please help me solve this problem
The features related to vectors are listed below:
Case A: u' = (- 4√41 / 41, - 5√41/ 41)
Case B: Tip coordinantes of vector v: (x, y) = (10, 10)
Case C: r = 11.402
How to determine vectors
In this question we must determine three features related to vectors: (a) unit vector, (b) the definition of a vector based on the coordinates of its base and its tip, (c) The magnitude of a resulting vector.
Case A - Unit vector
Unit vectors are vectors with magnitude 1, for the case of vector u we have the following definition:
u' = u / ||u||
Where:
u' - Unit vector.u - Vectoru - ||u|| - Magnitude of the vector.Please notice that the magnitude of the vector is determined by Pythagorean theorem:
r = √[(Δx)² + (Δy)²]
Where:
r - MagnitudeΔx - Change in the x-direction.Δy - Change in the y-direction.Thus, the unit vector of u is:
u' = (- 4, - 5) / √[(- 4)² + (- 5)²]
u' = (- 4, - 5) / √41
u' = (- 4 / √41, - 5 / √41)
u' = (- 4√41 / 41, - 5√41/ 41)
Case B - Definition of a vector
This can be found easily by vector subtraction:
v = Tip coordinates - Base coordinates
(3, 4) = (x, y) - (7, 6)
(x, y) = (3, 4) + (7, 6)
(x, y) = (10, 10)
Case C - Magnitude of a vector
The magnitude is found by means of Pyhtagorean theorem:
r = √[(- 4 - 3)² + (- 5 - 4)²]
r = √[(- 7)² + (- 9)²]
r = 11.402
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An electronics company has determined that the cost of producing MP3 players is $16 per MP3 player plus $16,380 per month and fixed cost the electronic company sells each MP3 player for $250 find the revenue function
Revenue function will be 17352.5
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
It is given that,
Cost of each MP3 player plus = $16
Additional cost = $16380
Fixed cost for each MP3 player = $250
Let C(x),P(x), R(x) be the cost function, profit function and revenue function respectively.
Let x be number of units of mp3 produced and sold
R(x)= 250x is required revenue function
We know that, C(x)= variable cost+ fixed cost
C(x)=16x+16380 is the required cost function
We know that, profit= revenue-cost
P(x)=R(x)-C(x)
P(x)= 250x-[16x+16380]=250x-16x-16380 = 236x-16380
We know that break even point occur when revenue function and cost function has same value.
R(x)=C(x)
250x=16x+16380
250x-16x=16380
236x=16380
x = 16380/236 = 69.41
Revenue function, R(x) = 250x = 250(69.41) = 17352.5
Therefore, revenue will be $17352.5
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Using Euler’s formular obtain trigonometric formulars for cos(1 + 2) and sin(1 + 2).
Step-by-step explanation:
Ruler's formula states that
\(e^{i\theta} = \cos{\theta} +i\sin{\theta}\)
We also know that
\(e^{i\theta_1} \cdot e^{i\theta_2} = e^{i(\theta_1+\theta_2)}\)
therefore,
\(e^{i(\theta_1+\theta_2)}= \cos{(\theta_1+\theta_2)}+ \sin{(\theta_1+\theta_2)}\) (1)
Similarly, we can write
\(e^{-i(\theta_1+\theta_2)} = \cos{(\theta_1+\theta_2)} - \sin{(\theta_1+\theta_2)}\) (2)
Adding Eqn(1) and Eqn(2) together, we get
\(2\cos{(\theta_1+\theta_2)} = e^{i(\theta_1+\theta_2)} + e^{-i(\theta_1+\theta_2)}\)
or
\(\cos{(\theta_1+\theta_2)} = \dfrac{e^{i(\theta_1+\theta_2)} + e^{-i(\theta_1+\theta_2)}}{2}\)
To get the expression for the sine function, we subtract Eqn(2) from Eqn(1) to get
\(2i\sin{(\theta_1+\theta_2)} = e^{i(\theta_1+\theta_2)} - e^{-i(\theta_1+\theta_2)}\)
or
\(\sin{(\theta_1+\theta_2)} = \dfrac{e^{i(\theta_1+\theta_2)} - e^{-i(\theta_1+\theta_2)}}{2i}\)
Please give me the answer and where it’s located at .
