The perimeter of the given composite figure is; 5¹/₂ cm
How to find the perimeter of the composite figure?
To get the perimeter of the given composite figure, what we will do is to dd up the given segment side lengths and we are given the following;
AE + DC = 1¹/₅ cm
AB = 1 ³/₄ cm
DE = 1 ¹/₄ cm
BC = 1 ³/₁₀ cm.
Thus, we can say that the Perimeter is;
Perimeter = AE + DE + DC + BC + AB
Perimeter = (AE + DC) + DE + BC + AB
= 1¹/₅ + 1 ¹/₄ + 1 ³/₁₀ + 1 ³/₄
= (1²/₁₀ + 1³/₁₀) +(1¹/₄ + 1³/₄)
= 2⁵/₁₀ + 3
= 5¹/₂ cm
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You can spend at most $6 at the market. Apples cost $0.44 each, and pears cost $0.85 each. Let x be the number of apples and let y be the number of pears. Write an inequality that represents the numbers of apples and pears you can buy.
Answer:
0.44x + 0.85y <= 6
Step-by-step explanation:
We can write the total cost of the apples as 0.44x, and the total cost of the pears as 0.85y. Since the total cost cannot exceed $6, we can write the following inequality:
0.44x + 0.85y <= 6
This inequality represents the numbers of apples and pears you can buy at the market, given that you can spend at most $6.
Answer:
0.44x + 0.85y ≤ 6
Step-by-step explanation:
To represent the number of apples and pears you can buy, you can use the following inequality: 0.44x + 0.85y ≤ 6. This inequality states that the total cost of the apples and pears, which is 0.44x + 0.85y, must be less than or equal to $6. This means that you cannot spend more than $6 at the market, and the number of apples and pears you can buy is limited by this budget constraint.
Solve the following inequality and plot the answer on the number line shown below.
Answer: n > 3
Step-by-step explanation:
A circle above 3 going right
Which congruence criterion do you use in the following? Given : EB = DB AE = BC ∠A = ∠C = 90° ∆ABE = ∆CDBSSS
SAS
RHS
ASA
By RHS congruence criterion, since it is given that EB=BD, AE=CB, ∠A=∠C=90°
RHS Congruence Property:
Two right triangles are congruent if the hypotenuse and one side of the first triangle are respectively equal to the hypotenuse and one side of the second.
If the length of the hypotenuse and one side of one triangle is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.
ΔABE ≅ ΔACD
The hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of another right-angled triangle.
Therefore,
ΔABE≅ΔCDB.
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NEED HELP ASAP PLEASE THANK YOU!!
Answer:
[tex]\sin(\theta ) = \dfrac{\textrm{opposite}}{\textrm{hypotenuse}}[/tex]
Hence,
[tex]\sin(A) =\dfrac{20}{29}[/tex]
If you can’t see the last part, it’s a 10.
Answer:
I don't know what is the answer
The prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500.
The price that is 3 standard deviations above the mean is $__
The price that is 2 standard deviations below the mean is $__
The percentage of buyers who paid between $16,500 and $17,500 is %__
The percentage of buyers who paid between $17,000 and $18,000 is %___
The percentage of buyers who paid less than $16,000 is %__
Answer:
Step-by-step explanation:
they are telling you the standard deviation , it's 500
then they ask, what's 3 times that. It's kinda obvious, when I put it in words like that so i'll let you do that math. 17,000 + (3*500) = ?
b)
17000 - (2*500) = ?
c)
This is the bell curve numbers of 1 deviation, it's 68%, if you don't recall
d)
it will be 1/2 of the 2nd deviation, or 95% * 0.5 = 47.5%
e)
this is the tiny amount outside of the main part of the 2 deviation on the bell curve.
5% is outside of the 2nd deviation. so it's half of that or 2.5%
Understand?????
:/
List five vectors in Span {v_1, v_2}. Do not make a sketch. v_1 = [8 2 -7], v_2 = [-6 4 0] List five vectors in Span {v_1, v_2} (Use the matrix template in the math palette. Use a comma to separate vectors as needed. Type an integer or a simplified fraction for each vector element.)
