The unit vectors that are orthogonal to both i+j and i+k are
± (-1/√3, 1/√3,1/√3 )
What are vector equations ?
Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.
a=i+j = < 1,1,0 > , b=i+k = < 1,0,1>
Let c= + < ( cos α,cos β ,cos γ )>
be the unit vectors (in opposite directions) orthogonal to a and b
the scalar product :
c.a = cos α +cos β = 0
c.b = cos α + cos γ = 0
It follows that ,
c= ± ( -cos α,cos α ,cos α )
cos α = ±1/√3
c= ± (-1/√3, 1/√3,1/√3 )
The unit vectors that are orthogonal to both i+j and i+k are
± (-1/√3, 1/√3,1/√3 )
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The unit vectors that are orthogonal to both i+j and i+k are
± (-1/√3, 1/√3,1/√3 )
What are vector equations ?
Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.
a=i+j = < 1,1,0 > , b=i+k = < 1,0,1>
Let c= + < ( cos α,cos β ,cos γ )>
be the unit vectors (in opposite directions) orthogonal to a and b
the scalar product :
c.a = cos α +cos β = 0
c.b = cos α + cos γ = 0
It follows that ,
c= ± ( -cos α,cos α ,cos α )
cos α = ±1/√3
c= ± (-1/√3, 1/√3,1/√3 )
The unit vectors that are orthogonal to both i+j and i+k are
± (-1/√3, 1/√3,1/√3 )
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3/7 of the tarts that Mrs Lee baked were pineapple tarts, 2/5 of the tarts were strawberry tarts and the rest were coconut tarts. There were 252 more pineapple tarts than coconut tarts. How many strawberry tarts did Mrs Lee bake?
Answer:
392
Step-by-step explanation:
...................
Solve the following initial value problem:
t* dy/dt+3y=8t
with y(1)=8.
Find the integrating factor, u(t)= ,
and then find y(t)=
Answer:
The integrating factor, u(t), for the initial value problem t* dy/dt+3y=8t with y(1)=8 is u(t) = e^(3t). The solution to this equation is y(t) = 8e^(-3t)+2te^(-3t).
Step-by-step explanation:
The integrating factor, u(t), for the given initial value problem t(dy/dt)+4y=3t with y(1)=8 is u(t) = e^(4∫t dt) = e^(2t^2).
Using this integrating factor, the solution to the initial value problem is y(t) = (3/8)te^(2t^2)+Ce^(-2t^2), where C is a constant of integration. Since y(1)=8, we can solve for C and find that C=-7/4. Therefore, the solution to the initial value problem is y(t) = (3/8)te^(2t^2)-7/4e^(-2t^2).
We are asked the solve the following differential equation, [tex]t\frac{dy}{dt}+3y=8t[/tex]. This is an ordinary, linear, first-order DE. We need it in the form [tex]\frac{dy}{dt}+P(t)y=Q(t)[/tex], where [tex]\mu(t)=e^{\int\ {P(t)} \, dt }[/tex], which is the integrating factor.
[tex]\Longrightarrow t\frac{dy}{dt}+3y=8t[/tex], multiply everything by t.
[tex]\Longrightarrow \frac{dy}{dt}+(\frac{3}{t} )y=8[/tex]
We now have the correct form for solving a linear, first-order DE.
Find [tex]\mu(t)[/tex].
[tex]\Longrightarrow \mu(t)=e^{\int\ {P(t)} \, dt } \Longrightarrow \mu(t)=e^{\int\ {\frac{3}{t} } \, dt }[/tex]
[tex]\Longrightarrow \mu(t)=e^{3\int\ {\frac{1}{t} } \, dt }\Longrightarrow \mu(t)=e^{3ln|t|} \Longrightarrow \mu(t)=e^{ln(t^3)}[/tex]
[tex]\Longrightarrow \mu(t)=t^3[/tex]
Now multiply the entire DE by [tex]\mu(t)[/tex].
