Answer:
[tex]\frac{dy}{dx}[/tex] = ([tex]\frac{dy}{dt}[/tex]) / ([tex]\frac{dx}{dt}[/tex]) = (36[tex]e^{4}[/tex]) / (-5) = -7.2[tex]e^{4}[/tex]
Step-by-step explanation:
To find the slope of the tangent line, we need to find [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex], and then evaluate them at t=1 and compute [tex]\frac{dy}{dx}[/tex].
We have:
x(t) = 2[tex]t^{3}[/tex] - 8[tex]t^{2}[/tex] + 5t + 3
Taking the derivative with respect to t, we get:
[tex]\frac{dx}{dt}[/tex] = 6[tex]t^{2}[/tex] - 16t + 5
Similarly,
y(t) = 9[tex]e^{4t-4}[/tex]
Taking the derivative with respect to t, we get:
[tex]\frac{dy}{dt}[/tex] = 36[tex]e^{4t-4}[/tex]
Now, we evaluate [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex] at t=1:
[tex]\frac{dx}{dt}[/tex]= [tex]6(1)^{2}[/tex] - 16(1) + 5 = -5
[tex]\frac{dy}{dt}[/tex] = 36[tex]e^{4}[/tex](4(1)) = 36[tex]e^{4}[/tex]
So the slope of the tangent line at t=1 is:
[tex]\frac{dy}{dx}[/tex]= ([tex]\frac{dy}{dt}[/tex]) / ([tex]\frac{dx}{dt}[/tex]) = (36[tex]e^{4}[/tex] / (-5) = -7.2[tex]e^{4}[/tex]
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What is the inverse of y=−4x+3?
The inverse of the equation y = - 4x + 3 is y = (3 - x)/4.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, An equation y = - 4x + 3.
To find the inverse we'll first solve for 'x'.
Therefore,
y = - 4x + 3.
4x = 3 - y.
x = (3 - y)/4.
Now, we'll interchange the positions of 'x' and 'y'.
Therefore,
x = (3 - y)/4 becomes,
y = (3 - x)/4.
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Draw all non-isomorphic simple graphs with three vertices. Do not label the vertices of the graph. You should not include two graphs that are isomorphic. Remember that it is possible for a graph to appear to be disconnected into more than one piece or even have no edges at all.
Three non-isomorphic simple graphs with three vertices are given in the figure below.
The first is a complete graph, in which all three vertices are connected to each other. It is represented by a triangle shape.
The second graph is a graph with one vertex connected to the other two, it is represented by a line with two branches.
The third graph is a graph with no edges, it is represented by three isolated points.
Remember that two graphs are isomorphic if one can be transformed into the other by relabeling the vertices. It's important to note that these are the only three possible non-isomorphic simple graphs with three vertices.
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suppose you spend $180 on equipment to make a new board game. In addition, each game costs $2 to make. After doing market research, you determine that the games will sell or $20 each.
what is the y-intercept of the cost equation?
Answer:
The y-intercept of an equation is the point where the line crosses the y-axis, i.e when x = 0.
In this case, the cost equation is C = 2x + 180, where C is the total cost and x is the number of board games produced.
So when x = 0, C = 2(0) + 180 = 180
Therefore, the y-intercept of the cost equation is (0,180)
So the y-intercept of the cost equation is 180.
Answer:
90
Step-by-step explanation:
What are the 4 transformations of a function?
The four transformations of a function are translation, reflection, stretching/shrinking, and rotation.
What is function?Function is a group of related statements that perform a specific task. It is a block of organized, reusable code which can be used to perform a single, related action. Functions help make code more reusable and efficient. It also reduces the complexity of a program by breaking it down into smaller and simpler parts.
Translation involves shifting the graph of a function along a given axis; reflection involves flipping the graph of a function about a given axis; stretching/shrinking involves changing the scale of a graph along a given axis; and rotation involves rotating the graph of a function about a given point. All of these transformations can be used to modify the graph of a function, allowing for a variety of different outputs.
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How can you isolate the term ?
3
f
3
+22=17
?