The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})
List five vectors in Span {v_1, v_2}?
1) V1+v2={8,2,-7 }+{-6,4,0 }
={2,6,-7}
2) 2v1+v2={16,4,-14}+{-6,4,0}
={10,8,-14}
3)2v1+2v2={16,4,-14}+{-12,8,0}
={4,12,-14}
4)V1-v2={8,2,-7}-{-6,4,0}
={14,-2,-7}
5)2v1-v2={16,4,-14}-{-6,4,0}
={22,0,-14}
All of these vectors are contained within the span.
{v1,v2}={av1+bv2:ab∈r}
A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram has 20 pens and 7 pencils,
Rohan has 15 pens and 5 pencils,
Yash has 12 pens and 3 pencils
Now, this could be arranged in tabular form as follows,
⎢20 7⎢
⎢15 5⎢
⎢12 3⎢
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Please help me I’m giving brainlyest
The angles ∠ 5 and ∠ 7 are supplementary angles.
What is supplementary angles?Supplementary angles are those angles that sum up to 180 degrees.
Given is a figure, with two parallel lines and a transversal
In the options,
(∠ 5 and ∠ 8) (∠ 2 and ∠ 3) are vertically opposite angles.
∠ 1 and ∠ 5 are corresponding angles
But ∠ 5 and ∠ 7 are forming linear pair, and we know that, two angles forming linear pairs are supplementary angles,
Hence, The angles ∠ 5 and ∠ 7 are supplementary angles.
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Phillip made a milkshake with 2 cups of ice cream and 3/4 cups of milk. Matthew made his milkshake with 1 cup of ice cream and 1/3 cups of milk. Whose milkshake was thicker?
Answer: Matthew’s milkshake
Step-by-step explanation: The ratio of ice cream to milk in Philips milkshake is 1:3/8. The ratio of ice cream to milk in Matthew’s milkshake is 1:1/3. 3/8>1/3. Since you want a thicker milkshake, you want less milk in the ratio, Matthew’s milkshake would be thicker.
Use the SOLVE Process to determine the missing coefficient
of a given polynomial. P(x)=x^4 - 3x^3 +ax^2 - 6x + 14
Answer:
To determine the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, we can use the SOLVE process as follows:
S: Write down the given information and identify the problem.
We are given the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, and we need to find the value of the missing coefficient "a".
O: Organize the information and decide on a plan.
To find the value of "a", we can substitute specific values for x into the polynomial and solve for a.
L: Carry out the plan.
For example, let's say we substitute x = 2 into the polynomial. We get:
P(2) = 2^4 - 32^3 + a2^2 - 6*2 + 14
= 16 - 24 + 4a - 12 + 14
= -4 + 4a + 2
= 4a - 2
We are given that P(2) = 4a - 2 = 0, so 4a = 2.
Solving for a, we get:
a = 2 / 4
= 0.5
V: Check the solution.
We can check the solution by substituting 0.5 for a in the original polynomial and verifying that it gives us the correct result for P(x) when x = 2.
P(x) = x^4 - 3x^3 + 0.5x^2 - 6x + 14
Substituting x = 2 and a = 0.5, we get:
P(2) = 2^4 - 32^3 + 0.52^2 - 6*2 + 14
= 16 - 24 + 1 - 12 + 14
= 0
Since P(2) = 0, our solution appears to be correct.
Therefore, the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14 is 0.5.
If you take 3 away from 100 every minute how long does it take to get to 0
Answer:
100÷3 = 33.33, so 33.33 minutes
Jacob i aving to buy an electronic tablet that cot $380 including tax and ha aved $150
The required Inequality is $12x + $150 ≥ $380 where x is the minimum number of lawns Jacob will need to mow in order to buy the ticket. The solution of inequation is x ≥ 19.2 ~ 19.
What is an Inequality?An inequality is a mathematical expression in which both sides are not equal. Unlike equations, inequalities compare two values. Equal signs between are replaced by less than (or less than and equal), greater than (or greater than and equal ) sign.
