Baby jacobs birth weight was 10 pounds one week after being born his weight was 9 pounds what was the percent of decrease in jacobs weight

The Laplace transform method is applied to solve the differential equation y' + 6y = e^4t with the initial condition y(0)=2. After transforming, simplifying, and solving for Y(s), we use inverse Laplace transform to find the solution y(t) in the time domain.

Laplace transform is a powerful tool in the field of mathematics used for solving differential equations. To solve the given initial value problem y' + 6y = e^4t ; y(0)=2, we can start by taking the Laplace transform of both sides of the equation.

The Laplace transform of y' is sY(s) - y(0) and the Laplace transform of y is Y(s). Therefore, the Laplace transform of y' + 6y gives sY(s) - y(0) + 6Y(s). Given that y(0)=2, this simplifies to sY(s) + 6Y(s) - 2.

On the right-hand side, the Laplace transform of e^4t is 1/(s-4). Thus, we have the equation sY(s) + 6Y(s) - 2 = 1/(s-4).

By solving for Y(s), we can find the inverse Laplace transform to get the solution y(t) in the time domain.

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To find the limit of the given expression [(ln(x+5) - ln5) / x ] as x approaches 0, we can apply L'Hospital's Rule.

To find the limit of the given expression, we can use L'Hospital's Rule. Let's first rewrite the expression:

[ln(x+5) - ln(5)] / x

As x approaches 0, when plugging in 0, we get an indeterminate form of 0/0. So, we can apply L'Hospital's Rule:

lim [(ln(x+5) - ln5) / x ] as x approaches 0 = lim [(1/(x+5)) / 1]

= lim (1 / (x+5)) as x approaches 0

Since x approaches 0, the expression approaches 1 / (0+5) = 1/5.

Answer: The simplified form of 48 over 192 is 1 over 4.

Step-by-step explanation:

Since, A fraction is in its simplest form when the numerator and denominator cannot be any smaller, while still being whole numbers.

Also, for find the simplified form of a fraction,

We divide both numerator and denominator by their H.C.F,

Here, the given fraction is,

[tex]\frac{48}{192}[/tex]

Since, 48 = 2 × 2 × 2 × 2 × 3

192 = 2 × 2 × 2 × 2 × 2 × 2 × 3

H.C.F(48,192) =  2 × 2 × 2 × 2 × 3  = 48

[tex]\implies \frac{48/48}{192/48}=\frac{1}{4}[/tex]

Hence, The simplified form of 48/192 is 1/4.

The simplified form of 48/192 is 1/4.

First, let's find the GCD of 48 and 192.

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

The factors of 192 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.

The common factors are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

So, the greatest common divisor (GCD) of 48 and 192 is 48.

Now, we divide both the numerator and denominator by 48:

48/48 = 1

192/48 = 4

Therefore, the simplified form of 48/192 is 1/4.

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Answer:

It enables you to explore and know more

Step-by-step explanation:

Purpose Of Questionnaire

The main purpose of a questionnaire is to extract data from the respondents. It's a relatively inexpensive, quick, and efficient way of collecting large amount data even when the researcher isn't present to collect those responses first hand

Answer:

{2, 1\2}

Explanation:

The correct option is:

d. x + (x+2) + (x+4) = 66

The scenario involves three consecutive even integers. Let's denote the first even integer as x, the second one as x+2 (since it is the next consecutive even integer), and the third one as x+4 (as it is two more than the second one).

The sum of these three consecutive even integers is given to be 66. Therefore, the equation that represents this scenario is:

x + (x+2) + (x+4) = 66

So, the correct option is:

d. x + (x+2) + (x+4) = 66

The probable question may be:

The sum of three consecutive even integers is 66. Which equation represents the scenario?

a. x=66

b. x+(x+1)+(x+2)=66

c. x+x+x=66

d. x+(x+2)+(x+4)=66

Answer:

The answer is 2 so C

Step-by-step explanation:

The correct answer is D. 4, The value of x is 4.

To find the value of [tex]\( x \)[/tex] in the diagram, we need to apply the properties of similar triangles. Assuming the diagram shows two similar triangles with corresponding sides labeled, we can set up a proportion between the sides of the similar triangles.

Let's denote the sides of the smaller triangle as [tex]\( a \), \( b \), and \( c \)[/tex], and the corresponding sides of the larger triangle as [tex]\( ka \), \( kb \), and \( kc \),[/tex] where [tex]\( k \)[/tex] is the scale factor between the two similar triangles.

Given that one side of the larger triangle is 4 times the corresponding side of the smaller triangle, we have [tex]\( k = 4 \)[/tex].

Now, if we let [tex]\( a = 21 \)[/tex] (as per the options given), then the corresponding side of the larger triangle is [tex]\( ka = 4 \times 21 = 84 \).[/tex]

The problem states that the side labeled [tex]\( x \)[/tex] in the larger triangle corresponds to the side labeled [tex]\( 1 \)[/tex] in the smaller triangle. Therefore, we have the proportion:

[tex]\[ \frac{x}{ka} = \frac{1}{a} \][/tex]

Substituting the known values, we get:

[tex]\[ \frac{x}{84} = \frac{1}{21} \][/tex]

To solve for [tex]\( x \)[/tex], we cross-multiply:

[tex]\[ x \times 21 = 84 \times 1 \][/tex]

[tex]\[ 21x = 84 \][/tex]

Now, we divide both sides by 21 to isolate [tex]\( x \)[/tex]:

