The cross product of
[tex](i+j) \times k[/tex]= 0.
To calculate the cross product of (i+j) and k,
Step 1: Assign unit vectors to the given vectors:
(i+j) = i + j + 0k
k = 0i + 0j + k
Step 2: Apply the cross product formula:
(i+j) × k = (i × 0i) + (i × 0j) + (i × k) + (j × 0i) + (j × 0j) + (j × k) + (0k × 0i) + (0k × 0j) + (0k × k)
Step 3: Simplify the cross product using the properties of the cross product:
(i × 0i) = (j × 0j) = (0k × 0i) = (0k × 0j) = 0
(i × k) = - (k × i)
(j × k) = - (k × j)
(k × k) = 0
Step 4: Substitute the simplified cross products into the formula:
(i+j) × k = 0 + 0 + (i × k) + 0 + 0 + (j × k) + 0 + 0 + 0
= 0 + 0 + (i × k) + 0 + 0 + (j × k) + 0 + 0 + 0
= (i × k) + (j × k)
Step 5: Calculate the cross products:
(i × k) = (0 - 0)k - (0 - 0)j = 0k - 0j = 0k
(j × k) = (0 - 0)i - (0 - 0)k = 0i - 0k = 0i
Step 6: Substitute the calculated cross products into the formula:
(i+j) × k = 0k + 0i
= 0k + 0
= 0
Therefore k=0.
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1. Write the following function using unit step functions and then find its Laplace transform: 0
The Laplace transformation in the given function is = 5 - 8e⁻⁷ˣ/ x
Rewrite f in terms of the unit step function:
f(t) = { y = 5 for 0 ≤ t ≤ 7
= { x = - 3 t > 7
f(t) = 5{u(t) -u(t -7) - 3u (t -7)}
= 5u(t) - 8u (t-7)
Recall the time-shifting property of the Laplace transform:
L I u(t - c)f(t -c) I
= e⁻ᵃˣ L[f(t)]
and the Laplace transform of a constant function,
L(K) = k/a
So we have
L{f(t)} = 5u(t) - 8u (t-7)
= 5 L[1] - 8e⁻⁷ˣ
= 5 - 8e⁻⁷ˣ/ x
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The given question is incomplete, the complete question is below
Write the following function using unit step functions and then find its Laplace transform:
f(t) = { y = 5 for 0 ≤ t ≤ 7
= { x = - 3 t > 7
In the experiment of throwing a dice and flipping a coin,
given:
A: getting a number less than 4
B: getting T on a coin
The probabilities of:
A: Getting a number less than 4 on the dice is 1/2
B: Getting tails (T) on the coin is 1/2
In the experiment of throwing a die and flipping a coin, let's define the following events:
A: Getting a number less than 4 on the dice (possible outcomes: 1, 2, 3).
B: Getting tails (T) on the coin.
To determine the probabilities of these events, we need to consider the number of favorable outcomes and the total number of possible outcomes.
For event A:
Number of favorable outcomes: 3 (numbers 1, 2, 3)
Total number of possible outcomes on the dice: 6 (numbers 1 to 6)
So, P(A) = favorable outcomes / total outcomes = 3/6 = 1/2
For event B:
Number of favorable outcomes: 1 (tails T)
Total number of possible outcomes on the coin: 2 (heads H, tails T)
So, P(B) = favorable outcomes / total outcomes = 1/2
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Sam raked 3 bags of leaves in 18 minutes. If he continues to work at the same rate, how long will it take him to rake 7 bags of leave ? PLEASE HELP
Answer:
Step-by-step explanation:
hope it helps make brainliest
Answer:
42 minutes
Step-by-step explanation:
18/3= 6
6*7=42
At a hospital emergency room, a doctor has determined that for every 14
patients injured in a car accident, 6 were not wearing seat belts.
6 no seat belts
14 injured total
If the emergency room saw 420 patients injured in car accidents last
month, what is the best prediction for how many patients were not wearing
seat belts? Round to the nearest WHOLE person.