How to solve an Inequality?When solving an inequality:
We can add the same quantity to each side We can subtract the same quantity from each side. We can multiply or divide each side by the same positive quantity . If we multiply or divide each side by a negative quantity, the inequality symbol must be reversed.We have, total cost of electronic ticket i.e with all taxes = $380
Saved cost = $150
Cost of one mowing lawn = $12
let "x" be the number of lawns mowed by Jacob for earning the rest of money .
Total cost of x mowed lawns by Jacob।
= $12x .
Now, $12x + $150 ≥ $380 --(*)
This is the required Inequality and x is minimum number of lawns which Jacob have to mowed .
The solution of above Inequality,
Substracts 150 from both sides in (*)
12 x + 150 - 150 ≥ 380 - 150
=> 12x ≥ 230
dividing by positive 12 both sides we get,
=> x/12 ≥ 230/12
=> x ≥ 19.16
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Complete question:
Jacob is saving to buy an electronic ticket that costs $380 including tax and has saved $150. Jared plans to earn the rest of the money by mowing lawns and will charge $12 for each lawn he mows. Write an inequality to find x, the minimum number of lawns Jacob will need to mow in order to buy the ticket. Show how to solve the inequality and what is solution.
The equation y=(1/4)x relate proportional quantitie x and y. What i the value of x when y i 7
To solve for x when y is given, we can use the given equation y=(1/4)x.By multiplying both sides of the equation by 4.x=28, we may find the value of x.
To solve for x when y is given, we can use the given equation y=(1/4)x. By multiplying both sides of the equation by 4.x=28, we may find the value of x. This gives us the equation 4y=x. Then, we can substitute the given value of y, 7, into the equation. This gives us 4(7)=x. Simplifying this equation gives us 28=x, which is the value of x when y is 7.
y=(1/4)x
4y=x
4(7)=x
28=x
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Help pls. Stuck on Khan Academy question in High School Geometry
Answer:
A
Step-by-step explanation:
Sequence A works.
With sequence B, the triangles will be next to each other.
Answer: A
i need help past due
Answer:
Unit price 12.16 for 4.07 pounds is $2.99 per pound
Unit price 14.99 for 5.11 pounds is $2.93 per pound
The best deal is the 14.99 per 4.11 pounds
Step-by-step explanation:
Unit price 12.16/4.07 = 2.99 rounded to the nearest cent
Unit price 14.99/5.11 = 2.93 rounded to the nearest cent.
Answer:
1) $2.99
2)$2.93
The better buy is the 4.07 pound bag
Step-by-step explanation:
To find the unit price you find the cost per pound
$12.16 : 4.07
? : 1
4.07x = 12.16
x = 2.98771499
$2.99
$14.99 : 5.11
? : 1
5.11x = 14.99
x= 2.9334638
A salesperson receives a 9.9% commission on her salesIf her total sales for the month are $3600, what is her commission ?
Answer:
$358.4
Step-by-step explanation:
To calculate the salesperson's commission, you can multiply the total sales by the commission rate. In this case, the commission is $3600 * 0.099 = $<<3600*0.099=358.4>>358.4. So the salesperson's commission would be $358.4.
Select the correct formula for the polyatomic ion. you can find a list of common polyatomic ions by clicking here. the formula for the ammonium ion: nh3 nh4 am
The chemical formula for ammonium carbonate is (NH₄)₂CO₃. Therefore, option (C) is correct.
When heated, ammonium carbonate, also known as ()2, rapidly breaks down into ammonia and carbon dioxide. It functions as a smelling salt and a leavening agent. Ammonium carbonate, often known as baker's ammonia, was used before baking soda and baking powder as leaveners.
Sal volatile contains ammonium carbonate, and salt of hartshorn when baked emits a strong odour. At standard pressure and temperature, two processes lead to the gradual breakdown of ammonium carbonate. The pure ammonium carbonate sample will combine with different byproducts.
Upon spontaneous dissociation, ammonium carbonate can separate into ammonium bicarbonate and ammonia. which results in the addition of more ammonia, carbon dioxide, and water.
