Answers
5 (9/12 - 3/12) + 0.5
5 (6/12) + 0.5
5(2.5) + 0.5
12.5 + 0.5
13
next we want to subtract 3/4 - 1/4 and we get 2/4
next we want to multiply 5 * 2/4 and we get 10/4
and lastly we want to add 5/2 + 0.5 to get our answer
Answer: 3
Related Questions
A car can travel 30 mi on a gallon of gas and has20 gallon gas tanks let g be the number of gallons the car has in its tank the function d=30 g gives the distance d in miles that the car travels on g gallons
Answers
[tex]30 \times 20 = 60[/tex]
A gas tank has a leak. Each hour it loses 3 gallons of gas. Write the equation that represents how much gas, g , the tank loses over h hours.
Answers
The rate of change, or the slope, of this relationship is -3 gal / hr
Glenda began the day with a golf score of -6 and ended with a score of -10. Which statement represents her golf score for that day?
A) -6 - ( - 10) = 4
B) - 10 - ( - 6) = - 4
C) - 6 + ( - 10) = - 16
D) - 10 + ( - 6) = - 16
Answers
She started with -6 and ended up with -10 so her score was 4 less than what she started with so it is -4
if you have 12 fish and 6 drown how many do you have left?
Answers
Cody saves all his nickles. Today he is getting them out of his piggy bank and wrapping them to take to the bank. He finds he has 360 nickels. It takes 40 Nicole's to fill each paper wrapper and make a roll. How many wrappers does he need? Explain how you solved this problem and how you know your answer is correct.
Answers
Divide 360 by 40
360/40 = 9
Cody needs 9 wrappers.
3rd grader explanation:
Explain that Cody wants to divide 360 into __ groups of 40.
Use an illustration of separating things into equal groups (you can simply use separating 6 objects into equal groups of 2).
Explain that subtraction, multiplication, or addition will not help.
Tell him/her to use division.
Although 360 and 40 are large numbers, explain that the 0's can be removed into 4 and 36.
36 / 4 = 9
Since the answer is 9, Cody needs 9 wrappers.
Have an awesome day! :)
Which graph represents the equation y=1/3x−4 ?
bottom picture is my answers
Answers
y = (1/3)x + -4.
we know that the y-intercept=-4, so we can rue out the top left and bottom left graphs.
m=slope= (1/3). We know the slope is positive, so we can rule out the bottom right graph.
The top-right graph is the correct one.
The graph of the equation y = 1/3x - 4 is a straight line that contains the points (3, -3) and (0, 04)
The bottom left is the correct answer.
We have,
To graph this equation, we can start by finding the y-intercept, which is the point where the line crosses the y-axis.
In this equation,
The y-intercept is -4, so we plot the point (0, -4).
Next, we can find another point on the line by choosing a value for x and calculating the corresponding y-value.
Let's choose x = 3.
Plugging this value into the equation, we get:
y = (1/3)(3) - 4
y = 1 - 4
y = -3
So point (3, -3) lies on the line.
Now we can plot these two points (0, -4) and (3, -3) and draw a straight line passing through them.
Since the coefficient of x is positive (1/3), the line will have a positive slope, meaning it rises as we move from left to right.
Thus,
The graph of the equation y = 1/3x - 4 would look like a straight line that slants upward as you move from left to right, crossing the y-axis at -4.
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Which number is a factor of 20 and also a prime number?
A.
4
B.
5
C.
7
D.
10
Answers
thus B is your Answer.
