Consider the system of differential equations x1' = -.5x1 + 2x2, 31(0) = -2 xz' = –261 – .5x2, 22(0) = 2 The below steps will walk through solving this system by recasting it as a second order differential equation. (a) Solve the first equation for x2 and substitute the result into the second equation obtaining a second order IVP in terms of X1. (b) Solve the second order IVP found in part (a). (c) Use your answer from part (b) along with an equation from the above system of differential equations to find 22. (d) Write the solution of the system in vector form.

Answer:

y = -2

Step-by-step explanation:

Answer:

13 units

Step-by-step explanation:
V = B • h

504.4 = 38.8 h

504.4 / 38.8 ( divide to isolate the variable)

Height = 13 units

Step-by-step explanation:

a) The probability that a tire will be too narrow is 0.252492. b)The probability that a tire will be too wide is 0.091211. c) , the probability that a tire will be defective is 0.252492 + 0.091211 = 0.343703.

a. To calculate the probability that a tire will be too narrow, we need to find the area under the normal distribution curve that falls below the lower specification limit.

Using the Z-score formula, we calculate the Z-score for the lower specification limit as follows:

Z = (Lower specification limit - Mean) / Standard deviation

Z = (22.8 - 23) / 0.15

Z = -0.666667

Next, we find the corresponding area from the standard normal distribution table or using a calculator. The area to the left of Z = -0.666667 is approximately 0.252492.

b. To calculate the probability that a tire will be too wide, we need to find the area under the normal distribution curve that falls above the upper specification limit.

Using the Z-score formula, we calculate the Z-score for the upper specification limit as follows:

Z = (Upper specification limit - Mean) / Standard deviation

Z = (23.2 - 23) / 0.15

Z = 1.333333

Next, we find the corresponding area from the standard normal distribution table or using a calculator. The area to the right of Z = 1.333333 is approximately 0.091211.

c. The probability that a tire will be defective is the sum of the probabilities of it being too narrow and too wide, since being outside the specification limits indicates a defect.

Therefore, the probability that a tire will be defective is approximately 0.252492 + 0.091211 = 0.343703.

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Step-by-step explanation:

Ans 3. C and D are not similar

Ans 4.less than 3

Ans 5. 3 or three

Ans 7.larger than 3

Ans 8. 3 or three

plz look these answers these all right don't see answers in the comment because those are confusing

the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.

There are no factors of 24 that are prime numbers. A factor of a number is a whole number that divides that number without leaving a remainder. Prime numbers, on the other hand, are numbers that are divisible only by 1 and themselves, and cannot be expressed as the product of any other numbers.

The prime factors of 24 are 2, 2, and 3. We can factorize 24 as 2 × 2 × 2 × 3 or 2^3 × 3. Here, 2 and 3 are both prime numbers, but they are not factors of 24 in isolation. They are only prime factors of 24 when combined in the manner shown.

This fact highlights an important concept in number theory: the uniqueness of prime factorization. Every composite number can be expressed as a unique product of prime numbers. This fundamental theorem of arithmetic is crucial in many areas of mathematics, including cryptography, where it is used to secure communications and protect sensitive information.

In summary, there are no factors of 24 that are prime numbers. However, the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.

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The value of the following equations by using the properties of logarithms: 1.x = 50000 2. x = (1 ± √5) / 4 3. x= 2√5.

In mathematics, an equation is a statement that asserts the equality of two expressions, usually separated by an equal sign (=). An equation typically consists of one or more variables, coefficients, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and roots. The purpose of an equation is to find the values of the variables that satisfy the equation. These values are called solutions or roots of the equation. Equations are used in many branches of mathematics, including algebra, calculus, geometry, and statistics, to model and solve various problems and phenomena in the natural and social sciences, engineering, and finance.

Here,

1. Log 2x = 5

We can rewrite this equation using the property that log_a(b) = c is equivalent to b = aˣ:

2x = 10⁵

Simplifying the right-hand side, we get:

2x = 100000

Dividing both sides by 2, we get:

x = 50000

Therefore, the solution is x = 50000.

2. Lnx - In(2x+1) = 2

Using the fact that ln a - ln b = ln(a/b), we can simplify the left-hand side of the equation:

ln(x/(2x+1)) = 2

Next, we can rewrite the equation in exponential form:

e² = x/(2x+1)

Multiplying both sides by 2x+1, we get:

e²(2x+1) = x

Expanding and simplifying the left-hand side, we get a quadratic equation:

4xe² + 2e² - x = 0

Solving for x using the quadratic formula, we get:

x = (-2e² ± √((2e²)² - 4(4e²)(-1))) / (2(4e²))

Simplifying, we get:

x = (-e² ± √(e⁴ + 4e₂)) / (4e²)

x = (-e² ± e²√5) / (4e²)

x = (1 ± √5) / 4

Therefore, the solutions are x = (1 + √5) / 4 and x = (1 - √5) / 4.