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Answer:
The formula for the ammonium ion: NH4+
The formula for the nitrate ion: NO3–
A chromate ion consists of four oxygen atoms bonded to a chromium atom. It has two extra electrons. The formula of this ion: CrO42–
Heres all three. Hope i helped
I need help with this. Please answer or explain how I have to do it.
\frac{x}{y} x^2+2*x-6/x+1
The division of the polynomial x^2 + 2*x - 6 by (x + 1), using the long division method of dividing polynomials is x + 1 - 7/(x + 1)
What is the long division method?The long division method allows the division of large numbers (which is the dividend) into the number of groups of the divisor and a remainder which is a value less than the expressed value of the divisor.
The expression \_f_rac{x}{y} x^2 + 2*x - 6/x + 1 can be presented as follows;
[tex]\dfrac{x^2+2\cdot x-6}{x + 1}[/tex]The long division showing the steps can be obtained using code found online as follows;
[tex]\begin{array}{*1r {\arraycolsep}{\arraycolsep} *{11}l} & && x + 1 \\\cline{4-3}& &x+1& \longdiv {) x^2 +2\cdot x - 6& & & & & \\ & & & x^2 +x \\\cline{4-} && &\ \ \ x -6& \\ & & \ \ \ & \ \ \ x +1 \\\cline{4-} & & & \ \ \ \ \ \ \ -7 & \\ \cline{4-} \end{array}[/tex]
The remainder of the long division is -7, therefore, we get;
[tex]\dfrac{x^2+2\cdot x-6}{x + 1} = x + 1 - \dfrac{7}{x+1}[/tex]
The value of the expression, \_f_rac{x}{y} x^2 + 2*x - 6/x + 1 following the long division is; x + 1 - 7/(x + 1)
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is the potential that a chosen action may lead to an undesirable outcome. group of answer choices chance probability negativity risk
Risk is the potential that a chosen action may lead to an undesirable outcome.
About riskIn simple terms, the definition of risk is a condition that is uncertain, but contains an element of danger as a consequence or result of something. Once again, this something is a business, business, activity, or decision that you make.
Types of RiskThe risks themselves are divided into several types, complete with different characteristics.
1. Pure Risk
This pure risk is certain, meaning that when the risk occurs, you will experience a loss. And vice versa, if pure risk does not occur, then you will make a profit.
2. Speculative Risk
There are three possibilities that will happen, if you experience speculative risk, namely profits, losses, or maybe break even. What is meant by break even is the break even point.
Conditions where there are no profits or losses, so it's normal. The most obvious examples of speculative risk are the lottery, stock exchange, exchange risk, and others.
3. Particular Risk or Special Risk
Specific risks originate from individual activities, so the impact can still be estimated or anticipated at the outset because they are local in nature. For example, a turbine explosion, a shipwreck, or maybe a crash.
How to anticipate it (example for collision risk). You can take out insurance to provide guarantees or protection, both for the vehicle and for yourself.
4. Fundamental Risk
Fundamental risks come from the surrounding environment or nature which can have quite a big impact, because humans are not able to control them.
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A certain amount of money wa divided between jaya and jyoti in the ratio 3:4. If jaya recieved R2700,then how much wa the total amount
By setting up the equation and solving we get the total amount of money was 1800.
What is ratio?A ratio is a way of comparing two or more quantities. It is expressed as a fraction or a decimal, and it represents the relative sizes of the quantities being compared.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. An equation typically consists of two expressions separated by an equals sign (=), and it states that the expressions are equal in value.
we can set up the following equation:
(2700 / X) = (3 / 4)
We can solve this equation for X by multiplying both sides by X:
2700 = (3 / 4) * X
2700 = (3 / 4) * X
5400 = 3X
X = 5400 / 3
X = 1800
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Solve the word problem below. Enter your answer as a fraction in simplest
terms, using the slash (/) as the fraction bar.
If
of all books at a library are nonfiction and of the nonfiction books are
biographies, then what fraction of the library's books are nonfiction
biographies?
The total number of non-fictional biography books in the library will be equal to 1/5.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
Let the total number of books is x.
3/5 of total books are non-fiction, then,
3/5 × x = 3/5x
1/3x of them are biographies.