Evaluate the triple integral of f(x,y,z)=z(x2+y2+z2)−3/2f(x,y,z)=z(x2+y2+z2)−3/2 over the part of the ball x2+y2+z2≤49x2+y2+z2≤49 defined by z≥3.5z≥3.5. ∫
Answers
[tex]f(x,y,z)=z(x^2+y^2+z^2)^{-3/2}=\dfrac z{(x^2+y^2+z^2)^{3/2}}[/tex]
(as opposed to subtracting 3/2, say)
Convert to spherical coordinates, taking
[tex]\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]
Now when [tex]z=\dfrac72[/tex], below the "cap" of the ball we have a right triangle with hypotenuse coinciding with the ball's radius and a leg of length [tex]\dfrac72[/tex], with the angle between them [tex]\varphi[/tex] satisfying
[tex]\cos\varphi=\dfrac{\frac72}7=\dfrac12\implies\varphi=\cos^{-1}\dfrac12=\dfrac\pi3[/tex]
Furthermore, when [tex]z=\dfrac72[/tex], we have
[tex]\dfrac72=\rho\cos\varphi\implies\rho=\dfrac72\sec\varphi[/tex]
Call the cap [tex]C[/tex]. Then the triple integral over [tex]C[/tex] is
[tex]\displaystyle\iiint_Cf(x,y,z)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi/3}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=7/2\,\sec\varphi}^{\rho=7}\frac{\rho\cos\varphi}{(\rho^2)^{3/2}}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]
[tex]=\displaystyle2\pi\int_{\varphi=0}^{\varphi=\pi/3}\int_{\rho=7/2\,\sec\varphi}^{\rho=7}\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi[/tex]
[tex]=\displaystyle\pi\int_{\varphi=0}^{\varphi=\pi/3}\sin2\varphi\left(7-\dfrac72\sec\varphi\right)\,\mathrm d\varphi[/tex]
[tex]=\displaystyle\frac{7\pi}2\int_{\varphi=0}^{\varphi=\pi/3}(2\sin2\varphi-\sin2\varphi\sec\varphi)\,\mathrm d\varphi=\frac{7\pi}4[/tex]
To evaluate a triple integral over a region of a sphere, we switch to spherical coordinates. We then express the integrand and the limits of the variables in terms of these new coordinates. Don't forget the Jacobian when changing variables.
Explanation:The subject is a mathematical problem that requires evaluating a triple integral over a specific part of a ball in three-dimensional space. The function to integrate is f(x,y,z)=z*(x2+y2+z2)-3/2 and the region of integration is defined as the part of the sphere with radius 7 (x2+y2+z2<=49) in which z >= 3.5. Unfortunately, the solution to such a problem requires advanced mathematical skills and knowledge, such as spherical coordinates and integration techniques, which cannot be elaborated within the word limit here.
However, to solve such problems, you typically switch to spherical coordinates, where x=r*cos(theta)*sin(phi), y=r*sin(theta)*sin(phi), z=r*cos(phi). Then, you express your function and the limits of your variables r, theta, and phi in terms of these new coordinates. You need to consider the Jacobian determinant when changing variables. Eventually, you integrate over the specified region. The solution needs careful elaboration of every step due to the complexity of the integral.
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Which statement best describes one of these transformations? Triangle 1 is rotated to result in triangle 2. Triangle 1 is dilated to result in triangle 3. Triangle 1 is reflected to result in triangle 4. Triangle 1 is stretched to result in triangle 5.
Answers
Answer:
Triangle 1 is rotated to result in triangle 2.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
GOT IT RIGHT
A boy walks for x hours at 33 mph and bicycles for (5−x) hours at 93 mph. If the total distance traveled is d miles, express d in terms of x.
Answers
distance = speed * time
Walking:
d = speed * time
d1 = 33 mph * x hours = 33x miles
Bicycling:
d = speed * time
d2 = 93 mph * (5 - x) hours = 93(5 - x) miles = (465 - 93x ) miles
The total distance traveled is the distance walked plus the distance bicycled
d = d1 + d2
d = 33x + 465 - 93x
d = -60x + 465
Answer:
d = 465 - 60x
Step-by-step explanation:
1. Find the distances of walking and bicycling. We can express the walking distance as 33x, because x is the time and 33 is the amount of miles, and we can express the bicycling distance as 93(5-x), because 93 is the speed and 5-x is the amount of hours.
