Find the solution to the differential equation y" + 2y' +10y=0 (0)=2. y(0) = 7.

Answer:

Area = 24.75 sqr units

Step-by-step explanation:

You will need these formulas:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

Midpoint = [tex](\frac{x_{1} + y_{1} }{2} , \frac{x_{2} + y_{2} }{2})[/tex]

Area = b x h

Let us treat CD as the base. Find the length of the base with the distance formula. Use the coordinates for points C & D.

[tex]d = \sqrt{(-2 - (-8))^2 + (-8-(-7))^2}[/tex]

[tex]d = \sqrt{37}[/tex]

The base is [tex]\sqrt{37}[/tex].

The height is the distance between point E and the midpoint of line CD.

Midpoint of CD = [tex](\frac{-8 + (-7) }{2} , \frac{-2 + (-8) }{2})[/tex] = ([tex]-\frac{15}{2}[/tex], [tex]-5[/tex])

Use the distance formula to find the height.

[tex]d = \sqrt{(-5 - (-\frac{15}{2} ))^2 + (-2-(-5))^2}[/tex]

[tex]d = \frac{\sqrt{61} }{2}[/tex]

Find the area with the two distances that were found.

Area = [tex](\sqrt{37}) (\frac{\sqrt{61} }{2})[/tex]

Area = [tex]\frac{\sqrt{2257} }{2}[/tex]

Area = 24.75 sqr units

Option D is the correct choice.

To evaluate the volume of D, the triple integral in cylindrical coordinates is required. So, let's derive the required triple integral.

Region D is bounded by two paraboloids z = 2x2 + 2y2 - 4 and z = 5 - x2 - y2 where x > 0 and y > 0.

In cylindrical coordinates,r = √(x^2 + y^2)z = zθ = tan-1(y/x)For the first paraboloid, the cylindrical equation of the paraboloid is: z = 2x2 + 2y2 - 4

By substituting the cylindrical coordinates values in this equation we get z = 2r2 sin2θ + 2r2 cos2θ - 4z = 2r2 (sin2θ + cos2θ) - 4z = 2r2 - 4 Now for the second paraboloid, the cylindrical equation of the paraboloid is: z = 5 - x2 - y2By substituting the cylindrical coordinates values in this equation we get:z = 5 - r2 The limits of r are 0 and √5; and the limits of θ are 0 and π/2.

Finally, the limits of z are obtained by equating the above two paraboloids.2r2 - 4 = 5 - r22r2 + r2 = 9r2 = 3z = 3We have got all the limits of cylindrical coordinates, we can now write the triple integral in cylindrical coordinates which evaluates the volume of D.

The triple integral is:∫(0 to π/2)∫(0 to √5)∫(2r2 - 4 to 3) r dz dr dθ

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To achieve this, the students must enter +31 (forward) to bring the robot back to its starting position of 0.

The robot can move forward or backward depending on the type of number entered into the control unit. For example, entering a negative number causes the robot to roll backward a specific number of inches,

while entering a positive number makes it move forward a certain number of inches. If −5 is entered, the robot moves backwards by 5 inches. As a result, the students entered the numbers −37, +22, and −16 to move the robot.

The question asks what number needs to be entered to bring the robot back to its starting position of zero. To do so, we must first calculate how far the robot has traveled in total.

When a negative number is entered into the control unit, the robot rolls backward.

As a result, when we add the negative numbers and subtract them from the positive number,

we can determine the total distance traveled by the robot.-37 (back) + 22 (forward) - 16 (back) = -31 (inches traveled)Since the robot moved a total of 31 inches,

the students must enter the opposite number to bring the robot back to its starting position of 0.

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A. the dimension of A is 3x3. the dimension of B is 3x2.

B. the dimension of AB will be 3x2.

C. The value of AB = [[ -15 14] [ 4 -2] [ 13 -9]]

A. The dimension of a matrix is given by the number of rows and columns it has.

For matrix A, we have:

A = [[-1 -4 1], [0 2 2], [2 3 0]]

The matrix A has 3 rows and 3 columns, so the dimension of A is 3x3.

For matrix B, we have:

B = [[2 0], [3 -3], [-1 2]]

The matrix B has 3 rows and 2 columns, so the dimension of B is 3x2.

B. To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, A has 3 columns and B has 3 rows, so we can multiply them.

The dimension of AB will be the number of rows of A and the number of columns of B. Therefore, the dimension of AB will be 3x2.

