line in slope-intercept form is:
y = x - 1
Solve the system of equations.
y=x−5 y=x^2−2x−9
Enter your answers in the boxes.
( , ) or ( , )
sub the first equation into the next one
The ratio of jakes money to joes money is 3:5. If joe gives jake $25, they will have an equal amount of money. How much money do they have altogether?
Answer: jake has 75 dollars and joe has 125 dollars
Step-by-step explanation:
3/5 = 75/125
joes gives 25 dollar
75 + 25 = 100
125 - 25 = 100
Which equation shows how (10, 8) can be used to write the equation of this line in point-slope form?
Answer:
y - 8 = m(x - 10). (h, k)
Step-by-step explanation:
If the slope is m, then the desired equation is y - 8 = m(x - 10). (h, k) represents the given point, which here is (10, 8).
Next time, won't you please share the answer choices?
Answer: y - 8 + 10x
ep-by-step explanation:
Factor completely 3x2+2x-1
Answer:
(x + 1) (3x - 1)
Step-by-step explanation:
Using the AC method, here a = 3, b = 2, and c = -1.
ac = 3 * -1 = -3
Factors of -3 that add up to +2 are +3 and -1.
Divide by a: +3/3, -1/3
Reduce: +1/1, -1/3
So the factors are x + 1 and 3x - 1.
3x² + 2x - 1 = (x + 1) (3x - 1)
Answer:
x = 1/3 or x = -1
Step-by-step explanation:
3x^2 + 2x - 1
=> 3x^2 + 3x - 1x - 1 product = -3 sum = 2
=> 3x( x + 1 ) - 1(x + 1 )
=> (3x - 1) (x + 1)
3x = 1
=>x=1/3 or x = -1
HOPE THIS HELPS YOU ~
A road crew must repave a rode that is 2/5 miles long. They can repave 1/30 miles each hour. How long will it take the crew to repave the road?
It would take 12 hours.
the equation would be 2/5=1/30x where x would equal the amount of hours it would take
Giselle works as a carpenter and as a blacksmith. She earns \$20$20dollar sign, 20 per hour as a carpenter and \$25$25dollar sign, 25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of 303030 hours, and earned a total of \$690$690dollar sign, 690. How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith? Giselle worked as a carpenter for hours and as a blacksmith for hours last week.
Answer:
Carpenter = 12 hours
Blacksmith = 18 hours
Step-by-step explanation:
Look at attachment:
Hope this helps! :)
Giselle worked as a carpenter for hours and as a blacksmith for hours, last week will be 18 hours and 12 hours, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Giselle works as a carpenter and as a blacksmith. She earns $20 per hour as a carpenter and $25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of 30 hours and earned a total of $690.
Let 'x' be the number of hours of a blacksmith and 'y' be the number of hours of a carpenter. Then the equations are given as,
x + y = 30 ...1
20x + 25y = 690 ...2
From equations 1 and 2, then we have
20(30 - y) + 25y = 690
600 - 20y + 25y = 690
5y = 90
y = 18
Then the value of 'x' is given as,
x + 18 = 30
x = 30 - 18
x = 12
Giselle worked as a carpenter for hours and as a blacksmith for hours, last week will be 18 hours and 12 hours, respectively.
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i go to school on the 4th of June Monday and i summer term is on 29th June i have 3 days a week at school Monday Tuesday Wednesday
how meany of my schooldays are left
11 school days are left.
In the attached picture of a calendar, I marked the days the person has left. There are 11.
Shamika's grandmother opens an account with a deposit of $5,000 for Shamika as a college savings account. The account pays 5 percent annual interest. How much money will be in the account after 10 years?
Answer:
$7500
Step-by-step explanation:
$5000 was deposited
5% annual interest of the $5000 is $250
so in ten years the interest will be 10 ×$250 =$2500
so the total sum that will be in the account is $5000 + $2500 =$7500
What is the surface area of the right prism given below?
Answer: Option D.
Step-by-step explanation:
You can calculate the surface area of this right prism by adding the area of its faces.
You can observe that the faces of the right prism are: Three different rectangles and two equal triangles.
The formula for calculate the area of a rectangle is:
[tex]A=lw[/tex]
Where "l" is the lenght and "w" is the width.
The formula for calculate the area of a triangle is:
[tex]A=\frac{bh}{2}[/tex]
Where "b" is the base and "h" is the height.
You can observe that the hypotenuse of the each triangle is the width of one of the larger rectangle, then , you can find its value with the Pythagorean Theorem:
[tex]a=\sqrt{b^2+c^2}[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.
Then, this is:
[tex]a=\sqrt{(8units)^2+(15units)^2}=17units[/tex]
Therefore, you can add the areas of the faces to find the surface area of the right prism (Since the triangles are equal, you can multiply the area of one of them by 2). This is:
[tex]SA=(10units)(8units)+(15units)(10units)+(17units)(10units)+2(\frac{(15units)(8units)}{2})\\\\SA=520units^2[/tex]
Answer:
520 units^2
Step-by-step explanation:
The equation yˆ=0.8579x+73.4728 models the mass of a mammal’s brain, in grams, where x is the mass of the mammal, in kilograms.
According to the regression equation, what is the approximate mass of a mammal's brain with a body that has a mass of 60 kg?
about 74 g
about 83 g
about 125 g
about 150 g
Answer:
Step-by-step explanation:
Answer:
125 grams.
Step-by-step explanation:
We have been given an equation , which models the mass of a mammal’s brain, in grams, where x is the mass of the mammal, in kilograms.