2. Construct an equation. We can say that the total distance is d = 33x + 93(5-x), the sum of both of the distances.
3. Simplify. If you simplify, you would get d = 465 - 60x
(This guy is going Super Saiyan)
Answer: d = 465 - 60x
A group of college students built a self-guided rover and tested it on a plane surface. They programmed the vehicle to move along the path A–B–C–D–A represented on the coordinate plane. What distance will the rover cover if it completes one circuit? 36 meters 40 meters 54 meters 60 meters 68 meters
Answers
https://brainly.com/question/1592171
Answer:
The answer is B. 40 meters on plato
What are the values of a and b
Answers
the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are 8 and [tex]\( 2\sqrt{7} \)[/tex], respectively.
The image depicts a right-angled triangle with a hypotenuse of length 10 and one leg of length 6, with the other leg labeled as [tex]\( a \)[/tex]. There is also a smaller right-angled triangle within it, sharing the leg of length 6 with the larger triangle, with the hypotenuse of the smaller triangle labeled as 8 and the other leg labeled as [tex]\( b \).[/tex]
To find the lengths of [tex]\( a \)[/tex] and [tex]\( b \)[/tex], we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse [tex](\( c \))[/tex] is equal to the sum of the squares of the lengths of the other two sides [tex](\( a \)[/tex] and [tex]\( b \)[/tex]): [tex]\( c^2 = a^2 + b^2 \).[/tex]
For the larger triangle:
[tex]\[ 10^2 = 6^2 + a^2 \][/tex]
For the smaller triangle:
[tex]\[ 8^2 = 6^2 + b^2 \][/tex]
We will solve these two equations to find [tex]\( a \)[/tex] and [tex]\( b \)[/tex]. Let's start with the calculations for [tex]\( a \)[/tex] and [tex]\( b \)[/tex] using the Pythagorean theorem.
Using the Pythagorean theorem for each triangle, we find:
For the larger triangle:
[tex]\[ a^2 = 10^2 - 6^2 \][/tex]
[tex]\[ a^2 = 100 - 36 \][/tex]
[tex]\[ a^2 = 64 \][/tex]
[tex]\[ a = 8 \][/tex]
For the smaller triangle:
[tex]\[ b^2 = 8^2 - 6^2 \][/tex]
[tex]\[ b^2 = 64 - 36 \][/tex]
[tex]\[ b^2 = 28 \][/tex]
[tex]\[ b = \sqrt{28} \][/tex]
[tex]\[ b = 2\sqrt{7} \][/tex]
So, the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are 8 and [tex]\( 2\sqrt{7} \)[/tex], respectively.
Doomtown is 300 miles due west of Sagebrush and Joshua is due west of Doomtown. At 9 a.m. Mr. Archer leaves Sagebrush for Joshua. At 1 p.m. Mr. Sassoon leaves Doomtown for Joshua. If Mr. Archer travels at an average speed 20 mph faster than Mr. Sassoon and they each reach Joshua at 4 p.m., how fast is each traveling?
Answers
Let the distance that Sassoon travels is d miles.
Let his average speed be x mph.
The time of travel is from 1 p.m. to 4 p.m., which is 3 hours.
Therefore
3x = d (1)
The distance that Archer travels is (d + 300) miles.
The time of travel is from 9 a.m. to 4 p.m., which is 7 hours.
The average traveling speed is (x + 20) mph, therefore
7(x + 20) = d + 300
That is,
7x + 140 = d + 300
7x = d + 160 (2)
Subtract (1) from (2).
7x - 3x = d + 160 - d
4x = 160
x = 40 mph (Sassoon's average speed)
x+20 = 60 mph (Archer's average speed)
From (1), obtain d = 120 mi
Answer:
Archer's speed is 60 mph.
Sassoon's speed is 40 mph.
Answer:Archer's speed is 60 mph.
Sassoon's speed is 40 mph.
Step-by-step explanation:
Let the distance that Sassoon travels is d miles.
Let his average speed be x mph.
The time of travel is from 1 p.m. to 4 p.m., which is 3 hours.