3. Log x = log (2/x) + 1

Using the fact that log_a(b) = log_a(c) is equivalent to b = c, we can simplify the equation:

x = 2/x * 10

Multiplying both sides by x, we get:

x² = 20

Taking the square root of both sides, we get:

x = ±√(20)

Since x cannot be negative (because log of a negative number is undefined), the only solution is:

x = √(20) = 2√5

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The given equation is cos(z) = sin(2z). To solve this equation, we'll use trigonometric identities and properties.

First, we can express sin(2z) in terms of cos(z) using the double angle identity for sine:

sin(2z) = 2sin(z)cos(z)

Now we substitute this expression into the equation:

cos(z) = 2sin(z)cos(z)

Since we're dealing with an equation involving trigonometric functions, it's essential to consider the possible values of z. In this case, we have the restriction that 0 < z < π/2.

Next, we can simplify the equation by canceling out cos(z) on both sides:

1 = 2sin(z)

Now we divide both sides by 2:

sin(z) = 1/2

To find the angle z that satisfies this equation, we consider the unit circle or use trigonometric reference angles. The reference angle for sin(z) = 1/2 is π/6. Since we're working in the first quadrant where sine is positive, we have:

z = π/6

So the angle that satisfies the given equation is z = π/6.

It's important to note that there can be multiple solutions for trigonometric equations. In this case, we considered the solution within the given range of 0 < z < π/2. If the range was different, such as -π/2 < z < 0, there would be other solutions as well. Therefore, the solution to the equation cos(z) = sin(2z) within the given range is z = π/6.

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Answer:

  t ∈ (-4.5, 2.25]

Step-by-step explanation:

You want to solve the compound inequality ...

  1/3t -5 < t -2 ≤ -3t +7

We can divide this into two inequalities.

  1/3t -5 < t -2   ⇒   -3 < 2/3t   ⇒   -4.5 < t

and

  t -2 ≤ -3t +7   ⇒   4t ≤ 9   ⇒   t ≤ 2.25

The solution interval is the intersection of these two solutions:

  -4.5 < t ≤ 2.25

  t ∈ (-4.5, 2.25]

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Answer:

-2n-6

Step-by-step explanation:

Answer: -2n+7

Step-by-step explanation:

-6n+4 equals 2n

3+4 equals 7

-2n+7

Answer:

18 tables: $143

t tables: $35 + $6t

Step-by-step explanation:

35 + 6t

35 + 6(18) = 35 + 108 = 143

1 gallon of milk is equal to 16 cups of milk (1 gallon = 4 quarts = 16 cups).

Mario poured 4 cups of milk for each of the 4 people, which is a total of 16 cups of milk.

So the amount of milk left is:

16 cups (total) - 16 cups (poured) = 0 cups

Therefore, there is no milk left.

The expression given is 30 x [(9 x 2) - (4 + 3)]. In order to find which expression has a value of 1, we must simplify the expression. First, we must solve the parentheses by adding 4 and 3 together, which equals 7, and multiplying 9 and 2 together, which equals 18.

So, the expression now becomes 30 x [18 - 7]. Next, we must solve the brackets by subtracting 7 from 18, which equals 11. So, the expression now becomes 30 x 11. Finally, we must multiply 30 and 11 together to get the final answer, which is 330. Therefore, the given expression does not have a value of 1.
Hello! Let's solve the given expression and check if its value is 1.

Expression: 30 x [(9 x 2) - (4 + 3)]

Step 1: Perform operations within the parentheses first.
9 x 2 = 18
4 + 3 = 7

Step 2: Substitute these values back into the expression.
30 x (18 - 7)

Step 3: Perform subtraction inside the parentheses.
30 x (11)

Step 4: Perform the final multiplication.
30 x 11 = 330

The given expression has a value of 330, not 1.

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Answer:

Around 376.99

Step-by-step explanation:

the formula is 2πrh+2πr²

so if we plug in everything we get 2π(4)(11)+2π(4)²

When we simplify that, we would get 376.99

Answer:

3.1

Step-by-step explanation:

go to the right and how it says 3 then when you go up to the dot go left and says 1 so answer is 3.1

Answer:

x=-3        x=-1            x=2         x=-2

Step-by-step explanation:

p(x) = (x^2 + 4x + 3)(x^2 – 4)

Set this equal to zero to find the x intercepts

0 = (x^2 + 4x + 3)(x^2 – 4)

Using the zero product property

(x^2 + 4x + 3) =0      (x^2 – 4)  =0

Factor

(x+3)(x+1) =0            (x-2) (x+2)=0

Using the zero product property

x+3 =0  x+1 =0          x-2 =0  x+2 =0

x=-3        x=-1            x=2         x=-2

The line perpendicular to y - 3 = 4(x+2) is y-3 = -1/4(x+2)

Two lines are said to be perpendicular if the product of their gradient is -1.

which means m1 x m2 = -1

Analysis:

y - 3 = 4(x+2)

y = 4x + 8+3

y = 4x + 11    m1 = 4

so m1 x m2 = -1

m2 = -1/4

so from the options, the equation with a gradient x = -1/4 is C, y-3 = -1/4(x+2)

In conclusion, the line that would be perpendicular to y - 3 = 4(x+2)

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The cost of fencing the field at ₹ 7.5 per meter is ₹810.