Is the range a subset or a proper subset of the codomain?
A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.
What is a subset?A set that includes all or a portion of another set's elements is known as a subset. For instance, because every even integer is also an integer, the set of even integers is a subset of the set of integers. A subset that contains some, but not all, of the members of another set is said to be a proper subset. Because it contains some, but not all, of the positive integers, the set of positive integers less than 10 is a valid subset of the set of positive integers.
A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.
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I NEED HELP ASAP!!!!
Samuel entered the following key strokes on his calculator.
5 EE (-) 9 divided by 2 EE 4
What did Samuel's calculator display?
A. 2.5E - 13
B. 2.5E - 4
C. 2.5E5
D. 2.5E14
Whoever gets this CORRECT may get MARKED BRAINLIEST.
In the case above about Samuel, one can say that Samuel's calculator has display option A. 2.5 E (- 13)
What is the calculation about?The function was \(\frac{5E (-9) }{2E(4) }\) :
We know that, E implies 10 to rise to power.
So, The equation above is Converted from scientific notation into standard form.
\(\frac{5 x 10^-9 }{2 x 10^ 4 }\)
= 5/2 x 10 ⁻⁹⁻⁴
=2.5 x 10⁻¹³
Therefore, In the case above about Samuel, one can say that Samuel's calculator has display option A. 2.5 E (- 13)
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Which expression can be used to convert 22 Australian dollars to US dollar
Answer:26.4
Step-by-step explanation:1.2 x22
What does the point (12,4) represent in this situation?
Answer:
what is the situation?
Step-by-step explanation:
Calc II Question
The base of s is an elliptical region with boundary curve 9x^2 + 4y^2 = 36
Cross sections perpendicular to the x axis are isoscelees right triangle with hypotension in the base.
Correct answer is 24 but I don't know how they go that
Answer:
See below for explanation
Step-by-step explanation:
The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:
\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)
As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).
Hence, the area function for our cross-sections are:
\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)
Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:
\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)
Therefore, this explanation confirms that the correct volume is 24!
Am I correct?? Plz need help
Find an equation of the line that (a) has the same y-intercept as the line y-3x+7=0 and (b) parallel to the line -2x-1x=-12
desmos calculator will help you to get the answer, hover I graph it say (-4,-19) that the line get togther
Step-by-step explanation:
Write the range of f(x) in all three notations if the domain is -2 < x < 6 . f(x)=x+3f(x)=x+3
Answer:
Interval notation: Range = (1,9)
Words notation: Range is between 1 and 9.
Inequality notation: Range = {f(x)| 1 < f(x) < 9}
Step-by-step explanation:
The given function is
\(f(x)=x+3\)
We need to find the range of f(x) for the domain -2 < x < 6 .
At x=-2,
\(f(-2)=-2+3=1\)
At x=6,
\(f(6)=6+3=9\)
So, the range of the function is 1 < f(x) < 9. It can be written as
Interval notation: Range = (1,9)
Words notation: Range is between 1 and 9.
Inequality notation: Range = {f(x)| 1 < f(x) < 9}
What’s the answer to the questions below? Plsss help
According to the information we can infer that the parallel line would be AD or CF. Additionally, the perpendicular lines would be CB or FE.
How to identify parallel lines?To identify the parallel lines we must look at the figure and find the lines that have the same direction as the line BE and that would never intersect with the segment BE, according to the above, we can infer that the parallel lines would be:
ADCFOn the other hand, the lines perpendicular to CF would be CB or FE because they make 90° angles with segment CF. Additionally, the face that would be parallel to ABC is DEF.