Therefore
3x = d (1)
The distance that Archer travels is (d + 300) miles.
The time of travel is from 9 a.m. to 4 p.m., which is 7 hours.
The average traveling speed is (x + 20) mph, therefore
7(x + 20) = d + 300
That is,
7x + 140 = d + 300
7x = d + 160 (2)
Subtract (1) from (2).
7x - 3x = d + 160 - d
4x = 160
x = 40 mph (Sassoon's average speed)
x+20 = 60 mph (Archer's average speed)
From (1), obtain d = 120 mi
Answer:
Archer's speed is 60 mph.
Sassoon's speed is 40 mph.
What is 0.63¯¯¯¯ expressed as a fraction in simplest form? Enter your answer in the box.
Answers
7
11
Explanation:
We let 0.63 (63 being repeated) be
x
.
x
=
0.6363
...
Since
x
is recurring in 2 decimal places, we multiply it by 100.
100
x
=
63.6363
...
Next, we subtract them.
100
x
−
x
=
63.6363
...
−
0.6363
...
99
x
=
63
The recurring digits '63' cancel off and the result is that
99
x
is non-recurring.
Lastly, we divide both sides by 99 to get
x
as a fraction.
x
=
63
99
=
7
11
To express 0.63¯¯¯¯ as a fraction, first set it up as x = 0.6363¯¯¯¯, then follow a process of subtraction, multiplication, and division to simplify it to 4063/9900.
Explanation:To express 0.63¯¯¯¯ as a fraction in simplest form, we can set it up as x = 0.6363¯¯¯¯.
Subtract the repeating part from the original number: x = 0.6363¯¯¯¯ - 0.6 = 0.03¯¯¯¯Multiply x by 100 to shift the decimal two places to the right: 100x = 63.6363¯¯¯¯ - 60 = 3.6363¯¯¯¯Subtract the first equation from the second equation: 100x - x = 3.6363¯¯¯¯ - 0.03¯¯¯¯Combining these steps, we get:
99x = 3.606363¯¯¯¯¯¯¯¯ x = 3.606363¯¯¯¯ / 99 = 4063/9900 as the fraction in simplest form.
If p(a) = 0.65, p(b) = 0.58, and p(a and
b.= 0.76, then p(a or
b.is:
Answers
The value of P( a or b)= 0.47.
what is Conditional Probability?The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier occurrence by the increased likelihood of the later, or conditional, event.
Conditional probability is the likelihood that any event A will occur in the presence of another event B that is related to A. P(A|B) illustrates it.
Given:
p(a) = 0.65, p(b) = 0.58, and p(a and b)= 0.76
Now, using the formula
P(a∪b) = P(a) + P(b) - P(a∩b)
= 0.65 + 0.58 - 0.76
= 0.47
Hence, the value of P( a or b)= 0.47.
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Find 14+1320
. Write your answer as a fraction in simplest form.
Answers
hope this helps
----------- --------------+---------------- =-----------------
10 4 20 10
WILL GIVE BRAINEST
Which system of inequalities is shown?
Answers
The system of inequalities are y > x and y > 4 option (C) y > x, y > 4 is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have a graph shown in the picture,
As we can see in the picture there two lines are shown which represent the inequality and the shaded region is the solution to the pair of the linear inequality.
y > x and
y > 4
Thus, the system of inequalities are y > x and y > 4 option (C) y > x, y > 4 is correct.
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Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system. x < 2 and y ≤ 4x + 1
(5, 6)
(5, –2)
(–3, –15)
(1, 11)
Answers
x < 2
y ≤ 4x + 1
Graph the lines:
x = 2
y = 4x +1
The solution to the system of inequalities is the shaded region shown in the graph below.
Test the given points to see whether they fall within the solution region.
Point Pass/Fail
-------- --------------
(5,6) Fail
(5,-2) Fail
(-3,-15) Pass
(1,11) Fail
Answer: (=3, -15)
Which phrase describes the variable expression k -7? A) 7 less then k B) 7 more then k C) The quotient of k and -7 D) The product of k and -7
Answers
hope this helps
Find three consecutive even integers such that the sum of twice the smallest number and three times the largest is 42.