6 no seat belts = ? no seat belts
___________ ___________
14 injured total 412 injured total
Answer:
A prediction of 177 people.
Step-by-step explanation:
6x412=2472
2472/14=176.571428571
Rounded to nearest whole person=177
Please mark me as brainliest.
Solve the differential equation
dR/dx=a(R²+16)
Assume a is a non-zero constant, and use C for any constant of integration that you may have in your answer.
R = ?
If anyone helps me, I will give away points.
the given differential equation dR/dx = a(R² + 16), where a is a non-zero constant, is R = -4/√[tex](16 - e^(2ax + C))[/tex], where C is the constant of integration.
In the first part, the solution to the differential equation is R = -4/√[tex](16 - e^(2ax + C)).[/tex]
In the second part, let's solve the differential equation step by step. We start by separating variables:
dR/(R² + 16) = a dx.
Next, we integrate both sides:
∫(1/(R² + 16)) dR = ∫a dx.
To integrate the left side, we can use a substitution. Let u = R² + 16, then du = 2R dR. This gives us:
(1/2) ∫(1/u) du = ∫a dx.
Simplifying the left side and integrating, we have:
(1/2) ln|u| = ax + C.
Substituting back for u and rearranging, we get:
ln|R² + 16| = 2ax + 2C.
Taking the exponential of both sides, we have:
|R² + 16| = [tex]e^(2ax + 2C).[/tex]
Considering the absolute value, we can rewrite it as:
R² + 16 = [tex]e^(2ax + 2C).[/tex]
Solving for R, we get:
R = ±√(e^(2ax + 2C) - 16).
Simplifying further:
R = ±√(e^(2ax + C) - 16).
Finally, we can rewrite it as:
R = -4/√(16 - e^(2ax + C)).
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You pick one card from each set and find the sum. How many different sums are possible? 4 5 6 5 6 7 1 2
There are a total of 9 possible sums. Suppose, the cards in the first set are 4, 5, and 6.
Similarly, the cards in the second set are 5, 6, and 7. A total of nine cards are there. If we choose one card from the first set and one card from the second set, then we get a total of nine possible pairs.
Hence, the sum of these pairs can be 4 + 5, 4 + 6, 4 + 7, 5 + 5, 5 + 6, 5 + 7, 6 + 5, 6 + 6, and 6 + 7. Therefore, there are nine possible sums possible.
Additionally, there are three possibilities in the first set (4, 5, and 6) and three possibilities in the second set (5, 6, and 7).
This means that there are 3 × 3 = 9 possible pairs of cards that we can choose, so there are 9 possible sums.We can list all of these sums as follows:4 + 5 = 96 + 5 = 116 + 5 = 116 + 6 = 127 + 5 = 127 + 6 = 137 + 7 = 14. Therefore, there are a total of 9 possible sums.
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• What is the diameter of the circle?
What is the circumference of the circle
What is the area of the circle
Answer:
Radius = r
Diameter = 2r
Circumference = 2πr
Area = πr²
a diameter of a circle is a line drawn through the center of a circle.
can anyone guess what game i was playing by the looks of it
Answer:
A VR car game and an iphone
Step-by-step explanation:
:)
PLEASE HELP THIS IS PYTHAGOREAN THEORM 3D
I MARK THE BRANILIEST
What is the vertical height, hh
Round your answer to the nearest tenth.
The height is
units
Answer:
The height is 6.3
Step-by-step explanation:
Pythagorean Theorm: a² + b² = c²
5² + b² = 8²
25 + b² = 64
b² = 39
b = 6.2449979984
What is the area of this shape can someone please help
Answer 10x8=80+3
Step-by-step explanation:
i.d.k 83?????
What is the slope of the line that passes through the
points (4,-7) and (9, 1)?