To find the approximate mass of a mammal's brain with a body that has a mass of 60 kg, we will substitute in our given equation.
Therefore, the mass of the mammal's brain is approximately 125 grams.
Please help me out????
Answer:
actually ASA and SAA is the same ASA stands for angle side angle while SAA stands for side angle angle .lets prove
Step-by-step explanation:
first name the triangle as i told earlier like ABC and PQR then
first side:AB=PQ,angleA=angleP,angleB=angleQ
One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero. Does this mean that when you analyze a body in equilibrium
Answer:
One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero. Does this mean that when you analyze a body in equilibrium
Step-by-step explanation:
One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero. Does this mean that when you analyze a body in equilibrium
There are 2 conditions for equilibrium require that the sum of all external forces acting on the body is zero (first condition of equilibrium), and the sum of all external torques from external forces is zero (second condition of equilibrium).
What is the torques?
Torque is the expression of a rotational or twisting force. The engines in vehicles rotate about an axis, thus creating torque.
One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero.
When a body or a system is in equilibrium, there is no net tendency to change.
In mechanics, equilibrium has to do with the forces acting on a body. When no force is acting to make a body move in a line, the body is in translational equilibrium; when no force is acting to make the body turn, the body is in rotational equilibrium.
There are 2 conditions for equilibrium require that the sum of all external forces acting on the body is zero (first condition of equilibrium), and the sum of all external torques from external forces is zero (second condition of equilibrium).
These two conditions must be simultaneously satisfied in equilibrium.
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NEEED HELP PLLZZZZZZ
Answer:
4
Step-by-step explanation:
In a 30-60-90 triangle, the short leg is half the length of the hypotenuse.
The path of a diver diving into the water is approximately parabolic. Diving Timelapse The function h(t)=-2t^2+3t+9 h ( t ) = − 2 t 2 + 3 t + 9 most closely represents the height (h) of the diver in feet after t seconds. How high does the diver reach? Round to the nearest tenth. Hint: Make sure you include units. A space is needed between the number and unit. Example: 34.8 feet
Answer:
10.125 feet
Step-by-step explanation:
h(t) = -2t² + 3t + 9
The maximum height is at the vertex of the parabola. For a parabola ax² + bx + c, the vertex is at x = -b/(2a).
t = -3 / (2×-2)
t = 3/4
h(3/4) = -2(3/4)² + 3(3/4) + 9
h(3/4) = -9/8 + 9/4 + 9
h(3/4) = 81/8
h(3/4) = 10.125 feet
Can someone help me out?
Answer:
40 degrees
Step-by-step explanation:
A triangle solver tool can find the angle easily. It is 39.8°, which rounds to 40°. Apps are available on some calculators, on the Internet, and for iOS and Android phones and tablets.
___
You may be expected to solve this using the Law of Cosines. If we name the sides ...
a = 1.75b = 3.00c = 2.00the law of cosines tells us the relationship is ...
c² = a² + b² -2ab·cos(θ)
Then the angle is ...
θ = arccos((a² +b² -c²)/(2ab)) = arccos((3.0625 +9 -4)/(2·1.75·3))
= arccos(8.0625/10.5) ≈ 39.838° ≈ 40°
Graph x^3 - 3x^2 + 2 = 0.1 - x What are the solutions of the equation?
To solve the equation
[tex]x^3 - 3x^2 + 2 = 0.1 - x[/tex], you can use the numerical method such as the Newton-Raphson method to approximate the solutions. The solutions are approximately x ≈ 0.84185 and x ≈ 2.725.
Explanation:To solve the equation
[tex]x^3 - 3x^2 + 2 = 0.1 - x[/tex], we first rearrange it as
[tex]x^3 - 3x^2 + x - 1.9 = 0[/tex]. Then, we can use a numerical method such as the Newton-Raphson method to approximate the solutions. Starting with an initial guess, we can iteratively apply the formula
[tex]x_n+1 = x_n - f(x_n) / f'(x_n)[/tex]until we reach an accurate solution. In this case, the solutions are approximately x ≈ 0.84185 and x ≈ 2.725.
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The solutions to the systems of equations graphically are (2, -2) and (1.52, -1.42)
Solving the systems of equations graphicallyFrom the question, we have the following parameters that can be used in our computation:
x³ - 3x + 2 = 0.1 - x
When splitted, we have
y = x³ - 3x² + 2
y = 0.1 - x
Next, we plot the graph of the system of the equations
See attachment for the graph
From the graph, we have solution to the system to be the point of intersection of the lines
These points are located at (2, -2) and (1.52, -1.42)
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The box is being pushed to the right with a force of 300 newtons, and to the left with a force of 400 newtons.
The magnitude of the net force on the box is 100 Newtons to the left.
What is force?A force is the result of the interaction between two things and can be either a push or a pull. Due to the fact that it is a vector quantity, it possesses both magnitude and direction. The object's state of motion, direction, size, and form might all change as a result.
Given, the box is being pushed to the right with a force of 300 newtons, and to the left with a force of 400 newtons.
Here,
400 newtons > 300 newtons
400 newtons is much more than 300 newtons,
The net force on the box will be the sum of F₁ and F₂.
Let the forces F₁ and F₂ act on the table in opposite direction,
F₁ is the greater than F₂,
the F net = F₁-F₂
And the magnitude of the net force on the box,
400 -300 = 100 newtons.
Therefore, net force on the box is 100 Newtons to the left.
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The complete question is:
A box is being pushed to the right with a force of 300 Newtons', and to the left with a force of 400 Newtons'. What is the magnitude of the net force on the box?