Answers
Let n be the smallest of the three even integers.
Then the next larger even integer is n + 2.
The largest even integer is n + 4.
Now we follow what the problem tells us.
Twice the smallest is 2n
3 times the larges is 3(n + 4)
2n + 3(n + 4) = 42
2n + 3n + 12 = 42
5n + 12 = 42
5n = 30
n = 6
n + 2 = 8
n + 4 = 10
The integers are 6, 8, 10
To find the consecutive even integers, we created an equation and solved for x, which represents the smallest integer. Upon solving, we found that the smallest integer is 6, and hence, the three consecutive even integers are 6, 8, and 10.
To find three consecutive even integers such that the sum of twice the smallest number and three times the largest is 42, we can form an equation based on the description. Let the smallest even integer be x. Since we are looking for consecutive even integers, the next two will be x+2 and x+4.
According to the problem, twice the smallest plus three times the largest equals 42:
2x + 3(x+4) = 42
Solving the equation:
Distribute the 3 into the parentheses: 2x + 3x + 12 = 42
Combine like terms: 5x + 12 = 42
Subtract 12 from both sides: 5x = 30
Divide both sides by 5: x = 6
Therefore, the smallest even integer is 6, and the other two are 8 and 10, which are the consecutive even integers that satisfy the given condition.
On your last credit card statement, you had a previous balance of $98.14, payments of $10, a periodic rate of 1.34 percent, and new charges totaling $34.89. What is your new balance?
A. $88.14
B. $100.58
C. $124.21
D. $189.35
Answers
An angle measures 54 less than the measure of a complementary angle. What is the measure of each angle?
Answers
A rectangle is 2 4/5 meters wide and 3 1/2 m long what is its area
Answers
I like to convert my fractions to decimals if that's alright with you☺
2.8 * 3.5
^ ^
2 4/5 , 3 1/2
=9.8m
hope this helped!
The area of the rectangle whose dimensions are 2 ⁴/₅ meters wide and 3 ¹/₂ m long will be 49/5 square meters.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L×W square units
A rectangle is 2 ⁴/₅ meters wide and 3 ¹/₂ m long. Then the area of the rectangle will be
A = (2 ⁴/₅)(3 ¹/₂)
A = (14/5) (7/2)
A = 49/5 square meters
The area of the rectangle whose dimensions are 2 ⁴/₅ meters wide and 3 ¹/₂ m long will be 49/5 square meters.
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Bill worked 24 hours last week and earns $8.25 per hour. Use front-end estimation to find an estimate of the total amount of money he earned.
Answers
Answer:
The total amount of money he earned was $160
Step-by-step explanation:
Bill worked 24 hours last week
He earns $ 8.25 per hour.
We have to use front-end estimation, we have to round to the first number all the values. So. Bill worked h = 20 hours and he earns 3 =$8 per hour.
Total amount (T) wil be the hours (h) multiplied by the earning (e)
T = h*e
T = (20 hours)(8 $/hours)
T = 160 $
After using front-end estimation, we can conclude that Bil earned $160.
labored 24 hours remaining week
He earns $ 8.25 in step per hour.
We should use the front-stop estimation, we have to round to the first number of all of the values. So. invoice worked h = 20 hours and he earns 3 =$eight according to an hour.
the entire amount (T) can be the hours (h) extended through the earning (e)
T = (20 hours)(eight $/hours)
T = 160 $
After using front-end estimation, we will conclude that Bil earned $one hundred sixty.
How do you calculate front-end estimation?front-cease estimation is a particular way of rounding numbers to estimate sums and variations. to apply the front-end estimation, add or subtract the handiest of the numbers in the finest location cost. Then upload the decimals rounded to the closest 10th.
what are front-end estimation examples?