A) 5/8
B) 8/5
C) -6/12
D)-13/6
Answer:
C) -6/12
Step-by-step explanation:
Sana nakatulong
match each correlation to the corresponding scatterplot. 13. true or false: r = 0.49 → (2) 14. true or false: r = −0.48 → (2) 15. true or false: r = −0.03 → (4) 16. true or false: r = −0.85 → (1)
Based on the given statistics, we will shape each correlation to the corresponding scatterplot as follows:
13.True or False: r = 0.49 → (2)
14.True or False: r = -0.48 → (4)
15.True or False: r = -0.03 → (3)
16.True or False: r = -0.85 → (1)
Based on the given records, we need to match each correlation fee to the corresponding scatterplot. Let's analyze every correlation and its corresponding scatterplot in more detail:
13.True or False: r = 0.49 → (2)
A correlation coefficient of 0.49 shows a tremendous correlation among the variables. This means that as one variable will increase, the alternative variable tends to grow as nicely, albeit not flawlessly. In the scatterplot categorized as (2), we'd assume to look at a trendy upward fashion wherein the factors are quite scattered around the road of satisfactory fit.
14.True or False: r = -0.48 → (2)
A correlation coefficient of -0.48 indicates a bad correlation between the variables. This manner that as one variable increases, the opposite variable has a tendency to lower. In the scatterplot labeled as (2), we'd expect to see a standard downward fashion wherein the points are rather scattered around the line of fine match.
15.True or False: r = -0.03 → (4)
A correlation coefficient of -0.03 shows a very weak terrible correlation between the variables. This method that there is almost no relationship between the variables. In the scatterplot categorized as (four), we would count on seeing factors scattered randomly, with no discernible pattern or fashion.
16. True or False: r = -0.85 → (1)
A correlation coefficient of -0.85 shows a sturdy poor correlation between the variables. This method that as one variable increases, the other variable has a tendency to decrease substantially. In the scatterplot labeled as (1), we might count on to peer a clear downward trend in which the factors are tightly clustered around the road of the first-rate match.
By analyzing the strengths and instructions of the correlations, we can suit each correlation value to its corresponding scatterplot as follows:
13. True or False: r = 0.49 → (2)
14.True or False: r = -0.48 → (2)
15.True or False: r = -0.03 → (4)
16.True or False: r = -0.85 → (1)
Please notice that scatterplots provide visible representations of statistics and relationships between variables, and the interpretations might also vary relying on the context and the statistics being analyzed.
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You put the names of all the students in your class in a paper bag. There are 14 boys and 20 girls. If you draw a name at random, what is P(boy’s name)?
Answer:
7/17
Step-by-step explanation:
you add the number of students which is 34. Then you take the number of boys and put it over 34 which would be 14/34. when you reduce it the answer will be 7/17.
let me know if this helps!
The sum of the first nine terms in a sequence is 49,205. Each term is 3 times the previous term. What is the third term?
Answer:
a₃ = 32 805Step-by-step explanation:
Each term is 3 times the previous term:
r = 3
The sum of the first nine terms in a sequence is 49,205:
[tex]S_n=a_1\cdot\dfrac{1-q^n}{1-q}\\\\\\49205=a_1\cdot\dfrac{1-3^9}{1-3}\\\\49205=a_1\cdot\dfrac{1-19683}{-2}\\\\49205=a_1\cdot9841\\\\a_1=5[/tex]
What is the third term?
[tex]a_n=a_1\cdot q^{n-1}\\\\a_3=5\cdot3^8=32805[/tex]
Enter values to complete the table below.
PLEASE HELP, DUE IN ONE HOUR AND HAVE LOTS TO DO.
20 POINTS!!
Answer:
6, 0, 2
Step-by-step explanation:
Divide y by x.
HA
2
-X
- 2
2
-2
-4
A.
ys1
B.
1 sys 6
Oc.
y21
D.
all real numbers
Answer:
Can you please explain this question more thoroughly?
Step-by-step explanation:
it is difficult to understand
The simplified expression is 4x - 23.
Option A is the correct answer.
We have,
To simplify the expression 3(2x - 5) - 2(x + 4), we need to apply the distributive property and combine like terms.
