Solve using the Laplace transform technique, y"(t) + y(t) = 48(t – 27), subject to the conditions i) y(0) = 1, y'(0) = 0, ii) y(0) = 0, y'(0) = 0.

In order to prove the triangles are similar, you have to use SAS, SSS and AA rule.

In triangle, the similarity theorem states that if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Here we have to find the 3 shortcuts to prove the triangles are similar.

According to the similarity theorem, here we have triangle that is similar to other if two pairs of angles are congruent (AA) or if two pairs of sides are proportional and the included angles are congruent whereas if three pairs of sides are proportional (SSS).

Here we must know that the term similarity and congruent are similar terms.

To know more about Triangle here.

https://brainly.com/question/8587906

#SPJ4

Answer:

A parallelogram is a quadrilateral with 2 pairs of parallel sides

Answer:

-2,2

Step-by-step explanation:

The difference between  the numbers 9.1 x 10⁹ and 7.8 x 10⁸ is 8.32 x 10⁹.

Given numbers are 9.1 x 10⁹ and 7.8 x 10⁸

Let's align the exponents by moving the decimal point to the right in the number with the smaller exponent, while incrementing the exponent accordingly.

We need to move the decimal point and increment the exponent of 7.8 x 10⁸ to match the exponent of 9.1 x 10⁹

7.8 x 10⁸ can be rewritten as 0.78 x 10⁹

Now that the exponents are aligned, we can subtract the coefficients:

9.1 x 10⁹ - 0.78 x 10⁹

= (9.1 - 0.78) x 10⁹

= 8.32 x 10⁹

Therefore, the difference between 9.1 x 10⁹ and 7.8 x 10⁸ is 8.32 x 10⁹.

To learn more on Difference click:

https://brainly.com/question/30241593

#SPJ1

Answer:

t is less  than or equal to 19

Step-by-step explanation:

t-7<12

+7

t is less than or equal to 19

The ratio that represent the quantities that are proportional to 15/10 and 10/15 are 3/2 and 2/3.

In mathematics, a ratio is the number of times one statistic equals another. A ratio can include any number, such as a count of people or products, or measurements of lengths, weights, and time, among other things.

Both numbers must be positive in most cases. As a result, a ratio can be defined as an ordered pair of integers, a fraction with the first and second numbers in the denominator, or the value represented by this fraction. Ratios of counts provided by (non-zero) two numbers are rational and, in some cases, natural numbers.

From the given equation we can see that the value of the proportion is given by 15/10 which can be simplified to 3/2 with common factor of 5.

Again the value of the proportion is given by 10/15 which can be simplified to 2/3 with common factor of 5.

hence the equal proportions will be 3/2 and 2/3.

to learn more about ratio visit:

https://brainly.com/question/13419413

#SPJ1

Answer:

A=l×w×h

Step-by-step explanation:

5×5×6×7

1050. or if we add 4 in the solution part 2400

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

To know more about MATLAB related question visit:

https://brainly.com/question/30763780

#SPJ11

The dot products of A = (1, 1, -1) and B = (3, 5, 8) are zero, so the cross product axb is orthogonal to both vectors A and B.

Step 1: Write down the components of the vectors A and B.
A = (A1, A2, A3) = (1, 1, -1)
B = (B1, B2, B3) = (3, 5, 8)

Step 2: Compute the cross product axb using the formula:
axb = (A2*B3 - A3*B2, A3*B1 - A1*B3, A1*B2 - A2*B1)

Step 3: Substitute the components of A and B into the formula.
axb = (1*8 - (-1)*5, (-1)*3 - 1*8, 1*5 - 1*3)

Step 4: Simplify the expression.
axb = (8 + 5, -3 - 8, 5 - 3)

Step 5: Calculate the final components of the cross product axb.
axb = (13, -11, 2)

Now, to verify if the cross product is orthogonal to both A and B, we will check if the dot product of axb with A and B is zero.

