Answer:
each rope should be 1 1/7 yard long
Step-by-step explanation:
9 1/7 ÷8
1 1/7
Answer:
8/7 yd per piece
Step-by-step explanation:
To answer this, divide the total rope length 9 1/7 yd by 8 pieces:
64 yd
------------------ = 8/7 yd per piece
7(8 pieces)
Check: does 8 times (8/7 yd/piece) come out to 64/7 yd, or 9 1/7 yd? YES
Find the general solution to the homogeneous system of DE: -11 x' = Ax where A = [-26 41 Hint: Write your answer x(t) in the form of eat [cos(ht) + sin(bt)].
The general solution to the homogeneous system of differential equations is:
x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |
|-1 |
where c₁ and c₂ are constants.
To find the general solution to the homogeneous system of differential equations -11x' = Ax, where A = [-26 4; 1 1], we first need to find the eigenvalues and eigenvectors of matrix A.
To find the eigenvalues, we solve the characteristic equation:
det(A - λI) = 0
Substituting the values, we get:
| -26-λ 4 |
| 1 1-λ |
Expanding the determinant, we have:
(-26-λ)(1-λ) - 4 = 0
Simplifying and solving the equation, we find the eigenvalues:
λ₁ = -7
λ₂ = -20
Next, let's find the corresponding eigenvectors.
For λ₁ = -7:
(A + 7I)v₁ = 0
| -19 4 |
| 1 8 |
Solving the system of equations, we find the eigenvector corresponding to λ₁:
v₁ = | 4 |
|-1 |
For λ₂ = -20:
(A + 20I)v₂ = 0
| -6 4 |
| 1 21 |
Solving the system of equations, we find the eigenvector corresponding to λ₂:
v₂ = | 2 |
|-1 |
Now that we have the eigenvalues and eigenvectors, we can write the general solution to the system of differential equations as:
Substituting the values of the eigenvalues and eigenvectors, we get:
x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |
|-1 |
Simplifying this expression, we get:
x(t) = | 4c₁ * [tex]e^{(-7t)[/tex] + 2c₂ * [tex]e^{(-20t)[/tex] |
|-c₁ * [tex]e^{(-7t)[/tex] - c₂ * [tex]e^{(-20t)[/tex]) |
Therefore, the general solution to the homogeneous system of differential equations is:
x(t) = c₁ * [tex]e^{(-7t)[/tex] * | 4 | + c₂ * [tex]e^{(-20t)[/tex] * | 2 |
|-1 |
where c₁ and c₂ are constants.
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Can someone help me please ASAP? Correct answer gets brainliest!! :)
Answer:
Blank 1: 6
Blank 2: 30
1/2 = 6/12 = 30/60
Blank 3: 30
1/4 = 3/12 = 15/60
How do you find the greatest common denominator, when comparing two numbers? Explain your thought process, in the example I provided. What is the greatest common Denominator for the numbers 20 and 40. Explain each step you do. Your answer will start with these words. "How to find the the greatest common denominator between 20 and 40?
Answer:
20 is the greatest common denominator. You can find this by listing the factors of each number. The highest number that can fit into both individual numbers is the common denominator. Since 40 is just 20 doubled, and 20 is just 20 once, it fits into both numbers and is also the highest number that can fit.
PLEASE HELP FAST I WIL MARK BRAINLIEST
Answer: AB = 15 because sides AB and AD are congruent
Step-by-step explanation:
six and fifty-three hundredths as a decimal-
Yes, I'm D-U-M-B!
Answer:
6.58
Step-by-step explanation:
ahahahaha lol
Answer:
6.58
i hope this helps:)
Step-by-step explanation:
brainliest please?
An element with a mass of 700 grams decays by 6.1% per minute. To the nearest
tenth of a minute, how long will it be until there are 220 grams of the element
remaining?