[tex]\Longrightarrow t^3[\frac{dy}{dt}+(\frac{3}{t} )y=8][/tex]
[tex]\Longrightarrow (t^3)\frac{dy}{dt}+(t^3)(\frac{3}{t} )y=(t^3)8[/tex]
[tex]\Longrightarrow (t^3)\frac{dy}{dt}+(3t^2)y=(t^3)8[/tex]
Verify that the L.H.S is a product rule of [tex]t^3y[/tex].
Product rule: [tex]\frac{d}{dx}[f(x)g(x)]=f(x)g'(x)+f'(x)g(x)[/tex]
[tex]\frac{d}{dt}[t^3y]=(t^3)(\frac{dy}{dt} )+(3t^2)(y)[/tex]
It is the product rule, so we can move forward by integrating both sides of the DE.
[tex]\Longrightarrow \int\ {[t^3y]'} \, =\int\ {8t^3} \, dt[/tex]
[tex]\Longrightarrow t^3y=2t^4+C[/tex]
Now using the initial condition to find the arbitrary constant, C.
[tex]t^3y=2t^4+C ;y(1)=8[/tex]
[tex]\Longrightarrow (1)^3(8)=2(1)^4+C[/tex]
[tex]\Longrightarrow 8=2+C[/tex]
[tex]\Longrightarrow 6=C \Longrightarrow C=6[/tex]
Now we have, [tex]t^3y=2t^4+6[/tex], solve for y.
[tex]\Longrightarrow t^3y=2t^4+6[/tex]
[tex]\Longrightarrow y=2\frac{t^4}{t^3} +\frac{6}{t^3}[/tex]
[tex]\Longrightarrow y=2t +6t^{-3}[/tex]
Thus the given differential equation with the initial condition is solved, [tex]y=2t +6t^{-3}[/tex].
Calculate an uncorrected creatinine clearance value given the following:urine creatinine = 76 mg/dLserum creatinine = 1.2 mg/dLtotal volume = 1430 mL in 24 hour collection.
The uncorrected creatinine clearance value is 62.7mL/min
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface
Given:
U=76 mg/dL
P= 1.2 mg/dL
Let V= volume of urine in mm/min
V=1430mL/1440min
V=0.99mL/min
Use the formula:
UV/P
=(76 x .99)/1.2=62.7mL/min
The uncorrected creatinine clearance value is 62.7mL/min
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if AD = 9 and DB = 4. Find the length of CD.
The length CD of the triangle is 6 units
How to determine the length CDFrom the question, we have the following parameters that can be used in our computation:
The triangle
Also, we have
AD = 9 and DB = 4
The length CD (x) is then calculated as
x/4 = 9/x
Cross multiply
This gives
x^2 = 36
Take the square roots
x = 6
Hence, the solution is 6
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BALL
AVENGER
Know When to Hold 'Em
Jack, Brooke and Caroline are chatting after school about a new special edition comic book
that just exploded on the scene. One of the friends owns a signed comic acquired before
the author and artist became famous, while the other two friends are eager to get their
hands on a signed copy. Read the scenarios below and decide if Jack should sell his comic
book to Brooke, make a trade with Caroline or hold on to his signed comic.
Time Required: 10 minutes
LESSON 21: STUDENT ACTIVITY SHEET 1
JACK (SELLER):
Jack collects comic books and last year he went to a local convention to check out some
new artists. He found one he thought was amazing and decided to buy an autographed
comic by him at the show for $5. Fast forward one year and the author is now hugely
popular, with everyone clamoring to buy his comics. Autographed comic books are flying
off local shelves at $25 each and some are even selling for $50 online. Jack's unsure if he
should keep the comic, make a trade or sell it now that it's worth so much money.
Should Jack sell, hold or trade? Why?
BROOKE (BUYER):
Brooke collects rare and original comic books. She loves the new series and needs an
autographed copy of the original comic book to add to her collection. She is willing to pay
whatever it takes to buy it and offers Jack $100 for it.
CAROLINE (TRADER):
Caroline would really like to have a signed copy of the comic book, but there's no way she
can afford to pay $25 or $50 to buy one. She does have three comic books from another
author that she, Jack and Caroline all like a lot. She offers Jack her three comic books for
his autographed comic.