Step 6: Calculate the dot product of axb with A and B.
(axb·A) = (13*1 + (-11)*1 + 2*(-1))
(axb·B) = (13*3 + (-11)*5 + 2*8)

Step 7: Simplify the expressions.
(axb·A) = (13 - 11 - 2)
(axb·B) = (39 - 55 + 16)

Step 8: Calculate the final dot product values.
(axb·A) = 0
(axb·B) = 0

Since both the dot products are zero, the cross product axb is orthogonal to both vectors A and B.

Know more about cross product here:

https://brainly.com/question/29164170

#SPJ11

Magnitude of impulse is I = FΔ t

What is impulse?

The concept of an impulse in it's most elementary kind could be a force integrated over a time. For a force with a relentless magnitude, we are able to notice the magnitude of the impulse by multiplying the magnitude of the force by the time that force is exerted.

Main body:

If the force is not constant, we simply integrate the force function over the set time period.

The direction of the impulse vector will be the direction of the force vector and the units will be a force times a time

Constant Magnitude Force:

J^=F^∗t

Impulse = Force × (final time – initial time)

Impulse = Force × Δt

I = F × Δt

Hence the magnitude of impulse is I = FΔ t

to know more about impulse , visit:

https://brainly.com/question/2193212

#SPJ4

Answer:

18.8

Step-by-step explanation:

Answer:

Option 4: 0

Step-by-step explanation:

Given the function, f(x) = 3x, and the domain. {-3, 1, 4}:

Substitute the values of each domain as inputs into the function:

f(-3) = 3(-3)

f(-3) = -9

f( 1 ) = 3( 1 )

f( 1 ) = 3

f(4) = 3(4)

f(4) = 12

Therefore, the correct answer is option 4) 0, because there is no input value that provides an output of 0. You were only given three domain values that provided its corresponding outputs.

Answer: 9 units

Step-by-step explanation:

Answer:

-6.25

Step-by-step explanation:

The answer is -6.25.

Answer:

1.5

Step-by-step explanation:

1.5 is the outlier because if one were to include it in the average, it would make the overall average higher than it should be.

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer: the total of the three- digit numbers which will satisfy the property that the middle digit is the average of the first and last digits is 45

Step-by-step explanation:

taking 1,2,3,4,5,6,7,8,9 as the numbers to form the first digits, we see

1 will take an odd number as the last digit so that there is a whole number as an average middle digit. the only numbers are 1,3,5,7,9

all the other odd numbers that is, 3,5,7,9 will also take 1,3,5,7,9 as their last digits

looking at the even numbers as the first digits that is 2,4,6,8, they will take 0,2,4,6,8 as their last digits

by this we see that we are forming five last digits to the first nine digits so that the property of the middle term becomes the average of the first and last digits

the total three-digit number which satisfy the property therefore, we get 9 as the first digits and five as the last digits therefore this gives a total of

9x5=45

#SPJ4

https://brainly.com/question/28203036

Answer:

x and y can be any two numbers greater than zero such that y is also greater than x

D.no more than 45

C.50 miles per hour

Step-by-step explanation:

Let the two numbers be such that x< y because we have been given y/x>1 and x/y< 1 .

Suppose we take y= 9 and x= 3 then

9/3 > 1

3>1

Also

3/9 < 1

1/3 < 1

x and y can be any two numbers greater than zero such that y is also greater than x

2. Total weight that can be carried is 3000 pounds.

The big machine is 300 pounds. The weight that the truck can carry beside the big machine is 3000-300= 2700 pounds.

The smaller machines weigh 60 pounds

The number of smaller machines that can be carried is 2700 ÷ 60= 45 other than the big machine.

3. Total distance = Speed * time

                           = 48 * (40/60) = 32 miles

New distance = 32+ 8= 40 miles

New time = 48 minutes

Speed = distance / time = 40/ 48/60=  50 miles per hour

A) If the triangle is a right triangle

The first step of an indirect proof of the phrase:

If the triangle is a right triangle. The correct statement is A.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

Given:

The Conditional statement:

If one of the angles of a triangle equals 90, then the triangle is classified as a right triangle.