First, distribute the 3 to the terms inside the parentheses:
3 * 2x = 6x
3 * (-5) = -15
Next, distribute the -2 to the terms inside the parentheses:
-2 * x = -2x
-2 * 4 = -8
Now, let's simplify the expression by combining like terms:
6x - 15 - 2x - 8
Combine the x terms: 6x - 2x = 4x
Combine the constant terms: -15 - 8 = -23
Thus,
The simplified expression is 4x - 23.
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The complete question:
Simplify the expression 3(2x - 5) - 2(x + 4).
A. 4x - 23
B. 4x - 7
C. 4x + 13
D. 4x + 7
Please help, promise I will mark ya if ur right
Find the value of x that makes the quadrilateral a parallelogram.
6x
3x + 2
X=
Answer:
15
Step-by-step explanation: simple math
Answer:
2/3
Step-by-step explanation:
6x = 3x+2
3x = 2
x = 2/3
-2( 3x - 1) = -6x - 1
Answer:
Yes, that equation is right
Step-by-step explanation:
I don’t know why this is a question, however
Answer:
0 = -3
Step-by-step explanation:
Distribution
− 2 ( 3 − 1 ) = − 6 − 1
− 6 + 2 = − 6 − 1
Subraction (2 from both sides)
− 6 + 2 = − 6 − 1
− 6 + 2 − 2 = − 6 − 1 − 2
Simplify
− 6 = − 6 − 3
Add 6 to both sides
− 6 +6 = − 6 − 3+6
Combine like terms
− 6 +6 = − 6 − 3+6
0=-(6)-3+(6)
0=-3
the area of a rhombus is 24 square inches. What is the are of a similar rhombus that is 7 times as big?
Answer: 1176
Step-by-step explanation: 7 times as big is an ambiguous term; it could mean that each side is 7 times larger, or that the shape as a whole is made 7 times larger. We'll assume that each side is made larger, because that is typically the type of question asked. The area is given as base times height, and obviously, if you dilate the non-base side by 7, the height will also become 7, because those two lines from a triangle with the third side being the base extended. I wish I could draw you a diagram but i can;t. Either way, think of it as a square, and if we dilate each side by 7, then we have lx7xwx7=Area, which is lw*49=49 times the given area, which is 24; 24*49=1176
A globe company currently manufactures a globe that is 16 inches in diameter. If the dimensions of the globe were reduced by half, what would its volume be? Use 3.14 for π and round your answer to the nearest tenth.
682.7 in^3
2143.6 in^3
85.3 in^3
267.9 in^3
If dimensions of the globe that is 16 inches in diameter were reduced by half, then its volume would be [tex]$V= 267.9 \text{ in}^{3}$[/tex]
What is volume ?The volume of an object is a measure of the amount of space occupied by that object.
Here given that originally diameter was 16 inches but then dimensions of the globe was reduced by half
The new diameter is equal to
[tex]$$D=16 / 2=8 \mathrm{in}$$[/tex]
Hence radius is equal to
[tex]$$r=8 / 2=4 \mathrm{in}$$[/tex]
The volume of the reduced globe is
[tex]$V=\frac{4}{3}(\pi)(r)^{3}$[/tex]
[tex]$V=\frac{4}{3}(3.14)(4)^{3}$\\[/tex]
[tex]$V= 267.9 \text{ in}^{3}$[/tex]
If dimensions of the globe that is 16 inches in diameter were reduced by half, then its volume would be [tex]$V= 267.9 \text{ in}^{3}$[/tex]
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Answer:
267.9 in3
Step-by-step explanation:
I took the test and got it right!
Two angles in a triangle have measures of 18 and 77º.
What is the measure of the third angle
Answer:
85 ° is the answer to the question
Answer:
85 degrees
Step-by-step explanation:
Angles in a triangle add up to 180 in total so to solve it add the two angles you know so 18+77 which is 95 than you subtract it from 180 so 180 - 95 is 85
Aliyah spent half of her weekly allowance playing arcade games. To earn more money her parents let her mow the lawn for $7. What is her weekly allowance (W) if she ended up with $16? The variable should always go in the first term
Answer:
who mows the lawn for 7 dollars :/
Step-by-step explanation:
What is the main cause of tides?
