Consider the initial value problem
my′′+cy′+????y=????(????), y(0)=0, y′(0)=0my′′+cy′+ky=F(t), y(0)=0, y′(0)=0
modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force ????(????)F(t), where the unit of force is the Newton (N). Assume that m=2m=2 kilograms, c=8c=8 kilograms per second, ????=80k=80 Newtons per meter, and the applied force in Newtons is
????(????)={400if 0≤????≤????/2,if ????>????/2.F(t)={40if 0≤t≤π/2,0if t>π/2.
Solve the initial value problem, using that the displacement y(????)y(t) and velocity y′(????)y′(t) remain continuous when the applied force is discontinuous.
For 0≤????≤????/20≤t≤π/2, y(????)=y(t)= help (formulas)
For ????>????/2t>π/2, y(????)=y(t)= help (formulas)
Determine the long-term behavior of the system. Is lim????→[infinity]y(????)=0limt→[infinity]y(t)=0? If it is, enter zero. If not, enter a function that approximates y(????)y(t) for very large positive values of ????t.
For very large positive values of ????t, y(????)≈y(t)≈
Answers
To solve the initial value problem, we first need to find the particular solution for the forced equation. Since the applied force is piecewise, we need to solve the differential equation separately for each interval.
For 0≤t≤π/2, the applied force is 40 N. So, we have:
my′′ + cy′ + ky = 40
Substituting the given values of m, c, and k, we get:
2y′′ + 8y′ + 80y = 40
Dividing both sides by 2, we get:
y′′ + 4y′ + 40y = 20
The characteristic equation is:
r^2 + 4r + 40 = 0
Using the quadratic formula, we get:
r = -2 ± 6i
So, the general solution of the homogeneous equation is:
y_h(t) = e^(-2t) (c1cos(6t) + c2sin(6t))
To find a particular solution, we assume that it has the form:
y_p(t) = A
Substituting this into the differential equation, we get:
0 + 0 + 80A = 40
So, A = 0.5
Therefore, the particular solution for 0≤t≤π/2 is:
y_p(t) = 0.5
The general solution of the forced equation for this interval is:
y(t) = y_h(t) + y_p(t) = e^(-2t) (c1cos(6t) + c2sin(6t)) + 0.5
Using the initial conditions, we get:
y(0) = c1 + 0.5 = 0
y′(0) = -2c1 + 6c2 = 0
Solving these equations, we get:
c1 = -0.5
c2 = 0.1667
So, for 0≤t≤π/2, the displacement and velocity are:
y(t) = e^(-2t) (-0.5cos(6t) + 0.1667sin(6t)) + 0.5
y′(t) = 2e^(-2t) (cos(6t) + 0.333sin(6t))
For π/2π/2, we have:
lim(t→∞) y(t) = 0
So, the long-term behavior of the system is that the displacement approaches zero as t approaches infinity.
Therefore, for very large positive values of t, we have:
y(t) ≈ 0
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Related Questions
2. The diameter of Earth is approximately 8,000 miles. What would the diameter of Earth be in your scale model?
Answers
The diameter of the moon is approximately 2,000 miles.
Explanation:
First, because we are solving for the approximate diameter of the moon, let's call the variable representing the diameter of the moon m.
The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both 25 2525 kilometers long. The population in Las Pythagoras is 100 , 000 100,000100, comma, 000 people. What is the population density of Las Pythagoras?
Answers
320
Step-by-step explanation:
Use the figure below to determine the length of sides b and c.
Question 5 options:
b = 5√3, c = 10
b =10, c = 5√3
b = 5√2, c = 10√3
b = 5, c = 10√2
Answers
Answer:
Option A
The value of the length of sides b and c is 5√3 and
10 respectively.
Step-by-step explanation:
Here, a given figure
Let the ΔABC
m∠B = 90°, m∠C = 30°, AB = 5, BC = b, AC = c
Now,
Sin θ = O/H
Sin 30° = 5/c
1/2 = 5/c
1 × c = 5 × 2
c = 10
Then,
tan θ = O/A
tan 30° = 5/b
1/√3 = 5/b
b × 1 = 5 × √3
b = 5√3
Thus, The value of the length of sides b and c is 5√3 and
10 respectively.