Answer:
11.2 minutes
Step-by-step explanation:
If the element decreases by 6.1, every minute, it means that the mass lost every minute = 0.061 x 700g = 42.7g
The mass remaining after a minute = 657.30g
The equation that can be used to solve this question is :
700 - 42.7m = 220
m = minutes
Collect like terms
700 - 220 = 42.7m
480 = 42.7m
divide both sides of the equation by 42.7
m = 11.241218 minutes
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
Here, the hundredth is less than 5, so zero would be added to 2. the answer is 11.2 minutes
Answer:
18.4
Step-by-step explanation:
I answered the question
A concrete slab has the dimensions 4 yd by 2 yd by 1.2 yd. What is the volume of 40 of these concrete slabs
The volume of 40 of the concrete slabs given the dimensions of one concrete slab is 384 yd³.
What is the volume of one concrete slab?The concrete slab has the shape of a rectangular prism. So, the volume of a rectangular prism would be used to determine the volume of the concrete slabs.
Volume of one concrete slab = length x width x height
4 x 2 x 1.2 = 9.6 yd³
Volume of 40 concrete slabs = 40 x 9.6 = 384 yd³
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Please help me in it! It's very difficult, i'm in 6th and I still don't understand this. Please, help me in this!!!
Answer:
40
where the line starts (75) and ends (115)
115-75=40
thats the quick way to solve... hope this helps!
Step-by-step explanation:
Brainliest?
A sphere has a radius of 9 feet. A second sphere has a radius of 6 feet. What is the difference of the volumes of the spheres? The volume of the larger sphere is π cubic feet greater than the volume of the smaller sphere.
Answer:
684 π
Step-by-step explanation:
volume of a sphere = (4/3) x (n) x (r^3)
n = 22/7
r = radius
volume of larger sphere
4/3 x n x 9³ = 972 n
4/3 x n x 6³ =288n
972n - 288n = 684n
Can someone help me with this. Will Mark brainliest.
Answer:
the distance between the two points is √130.
Step-by-step explanation:
a^2 + b^2 = c^2
a^2 = 9^2 = 81
b^2 = 7^2 = 49
c^2 = 81 + 49 = 130
c = √130
Jasmine bought four potted plants. Two of the plants cost $6.65, and the others cost $4 and $7.15. How much money did jasmine spend in all?
Answer:
$24.45
Step-by-step explanation:
6.65 + 4 + 7.15 + 6.65 = 24.45
True or false: On average, eta-squared, partial eta-squared, and R-squared are all measures of effect size that refer to the proportion of variance explained within a study.
The statement that eta-squared, partial eta-squared, and R-squared are all measures of effect size that refer to the proportion of variance explained within a study. This statement is true.
In order to better understand what eta-squared, partial eta-squared, and R-squared are, we must first understand what the proportion of variance explained is. The proportion of variance explained refers to the amount of variation in one variable that is accounted for by another variable or variables. All three of these measures are measures of effect size, which means they are used to determine the strength of the relationship between two variables. They also all refer to the proportion of variance explained within a study. However, they differ in terms of how much variance they account for. Eta-squared is a measure of effect size that is used in ANOVA to determine the proportion of variance in the dependent variable that is accounted for by the independent variable. Partial eta-squared, on the other hand, is used to determine the proportion of variance that is accounted for by the independent variable when controlling for other variables.
Finally, R-squared is a measure of effect size that is used in regression analysis to determine the proportion of variance in the dependent variable that is accounted for by the independent variable.
In conclusion, all three of these measures of effect size are used to determine the proportion of variance explained within a study.
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find the area of the triangle
Rico and Darla each measured a side and height on the triangle below to find its area.
Rico’s side measured 7.5 m and Darla’s side measured 9 m.
Choose True or False for each statement.
A triangle with two base and side length measurements. One side length is nine meters, and the height from that side is five meters. The other side length is seven and five-tenths meters and the height from that side is six meters.
Darla can use either the height of 6 meters or the height of 5 meters to find the area of the triangle.
Choose...
If Darla uses the height of 6 meters and Rico uses the height of 5 meters, they will find the same area of the triangle.
Choose...
If Rico uses the height of 6 meters and Darla uses the height of 5 meters, they will find the same area of the triangle.
Choose...
The area of the triangle is 22.5 square meters.
Choose...