?
on both sides.
Answer: How you can isolate the term f/3 is to
subtract 22 from both sides.
Yesterday a chef used 30 eggs to make 6 chocolate souffles and 6 lemon meringue pies. The day before, he made 4 chocolate souffles and 8 lemon meringue pies, which used 24 eggs. How many eggs does each dessert require?
Answer:
Let the chocolate souffles be x and lemon meringue pies be y.
For yesterday, it will be 6x+6y=30
For the day before, 4x+8y=24
By solving the two equations, the answers will be obtained.
4 eggs is required for chocolate souffles and an egg for lemon pie.
What is the exponential form of 2 * 2 * 2 * 2 * 2?
(y+x)-:2+x; use x=1, and y=1
Value of expression (y + x) ÷ (2 + x) is 2 if x =1 and y = 1.
What is expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Coefficient: A coefficient is a number that is multiplied by a variable in an expression.
Given
In expression
(y + x) ÷ 2 + x
x = 1
y = 1
Substituting value of x and y in the expression
(1 + 1) ÷ 2 + 1
= 2 ÷ 2 + 1
= 1 + 1
= 2
Hence, 2 is the value of expression (y + x) ÷ (2 + x) if x= 1 and y = 1.
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Factor the following expression
x²- 15 x 56 =
Multiply the numbers X²-15x56
x²-840
What is factor expression?A factor in an expression is something that is multiplied by something else. It can be a number, variable, term or any other longer expression. For example, the factors of 2xy are 2, x and yWrite each term as the. prime factorization. of the coefficient or constant, listing any variables separately. For example, write. x. y. as. x. y. , and write. x. as. x. x. .Identify the factors that all of the terms have in common.Multiply those common factors.When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5).To learn more about factor expression refers to:
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what is a definition of a circle
Answer:
A round-shaped figure with no corners or edges.
Step-by-step explanation:
Answer: A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
Step-by-step explanation:
NEED HELP ASAP!!!!!!!!
Answer:
A = 5, B= 4, C = 2, D = 1, E= 3
Step-by-step explanation:
x^5 times x^8 = x^13 following the x^n times x^m = x^n+m [rule]
The 1 and 3 for D and E satisfy this. Each number is used only once.
Hope this helps!
Help With Both Please!
Answer:
1. (0,2)
2. (-2,-1)
Step-by-step explanation:
1.
y = 2x + 2
y = x + 2
2x + 2 = x + 2
2x = x
x = 0
Now we put 0 back in for x and solve for y
y = 2(0) + 2
y = 2
So, our answer for Q1 is (0,2)
2.
y = 3x + 5
y = -x - 3
3x + 5 = -x - 3
4x + 5 = -3
4x = -8
x = -2
Now we put -2 back in for x and solve for y
y = 3(-2) + 5
y = -6 + 5
y = -1
So, our answer for Q2 is (-2,-1)
In a company, 65% of the workers are women. If 945 people work for the company who aren't women, how many workers are there in all?
Answer:
32123456789098765443
what is The distance from Phoenix, Arizona, to Jacksonville, Florida, is 1 795 miles. 5.1 Use the line of best fit to predict the length, in minutes, of a direct flight from Phoenix to Jacksonville
Answer:
this is your answe
Step-by-step explanation:
The total straight line flight distance from Jacksonville, FL to Phoenix, AZ is 1,795 miles. This is equivalent to 2 888 kilometers or 1,559 nautical miles.
How do I find the solution to a system?
If the system consists of 2 variables we can use the method of elimination or substitution to get the answer easily.
In the method of elimination from the two given sets of equations, we make one of the coefficients of a variable the same so that when in the next step when we will subtract them they will get canceled out and we will get the value of one of the variables which after substituting in one of the equation we'll get the value of another variable.
If we have more than 2 variables the method of row reduction using a matrix is the best way to solve the system. In the system we make an augmented matrix of the coefficients of the variables and row reduce them in such a way that when we multiply the matrix with the row matrix we get the values of the variables easily.
