Evaluate the integral. 2 (6t i − t3 j + 2t3 k) dt 0
The integral of the vector field 2 (6t i − t3 j + 2t3 k) from 0 to t can be broken down into three separate integrals for each component, yielding the resulting integral vector of (6t^2)i - (0.5t^4)j + (t^4)k.
Explanation:The integral you're asking about is a vector field integral, which comes up primarily in physics-related problems. The integral of a vector field, in this case, 2 (6t i − t3 j + 2t3 k) with respect to time, can be broken down into three separate integrals, each corresponding to a different component.
To solve, you would perform each integral separately:
Integral from 0 to t of 2*6t dt = 6t^2 between 0 and t = 6t^2 Integral from 0 to t of 2*-t^3 dt = -0.5*t^4 between 0 and t = -0.5t^4 Integral from 0 to t of 2*2t^3 dt = t^4 between 0 and t = t^4Combine these answers to yield the integral vector (6t^2)i - (0.5t^4)j + (t^4)k as the solution. Please remember to always check your calculations to ensure accuracy!
Learn more about Vector Field Integral here:https://brainly.com/question/30450980
#SPJ12
What is another way to write 9×200?
A rectangular prism is completely packed with 90 cubes of edge length fraction 1 over 2 inch, without any gap or overlap. Which of the following describes the volume of this rectangular prism? 11 unit cubes and 1 smaller cube of volume fraction 1 over 8 cubic inch 22 unit cubes and 4 smaller cubes of volume fraction 1 over 8 cubic inch each 11 unit cubes and 2 smaller cubes of volume fraction 1 over 8 cubic inch each 22 unit cubes and 2 smaller cubes of volume fraction 1 over 8 cubic inch each Could someone teach me the steps please? I reviewed the lesson, I still don't understand
Answer:
A
Step-by-step explanation:
ur welcomes
a candle maker has 4 1/2 pounds of wax. He wants to cut the wax into pieces that are 2/3 pound each. How many 2/3 pound pieces can he divide the wax into?
Answer:
[tex]6\frac{3}{4}[/tex] pieces.
Step-by-step explanation:
Let x represent number of pieces.
The amount of wax used in making x pieces would be [tex]\frac{2}{3}x[/tex].
We have been given that a candle maker has 4 1/2 pounds of wax. We can represent this information in an equation as:
[tex]\frac{2}{3}x=4\frac{1}{2}[/tex]
[tex]\frac{2}{3}x=\frac{9}{2}[/tex]
[tex]\frac{3}{2}*\frac{2}{3}x=\frac{3}{2}*\frac{9}{2}[/tex]
[tex]x=\frac{27}{4}[/tex]
[tex]x=6\frac{3}{4}[/tex]
Therefore, the candle maker can make [tex]6\frac{3}{4}[/tex] pieces.
Ted can wax a car in 20 minutes or wash a car in 60 minutes. tom can wax a car in 15 minutes or wash a car in 30 minutes. what is each man’s opportunity cost of washing a car?
Trish has 9 boxes of pencils. Raj has 2 boxes of pencils. There are 10 pencils in each box. How many they have
Determine whether the statement is always, sometimes, or never true. If △ABC has angles that measure 10° and 40°, and △DEF has angles that measure 40° and 120°, then △ABC ≅ △DEF.
The statement is sometimes true. If two triangles have congruent angles, they are similar but not necessarily congruent.
Explanation:The statement is sometimes true. If △ABC has angles that measure 10° and 40°, and △DEF has angles that measure 40° and 120°, we can determine their congruence by comparing their angles. If two triangles have congruent angles, they are similar but not necessarily congruent. Therefore, △ABC and △DEF are similar triangles but not necessarily congruent.
Learn more about Triangles here:https://brainly.com/question/12113882
#SPJ3
if y is directly proportional to x^2 and y=216 when x=9 find y if x=19
round 101 to the nearest ten
101 rounded to the nearest ten is 100.
What is Rounding Off?Rounding off of a number is defined as the simplification of the number by keeping the value of the number same but is made closer to the next number.
Rounding can be done for whole numbers as well as decimals.
Here the given number is 101.
101 is between 100 and 110. We can round it to either of these two.
We have to round it to the nearest ten.
The number in the tens place is 0.
Look at the number next to tens place, which is at ones place.
The digit at ones place is 1, which is less than 5.
So keep the number in tens place as such and add 0 to ones place.