A.
Earth's gravitational pull
B.
the moon's gravitational pull
C.
the moon's rotation around its axis
D.
Earth's revolution around the sun
The main cause of tides is the moon's gravitational pull.
Hope it helps you...
Answered by Benjemin ☺️
✅
Find the answer
A.
B.
C.
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
A) (2,5)
Step-by-step explanation:
longest side is between points (1,4) and (3,6)
so midpoint is ((1+3)/2), ((4+6)/2), which equals (2, 5)
I need help with this question ( see image). Please show workings.
Answer:
13. (a) 120°, 120°, (b) 8.94 cm14. (a) 17.9 cm, (b) 22.4 cmStep-by-step explanation:
Refer to the attached sketch (not to scale)Question 13(a) The center of the circle is also the circumcenter of the triangle PQR.
Since ΔPQR is equilateral, all sides are equal, therefore opposite angles are also congruent:
∠POQ ≅ ∠QOR ≅ PORSum of the three angles is 360° as cover the full circle.
Each angle measure is:
∠POQ = ∠QOR = ∠POR = 360°/3 = 120°(b) Each side is 16 cm and the radius is 12 cm.
The distance of the midpoint M of PQ from the center O is perpendicular bisector of ΔPOQ.
The segment MO is:
MO² = PO² - PM² = PO² - (PQ/2)²MO² = 12² - (16/2)² = 80MO = √80 = 8.94 cm (rounded)Question 14ΔXYZ is isosceles with:
XY = XZ = 20 cmYZ = 18 cm(a) The altitude of ΔXYZ is a perpendicular bisector of YZ. h = XM is the altitude
Find h:
h² = XZ² - ZM² = XZ² - (ZY/2)²h² = 20² - (18/2)² = 319h = √319h = 17.9 cm (rounded)(b) Note the ∠ZXM is half of the ∠ZOM as both the angles intercept half of the arc ZY and ∠ZOM is a central angle.
Find ∠ZXM:
sin ∠ZXM = ZM/ZX = 9 / 20m∠ZXM = arcsin (9/20) = 26.7° (rounded)Find ∠ZOM:
m∠ZOM = 2*m∠ZXM = 2*26.7 = 53.4°Find the measure of the radius:
sin ∠ZOM = ZM/rsin 53.4° = 9/rr = 9 / sin 53.4°r = 11.2 cm (rounded)Find the measure of the diameter:
d = 2r = 2*11.2 cm = 22.4 cmmartin has read 20% of a book. He has 8 more pages to finish. How many pages are there in the book?
Answer:
10 pages are in the page if im correct
What is the solution set for -4m ≥ 96?
m ≥ -384
m ≤ -24
m ≤ -384
m ≥ -24
Answer:
Step-by-step explanation:
-4m≥96
-m≥24
m≤-24
Determine if the following systems is a) Linear b) Time-invariant c) Causal, Justify your answer. y(0) = x(t)sinwet
The given system y(0) = x(t)sin(wt) is linear, time-invariant, and causal. It satisfies the properties of superposition and homogeneity, exhibits the same time shift in the output as in the input, and the output at any given time depends only on the current and past values of the input.
a) Linearity: A system is linear if it satisfies the properties of superposition and homogeneity. In this case, the system is linear because it satisfies both properties. The input signal x(t) can be scaled or added together, and the corresponding output y(t) will also be scaled or added accordingly.
b) Time-invariance: A system is time-invariant if a time shift in the input signal results in the same time shift in the output signal. In this case, the system is time-invariant because shifting the input signal x(t) by a time delay will result in the same time delay in the output signal y(t).
c) Causality: A system is causal if the output at any given time depends only on the current and past values of the input. In this case, the system is causal because the output y(t) at any time t depends only on the values of the input x(t) for t' ≤ t.
In conclusion, the given system y(0) = x(t)sin(wt) is linear, time-invariant, and causal based on the justification provided above.
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