C. [-1 -4 1] * [2 0]

   [0 2 2]    [3 -3]

   [2 3 0]    [-1 2]

  [-2-12-1   0+12+2]

= [0+6-2    0-6+4]

  [4+9+0   0-9+0]

  [ -15     14]

= [ 4         -2]

  [ 13       -9]

The value of AB = [[ -15 14] [ 4 -2] [ 13 -9]]

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Given question is incomplete, the complete question is below

For matrices: A =[[ -1 -4 1] [0 2 2][ 2 3 0]] B =[[2 0] [3 -3 ][-1 2] ]

A. What is the dimension of A and B?

B. What is the dimension of A*B?

C. What is A*B?

The surface area of the trumpet is [tex]\( 1256.64 \pi \)[/tex] square feet.

To find the surface area of the trumpet, we need to calculate the areas of the curved surface and the base separately, and then sum them.

The curved surface area of a truncated cone can be calculated using the formula:

[tex]\[ CSA = \pi \times (r_1 + r_2) \times l \][/tex]

Where [tex]\( r_1 \) and \( r_2 \)[/tex] are the radii of the two bases, and [tex]\( l \)[/tex] is the slant height of the truncated cone.

Given that the base diameter is [tex]40[/tex] feet, the radius of the larger base [tex](\( r_1 \))[/tex] is half of that, which is [tex]20[/tex] feet. The slant height [tex](\( l \))[/tex] can be calculated using the Pythagorean theorem:

[tex]\[ l = \sqrt{(h^2 + (r_1 - r_2)^2)} \][/tex]

The height [tex]h[/tex] of the truncated cone is [tex]30[/tex] feet, and the radius of the smaller base [tex](\( r_2 \))[/tex] can be calculated as half the diameter, which is [tex]10[/tex] feet.

Substituting the values into the equations:

[tex]\[ l = \sqrt{(30^2 + (20 - 10)^2)} = \sqrt{(900 + 100)} = \sqrt{1000} = 10\sqrt{10} \]\[ CSA = \pi \times (20 + 10) \times (10\sqrt{10}) = 30\pi\sqrt{10} \][/tex]

The base area of the truncated cone is the area of a circle with radius [tex]\( r_1 \):\[ BA = \pi \times r_1^2 = \pi \times 20^2 = 400\pi \][/tex]

Finally, we can find the total surface area by adding the curved surface area and the base area:

[tex]\[ Surface \, Area = CSA + BA = 30\pi\sqrt{10} + 400\pi \][/tex]

[tex]\[ Surface \, Area = 30\pi\sqrt{10} + 400\pi \]\[ Surface \, Area = \pi(30\sqrt{10} + 400) \]\[ Surface \, Area \approx 1256.637 \pi \]\[ Surface \, Area \approx 1256.64 \pi \][/tex]

Therefore, the simplified surface area of the trumpet is approximately [tex]\( 1256.64 \pi \)[/tex] square feet.

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Answer:

It's 11.72

Step-by-step explanation:

Area=)1/2×15/4×25/4

Answer》11.72

Hope it helps...

Have a great day

Answer:

i have made it in above picture

Answer:

Hey Aryabd interested to talk with me. Come in comments.

The  US Dollars for Rs 21000 would be 200 USD

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that  the rate of Rs 105 per US Dollar,

We have to calculate the US Dollars for Rs 21000.​

105 Rs = 1 USD

21000 Rs = x USD

Now the proportion can be;

105x =21000

x =21000 /105

x= 200 USD

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Answer:

139°

Step-by-step explanation:

Corresponding angles theorem:

When a transversal line intersects two parallel lines, the angles formed from the intersection are congruent in pairs. For example with your problem, using the Corresponding Angles Theorem (one of the few theorems/postulates used to find angles on transversals), the angles are paired on the same place on the first parallel line as they are on the second. Since the corresponding pair of (x)° is given, the angle of x is given. (x)° = 139°

I've provided an image courtesy of tutors.com that will help remember corresponding angles for you.

Answer: 1/6 is its simplest form :)

The integral oſ sin(x - 2) dx is transformed into g(t)dt by applying an appropriate change of variable is g(t) = sin(t).

To transform the integral ∫sin(x - 2) dx into the form ∫g(t) dt using a change of variable, we can let u = x - 2.

Then, differentiating both sides with respect to x gives du = dx.

Substituting these values in the integral, we have:

∫sin(x - 2) dx = ∫sin(u) du

The integral has now been transformed into the integral of sin(u) with respect to u, denoted as g(t) dt.