So the number is 100.
Hence 101 when rounded to nearest ten is 100.
Learn more about Rounding Off Numbers here :
https://brainly.com/question/13391706
#SPJ2
5x - x + 12 +2x - 7 = 10
1/10 of 400,000 is 10 times as much as?
Complete the following proof. Given: 2x 11 = 15 Prove: x = 2
Answer:
Hence, x = 2.
Step-by-step explanation:
Given : Given: 2x + 11 = 15 .
To find : Prove: x = 2.
Solution : We have given 2x + 11 = 15 .
On subtracting both sides by 11
2x = 15 - 11
2x = 4
On dividing both sides by 2
x = 2
Hence, x = 2.
Therefore, Hence, x = 2.
what is 3a^2 +a^2 added to a+6?
Answer:
Step-by-step explanation:
not sure if i am doing it right help please?
3a^2+a^2+a+6
3a^4+a+6
5/8(x-1/3)=5/12 can someone help me figure out what x is?
The above answer is correct, this answer I am sure is correct, I hope you can adopt.
One and two thirds times a right angle
Answer:
150 Degrees
Step-by-step explanation:
We have to find one and two third of a right angle.
That is we have to basically find [tex]1\displaystyle\frac{2}{3}\text{ of a right angle.}[/tex]
The measure of a right angle in degrees is 90 degrees.
[tex]1\displaystyle\frac{2}{3}\times 90[/tex]
We convert the mixed fraction into unlike fraction
[tex]\displaystyle\frac{5}{3}\times 90 = 150[/tex]
Thus, one and two third of a right angle is 150 degrees or [tex]150^\circ[/tex]
How much greater is the weight of the large box at 3/4lb than the small box at
1 1/8lbs
When the r2 of a regression equation is very high, it indicates tha?
What value of x will give the minimum value for x^2- 14x + 3?
Please help me!!
How much pizza will each person get if 4 people share 3/4 of a pizza equally?
what times what equals 46
What times what equals 46 is 2 times 23, or 2 x 23 = 46.
We have,
To find what times equal 46, we can look for pairs of numbers that, when multiplied together, result in 46.
We can start by listing the factors of 46:
1 x 46 = 46
2 x 23 = 46
From these factor pairs, we can see that 2 and 23 are the numbers that multiply to 46.
Therefore,
What times what equals 46 is 2 times 23, or 2 x 23 = 46.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
PLEASE HELP ASAP!!(3 QUESTIONS) I WILL GIVE BRAINLIEST AND 5 STARS!!
Identify the corresponding word problem given the equation: 5.59x = 27.95
A) How many boxes of nectarines can you buy with $27.95.
B) How much does a box of nectarines cost if five boxes costs $27.95?
C) How much does five boxes of nectarines cost if one box costs $5.59?
D) How many boxes of nectarines can you buy with $27.95 if one box costs $5.59?
Tom has saved $128, and his goal is to save $500. How much more must he save?
Which equation BEST represents this situation?
A) x + 128 = 500
B) x - 128 = 500
C) x + 500 = 128
D) x - 500 = 128
8, minus some number divided by 3, equals 6. Find the number.
A) -14/3
B) 4
C) 6
D) 2/3
Answer:
The first one is
1.) D)How many boxes of nectarines can you buy with $27.95 if one box costs $5.59?
2.) is B
3.) D
Step-by-step explanation:
You are given two sides of a triangle, a = 4.5 and b = 6. the angle between them is 35 degrees. write a script to find the length of the third side and the area of the triangle. hint: use trigonometric formula.
A rectangular rug is 12.5 feet long and 10 feet wide. The rug needs to be reduced by a factor of 1/5 to be placed near a door. What is the area of the reduced rug in square feet?
_______ft2
The temperature of dry ice is -109.3°F, which is 183.6°F less than the outside temperature. What is the outside temperature?
To find the outside temperature, add the difference of 183.6°F to the dry ice temperature of -109.3°F, yielding an outside temperature of 74.3°F.
Explanation:The student is asking to find the outside temperature given that dry ice temperature is -109.3°F and that the outside temperature is 183.6°F higher than the dry ice. We can solve this by adding the temperature difference to the dry ice temperature.
Let's denote the outside temperature as T.
T = (-109.3°F) + 183.6°F
Now, let's perform the addition:
T = 74.3°F
Therefore, the outside temperature is 74.3°F.