-TheUnknownScientist
[8 + (24 x 3)] divided by 7
Use PEMDAS &’ show work .
![[8 + (24 x 3)] divided by 7 Use PEMDAS & show work .](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/vH1EfCPA4ruq9XVnWstjkqEBeGjoeTKL.png)
Answers
Answer:
11.43
Step-by-step explanation:
[8 + (24 x 3)] divided by 7
[8 + (72)] divided by 7
80/7
11.42857142857143
11.43 (I rounded it)
Answer:
11.42
My explanation:
P( )
E *
M x
D /
A +
S -
the first step is to multiply 24x3 because parenthesses go first
the second step is that get the 72 form multiplying and add 8 to it becasue its inside the lines
third step is to divide by 7 and then you get 11.42
Feel free to ask for more help :)
George has 24 fluid ounces of honey. How many cups of honey does he have? A. 1 cup B. 2 cups C. 3 cups D. 4 cups please help
Answers
Answer: 8
24 divided by 8 is 3
So 3 cups!
C. 3 cups
Answer:3
Step-by-step explanation:
1. A triangle has side lengths of 1, 2, and 3. Can these lengths form a triangle? Use the Triangle Inequality Theorem to prove whether these lengths form a triangle. Show all work. DUE IN 1 HOUR
Answers
Step-by-step explanation:
step 1. the 3rd side of a triangle must be less than the addition of the other two sides
step 2. 3 is not less than the addition of 1 and 2
step 3. no. this cannot be a triangle.
6 of 6
Lena and Ras drive to work.
Lena drives 24 miles in 1.5 hours.
Ras drives 36 km in 1 hour 15 min.
Work out the difference between their average speeds in km/h.
1 mile = 1.6 km
km/h
Answers
Answer:
3.2 km/h
Step-by-step explanation:
1. Approach
The average speed is the rate at which one travels. It can be found by diving the total distance traveled over the total time it took to cover that distance. In essence, the following formula can be used to find the average speed:
\(\frac{total\ distance}{total\ time}=average\ speed\)
In this situation, one is asked to find the difference between two people's average speed. One is given the following information:
Lena: 24 miles 1.5 hours
Ras: 36km 1 hour 15 minutes
First, convert all of the numbers into the correct units (km) and (hours). Then find the average speed for each person. Finally, subtract the smaller speed from the larger speed to find the difference in the average speeds.
1. Find Lena's average speed
The problem asks one to find the average speed in the units (km/h). However, the distance Lena covered is given in (miles). Therefore, one has to multiply it by the conversion factor (1.6) in order to convert it from (miles) to (km).
24miles * 1.6 = 38.4
Now find the average speed by using the formula:
\(\frac{total\ distance}{total\ time}=average\ speed\)
Substitute,
\(\frac{38.4}{1.5}\\\\=25.6\)
2. Find Ras's average speed
Use a similar approach to work out Ras's average speed, as was used to find Lena's average speed. Since Ras's time spent is given in both hours and minutes, one must convert it to just minutes. There are (60) minutes in an hour, thus, one can rewrite the number as the following:
\(1\ hour \ \ 15\ minutes= 1 \frac{15}{60}\ hours = \frac{75}{60}\ hours\)
Now find the average speed:
\(\frac{total\ distance}{total\ time}=average\ speed\)
Substitute,
\(\frac{36}{\frac{75}{60}}\\\\=28.8\)
3. Find the difference between the speeds
Since Ras's speed is greater, subtract Lena's speed from Ras's speed.
Ras - Lena
= 28.8 - 25.6
= 3.2
Let ????be a group and ????∈????an order element m????, where mand ????are relatively prime positive integers. Prove that there are x,y∈????such |x|=mand |y|=????and ????=xy.
Answers
The extended Euclidean algorithm, we have shown that there exist x,y∈G such that |x|=m and |y|=G and G=xy.