It depends on Jack's personal preference and priorities. If he values having a large collection of comics.
Describe Comics?Comics are visual storytelling medium that combines text and images to convey a narrative or illustrate a story. They can come in many forms, including comic books, graphic novels, manga, and webcomics, and often feature characters, settings, and events that are fictional or based on real-life events. Comics can be serious or humorous and can be aimed at a wide range of audiences, from children to adults. The format of comics allows for a unique combination of text and illustration that can create an immersive experience for the reader.
It depends on Jack's personal preference and priorities. If he values having a large collection of comics, he may choose to make a trade with Caroline for three of her comic books. If he values money, he may choose to sell the comic to Brooke for $100. If he values the sentimental attachment to the comic book or the rarity of a signed copy, he may choose to hold onto the comic. Ultimately, the decision is up to Jack and what he values the most.
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Ariana loves making things she can wear. She makes a necklace by joining together 10 large pink paper clips. Each paper clip has a mass of 2 grams.
The total mass of the necklace is 20 grams.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that,
Ariana loves making things she can wear. She makes a necklace by joining together 10 large pink paper clips. Each paper clip has a mass of 2 grams.
Total number of paper clips used to make necklace = 10
Mass of each clip = 2 grams
To find the total mass of the necklace, multiply the number of clips used to make necklace with the mass of each clip.
Mass of necklace = 10 × 2 grams = 20 grams
Hence 20 grams is the mass of the necklace.
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A bicycle has a listed price of 691.95 before tax. If the sales tax rate is 7.75% , find the total cost of the bicycle with sales tax included.
Answer:
745.57
Step-by-step explanation:
[tex]691.95 \times \frac{7.75}{100} = 53.62[/tex]
[tex]53.62 + 691.95 = 745.57[/tex]
(~P ∧ ~Q) ∨ (~P ∧ ) ∨ (P ∧ ~Q),
For the circuit corresponding to the Boolean expression given above, there is an equivalent circuit with at most two logic gates. Construct such a circuit and explain the construction in detail.
Answer:
The equivalent circuit can be constructed using two NAND gates. The NAND gate is universal and can be used to implement all other logic gates including AND, OR, NOT, etc.
Here's the construction of the equivalent circuit:
First NAND gate: The first NAND gate implements the expression (~P ∧ ~Q). The inputs to the gate are P and Q, and the output is connected to the first input of the second NAND gate.
Second NAND gate: The second NAND gate implements the expression (~P ∧ (output of first NAND gate)) ∨ (P ∧ ~Q). The second input of the second NAND gate is connected to the output of the first NAND gate. The output of the second NAND gate is the final output of the circuit.
This circuit implements the given Boolean expression and has at most two logic gates.
Find the value of a by substituting the point (0,4) in for x and y to determine the value of b
The value of {b} is equivalent to 4.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is to find the value of {b}.
The function is not given. Assume that the function is -
y = ρx + b
For the point (0, 4), we can write -
4 = ρ x 0 + b
b = 4
Therefore, the value of {b} is equivalent to 4.
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Could this input and output table represent a function?
Yes, the given input and output values represent a function, f(x) = x²
What are functions?
In mathematics, a function is an expression, rule, or law that specifies the relationship between an independent variable x and a dependent variable y.
y and x are related in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x). In other words, for the same x value, there cannot be more than one value for f(x).
If we look at the table, we can see a relationship between the x (input) and y (output) values.
The output values (y) are the squares of the corresponding input values(x).
Also, there is only one distinct value of y for each x value.
Therefore the given values represent a function, f(x) = x².
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Omari drives a car that gets 18 miles per gallon of gasoline. The car's gasoline tank holds 15 gallons. The distance Omari drives before refueling is a function of the number of gallons of gasoline in the tank. Identify a reasonable domain for this situation.
(A) 0 to 18 miles
(B) 0 to 270 miles
(C) 0 to 15 miles
(D) 0 to 60 miles
Identify a reasonable range for the function in the question above.