The first step of an indirect proof of the phrase:

If the triangle is a right triangle.

That means, the triangle have an angle equals to 90°.

Therefore, the correct statement : If the triangle is a right triangle.

To learn more about the right-angled triangle;

brainly.com/question/3772264

#SPJ2

Answer:

$548.9

Step-by-step explanation:

$499 x (1+10%) = $ 548.9

The expected value of the product of two independent random variables X and Y is equal to the product of their individual expected values, given that the expected values of X and Y exist.

Let X and Y be two independent random variables. Then, the expected value of the product XY is given by:

E[XY] = ∫∫ xy fX(x) fY(y) dx dy

where fX(x) and fY(y) are the probability density functions of X and Y, respectively. Since X and Y are independent, their joint probability density function is given by:

fXY(x,y) = fX(x) fY(y)

Thus, the expected value of XY can be written as:

E[XY] = ∫∫ xy fX(x) fY(y) dx dy = ∫∫ xy fXY(x,y) dx dy

Now, we can use the linearity of expected value to split up the integral:

E[XY] = ∫∫ xy fXY(x,y) dx dy = ∫∫ x fX(x) y fY(y) dx dy

      = (∫ x fX(x) dx) (∫ y fY(y) dy) = E[X] E[Y]

Therefore, we have shown that E[XY] = E[X] E[Y], given that X and Y are independent and that the expected values of X and Y exist.

Learn more about expected values here:

https://brainly.com/question/18523098

#SPJ11

Answer:

44

Step-by-step explanation:

The number of zeros which this graphed polynomial function have is: B. 3.

A polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

Additionally, a polynomial graph simply refers to a type of graph that is commonly used for the representation of only positive (non-negative) integer exponents of a variable in an equation.

This ultimately implies that, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

In this context, we can reasonably and logically deduce that the zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and these include the following:

Zeros = (-2, 0)

Zeros = (-1, 0)

Zeros = (1, 0)

Read more on polynomial function here: brainly.com/question/14625910

#SPJ1

Answer:

Option (1)

Step-by-step explanation:

Given linear inequalities in the graph are,

\(y\geq -\frac{1}{3}x+2\)

y < 2x + 3

Here shaded area above the solid line represents the inequality,

\(y\geq -\frac{1}{3}x+2\)

And shaded area on the right side of the dotted line represents the solution set of the inequality,

y < 2x + 3

And the solution set of the system of linear inequalities will be represented by the common area of these inequalities.

Therefore, ordered pairs (2, 2), (3, 1) and (4, 2) will lie in the common shaded area.

Option (1) will be the answer.

Answer:

$60

Step-by-step explanation:

180/3 = 60

I hope this helps :)

Answer:60 per hour

Step-by-step explanation: you divide 180 by 3

Answer:

B

Step-by-step explanation:

Answer:

the 90th percentile is 9.

The 90th percentile of the distribution is 9.

The 90th percentile of the distribution in the table is 9.

To find the 90th percentile, we need to look at the values of X and their corresponding cumulative percentages (C%). The 90th percentile is the value of X at which 90% of the data falls below.

Looking at the table, we can see that the value of X at the 90th percentile is 9, as it corresponds to a cumulative percentage of 100%. This means that 90% of the data falls below the value of 9.

Therefore, the 90th percentile of the distribution is 9.

To know more about percentile refer here:

https://brainly.com/question/4001098#

#SPJ11

Answer:

35%

Step-by-step explanation:

Xavier downloaded 40 songs last week,

14 of them were jazz songs.

Therefore, \(\frac{14}{40}\) of Xavier's downloads were jazz songs.

In order to convert it into a percentage, we need to multiply 100 to the fraction.

We get \(\frac{1400}{40}\), which is equal to 35%.

I would appreciate it if you mark my answer as brainliest.