Let G be a group and m∈G an order element, where m and G are relatively prime positive integers. To prove that there exists x,y∈G such that |x|=m and |y|=G and G=xy, we can use the fact that since G and m are relatively prime, there exist integers a and b such that am + bG = 1 (by the extended Euclidean algorithm). This implies that m = (1-bG)/a and G = (1-am)/b.
Let x = (1-bG)/a and y = (1-am)/b, then since |x| = |(1-bG)/a| = m and |y| = |(1-am)/b| = G, we have that |x| = m and |y| = G.
Additionally, since xy = (1-bG)/a * (1-am)/b = 1-bG -am + (abGm)/ab = 1, we have G=xy, proving our statement.
Therefore, by using the extended Euclidean algorithm, we have shown that there exist x,y∈G such that |x|=m and |y|=G and G=xy.
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geometry a farmer uses 24 yd of fencing to make a rectangular pen. the pen is 6 yd longer than it is wide. what are the dimensions of the pen?
Answers
So, the dimensions of the pen are 3 yards by 9 yards.
Let's assume the width of the rectangular pen is x yards.
According to the given information, the length of the pen is 6 yards longer than the width, so the length would be x + 6 yards.
The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
In this case, the perimeter is given as 24 yards, so we can write the equation:
2(x + 6) + 2x = 24
Simplifying the equation:
2x + 12 + 2x = 24
Combining like terms:
4x + 12 = 24
Subtracting 12 from both sides:
4x = 12
Dividing both sides by 4:
x = 3
Therefore, the width of the pen is 3 yards, and the length is 6 yards longer, which is 9 yards.
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Write a ratio for the situation in three ways, comparing the first quantity to the second quantity. A zoo has 17 monkeys and 12 chimpanzees. 12 to 17, 12:17, 17 60 12, 17:12, 1 C 17 to 22. 17:22 • D 1740 12. 12:12 17 to 12. 12:17 12
Answers
Answer: B
in three ways we have;
\(17\text{ to }12,\text{ }17\colon12,\text{ }\frac{17}{12}\)Explanation:
We want to write the ratio of the situation in three ways, comparing the first quantity to the second quantity.
Given that;
A zoo has 17 monkeys and 12 chimpanzees
so, we want to compare the number of Monkeys to the number of Chimpanzees.
There are 17 Monkeys to 12 Chimpanzees.
\(17\text{ to }12\)Writing in other ways, we have;
\(17\colon12\)and lastly in fraction;
\(\frac{17}{12}\)Therefore, in three ways we have;
\(17\text{ to }12,\text{ }17\colon12,\text{ }\frac{17}{12}\)
Find the distance between the two points.|(1,4)✓ [?](-2,-3)Enter the number thatgoes beneath theradical symbol.Enter
Enter the number thatgoes beneath theradical](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/6OUOIQIZzSrDDT2ilpCfsa0UdLwMj77d.jpeg)
Answers
The distance between two points is given as;
\(D=\sqrt[]{(y_2-y_{1_{}})^2+(x_2-x_1)^2}\)\(\begin{gathered} \text{Where x}_1=-2 \\ y_1=-3 \\ x_2=1 \\ y_2=4 \end{gathered}\)\(\begin{gathered} D=\sqrt[]{(4-(-3)^2+(1-(-2)^2} \\ D=\sqrt[]{7^2+3^2} \\ D=\sqrt[]{49+9} \\ D=\sqrt[]{58} \end{gathered}\)The number beneath the radical symbol is 58.
the average of 8 girls is 15 and the average of 6 girls is 13 find the average of the other two girls with equal age
Answers
Answer:
21
Step-by-step explanation:
Since the girls have the same age, let their age be x.