Answer: not sure
Step-by-step explanation:
Calculate the integral ∫ [(1+cos(arctan (3x))+(arctan (3x))^5)/(1+9x^2]dx.
The solution of the integral (1/6)ln|9x²+1| +(1/3)arctan (3x) +(1/6)arctan((3x)²)- (1/18)(3x)²/(9x²+1) + (1/90)(3x)⁴/(9x²+1) + C.
We have the following integral to solve.∫ [(1+cos(arctan (3x))+(arctan (3x))⁵)/(1+9x²2)]dx
Let's begin by using the substitution u = arctan(3x).
We need to convert this integral into a U-form. By substituting the above expression, we have the following new expression.
∫ [(1+cos u)+u⁵]/[1+9(3tanu)²] *(1/3) du=∫ [(1+cos u)+u⁵]/(9tan²u+1) *(1/3) du
Let's now consider the numerator.
We have 1+cosu+u⁵ in the numerator. Let's break down the integral into 3 parts. The first part is ∫(1)/(9tan²u+1) *(1/3) du.
We can convert the denominator to a perfect square of the form 3²tan²u+1 which simplifies to (3tanu+1)(3tanu-1)+2.
Let's now factorize
= ∫(1)/(9tan²u+1) *(1/3) du
=∫(1)/[(3tanu+1)(3tanu-1)+2] *(1/3) du
Now let's perform partial fraction decomposition. We have 1/[(3tanu+1)(3tanu-1)+2] which we can write as
= A/(3tanu+1)+B/(3tanu-1)+C/(3tan²u+1) where A, B, and C are constants to be determined.
We now have 1= A(3tanu-1)(3tan²u+1)+ B(3tanu+1)(3tan²u+1)+ C(3tanu+1)(3tanu-1).
Let's now set up the system of equations.
The first equation is
1= A(3tanu-1)(3tan²u+1)+ B(3tanu+1)(3tan²u+1)+ C(3tanu+1)(3tanu-1)
Putting u=0, we get
A = 1/4
Putting u =pi/3, we get
B=1/4 Putting
u = arctan(1/√(3)), we get C=1/2. Now that we have A, B, and C, let's substitute them back to our integral.
We have
= ∫(1)/[(3tanu+1)(3tanu-1)+2] *(1/3) du
= (1/4)∫(1)/(3tanu+1) du + (1/4)∫(1)/(3tanu-1) du +(1/2)∫(1)/(3tan²u+1) du
Let's now solve the integral and simplify.
= ∫(1)/(3tanu+1) du
= (1/6)ln|3tanu+1|- (1/6)ln|3tanu-1|+ (1/3)arctan (3tanu).
Similarly,
= ∫(1)/(3tanu-1) du
= (-1/6)ln|3tanu+1|+ (1/6)ln|3tanu-1|+ (1/3)arctan (3tanu).
The third integral we can solve by substitution
v = √(3)tanu.
We then get
= ∫(1)/(3tan²u+1) du= (1/√(3))∫(1)/(v²+3) dv
= (1/sqrt(3))arctan(v/√(3))
= (1/√(3))arctan((√(3)tanu)/√(3)).
We can now put back all the values to get the solution.
= ∫ [(1+cos(arctan (3x))+(arctan (3x))⁵)/(1+9x²)]dx
= (1/3)∫ [(1+cos u)+u⁵]/(9tan²u+1) du
=(1/3)[(1/4)(ln|3tanu+1|- ln|3tanu-1|+ 2arctan (3tanu))+(1/4)(-ln|3tanu+1|+ ln|3tanu-1|+ 2arctan (3tanu))+(1/2)(1/√(3))(arctan((sqrt(3)tanu)/√(3)))]+ C
We can simplify the above expression to get
=- ∫ [(1+cos(arctan (3x))+(arctan (3x))^5)/(1+9x²)]dx
= (1/6)ln|9x²+1| +(1/3)arctan (3x) +(1/6)arctan((3x)²)- (1/18)(3x)²/(9x²+1) + (1/90)(3x)⁴/(9x²+1) + C
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Solve.