(A) 0 to 18 miles
(B) 0 to 270 miles
(C) 0 to 15 miles
(D) 0 to 60 miles
a) The domain of the function is 0 to 15 miles
b) The range of the function is 0 to 270 miles
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the mileage of the car = 18 miles per gallon
The amount of gasoline the car can hold = 15 gallons
Let the distance to empty be a function of mileage of the car × amount of gas in gallons
Now , the domain of a function is the set of values that we are allowed to plug into our function which ranges from 0 to 15
So , distance to empty = 18 x 15 = 270
So , the range of the function is the set of output values which ranges from 0 to 270
Hence , the domain of the function is 0 to 15 miles and the range of the function is 0 to 270 miles
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(X-2)^2 - (x-4)^2 simplify
A sweater is on sale for a 20% discount. The amount of the discount is $12. What is the original cost of the sweater? Do not include a dollar sign in your answer.
The original cost of the sweater that is on sale for a 20% discount will be $60.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A sweater is on sale for a 20% discount. The amount of the discount is $12.
Let 'C' be the original cost. Then the equation is given as,
20% = ($12 / C) x 100
Simplify the equation, then we have
20% = ($12 / C) x 100
0.20 = ($12 / C)
C = $12 / 0.20
C = $60
The original cost of the sweater that is on sale for a 20% discount will be $60.
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Sandra bought 4 pounds of sweet potatoes for $6.40. What is the cost per pound of the sweet potatoes?
Answer: Sandra bought 4 pounds of sweet potatoes for $6.40. What is the cost per pound of the sweet potatoes?
$1.57
Step-by-step explanation: pls give brainiest
Answer:
The answer to your question is $1.57.
Step-by-step explanation:
To find the cost per pound of sweet potatoes, divide $6.28 by 4.
6.28 ÷ 4= $1.57
I hope this helps and have a wonderful day!
Find the distance between the points on a number line. -8,9
Answer:
17
Step-by-step explanation:
Find the absolute value of -8, which is 8, and add 9 to that, which gives you 17.
A furniture worker tells an apprentice, "Always use coarse steel wool at the start of a major wood refinishing project. As you progress, use finer steel wool.” Which information in the graphic supports this advice? The grade levels of steel wool range from 0000, which is fine, to 4, which is coarse. Grade 1 should be used to remove paint, and grade 000 to remove paint drips. The grade levels of steel wool used for metalwork are comparable to the levels used for woodworking. Grade 4 steel wool is used to remove paint and other materials, while grade 0000 is used for the final finish on fine woodwork.
Therefore, the project progresses and the unitary method wood becomes smoother, finer steel wool (i.e. grades 3, 2, 1, and 0000) can be used to achieve a smoother finish..
What exactly is a unitary method?To finish a task using unitary procedure, multiply this same sum by two after finding the measurements of one tiny slice. To differentiate a coded unit from a specific group or collection of groups, use the unit variable method, which only needs an expression. For instance, 40 pencils could cost. 4,000, which really is equivalent to $1.01 as well as 4000 pounds.
Here,
The information in the graphic that supports the advice to use coarse steel wool at the start of a major wood refinishing project is:
"Grade 4 steel wool is used to remove paint and other materials, while grade 0000 is used for the final finish on fine woodwork."
This suggests that coarse steel wool (i.e. grade 4) is more effective at removing paint and other materials, which is often necessary at the beginning of a wood refinishing project.
As the project progresses and the wood becomes smoother, finer steel wool (i.e. grades 3, 2, 1, and 0000) can be used to achieve a smoother finish..
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Greg plants two-thirds of his garden in potato’s and one-eighth in carrots.what fraction of the garden remains for his other crops?
The fraction to the garden that would probably remain for his other crops would be = 5/24
How to calculate the fraction of the garden left?The portion of the garden in which potatoes are being planted = 2/3
The portion of the garden in which carrots are being planted = 1/8
Therefore,the fraction of the garden that is left without plants = X
But;
The whole garden is represented as 1.
That is;
1 = 2/3+1/8 +X
Make X the subject of formula;
X = 1 - (⅔+⅛)
X = 1-(19/24)
X = 1-19/24
X= 5/24.