We already know that the area of a rectangle can be calculated using the formula = l*b

We have been told that the rate is ₹ 4 per sq. meter is ₹ 2340 and the breadth is 15 m.

Using these values, we can conclude that -

= l*b * 4 = 2340

= l = 2340 / 60

= l = 39 m

We also know that the perimeter of a rectangle can be calculated using -

= 2(l+b) and the rate of fencing this perimeter is  ₹ 7.5 per meter.

Using the values, we get -

= 2(39+15) * 7.5

= ₹ 810

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Answer:

B

Step-by-step explanation:

The graph of function is |x + 2| – 5= -(x - 1)(x - 3) which is represented in the graph option first is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we can see in the graph, there are two graphs of a function shown.

First one is a graph of a mod function and second one is a graph of a quadratic equation.

|x + 2| – 5= -(x - 1)(x - 3)

f(x) = |x + 2| - 5

g(x) = -(x - 1)(x - 3)

Thus, the graph of function is |x + 2| – 5= -(x - 1)(x - 3) which is represented in the graph option first is correct.

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g(x) = 400 when x = 4. To find the value of g(0) and g(x) for the given function g(x) = 5x³(x² - 4x + 5) / 4, we can substitute the respective values into the expression.

The value of g(0) can be found by setting x = 0, while the value of g(x) can be determined by substituting the given value of x into the function.

To find g(0), we substitute x = 0 into the expression:

g(0) = 5(0)³(0² - 4(0) + 5) / 4

    = 0

Therefore, g(0) = 0.

To find g(x), we substitute x = 4 into the expression:

g(x) = 5(4)³((4)² - 4(4) + 5) / 4

    = 5(64)(16 - 16 + 5) / 4

    = 5(64)(5) / 4

    = 5(320) / 4

    = 400

Therefore, g(x) = 400 when x = 4.

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The amount of money in sales that Nolvia needs to earn a salary that exceeds $40,000 is greater than or equal to $19,000.

Given that:-

Fixed salary of Nolvia = $21,000

Commission tax that Nolvia gets = 4 %

Linear equation of Nolvia's salary and commission tax = 21000 + 0.04x

Where,

s represents her salary

x represents total sales

We have to find the amount of money in sales that Nolvia needs to earn a salary that exceeds $40,000.

The amount of money in sales that Nolvia needs to earn a salary that exceeds $40,000 = 40000 - 21000 ≥ $ 19,000

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The coordinates of vertex A in the image triangle are (-7, 4)

The vertex of A is given as:

A = (-4, -1)

The rule of 90° clockwise rotation is

(x,y) => (y,-x)

So, we have:

A' = (-1, 4)

The rule of shifting the triangle left by 6 units is

(x,y) => (x - 6,y)

So, we have:

A" = (-1 - 6, 4)

Evaluate

A" = (-7, 4)

Hence, the coordinates of vertex A in the image triangle are (-7, 4)

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Complete question

Triangle ABC is rotated about the origin 90° clockwise and then translated 6 units to the left. This sequence of transformations produces the image, triangle.

The coordinates of vertex A in the preimage triangle are A(-4, -1), what are the coordinates of vertex A in the image triangle

Answer:

Step-by-step explanation:

The width of the rectangle is 40in.

A rectangle can be divided into two right angles by a diagonal. Then we can use the Pythagorean theorem to find the width.

Here,

Length = a

Width = b

Length of the diagonal = c

The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Therefore,

a² = b² + c²

30² +  b² = 50²

900 + b² = 2500

b² = 1600

b = √1600

b = 40in.

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\(ans = \boxed{ 0.6}\)

\(since \: cot( \theta)= \frac{1}{ \tan( \theta) } \\ \frac{1}{ \tan( \theta) } = 1.5 \\ (1.5)\tan( \theta) = 1 \\ \tan( \theta) = \frac{1}{1.5} = 0.6666666667 \\ \theta = { \tan}^{ - 1} (0.6666666667) \\ \theta = 33.69 \\ hence: \sin( \theta) = \sin(33.69) = 0.5546992156\)