t
8.4=
1.5
=
Help plzzzz
Answer:
t = 12.6
Step-by-step explanation:
8.4 x 1.5 = 12.6
to check it, do 12.6 ÷ 1.5 = 8.4
сть
b
d
a
If mza = 2.m2b, mzc = 60', and the right angles are labeled in the figure, which of the following
produce an acute angle? Select all that apply
Answer:
a and c
Step-by-step explanation:
Please help, i need it done by today,
Answer:
x= 28
do i have to explain
Step-by-step explanation:
3. A runner sprints 50 ft each day for 7 days. How many inches does she sprint during this week? (Again please hurry)
Answer: The runner will sprint 4,200 inches during this week
Step-by-step explanation:
50 * 7 = 350
350 * 12 = 4200
Answer:
It's 4200in
in feets its 350ft
Step-by-step explanation:
Find the volume of the cylinder. Use 3.14 for T.
height of 3 radius of 3
Answer:
84.82
Step-by-step explanation:
π·32·3≈84.823
Answer:
The volume of a cylinder with a height of 3 and a radius of 3 is 84.823 or you could say 84.8.
Step-by-step explanation:
Find the formula for the nth term in this arithmetic sequence a1=0 a2=.5 a3=1 a4=1.5
Answer:
Step-by-step explanation:
The arithmetic sequence usually write as [tex]a_{n}=a_{1} +(n-1)d[/tex], where a1 is the first term and d is a common difference.
[tex]a_{n} = a_{1}+(n-1)d\\a_{n} = 0+(n-1)0.5\\[/tex]
Can someone plzzz helppp meee!!!
Answer:
Step-by-step explanation:
x-4.88=-5.78
solve for x
Answer:
-0.9
Step-by-step explanation:
Answer:
x =-.9
Step-by-step explanation:
x-4.88=-5.78
Add 4.88 to each side
x-4.88+4.88=-5.78+4.88
x =-.9
The quotient of a number more than 1 and 3 is 5
Answer:
https://brainly.com/question/13518166
Step-by-step explanation:
Figure 222 is a scaled copy of Figure 111.
Identify the side in Figure 222 that corresponds to side \overline{CD}
CD
start overline, C, D, end overline in Figure 111.
Answer:
if im corect the anwser is 3.14 (Side note) this is the wrong question i was anwsering to
These cones are similar. Find the surface
area of the smaller cone. Round to the
nearest tenth.
2 cm
5 cm
Surface Area = [? ] cm2 Surface Area = 111 cm?
9514 1404 393
Answer:
17.8 cm²
Step-by-step explanation:
The ratio of surface areas is the square of the ratio of the linear dimensions. The small/large linear dimension ratio is 2/5, so the surface area of the smaller cone is ...
A = (2/5)²(111 cm²) = 17.76 cm²
The area of the smaller cone is about 17.8 cm².
Answer: [tex]17.8 cm^{2}[/tex]
how do you find the radius when given the volume and height?
Answer:
Calculate the area of the base (which is a circle) by using the equation πr² where r is the radius of the circle. Then, multiply the area of the base by the height of the cylinder to find the volume. SOO just remember to divide the diameter by two to get the radius. If you were asked to find the radius instead of the diameter, you would simply divide 7 feet by 2 because the radius is one-half the measure of the diameter. The radius of the circle is 3.5 feet. You can also use the circumference and radius equation.
Step-by-step explanation:
brainliest?
the area is ___ square units
Answer:
12 units²
Step-by-step explanation:
The height is 2, and the width is 12.
Now multiply and that gives us 24. But that's not the full answer.
Since a triangle's area is half of a square, we divide by 2, leaving us with 12. (plus the label which is units²)
Tema: valor numérico de expresiones algebraicas
A= 2
B= 1
X= 3
Y= 5
Z= -3
Answer:
1. 61
2. -8
3. 731
4. -16
5. -5
Step-by-step explanation:
what is the value of x ?
Step-by-step explanation:
The line JK is tangent to the circle h so <KJH is a right angle.
[tex]a^2+b^2=c^2[/tex]
[tex]15^2+20^2=x^2[/tex]
[tex]625=x^2\\x=25[/tex]
Hope that helps :)