In the front-cease estimation, we replace the original quantity with quite a number it is close by but the handiest has one non-zero digit. as an example, 20, three hundred, -50, 1,000, eighty,000. Take the quantity 32; the selections to update it with are 30 or forty (they both have the handiest one non-0 digit).
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a moving company charges $250 to rent a truck and $0.40 for each mile driven. Mr. Lee paid a total of $314. Which equation can be used to find m, the number of miles he drove the moving truck?
Answers
314 = 0.4(x) + 250
Would you like me to explain?
To find the number of miles Mr. Lee drove the moving truck, we can set up an equation using the given information and solve for 'm'. The equation is $250 + $0.40x = $314, where 'x' represents the number of miles driven. Simplifying the equation, we find that Mr. Lee drove a total of 160 miles in the moving truck.
Explanation:To find the number of miles Mr. Lee drove the moving truck, we can set up an equation using the given information. The moving company charges $250 to rent the truck and $0.40 for each mile driven. Let's let 'm' represent the number of miles he drove. The total cost Mr. Lee paid, including the rental fee and the cost per mile, is $314. So, the equation can be written as:
$250 + $0.40x = $314
To solve for 'm', we can subtract $250 from both sides of the equation:
$0.40x = $314 - $250
$0.40x = $64
Finally, we can divide both sides of the equation by $0.40 to find the value of 'm':
x = $64 / $0.40
x = 160
Therefore, Mr. Lee drove a total of 160 miles in the moving truck.
Which situation could best be represented by this linear equation?
2.75x + 3.25y = 215
Answers
answer is the last one (D)
Answer:
The correct option 4.
Step-by-step explanation:
The given equation is
[tex]2.75x+3.25y=215[/tex] .... (1)
Let x is the number of pretzels sold and y is the number of popcorn bags sold.
Total sales is defined as
[tex]Sales=C_1x+C_2y[/tex] ... (2)
From (1) and (2) it is clear that,
The cost of each pretzel is $2.75 or 275 cents. The cost of each popcorn bag is $3.25 or 325 cents ($1 = 100 cents). Total sales is $215.
[tex]325-275=50[/tex]
Pretzels cost is 50 cents less than popcorn bags. The variable x represents the number of pretzels sold and y represents the number of popcorn bags sold. The total sales was $215.
Therefore the correct option 4.
I need help! Rewrite each product below using Distributive property.
a: 18(26)
b: 6(3405)
c: 21(35)
Thanks!!!p
Answers
a. 18(26) →18 × 26 = 468
b. 6(3405) → 6 × 3405 = 20,430
c. 21(35) → 21 × 35 = 735
The numbers in bold are the answers. Hope this helps and have a phenomenal day!
By using distributive property, the answers are :(a)468, (b) 20430, (c) 735.
Explain, distributive property.Distributive property is the mathematical property to solve expressions in the form of a(b + c), in which firstly bracket term is solve and then other terms are solved.
(a)
The given term is,
18(26),
According to distributive property, bracket changes in multiply.
Therefore, 18(26)⇒18×26=468.
(b)
The given term is,
6(3405),
According to distributive property, bracket changes in multiply.
Therefore, 6(3405)⇒6×3405=20430.
(c)
The given term is,
21(35),
According to distributive property, bracket changes in multiply.
Therefore, 21(35)⇒21×35=735.
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20,880 times 2/5 worked out
Answers
= (20,880 x 2)/5
= (41,760)/5
= 8,352
The multiplication [tex]20880 \times \dfrac{2}{5}[/tex] is [tex]\boxed{8352}.[/tex]
Further explanation:
Always use the PEDMAS rule to solve the grouping of multiplication, addition, subtraction and division.
Here, P is parenthesis, E is exponents, M is multiplication, D is division, A is addition and S is subtraction.
Given:
The expression is [tex]20880 \times \dfrac{2}{5}.[/tex]
Explanation:
The given expression is [tex]20880 \times \dfrac{2}{5}.[/tex]
Consider the expression [tex]20880 \times \dfrac{2}{5}[/tex] as A.