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30% sugar syrup using 75 g sugar
Answer:
22.5 g suger!
Step-by-step explanation:
100% is 75 g
10% is 7,5 g
30% is 22.5 g
10% x 3
( 7,5 g x 3 = )
7 x 3 = 21
0.5 x 3 = 1.5
21 + 1.5 = 22.5 g!
consider the set of replicate measurements. 23.4 g,23.9 g,22.6 g,24.5 g,23.0 g,23.6 g for this data set, calculate the mean, range, standard deviation, and percent relative standard deviation.
The mean of the measurements is 23.3 g.
The standard deviation of the measurements is 0.65 g.
The range of the measurements is 1.9 g
The percent relative standard deviation of the measurements is 2.77%.
What is the mean, range, standard deviation, percent relative standard deviation?
Mean: The mean is the average of all the measurements. To find the mean, add up all the measurements and divide by the number of measurements:
(23.4 + 23.9 + 22.6 + 24.5 + 23.0 + 23.6) / 6 = 23.3
So, the mean of the measurements is 23.3 g.
Range: The range is the difference between the largest and smallest measurements. To find the range, subtract the smallest measurement from the largest measurement:
24.5 g - 22.6 g = 1.9 g
So, the range of the measurements is 1.9 g.
Standard Deviation: The standard deviation is a measure of the spread of the data around the mean. To find the standard deviation, we first calculate the difference between each measurement and the mean, square each difference, and then average the squared differences. The square root of this average gives us the standard deviation.
(23.4 - 23.3)^2 + (23.9 - 23.3)^2 + (22.6 - 23.3)^2 + (24.5 - 23.3)^2 + (23.0 - 23.3)^2 + (23.6 - 23.3)^2 = 0.09 + 0.16 + 0.49 + 1.16 + 0.09 + 0.16 = 2.55
2.55 / 6 = 0.425
√0.425 = 0.65
So, the standard deviation of the measurements is 0.65 g.
Percent Relative Standard Deviation (RSD): The percent RSD is the standard deviation expressed as a percentage of the mean. To find the percent RSD, divide the standard deviation by the mean and multiply by 100:
0.65 g / 23.3 g * 100 = 2.77%
So, the percent relative standard deviation of the measurements is 2.77%.
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A baseball pitcher won 80% of the games h pitched. If he pitched 35 ballgames, how many games did he win?
Answer:
The pitcher won 28 games out of 35.
Step-by-step explanation:
A baseball pitcher won 80% of the games he pitched, so the formula to calculate the number of games won is:
G = 80/100 * n
where
G is the number of games won
n is the number of games pitched
We know that the pitcher pitched 35 games, so:
G = 0.8 * 35
G = 28
So, the pitcher won 28 games out of 35.
Answer: 28
Step-by-step explanation: times 35 by 0.80 to get your answer, also not really a collage level question.
PS pls help me by answering one of my questions (:
A graphic company charges $60 per hour for the work of its most senior graphic artists, $30 per hour for the work of a production designer, and $19 per hour for the
work of a trainee. A recent project required 34 hours of work from a senior artist, 13 hours from a production designer, and 35 hours from a trainee. Write out a
mathematical statement for calculating the total labor cost, and then compute this cost.
Select the correct choice below and fill in the answer box to complete your choice.
(Simplify your answer.)
OA. $60+34+$30+13+$19+35-$
OB. (34+13+35) x ($60+$30+$19)=$
OC. 34x13x35+$60 × $30x$19=$
OD. 34×$60+ 13× $30+35x$19=$
Considering the definition of an equation, a mathematical statement for calculating the total labor cost is Total labor cost= 60×S + 30×PD + 19×T and the total labor cost for the recent project is $3,160.
Definition of equation
An equation is the equality between two algebraic expressions connected by the equals sign in which some known data are included together with one or more unknown values, also known as unknowns.
The terms of an equation are the addends that make up the members of an equation, whereas the members of an equation are each of the expressions that appear on both sides of the equal sign.