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-4(1.75+x)=18. ;;;;;;;;;;;;;;;;
Answer:
Step-by-step explanation:
1.75+x=-9/2
7/4+x=-9/2
x=-25/4
How do you find the equation of a line with 2 points in Class 10?
Steps to find the equation of a line with 2 points mentioned below:
What is equation of line?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The ratio of y to x is known as the slope. A slope triangle should be drawn connecting any two spots you find along the line.
To determine a line's equation from two points following steps are there:
1. Determine the slope and used the slope formula.
Slope(m) = (y₂ - y₁) / (x₂ - x₁)
2. To determine the y-intercept, use the slope and one of the points(b).
The x and y in your equation y = mx + b may be replaced by one of your locations, and the m can be replaced by the slope you just computed. The only variable remaining is b in such case. To solve for b, use the same methods you would to solve for a variable.
3. Once you have the values for m and b, you can use them to solve for the line's equation in the slope-intercept form (y = mx + b).
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How do you change to base 5?
Change to base 5 can be done by dividing the decimal number by 5 and then taking the remainder of the division in reverse order.
The number base is the number that forms the basis for the formation of other numbers in a number system.
The number base that we use a lot every day is the decimal system, which consists of 10 numbers, from 0 to 9. This decimal system is usually called the base 10 number system. Apart from base 10, there are also other base systems, for example, base 2 (biner system), 8 (octal system), and 16 (hexadecimal system) which are usually used in computer / digital systems.
Change of base 10 numbers to other base numbers is done by:
dividing the decimal number by the intended base number, writing the remainder down, repeating the division until the remainder is zero, taking a look at the remainder in reverse order.For example, we want to change 214₁₀ to a base 5 number:
214 : 5 = 42 remainder 4
42 : 5 = 8 remainder 2
8 : 5 = 1 remainder 3
1 : 5 = 0 remainder 1
Thus 214₁₀ = 1324₅
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A local boys club sold 136 bags of mulch and made a total of $532. It sold two types of mulch: hardwood for $4.25 a bag and pine bark for $3.75 a bag. How many bags of each kind of mulch did it sell?
The local boys club sold 91 bags of hardwood mulch at $4.25 each, and 45 bags of pine bark mulch at $3.75 each.
What is selling?Selling is the action of exchanging goods or services in exchange for money. It is the process of persuading someone to buy a product or service. Sellers use various methods to persuade potential buyers, such as advertising, discounts, and promotions. Sellers must understand the needs and wants of their customers in order to effectively sell their products or services.
This totaled $532, with 91 bags of hardwood mulch costing $385.75 and 45 bags of pine bark mulch costing $168.75.
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What does 3 2 mean in math?
Answer: In math, 3 2 would typically be written as 3^2, which means "3 raised to the power of 2" or "3 to the second power." It is the same as 3 multiplied by itself, which equals 9.
In some contexts, 3 2 could also be interpreted as "3, 2" which would be read as "3 and 2" and it can mean a collection of 3 and 2 items.
Step-by-step explanation:
Given below are lease terms at the local dealership. What is the total cash
due at signing?
Terms:
• Length of lease: 24 months
• MSRP of the car: $27,500
• Purchase value of the car after lease: $19,500
• Down payment: $3400
Monthly payment: $425
Security deposit: $375
.
• Acquisition fee: $550
●
The total cash due at signing is $4750.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To get the cash due at signing, we just add up the following quantities:
Down payment = $3300
First Monthly payment = $475
Security deposit = $475
Acquisition fee = $500
Hence the total cash due at signing is calculated as follows:
(Total cash due at signing) = (Down payment) + (First Monthly payment) + (Security deposit) + (Acquisition fee)
= $3300 + $475 + $475 + $500
= $4750
Hence, the total cash due at signing is $4750.
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Seven more than the product of a number and 3 is 8.
Answer:
x = 1/3
Step-by-step explanation:
Seven more than the product of a number and 3 is 8.