Final answer:
The outside temperature can be calculated by subtracting 183.6°F from the temperature of dry ice (-109.3°F).
Explanation:
The outside temperature can be calculated by adding the temperature difference to the temperature of dry ice. The temperature difference is given as 183.6°F less than the outside temperature, which means we need to subtract 183.6°F from the temperature of dry ice (-109.3°F). So, the outside temperature would be -109.3°F + (-183.6°F) = -293.9°F.
A restaurant uses 8 1/4 pounds of carrots to make 6 carrot cakes. Frank wants to use the same recipe. How many pounds of carrots does Frank need to make one carrot cake?
Frank needs [tex]\( \frac{11}{8} \)[/tex] pounds of carrots to make one carrot cake.
To find out how many pounds of carrots Frank needs to make one carrot cake, we first need to determine how many pounds of carrots are used per carrot cake in the original recipe.
Given that the restaurant uses 8(1)/(4) pounds of carrots to make 6 carrot cakes, we divide the total pounds of carrots by the number of cakes to find the amount per cake.
[tex]\( \text{Carrots per cake} = \frac{8\frac{1}{4}}{6} \)[/tex]
First, we convert the mixed number [tex]\(8\frac{1}{4}\)[/tex] to an improper fraction:
[tex]\(8\frac{1}{4} = \frac{(8 \times 4) + 1}{4} = \frac{33}{4}\)[/tex]
Then, divide by 6:
[tex]\( \frac{33}{4} \div 6 = \frac{33}{4} \times \frac{1}{6} = \frac{33}{24} = \frac{11}{8} \)[/tex]
So, Frank needs [tex]\( \frac{11}{8} \)[/tex] pounds of carrots to make one carrot cake.
NEED HELP 25 POINTS PLEASE HELP.The students at Harrison Middle School are being split into groups for a community service project. The school faculty has decided that each grade (6th, 7th, and 8th) will be split up into their own set of groups. The faculty has also decided that it is important for each grade to be split evenly into groups, with no leftover students, so that each group in a grade has exactly the same number of boys and girls. For each of the following grades, determine the largest number of groups that can be made and the number of boys and girls that will be in each group. The 6th grade has 64 girls and 72 boys. The 7th grade has 81 girls and 63 boys. The 8th grade has 68 girls and 60 boys. Please list down how many groups each grade has for both boys and girls.
Solve for y 1.2x - 4y = 28
Each time Gertrude gets paid, 10% of her pay check goes to taxes. Last week, $ 40 was taken out of her check for taxes. What was the amount of Gertrude's pay check last week?
Gertrude's paycheck last week was $400.
Explanation:To find the amount of Gertrude's paycheck last week, we can set up an equation using the information given. Let's assume her paycheck amount is represented by 'x'. According to the problem, 10% of her paycheck, or 0.10x, is taken out for taxes. This amount is given as $40. So we can write the equation as 0.10x = 40. To solve for x, we divide both sides of the equation by 0.10: x = 40 / 0.10 = $400.
Standard form of 210 million, 64 thousands, and fifty
The standard form of 210 million, 64 thousands, and fifty is 210,064,050. This is found by adding the values of each place: 210,000,000 for million, 64,000 for thousand, and 50 for the units.
The standard form of a number is a way of writing numbers that is commonly used in mathematics, especially in arithmetic and place value studies. To write the number 210 million, 64 thousands, and fifty in standard form, one combines these values considering their place values.
The value of 210 million is simply 210,000,000. The value of 64 thousands is 64,000, and the value of fifty is 50. When these are combined, we get:
210,000,000 (Two hundred and ten million)+ 64,000 (Sixty-four thousand)+ 50 (Fifty)Adding these together:
210,000,000 + 64,000 + 50 = 210,064,050
Therefore, the standard form of 210 million, 64 thousands, and fifty is 210,064,050.
The ratio of a quarterback completed passes to attempted passes is 7 to 8. If he attempted 24 passes, how many did he complete? Round to nearest whole number if needed.
If he attempted 24 passes, he completes 21 pass.
What is ratio?The numerical association of two values that shows how frequently one value includes or is contained inside another is called ratio.
Given, The ratio of a quarterback completed passes to attempted passes is 7 to 8.
If he attempted 24 passes.
To find the number of passes, he completes:
24 x 7/8
= 3 x7
= 21
Hence, he completes 21 passes.
To learn more about the ratio;
https://brainly.com/question/13419413
#SPJ3