Finding the value that satisfies an equation is what is meant by finding its solution. By converting the unknown to the answer in this manner, the equality must be true.
This case
In this case, you consider:
S= hours of work from a senior artist.
PD= Production designer labor hours.
T= hours of work from a trainee.
On the other hand, you know that Girilla Graphics charges:
For the work of its most senior graphic artists, they charge $60 per hour.
For production designer work, the hourly rate is $30.
$19 per hour for a trainee's labor.
Therefore, the following equation can be used to determine the project's overall labor costs:
Total labor cost= 60×S + 30×PD + 19×T
A recent project required:
A senior artist's 34 hours of labor.
13 hours from a production designer.
35 hours from a trainee.
So, the following formula can be used to determine the project's overall labor costs:
Total labor cost= 60×34 + 35×13 + 19×35
Solving:
Total labor cost= $3,160
In summary, a mathematical statement for calculating the total labor cost is Total labor cost= 60×S + 30×PD + 19×T and the total labor cost for the recent project is $3,160.
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Title: ....Home Lork Date: 6/02/2025. 42 students in a class took a test in Science and English. 13 students took both subjects and students did not pass in any of the two subjects. Those who took Science is 7 less than thos who took only English. Work 1.5 (a) Illustrate the information on a Venn diagram. (b) Find the number of students who passed: (ii) English; (i) Science; Solution Let u 1.(u). universal set 4.2. .... .4/1.2 (iii) exactly one subject. Correction
(a) To illustrate the information on a Venn diagram:
Draw two circles, one for Science and one for English.Label the circles with the names of the subjects.Calculate the number of students who took both Science and English (13 students).Label the overlapping region of the two circles with the number of students who took both subjects (13).Calculate the number of students who took only Science (7 less than those who took only English).Label the region outside the overlapping region and inside the Science circle with the number of students who took only Science.Calculate the number of students who took only English.Label the region outside the overlapping region and inside the English circle with the number of students who took only English.Calculate the total number of students in the class (42).Label the area outside both circles as the universal set, and write the total number of students in the class (42).What is a Venn Diagram?A Venn diagram is a graphical representation of the relationship between sets of items
This Venn diagram will visually represent the information given in the question and help to answer the questions about the number of students who passed each subject and the number of students who passed exactly one subject.
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Need help with this math problem please!
Answer:
The top one is: 1/2x + 6
The bottom one is: -2x + 5
Step-by-step explanation:
The top function:
f(x) = mx + b
m is the slope and b in the y-intercept. This is what you need to write the function.
The slope is 1/2. The slope is the rise over the run. If you start at the point (-6,3) and go up one unit and 2 units to the right, you end up back on the line. This is the slope. If you follow that pattern, you will cross the y axis at (0,6). 6 is the y intercept.
The bottom function:
The slope is -2. I you start at the point (1,3) and you go down 2 and one to the right, you will end up back on the line. 2/1 equals 2.
If you follow that pattern going backwards, 2 up and one to the left, you will be at the y-intercept (0,5) 5 is the y-intercept.
find the value of x. show process please!
Therefore, since the total of all the angles is 180°, the value of the other angle is 100°, 40°, and 40°.
what is angles ?In Trigonometry, an angle is a curve made up of two rods, referred to as the angle's sides, which thus converge at a center point regarded as the ball's vertex. Two rays can create an angle in the region where they are arranged. Additionally, when airplane collide, an angle is created. Dihedral angles are what they are called. An offset is a possible shape spanning two radiation or lines with an identical termination in planar geometry. The English term "angle" comes from the Latin word "angulus," which meaning "horn." The vertex is the common endpoint of the two rays, also know as the faces of the angle.
given
one angle = 40°
other angle = (11x - 18)°
in triangle sum of all angle = 180°
40° + 11x - 18 + 40 = 180
80 + 11x - 18 = 180
62 + 11x = 180
11x = 180 - 62
11x = 118
x = 10 . 2
Therefore, since the total of all the angles is 180°, the value of the other angle is 100°, 40°, and 40°.
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can someone help me please
here is the picture i need step by step
Answer:
Can you please post the picture of the question, then I can help.