7 + 3x = 8
3x = 8 - 7
3x = 1
x = 1/3
-------------------
check7 + 3 x 1/3 = 8 (remember PEMDAS)
7 + 1 = 8
8 = 8
the answer is goodHelp me figure this mf out
Answer:
m∠COQ = 60°
Step-by-step explanation:
(2x)° = (3x-30)° (corr angles, l//m)
2x - 3x = -30
∴ x = 30
∴ m∠COQ = 2x°
= 60°
What is the value of the missing angle?
Answer: Missing angle= 42°
Step-by-step explanation:
Since the whole angle is a right-angled triangle the angle will obviously be 90 degrees therefore subtract the given value in order to find the missing angle.
Missing angle= 90°- 48°
= 42°
Lisa worked 26 hours last month and earn seven dollars per hour she spent $17 on her earring since then how much money does she have left?
After spending $17 the amount of money left with Lisa is $165.
What is equation?
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
Lisa worked 26 hours last month.
For each hour she earns $7.
Total earnings of Lisa in last month is equated as -
Earning = 26 × 7
Earning = $182
She spent $17 dollars on earring.
The amount of money left with her is equated as -
Total Earning - Money spent
Money Left = 182 -17
Money Left = $165
Therefore, the money left with Lisa is $165.
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What is the exponential form of 8 * 8 * 8 * 8?
Answer:
8^4
Step-by-step explanation:
Isa earns a salary of $32,500 per annum. If he works an average of 34 hours a week calculate his hourly rate of pay
His hourly pay rate is $18.38 if he works 34 hours a week an earns $32,500 per annum.
What does per annum mean?Per annum denotes yearly or annually. It is a phrasing used frequently to describe interest rates. In sentences like "I have a 4% mortgage loan" or "This bond pays interest at a rate of 6%," "per annum" is frequently left out.
An illustration is when a supplier offers a credit customer a 2% early-payment discount for paying an invoice in 10 days as opposed to the full amount in 30. In this instance, the supplier forfeits 2% of the invoice amount in exchange for receiving payment 20 days early.
We recalculate the amounts and multiply both the "2%" and the "20 days" by 18 to get the rate per year. The annual rate that results is roughly 36%.
Isa works 34 hours a week
There are total 52 weeks a years
In a year the time he works is = 52 × 34 h
= 1768 hours
His annual salary is $32,500
Then his hourly rate of income = 32500/1768
= 32500/1768
= $18.38
Thus, his hourly pay rate is $18.38 if he works 34 hours a week an earns $32,500 per annum.
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An oil company fills 1 over 12 of a tank in 1 over 3 hour. At this rate, which expression can be used to determine how long it will take for the tank to fill completely? (1 point) Group of answer choices
7th grade
Answer:
12 × 1/3 hour
Step-by-step explanation:
1/12 tank in 1/3 hour.
1/12 is one-twelfth of the tank.
there are 12 twelfths in an unit. The tank has 12 one-twelfth parts, so you need to fill 12 times 1/12 of the tank.
Since it takes 1/3 hour to fill 1/12 of the tank, it will take 12 × 1/3 ghour tio fill the entire tank.
The expression is
12 × 1/3 hour
How many groups of ten make 120?
12
12 times ten is 120
Answer: 12 groups of ten makes it 120
Step-by-step explanation:
here one group consists of ten.
and to make 120 we will need 12 groups of ten.
How do you write coordinates in quadratic form?
To write coordinates in quadratic forms,
Obtain the equation y = ax2 + bx + c.Determine -b / 2A. The vertex's x-coordinate is given here.Simply enter the value of -b / 2a into the equation for x and solve for y to obtain the vertex's y-coordinate. The vertex's y-coordinate is given here.What is coordinate quadratic function?When a quadratic equation is written in standard form, the vertex's coordinates are (-b/2a, f(-b/2a)), where x = -b/2a and y = f(-b/2a). This suggests that the formula x = -b/2a should be used to determine the x-value of the vertex in the equation y = -3x2 + x + 1. The equation for a straight line, y = mx + c, is one of the key coordinate geometry formulas. The angle that the line makes with the positive x-axis is represented by the symbol, where m is the slope and c is the y-intercept (tan = m).When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point.To learn more about quadratic form refer to:
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