[tex]\[ x = \frac{84}{21} \][/tex]

[tex]\[ x = 4 \][/tex]

we have

[tex]f(x)=(x-4)(x+1)[/tex]

using a graph tool  

see the attached figure

we know that

The function is increasing for all real values of x where [tex]x > 1.5[/tex]

and

The function is decreasing for all real values of x where [tex]x < 1.5[/tex]

therefore

Statements

case a) The function is increasing for all real values of x where x < 0

The statement is false

case b) The function is increasing for all real values of x where x < –1 and where x > 4

The statement is false

case c) The function is decreasing for all real values of x where –1 < x < 4

The statement is false

case d) The function is decreasing for all real values of x where x < 1.5

The statement is true

Answer:

The correct option is:

The function is decreasing for all real values of x where x < 1.5.

Step-by-step explanation:

We are given a function f(x) which is a product of two linear polynomial as:

[tex]f(x)=(x-4)(x+1)[/tex]

Now, we know that on multiplying the two linear polynomial we will obtain a quadratic polynomial.

So, the function f(x) will be represented as:

[tex]f(x)=x(x+1)-4(x+1)\\\\f(x)=x^2+x-4x-4\\\\f(x)=x^2-3x-4[/tex]

So, we will plot the graph of the function and check which statements about the function hold true.

1)

The function is increasing for all real values of x where x < 0.

This statement is false.

Since we get from the graph that function f(x) is decreasing for x<0.

2)

The function is increasing for all real values of x where x < –1 and where x > 4.

This option is incorrect as the function is decreasing for x<-1

whereas it is increasing for x>4.

3)

The function is decreasing for all real values of x where –1 < x < 4.

This option is incorrect.

Since, the function is both decreasing as well as increasing in the interval (-1,4).

4)

The function is decreasing for all real values of x where x < 1.5.

This option is correct.

Since it could be observed from the graph that the function is decreasing for x<1.5.

Answer:

p ↔ q

Step-by-step explanation:

Given :

Let p: The integer has one digit.

Let q: The integer is less than 10.

To Find:Which represents "The integer has one digit if and only if the integer is less than 10”?

Solution:

1. p ∧ q denotes “p and q”

2.p ∨ q denotes “p or q" (or both)

3.p → q denotes “if p then q”

4. Biconditional p ↔ q denotes “p if and only if q"

Thus Biconditional p ↔ q represents "The integer has one digit if and only if the integer is less than 10”

Hence Option D is correct p ↔ q

Answer: Answer is second and fifth option.

Step-by-step explanation:  

m = –2 and b =

m = –2 and b =  

Answer:

Step-by-step explanation:

A relation from a set X to a set Y is called a function, if each element of X is related to one and exactly one element in Y. Though many elements of X can be related to one element in Y (many to one).

{(3, 7),(3, 6),(5, 4),(4, 7)} → is not a Function (as (3, 7), (3, 6) share same x)

{(1, 5),(3, 5),(4, 6),(6, 4)} → is a Function

{(2, 3),(4, 2),(4, 6),(5, 8)} → is not a Function (as (4, 2), (4, 6) share same x)

{(0, 4),(3, 2),(4, 2),(6, 5)} → is a Function

Answer: ^^^ that person was correct

Step-by-step explanation:

The required, 60 percent of 22.5 is equal to 13.5, as of the given condition.

The percentage is a way of expressing a fraction or a decimal number as a portion of 100. It is denoted by the symbol '%'. For example, the percentage of 0.75 can be calculated as 0.75 x 100% = 75%. In other words, we are expressing 0.75 as a fraction of 100.

Here,
To find out what number 60% of is equal to 13.5, we can use algebra. Let x be the number we are looking for. Then we can write:

60% of x = 13.5

We can convert 60% to a decimal by dividing by 100:

0.6x = 13.5

Finally, we can solve for x by dividing both sides of the equation by 0.6:

x = 13.5 ÷ 0.6

x = 22.5

Therefore, 60% of 22.5 is equal to 13.5.

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B.

He has used the highest recommended percentages to calculate the amounts for the three categories.

Step-by-step explanation:

It is given that, the total distance an object travels varies directly with the length of time it travels.

[tex]d\propto t[/tex]

If an object travels 32 meters in 18 seconds so,

[tex]32= 18k[/tex].....(1) (k is a constant)

If distance travelled is 80 meters, then the time taken is t say.

[tex]80= kt[/tex].....(2)

On solving equation (1) and (2), we get the value of t as,

t = 45 seconds

Hence, this is the required solution.

The value of the positive integer is,

⇒ 11

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Here, 12 is added to the square of a positive integer, the result is 133.

Let a positive integer = x

Hence, We can formulate;

⇒ 12 + x² = 133

⇒ x² = 133 - 12

⇒ x² = 121

⇒ x = √121

⇒ x = 11

Thus, The value of the positive integer is,

⇒ 11

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Answer:

The answer is the option B

see the attached figure

Step-by-step explanation:

we have

[tex]x\geq4[/tex]

The solution is the interval ------> [4,∞)

All real numbers greater than or equal to [tex]4[/tex]

therefore

the answer  in the attached figure

When there is the no of ways where the president and the vice president should be selected from the grouping of 10 people does not represent the combination.

The following information should be considered:

Therefore we can conclude that when there is the no of ways where the president and the vice president should be selected from the grouping of 10 people does not represent the combination.

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