Which of these is the standard form of the polynomial function y=x(x+5)(x−3)
The standard form of the polynomial function y = x(x + 5)(x - 3) is
y = x³ + 2x² - 15x
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
The polynomial function,
y = x(x+5)(x−3)
To obtain the standard form, we need to multiply out the expression and then arrange the terms in decreasing order of the degree of the monomials. The degree of a polynomial is the highest degree of its monomials.
x(x + 5)(x - 3) = x³ + (5x²) - (3x²) + (5x²) + (-15x) = x³ + 2x² - 15x
In the standard form, the coefficient of the monomial with the highest degree is 1, and the rest of the terms are arranged in decreasing order of the degree.
Thus, the standard form is x³ + 2x² - 15x
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Help pls I need this quick thx :D
Draw an accurate sketch of the function f(x) = x^4-3x^3 + 2x. Where are the zeros? Where are the critical values? Where are the maxima and/or minima? What are the intervals on which the function is increasing and decreasing, respectively? What is the behavior as x approaches ±∞? Justify your answers with calculus rather than merely copying a graph from your calculator.
Due to length restrictions, we kindly invite to read the explanation below to know how the graph of the quartic function is made. Here is a summary:
Zeros: x = - 0.732, x = 0, x = 1, x = 2.732
Critical values: x = - 0.432 (minimum), x = 0.541 (maximum), x = 2.141 (minimum)
Increasing: - 0.432 < x < 0.541 and x > 2.141
Decreasing: x < - 0.432 and 0.541 < x < 2.141
How to construct a precise sketch of a quartic function
Herein we find the definition of a quartic function, that is, a polynomial with grade 4, of which we must sketch its graph. This can be done from the understanding of the following information:
ZerosCritical values.Interval behaviorZeros
Let be equal the polynomial to zero. All roots can be found by means of numerical methods:
x⁴ - 3 · x³ + 2 · x = 0
x = - 0.732 or x = 0 or x = 1 or x = 2.732
Critical values
Determine the first derivative, equal it to zero and find the roots of the expression:
4 · x³ - 9 · x² + 2 = 0
x = - 0.432 or x = 0.541 or x = 2.141
Determine the second derivative and evaluate it at each root found in previous step:
f''(x) = 12 · x² - 18 · x + 2
x = - 0.432
f''(- 0.432) = 12.015 (MINIMUM)
x = 0.541
f''(0.541) = - 4.226 (MAXIMUM)
x = 2.141
f''(2.141) = 18.469 (MINIMUM)
Finally, find the coordinates of the quartic function:
f(- 0.432) = - 0.587
f(0.541) = 0.693
f(2.141) = - 4.148
Interval behavior
Use the first derivative find the roots of the following inequalities:
Increasing
4 · x³ - 9 · x² + 2 > 0
- 0.432 < x < 0.541 and x > 2.141
Decreasing
4 · x³ - 9 · x² + 2 < 0
x < - 0.432 and 0.541 < x < 2.141
Finally, we build the sketch with the help of a graphing tool.
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A rectangular vegetable garden will have a width that is 2 feet less than the length area of 48 square feet. If represents the length, then the length can be found by s equation:
x(x - 2) = 48
What is the length, x, of the garden?
The length is
feet.
Answer: The equation for the area of the garden is x(x - 2) = 48. To find the length, we need to solve for x:
x^2 - 2x - 48 = 0
Using the quadratic formula:
x = (-(-2) ± √((-2)^2 - 4(1)(-48)))/2(1)
x = (2 ± √(4 + 192))/2
x = (2 ± √196)/2
x = (2 ± 14)/2
x = 8 or x = -6
Since the length cannot be negative, the length of the garden is 8 feet.
Step-by-step explanation:
PLEASE HELPP MEEEEEEEEEEEEEEEEEEEEEE
Answer: the new points are A=(2,4) B=(2,3) C=(4,6) D(4,2)
Step-by-step explanation:
If the scale factor is 2, then every coordinate point of the original triangle is multiplied by the scale factor 2.