Then, the number of non-fictional biographies are,
3/5 × 1/3
=1/5
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Erik is carrying stones in a small wagon. His
wagon can carry 1.2 kg without falling apart. The
stones are in a wooden box that weighs 150 grams,
and each stone weighs 35 grams. What is the
largest number of stones that could be in the box
in the wagon? (Hint: 1 kg = 1000 grams)
The largest number of stones that could be in the box in the wagon will be 30.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
His wagon can carry 1.2 kg without falling apart.
And, The stones are in a wooden box that weighs 150 grams, and each stone weighs 35 grams.
Now,
Let the number of stones = x
So, We can formulate;
⇒ 150 + 35x = 1200
Solve for x as;
⇒ 35x = 1200 - 150
⇒ 35x = 1050
⇒ x = 1050/ 35
⇒ x = 30
Thus, There are 30 largest number of stones that could be in the box in the wagon.
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A metal i made up of copper and zinc in the ratio 3:2 by volume. 1cm cube of copper ha a ma of 8. 9g and 1cm cube of zinc ha a ma of 7. 1g. Find the ma of 100cm cube of the metal
When metal is composed of copper and zinc in a 3:2 by volume ratio, the mass of metal in a 100cm cube is 1600g.
What is proportion?A percentage is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province. The population percentage is marked by the letter p, whereas the sample proportion is denoted by the letter p. Thus, p=0.43 if 43% of individuals visiting a business make a purchase before leaving. If 78 customers out of 200 enter the store and make a purchase, p=78200=0.39.
Here,
1/8.9=100/x
x=890g
1/7.1=100/x
x=710g
Total mass of metal=890+710
=1600g
The mass of metal in 100cm cube is 1600g when metal is made up of copper and zinc in the ratio 3:2 by volume.
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Enter the letter of the graphed function.
a. y = (x + 2)(x - 1)³(x-3)
b. y = (x + 2)(x - 1)(x-3)³
c. y = (x + 2)(x - 1)²(x - 3)²
d. y = (x - 1)(x-3)²(x + 2)²
e. y = (x + 2)²(x-1)²(x-3)
10
Answer:
d. y = (x - 1)(x-3)²(x + 2)²
Step-by-step explanation:
When there is a local max or local min on the x-intercept, then the function on the x-intercept is raised to an even power.
At x=3 and x=-2, the function goes up then down, or down then up.
If the function goes through an x-intercept when there is no local max or local min on the x-intercept, then the function on the x-intercept is raised to an odd power.
At x=1, the function goes through the x-intercept.
Hence, d is the answer.
Can someone help me with Question 1, a-b of this assignment? I'd deeply appreciate it! :) I am trying to figure these questions out, and I need help.
Answer:
Step-by-step explanation:
so we start with Sara's
-3x+14=18-5x
for properties of equality, we need to isolate the x variable
-3x=4-5x
2x=4
x=2
that is correct
now we go to Ethan's
2x=5-1/2x
2 1/2x=5
x=2
now we have confirmed that x is equal to 2
hope this helped
how many ways are there for eight blue-shirt and five red-shirt to stand in a line so that no two red-shirts stand next to each other?
The total number of ways there are for eight blue-shirt and five red-shirt to stand in a line so that no two red-shirts stand next to each other is 609638400.
What is permutation?A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already ordered, or arranging its members into a sequence or linear order.
Given:
The eight blue-shirt and five red-shirt stands in a line,
Calculate the number of ways as shown below,
The total number of ways = Total no of permutations of blue ones × Total permutation of 9 positions, taken 5 at a time,
N = 8! × 9! / (9 - 5)!
N = 40320 × 362880 /24
N = 609638400
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a university student wishes to explore whether gender (man, woman, trans, non-binary) is associated with agreement (agree, disagree, neutral) to endorse the existence of a social media platform that allows almost all forms of non-violent free speech, with minimal content moderation to censure only the most egregious of posts. of the 47 men polled, 25 agreed and 10 were neutral. of the 50 women polled 14 agreed and 5 were neutral. of the 41 transgendered people polled 18 agreed and 4 were neutral. of the 50 non-binary people, 6 agreed and 12 were neutral. the rest disagreed with such a platform being allowed to exist in our society. the student wishes to test the hypothesis of independence using pearson's chi square test. how many transgendered people (round to the nearest thousandth) would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis?