Then, their average is
\(\frac{x+x}{2} = \frac{2x}{2} = x\)
Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)
Also, we have,
\(\frac{S_{8}}{8} =15 - eq(2)\)
\(\frac{S_{6}}{6} =13 - eq(3)\)
Then eq(2):
(from eq(1) and eq(3))
\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)
The average of the other two girls with equal age is 21
£2,000 is invested for 3 years at a rate of 1.5% per annum compound interest work out the amount of interest at the end of 3 years
Answers
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 1.5\%\to \frac{1.5}{100}\dotfill &0.015\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}\)
\(A=2000\left(1+\frac{0.015}{1}\right)^{1\cdot 3}\implies A\approx 2091.36~\hfill \underset{earned~interest}{\stackrel{2091~~ - ~~2091.36}{\approx 91.36}}\)
what is the value of y in the following equations y=3x-5 6x+3y=15
Answers
y = 3x - 5
6x + 3(3x - 5) = 15
6x + 9x - 15 = 15
15x -15 + 15 = 15 + 15
15x = 30
15x/15 = 30/15
x = 2
6x + 3y = 15
6(2) + 3y = 15
12 + 3y = 15
12 - 12 + 3y = 15 - 12
3y = 3
3y/3 = 3/3
y = 1
The value of y is 1
..........................
a) Factor f(x)=−4x^4+26x^3−50x^2+16x+24 fully. Include a full solution - include details similar to the sample solution above. (Include all of your attempts in finding a factor.) b) Determine all real solutions to the following polynomial equations: x^3+2x^2−5x−6=0 0=5x^3−17x^2+21x−6
Answers
By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.
Find all real solutions to the polynomial equations \(x³+2x ²-5x-6=0\) and \(5x³-17x²+21x-6=0\).Checking for Rational Roots
Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).
The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.
By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).
Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:
-4x⁴ + 26x³ - 50x² + 16x + 24 = (x + 2)(-4x³ + 18x² - 16x + 12)Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).
Attempt 2: Factoring by Grouping
Rearranging the terms, we have:
-4x³ + 18x² - 16x + 12 = (-4x^3 + 18x²) + (-16x + 12) = 2x²(-2x + 9) - 4(-4x + 3)Factoring out common factors, we obtain:
-4x³+ 18x² - 16x + 12 = 2x²(-2x + 9) - 4(-4x + 3) = 2x²(-2x + 9) - 4(3 - 4x) = 2x²(-2x + 9) + 4(4x - 3)Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:
2x²(-2x + 9) + 4(4x - 3) = 2x² (-2x + 9) + 4(4x - 3) = 2x²(-2x + 9) + 4(4x - 3) = 2x²(-2x + 9) + 4(4x - 3) = (2x² + 4)(-2x + 9)Therefore, the fully factored form of \(f(x) = -4x⁴ + 26x³ - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).
Solutions to the polynomial equations:
\(x³ ³ + 2x² - 5x - 6 = 0\)Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +
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a contractor needs to buy nails to build a house. the nails come in a small boxes and large boxes. each small box has 200 nails and each large box has 600 nails. the contractor bought twice as many small boxes as large boxes, which altogether had 3000 nails. graphically solve a system of equations in order to determine the number of small boxes purchased,x, and the number of large boxes purchased,y.
Answers
By using simultaneous linear equation the results obtained are-
Number of small boxes = 6 and number of large boxes = 3
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Let the number of small boxes purchased be x, and the number of large boxes purchased be y.
Each small box has 200 nails and each large box has 600 nails.
Total number of nails = 3000
\(200x +600y = 3000\\200(x+ 3y)=3000\\x + 3y = \frac{3000}{200}\\x + 3y = 15\) .............. (1)
The contractor bought twice as many small boxes as large boxes
So,
\(x = 2y\\x - 2y = 0............(2)\)
The equations are solved graphically. The graph has been attached.
From the graph, it can be said that the two lines meet at (6, 3)
So x = 6, y = 3
Number of small boxes = 6 and number of large boxes = 3
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Using the function g( x) = -2 x – 11, calculate g(-3).
Answers
════════ ∘◦❁◦∘ ════════
Answer = -5════════════════════
Knowng(x) = -2x - 11
════════════════════
Questiong(-3) = ..?