Therefore, g(t) = sin(t).

So, the correct option is g(t) = sin(t).

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Answer:

52.81

Step-by-step explanat

Answer:

The equation is 157+28=185.

157+ 28= 185

I think that’s right

Answer:

25

Step-by-step explanation:

4x25=100

100-25=75 degrees

Answer:

25°

Step-by-step explanation:

(4x-25)=75

4x=100

x=25

At t = 0.03 s, the charge on the capacitor in the LRC-series circuit is 0.8630 C.

In an LRC-series circuit, the charge on the capacitor can be calculated using the formula Q(t) = Q(0) * e^(-t/(RC)), where Q(t) is the charge at time t, Q(0) is the initial charge on the capacitor, R is the resistance, C is the capacitance, and e is the base of the natural logarithm.

Given the values L = 0.05 H, R = 3.12 Ω, C = 0.008 F, E(t) = 0 V, Q(0) = 4 C, and i(0) = 0 A, we can substitute these values into the formula. Using the given time t = 0.03 s, we can calculate the charge on the capacitor.

Plugging in the values, we have Q(0.03) = 4 * e^(-0.03/(3.12*0.008)). Evaluating this expression gives us Q(0.03) ≈ 0.8630 C, rounded to four decimal places.

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Answer:

theres no answer

Step-by-step explanation:

Answer:

(a) 100

(b) 10.27

Step-by-step explanation:

We are given  

No of elements = 15  

Σ(x-c) = 72,Σ(x-c)^2 = 499.6

,where c is a constant

and the sample mean is 104.8.

(a)  lets take into account Σ(x-c) = 72

this means that we have the sum of the 15 elements of x and each element of x is subtracted by the constant c

so the equation becomes Σxi -15c = 72, ............(1)

where xi means the sum of the elements of x from 1 to 15.

we are given the mean as 104.8

this means that Σxi/15 = 104.8

Σxi = 15*104.8 = 1572 .............(2)

substituting (2) in (1)

we get  

1572 - 15c = 72  

15c = 1500  

c = 100

(b) We will use the property that variance does not change when a constant value is added or subtracted to the elements. This we can observe in the given equation that c is a constant that has the value of 100.

so the variance is  

σ^2 = Σ(x-c)^2/15  - (Σ(x-c)/15 )^2

      = 499.6/15  - (72/15)^2

      = 33.31 - 23.04

   σ^2   = 10.27

Therefore the variance of the given problem is 10.27.

Answer:

[tex] - 49 \times (49 \times 5982 + 3) {}^{2} \\ = - 49 \times 85919920641 \\ = - 4,210,076,111,409[/tex]

Answer:

1).  (x - 4 = 13)

2).  (r + 17 = 51)

3). (7/9x =28)

4). (2/3x = 2)

5). { 3(x-2) = -9 }

6). (x -1.75 = 8.85)

7). Natalie buys organic almonds priced at $77 from the grocery store. How much did

she pay the cashier, if she received $23 in change?

Step-by-step explanation:

1. add 4 on both sides and it will be x=17

2. subtract 17 on both sides and it will be x= 34

3. multiply 9/7 on both sides and it will be x= 257/7 then you divide 257 by 7 then the final answer will be x= 36

4. multiply 3/2 on both sides and it will be x=6/2 then you divide 6 from 2 and the finial answer will be x= 3

5. you will distribute 3 into x and 2 and you will be 3x-6=-9 then you will add 6 on both sides so you will get 3x=3 and then divide 3 on both side so you will get x=1

6. add 1.75 on both sides so x= 10.6

7. the equation will be 23 +x = 77 so first you will subtract 23 on both sides and x will equal 54 so Natalie paid $54

Answer:

i'm taking that test rn

Step-by-step explanation:

The expectation (mean) of the company's daily loss due to blackouts is $200, and the variance is $350.

To compute the expectation of the company's daily loss, we multiply each possible loss value by its corresponding probability and sum them up. In this case, we have three possible loss values (0, 1, and 2) with their respective probabilities (0.7, 0.2, and 0.1). Multiplying each loss value by its probability and summing them gives us the expected value of $200.

To calculate the variance, we need to find the squared differences between each possible loss value and the expected value, multiply them by their respective probabilities, and sum them up. Squaring the differences ensures that negative differences do not cancel out positive differences. In this case, the variance is calculated as (0 - 200)^2 * 0.7 + (1 - 200)^2 * 0.2 + (2 - 200)^2 * 0.1, resulting in a variance of $350.