The number of transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis is 19.00
What Is a null hypothesis?A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is H0.
To determine if a theory regarding markets, investing methods, or economies is correct or wrong, quantitative analysts employ the null hypothesis, often known as the conjecture.
The number of transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis is 19.00
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How many solutions does 1/2(6x-2)=2 have
One solution for the equation [tex]\frac{1}{2} (6x - 2) = 2[/tex] is x = 1
What is an equation ?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
According to the given information
The equation given to us is
[tex]\frac{1}{2} (6x - 2) = 2[/tex]
Solving the above equation
We get
3x - 1 = 2
3x = 2 + 1
3x = 3
x = 1
We have only
One solution for the equation [tex]\frac{1}{2} (6x - 2) = 2[/tex] is x = 1
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if r(t) = 3t, 2t2, 4t3 , find r'(t), t(1), r''(t), and r'(t) × r ''(t).
The value of [tex]r^{\prime}(t)[/tex] is [tex]\left\langle 3,4 t, 12 t^2\right\rangle[/tex].
The value of unit tangent vector T(1) is [tex]\left\langle\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right\rangle \quad[/tex]
The value of r''(t) is [tex]\langle 0,4,24 t\rangle[/tex]
The value of r'(t) × r ''(t) is [tex]\left(48 t^2\right) \vec{i}-(68 t)\vec{j}+(12)\vec{k}[/tex]
As per the data given in the question r(t) = 3t, [tex]2t^{2}[/tex], [tex]4t^{3}[/tex]
From r(t) we can find the value of [tex]r^{\prime}(t)[/tex].
For that we have to differentiate each term of r(t).
[tex]r^{\prime}(t)=\left\langle 3,4 t, 12 t^2\right\rangle[/tex]
Tangent and Normal Vectors:
The tangent and unit normal vectors are calculated from the derivatives of the parameter settings of the curve.
In particular, to determine the unit tangent vector, we have:
[tex]& \vec{T}(t)=\frac{\partial^{\prime}(t)}{\left|r^{\prime}(t)\right|} \\[/tex]
Therefore [tex]\vec{T}(1)=\frac{\partial^{\prime}(1)}{\left|\partial^{\prime}(1)\right|}[/tex]
[tex]\partial^{\prime}(1)=\langle 3,4,12\rangle \\& \therefore\left|r^{\prime}(1)\right|=\sqrt{9+16+144}\\=\sqrt{169}\\=13[/tex]
[tex]\vec{T}(1)=\frac{\langle 3,4,12\rangle}{13}[/tex]
[tex]& =\left\langle\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right\rangle[/tex]
[tex]\vec{T}(1)=\left\langle\frac{3}{13},\frac{4}{13}, \frac{12}{13}\right\rangle[/tex]
[tex]\vec{T}(1)=\left\langle\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right\rangle \quad[/tex]
Now [tex]r^{\prime}(t)=\left\langle 3,4 t, 12 t^2\right\rangle \\[/tex]
From r'(t) we can find the value of r''(t).
For that we have to differentiate each term of r'(t)
[tex]r^{\prime \prime}(t)=\langle 0,4,24 t\rangle[/tex]
Now we have to find the value of r'(t) × r ''(t).
[tex]\partial^{\prime}(t) \times \partial^{\prime \prime}(t)=\left|\begin{array}{ccc}i & j & k \\3 & 4 t & 12 t^2 \\0 & 4 & 24 t\end{array}\right|[/tex]
[tex]&=i\left(96 t^2-48 t^2\right)-j(68 t)+k(12) \\&=\left(48 t^2\right) \vec{i}-\vec{j}(68 t)+\vec{k}(12) \\[/tex]
[tex]r^{\prime}(t) \times r^{\prime \prime}(t)=\left(48 t^2\right) \vec{i}-\vec{j}(68 t)+\vec{k}(12)[/tex]
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