════════════════════
Way to do#since x inside (x) change into (-3) then it means that you only need to change x into -3
g(-3) = -2(-3) - 11
g(-3) = 6 - 11
g(-3) = -5
════════════════════
please help, show your work first then choose the answer, thank you
Answers
Answer:your mom
Step-by-step explanati
Help PLZZZ
Describe the change in the graph of the parabola f(x) when it transforms into g(x) = two thirdsf(x).
A The parabola g(x) will open in the opposite direction of f(x), and the parabola will be narrower than f(x).
BThe parabola g(x) will open in the same direction of f(x), and the parabola will be narrower than f(x).
CThe parabola g(x) will open in the opposite direction of f(x), and the parabola will be wider than f(x).
D The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Answers
Answer:
The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Step-by-step explanation:
Answer:
It's B.
Step-by-step explanation:
I took the test.
I need some help with this
Answers
Answer:
a. 121
b.2
Step-by-step explanation:
a.
33/3×11>11
11×11>11
121>11
b.
5×2/8<5
10/8<5
1.25<5
9_12-15-22-5_25-15-21
translate the code
Answers
Answer:
this is sum u made up
Step-by-step explanation:
The label on a car's antifreeze container claims to protect the car between −30°C and 130°C. To covert Celsius temperature to Fahrenheit temperature, the formula is C equals five ninths times the quantity F minus thirty two.. Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car.
Answers
Answer:
he. haha. shyw sjIana d auhaabab ssbajiaan s
Joshua had two-sevenths of all the goals scored by is soccer team. His team scored 28 goals this past season. How many goals did the rest of the team score? 1 point
Answers
Answer:
Rest of the team= 20 goals
Step-by-step explanation:
Giving the following information:
Joshua= (2/7)
His team scored 28 goals this past season.
First, we determine hoy many goals Joshua score:
Joshua= (2/7)*28
Joshua= 8 goals
Now, the rest of the team:
Rest of the team= 28 - 8
Rest of the team= 20 goals
Dilation / Scale factor = 1/3 / COD = Origin REPOST ASAP
Lindsay is designing a dog pen. The original floor plan is represented by figure PQRS. Lindsay dilates the floor plan by a scale factor of 1/3 with a center of dilation at the origin to form figure P'Q'R'S'. Then she translates figure P'Q'R'S' 4units to the left and 2 units down. The final figure is P''Q''R''S''. Draw or explain Lindsay’s transformations in the coordinate plane.
Basically, I think I just need the coordinates of both P'Q'R'S' and P''Q''R''S''
Answers
Below are the Lindsay's dog pen's coordinates both before and after dilation and translation.
preimage image (translation) image (translation and dilation)
P (-6, 9) → P' (-2, 3) → P'' (-4, 1)
Q (3, 9) → Q' (1, 3) → Q'' (-1, 1)
R (3, 3) → R' (1, 1) → R'' (-1, -1)
S (-6, 3) → S' (-2, 1) → S'' (-4, -1)
How to perform the required transformationDilation is a transformation technique that can either enlarge or reduce the preimage depending on the scale factor.
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
Rule for translation 2 units down and 4 units to the left is below
(x, y) → (x - 2, y - 2)
Applying the rules to get the coordinates of the image
preimage dilation image translation image
P (-6, 9) → (-6 * 1/3, 9 * 1/3) → P' (-2, 3) → (-2 - 2, 3 - 2) → P'' (-4, 1)
Q (3, 9) → (3 * 1/3, 9 * 1/3) → Q' (1, 3) → (1 - 2, 3 - 2) → Q'' (-1, 1)
R (3, 3) → (3 * 1/3, 3 * 1/3) → R' (1, 1) → (1 - 2, 1 - 2) → R'' (-1, -1)
S (-6, 3) → (-6 * 1/3, 3 * 1/3) → S' (-2, 1) → (-2 - 2, 1 - 2) → S'' (-4, -1)
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Boston, Massachusetts had a population of 617,594 people during January 1 2010, and 675,647 people on January 1 2020.
Write an exponential function to represent the cities population, y, based on the number of years that pass, x after period of exponential growth. Describe The variables in numbers that you used in your equation.