The expectation and variance provide useful measures of the central tendency and variability, respectively, of the company's daily loss due to blackouts.

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a) The solution to x²-2x-3≥0 is x ≤ -1 or x ≥ 3, expressed in interval notation as (-∞, -1] ∪ [3, ∞).

b) The solution to 6x-2x² > 0 is x < 0 or x > 3, expressed in interval notation as (-∞, 0) ∪ (3, ∞).

c) The solution to 9x+17 ≤ 0 is x ≤ -17/9, expressed in interval notation as (-∞, -17/9].

a) To solve the inequality x²-2x-3≥0, we can factor the quadratic expression as (x-3)(x+1) ≥ 0. We find that the inequality is satisfied when x ≤ -1 or x ≥ 3. The solution is expressed in interval notation as (-∞, -1] ∪ [3, ∞).

b) To solve the inequality 6x-2x² > 0, we can factor out 2x from the expression to get 2x(3-x) > 0. We find that the inequality is satisfied when x < 0 or x > 3. The solution is expressed in interval notation as (-∞, 0) ∪ (3, ∞).

c) To solve the inequality 9x+17 ≤ 0, we isolate x by subtracting 17 from both sides to get 9x ≤ -17. Dividing both sides by 9, we find x ≤ -17/9. The solution is expressed in interval notation as (-∞, -17/9].

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Answer:

the answer is C

Step-by-step explanation:

BABYSHARK

Answer:

I think its c?

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

ok, i will help you.

For the first equation, we have points

(-1, -4)

and

(1, -1)

we also know the y-intercept is

(0, -2)

we can make systems of equations to solve for the equation of this exponiental function

y=ab^x

-1=ab

-2=a*1

a=-2

-1=-2(b)

b=1/2

The exponiental fufnction here is y=(-2)(1/2)^x

2nd equation

(0, 6)

(1, 12)

12=ab

6=a*b^0=6

a=6

12=6(b)

b=2

2nd equation is

y=6(2)^x

Step-by-step explanation:

Use soh cah toa to solve

it is cos(α)=.839

so the angle of α is 32.9653

Hope that helps :)

Trigonometric identity is cosine. And a is 32.965327740597°.

Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.

Given:

A triangle with an adjacent leg to hypotenuse ratio value of 0.839.

Assume the triangle is a right-angled triangle.

In the right-angled triangle,

the ratio of adjacent leg to hypotenuse is cosine.

So,

Cos(a) = Adjacent leg/Hypotenuse

Cos(a) = 0.839

a = Cos⁻¹(0.839)

a = 32.965327740597°

Therefore, angle measure of a is 32.965327740597°.

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The length of the hypotenuse is approximately 19.8 units.

In a right-angled triangle, the hypotenuse is the longest side, and it is opposite to the right angle. To find its length, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, we have:

h^2 = 14.3^2 + 13.7^2

h^2 = 204.49 + 187.69

h^2 = 392.18

h = sqrt(392.18)

h ≈ 19.8

We can round the answer to one decimal place, as this is the nearest level of precision to the data provided. Note that for a right-angled triangle, the hypotenuse is always the longest side, so it makes sense that the hypotenuse is longer than both of the other sides in this case.

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The interval value at 98% confidence level for the given scenario is (73.51 ; 89.79)

From the data :

Mean(x) = (79.5+102.8+80.8+76.8+80.4+79.2+86+67.7)/8

Mean = 81.65

Sample standard deviation :

s = √[(x1 - mean)² + (x2 - mean)² + ... + (x(n) - mean)²] / n

Using a statistical calculator :

s = 9.98

The confidence interval is defined thus :

Mean ± Tcritical × s/√n

Tcritical at 98% = 2.306

Substituting values into the formula :

81.65 ± (2.306 × 9.98/√8)

81.65 ± 8.137

(73.51, 89.79)

Therefore, the confidence interval for the given scenario is (73.51 ; 89.79)

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Answer:

2

Step-by-step explanation:

The formula to find the slope given 2 points is y2-y1/x2-x1. Now lets plug in the numbers. (2,2) is the first set of points and (-1,-4) is the second set of points. So we have -4-2/-1-2. We have -6/-3. Now we must simplify, giving us 2.

Answer:

-6=2/3*-6

Step-by-step explanation:

y=mx+b

slope = m b=y intercept