[tex]A = 20880 \times \dfrac{2}{5}[/tex]
Solve the above expression to obtain the simplest form.
[tex]\begin{aligned}A&= 20880 \times \frac{2}{5}\\&= \frac{{41760}}{5}\\&= 8352\\\end{aligned}[/tex]
Another way of solving the expression can be expressed as follows,
First divide 2 by 5.
[tex]\begin{aligned}b&= \frac{2}{5}\\&= 0.4\\\end{aligned}[/tex]
Now multiply 20880 to 0.4.
[tex]\begin{aligned}A&= 20880 \times 0.4\\&= 8352\\\end{aligned}[/tex]
The multiplication [tex]20880[/tex] times [tex]\dfrac{2}{5} \:{\text{is}\: \boxed{8352}.[/tex]
Learn more
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: factor, factorization, 20880, 2/5, times, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.
Evaluate the line integral ∫cx4zds, where c is the line segment from (0,6,5) to (8,4,1).
Answers
[tex]\mathbf r(t)=\langle0,6,5\rangle(1-t)+\langle8,4,1\rangle t=\langle8t,6-2t,5-4t\rangle[/tex]
with [tex]0\le t\le1[/tex]. Then
[tex]\displaystyle\int_{\mathcal C}x^4z\,\mathrm dS=\int_{t=0}^{t=1}(8t)^4(5-4t)\sqrt{8^2+(-2)^2+(-4)^2}\,\mathrm dt=8192\sqrt{21}-16384\sqrt{\frac73}[/tex]
To evaluate the line integral, we need to parameterize the line segment and calculate the differential arc length. After simplifying the integrand, we can evaluate the line integral by integrating the simplified expression.
Explanation:To evaluate the line integral ∫cx^4zds, where c is the line segment from (0,6,5) to (8,4,1), we need to parameterize the line segment c. Let's parameterize it with t, where t varies from 0 to 1. The parameterization of c is given by:
x(t) = 8t, y(t) = 6 - 2t, z(t) = 5 - 4t.
Next, we need to calculate ds, which is the differential arc length along the line. The differential arc length ds is given by:
ds = √(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt.
Substituting the parameterized values of x(t), y(t), and z(t) into the above equation, we get:
ds = √[(8)^2 + (-2)^2 + (-4)^2] dt = √84 dt.
Now, we can rewrite the line integral as:
∫cx^4zds = ∫(8t)^4(5 - 4t)√84 dt.
Next, we simplify the integrand:
(8t)^4(5 - 4t) = 4096t^4(5 - 4t).
Finally, we evaluate the line integral by integrating the simplified integrand over the interval [0, 1]:
∫(8t)^4(5 - 4t)√84 dt = √84 ∫4096t^4(5 - 4t) dt.
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Find the length of the curve. r(t) = 3 i + t2 j + t3 k, 0 ≤ t ≤ 1
Answers
[tex]\displaystyle\int_C\mathrm dS=\int_{t=0}^{t=1}\|\mathbf r'(t)\|\,\mathrm dt=\int_{t=0}^{t=1}t\sqrt{9t^2+4}\,\mathrm dt=\frac{13\sqrt{13}-8}{27}[/tex]
To determine the length of the curve, we find the derivative of the given vector function, compute its magnitude, and then compute the integral of the magnitude from 0 to 1. This involves calculus techniques.
Explanation:To find the length of the curve, we have to compute the integral of the magnitude of the derivative on the interval from 0 to 1. First, we find the derivative of r(t) = 3 i + t^2 j + t^3 k which is r'(t) = 2t j + 3t^2 k. The magnitude of r'(t) is |r'(t)| = sqrt((0)^2 + (2t)^2 + (3t^2)^2) = sqrt(4t^2 + 9t^4). Thus the length of the curve is the integral of this magnitude from 0 to 1: ∫ from 0 to 1 of sqrt(4t^2 + 9t^4) dt. This integral can be evaluated using techniques from calculus.
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