Answers
Answer:
See belowStep-by-step explanation:
Exponential function is:
y = abˣIf we consider the time difference in years as x and the initial population as a, then we get:
675647 = 617594*b¹⁰Find the value of b:
b¹⁰ = 675647/617594b¹⁰ = 1.09399864636b = 1.09399864636^(1/10)b = 1.009 (rounded)The equation we got is:
y = 617594*1.009ˣHere we have y- population after x years since 2010, x - the number of years since 2010 and 1.009 is the population growth rate.
General equation
y=ab^xTotal years(x)=2020-2010=10
Now
675647=617595b¹⁰b¹⁰=675647/617595b=1.009(Approx)So.our equation
y=617595(1.009)^xCan you simply these fractions?
Answers
Answer:
\( \frac{1}{5 } = \frac{3}{8} = \frac{3}{5} = \frac{3}{4} = \frac{3}{7} = \frac{1}{9} = \frac{4}{5} = \frac{5}{6} = \frac{2}{3} = \frac{1}{10} \)
Answer:
4/20= 1/5
9/24= 3/6
18/30= 3/5
5/45= 1/9
20/25= 4/5
10/12= 5/6
6/9= 2/3
4/40= 1/10
Step-by-step explanation:
What i did was use different numbers to divide them with the numerator and denominator.
4 glasses of milk and 3 snack bars have a total of 80 carbohydrates (carbs), and 2 glasses of milk and 4 snack bars have a total of 70 carbs. Determine how many carbs are in one glass of milk and
in one snack bar.
Answers
The carbs that are in one glass of milk and
in one snack bar is 27 carbs
How to calculate the number of carbs?Since 4 glasses of milk and 3 snack bars have a total of 80 carbohydrates (carbs), this will be:
4m + 3b = 80
2 glasses of milk and 4 snack bars have a total of 70 carbs. This will be:
2m + 4b = 70
Collect both equations and solve
4m + 3b = 80 ..... i
2m + 4b = 70 ..... ii
m = milk
b = snack bars
Multiply equation i by 2
Multiply equation ii by 4
8m + 6b = 160
8m + 16b = 280
Subtract
10b = 80
Divide
b = 80/10 = 8
Snack bars = 8 carbs
Since 2m + 4b = 70
2m + 4(8) = 70
2m + 32 = 70
2m = 70 - 32
2m = 38
Divide
m = 38/2 = 19
Milk = 19 carbs
The total carbs will be:
= Milk + Snack
= 19 + 8
= 27 carbs
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which is more, 34 quarts or 8 gallons
Answers
To solve this problem both units must have the same units.
So, let's convert quarts to gallons
1 quart ----------------------- 0.25 gallon
34 quarts -------------------- x
x = (34 x 0.25) / 1
x = 8.5 gallons
8.5 gallons or 34 quarts > 8 gallons
Help please!!!!!!!
Find the area of the figure. (Sides meet at right angles.)
10 ft
5 ft
6 ft
4 ft
5 ft
Answers
Write the equation in slope-intercept form of a line that has a slope of and passes through the point (-6, 0)
3
0 >=²x
xy=
y=x-6
O 0y=x-2
O
0 >=²x+2
Answers
The equation of the line in slope intercept form with slope 1/3 and passes through ( - 6, 0) is y = 1/3x + 2.
In mathematics, the slope or gradient of a line is a number that indicates the line's steepness as well as its X and Y directions. The letter "m" stands for slope. The ratio of the "vertical change" to the "horizontal change" between any two separate points on a line is used to compute the slope.
The equation of the line in point-slope form is expressed as:
y - y₁ = m( x - x₁ )
where m is the slope.
So, m = 1/3
( x₁, y₁ ) is the point on the line = ( - 6, 0)
Substituting the values,
y - 0 = 1/3( x + 6 )
y = 1/3( x + 6 )
y = 1/3x + 6/3
y = 1/3x + 2
Hence, the equation in slope-intercept form of the line is y = 1/3x + 2.
Learn more about slope intercept form here:
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