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The parking fee at the amusement park is $15. Each
ride requires a ticket that costs $4. Grams spent $71
for her grandchildren. How many ride tickets did
Grams purchase?
Answer:
Step-by-step explanation:
Total money spent = 71
Parking fee = 15
71 - 15 = 56
Each ride costs = 4
Total rides = 56 ÷ 4 = 14 rides
Solve the system of linear equations by elimination. x+6y=28 2x−3y=−19
In this polygon, all angles are right angles.
What is the area of this polygon?
Enter your answer in the box.
Divide the shape into a square and a rectangle, multiply 7 by 10, and subtract 10 from 21 to get 11. then multiply 11 by 24. Lastly, add the products together and you get 334 feet squared. Have a good day my friend!
The area of the polygon is: 334 ft²
What is the Area of a Polygon?To find the area of a polygon, decompose the polygon into known shapes and find the area of each shape, then add all.
Thus:
Decomposing the polygon given, we would have rectangle 1 and rectangle 2.
Area of rectangle 1 = length × width = 7 × 10 = 70 ft²
Area of rectangle 2 = length × width = 24 × (21 - 10) = 264 ft²
Area of the polygon = 264 + 70 = 334 ft²
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3e + c = 38
3e +2c = 52
u= ab/k, for a
Solve form A
a = uk/b
Step-by-step explanation:u = ab/k
uk = ab
a = uk/b
Which expression is positive?
Answer:
A
Step-by-step explanation:
the answer is A
.......
Answer: A
Step-by-step explanation: if you add A and B you get a positive number
A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/25 for green, 1/15 for blue, 1/20 for pink, and 1/5 for red. What is the probability of pulling a red or pink card, written as a reduced fraction?
Answer:
Step-by-step explanation:
0.2(red) + 0.05(pink)
=0.25
=1/4
ALLWAYS REMEMBER OR MEANS ADD AND AND MEANS MULTIPLY
The probability of pulling a red card or a pink card is \(\frac{1}{4}\).
Probability:The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.Step-by-Step Solution -To remember -
'OR' means add.'AND' means multiply. \(0.2(red)+0.05(pink)\\= 0.25\\=\frac{1}{4}\)Therefore, the probability of pulling a red card or a pink card is \(\frac{1}{4}\).
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What is the x-intercept of the logarithmic function below?
F(x) = log3 x
OA. (3,0)
OB. (1,0)
O C. (-3,0)
O D. (-1,0)
The x-intercept of the function is (-3, 0).
What is x-intercept of a function?
A function's x-intercepts are the point(s) at which its graph crosses the x-axis. The term "x-value" is commonly used to describe the x-intercept.
Where a line on a graph crosses the x-axis is known as the x-intercept. At that time, the y coordinate's value is zero. For instance, the x-intercept would be where the equation y = x + 5 crosses the x-axis at the location (-5, 0).
The x-intercept of the given function is in option (c).
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What’s the correct answer for this? Select the ones that apply
PLEASE HELP!
Which value is MOSTLY closely associated with the fundamental principles of Buddhism?
A submission to authority
B devotion to one god
C giving up worldly desires
D honoring ancestors' spirits
Real answers only please!
Answer:
C
Step-by-step explanation:
The ultimate aim of a Buddhist disciple is to reach peace, or nirvana. To do so, the Buddha preached to give up worldly desires. So, the answer is C. Good luck ^^
Two cities,a and are mapped on the coordinate plane. How far apart are they from each other?
Answer:
\(\sqrt{97} \\ \sqrt{9^{2}+4^{2} }\)
Step-by-step explanation:
Which of the following is equivalent to the expression below?O A SiOB. -5,5O C. -2,5O D. 225
SOLUTION
We want to solve
\(\sqrt[]{-20}\)This becomes
\(\begin{gathered} \sqrt[]{-20} \\ \sqrt[]{-4\times5} \\ \sqrt[]{-1\times4\times5} \\ i\times\sqrt[]{4\times5} \end{gathered}\)The square root of a negative number is a complex number, so the square root of -1 is i
The answer becomes
\(\begin{gathered} i\times\sqrt[]{4\times5} \\ i\times2\sqrt[]{5} \\ 2i\sqrt[]{5} \end{gathered}\)At the last minute, two families (a total of 11 people) cancel because of illness. Does this effect
which company is the better deal? Why or why not?
The last-minute cancellations of two families (11 people in total) due to illness may affect the decision as to which company offers more favorable terms, depending on the specific circumstances and fee structures of the companies involved.
Why is this scenario so?If the rate is based on per person, canceling 11 people would significantly reduce the total cost for both companies. In this case, one would compare the changed prices of each company to determine which one offers the better deal.
However, with flat-rate pricing regardless of the number of participants, the cancellation of 11 people would not affect costs for either company. In such a scenario, the cancellation will not affect the evaluation of which company presents the better offer.
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Suppose carpet for a 12ft by 14ft room costs $400 find the cost to carpet a room 48ft by 56ft
Answer:
\(\$\ 6400\)
Step-by-step explanation:
1. Approach
The easiest way to solve this problem is to find the area of the first room with the dimensions of (12ft) by (14ft). Then one will divide the cost of carpeting the room by the area of the room, this will yield the price of carpeting per square foot. After finding the price of carpeting per square foot, one will find the area of the second room, with the dimensions of (48ft) by (56ft). Finally, one will multiply the price per square foot of carpeting by the area of the second room to find the price for carpeting the second room.
2. Find the area of the first room
Assume that the first room is a rectangle. the following formula can be used to find the area of a rectangle,
\((length)(width)=Area\)
The following are the dimensions of the given room,
\(length = 14\\width = 12\)
Substitute into the formula to find the area and simplify to solve,
\((length)(width)=Area\)
\((14)(12)=Area_1\)
\(168=Area_1\)
3. Find the price of carpeting per square foot
To find the price of carpeting per square foot, divide the total price for carpeting the first room by the area of the first room.
\(\frac{carpeting\ price_1}{area_1}\)
\(=\frac{400}{168}\)
Simplify,
\(=\frac{400}{168}\)
\(=\frac{50}{21}\)
4. FInd the area of the second room
Assume that the second room is also a rectangle. Use a similar strategy to find the area of this room as used for the area of the first room.
\((length)(width)=Area\)
\(length = 48\\width = 56\)
Substitute and simplify to sovle,
\((length)(width)=Area\)
\((48)(56)=Area_2\)
\(2688=Area_2\)
5. Find the price for carpeting the room
Multiply the area of the room by the price for carpeting per square foot to find the price for carpeting the second room.
\((Area_2)*(carpeting\ price)\)
\(2688=Area_2\)
\(\frac{50}{21}=carpeting\ price\)
\((Area_2)*(carpeting\ price)\)
\(=(2688)*(\frac{50}{21})\)
Simplify to solve,
\(=(2688)*(\frac{50}{21})\)
\(=(2688)*(\frac{50}{21})\)
\(=6400\)
Find the perimeter of abc with vertices (1,-6) (1,-3) (-4,-6)
Answer:
8+√34
Step-by-step explanation:
use distance formula d =√(x2-x1)² +(y2-y1)² to find the sides
√ (1 -1)²+( -6+3)² = √9 = 3
√ (1+4)²+( -6+6)² = √25 =5
√ (1+4)² + (-3+6)² = √25+9 =√34
Perimeter is P = 3+5+√34 = 8+√34
Suppose that 14 inches of wire costs 84 cents. At the same rate, how many inches of wire can be bought for 42 cents
please help!!!!!!!!!!!!
Answer: 43
Step-by-step explanation: i am thinking i did something like this in ixl