Use a technique of integration or a substitution to find an explicit solution of the given differential equation. dy/dx = sin(root(x))/root(y)

\(❖\qquad\qquad\huge\underline{{\sf Answer}} \qquad \normalsize❖\)

Let's simplify ~

\(\qquad \sf  \dashrightarrow \: \cos(x) \times \tan(x) \times \csc(x) \)

\(\qquad \sf  \dashrightarrow \: \cancel{ \cos(x) }\times \dfrac{ \cancel{ \sin(x)} }{ \cancel{ \cos(x) }} \times \dfrac{1}{ \cancel{\sin(x)} } \)

\(\qquad \sf  \dashrightarrow \:1\)

The equivalent value is 1

Answer:

Start from (0,0) and do rise over run

Step-by-step explanation:

Rise 4

Run 3

For the III (3rd) quadrant use

Rise -4

Run -3

Answer:

The new median would be 15.

Step-by-step explanation:

This is because the median means the middle number so we can cross out 2 and 25. Then cross out 6 and 23. Then cross out 7 and 21. Next, cross out 14 and 20. Since there is only one number left, 15, that number is therefore the median.

Answer:

List the numbers in order including 25

2,6,7,14,15,20,21,23,25

choose the number in the middle

15 has 4 numbers to the left and right so it is in the middle so it is the median

hope this helps

Step-by-step explanation:

The angle of rotation for the described transformation is

The movement or transformation described is form quadrant 4 to quadrant  2.

The transformation will require 180 degrees transformation.

In this type of transformation, both clockwise and the counter clockwise have similar effects

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The graph of the given line is attached below.

We are given the line:-

y = (3/5)x - 4

We will find the x and y intercepts of the line to plot in the graph.

As the equation is already in the slope intercept form, we can write,

The y-intercept of the line is -4.

Hence, the coordinates of the point will be (0,-4).

To find the x - intercept of the line we will put y = 0 in the given line.

0 = (3/5)x - 4

4 = 3x/5

x = 20/3

The coordinates of the point will be (20/3,0).

We can plot these points to get the desired graph.

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Answer:24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

12+12=24

Answer:

\(72\)

Step-by-step explanation:

\(4^2+7\times \:2^3\)

\(16+7\times 2^3\)

\(16+7\times 8\)

\(7\times 8=56\)

\(16+56\)

\(72\)

Answer:

x = 10 yd

Explanation:

These triangles are based on proportions. 12 yd is proportional to 18 yd, and x yd to 15 yd. We want to find x. We'll use the rule of three to calculate the unknown number.

12/18 = x/15

x = (12 · 15)/18

x = 10 yd (10 yards from the hut to the gold coins)

Answer:

The factored expression is 12(2k + 3q - 1)

Step-by-step explanation:

To factor the expression, we identify the greatest common factor between 24, 36 and 12. Between the variables(k, q, and 1), there is no gcf, so no need to find.

GCF between 24, 36 and 12:

We factore these numbers simultaneously, while all of them can be factored by the same value. So

24 - 36 - 12|2

12 - 18 - 6|2

6 - 9 - 3|3

2 - 3 - 1

So gcf(24,36,12) = 2*2*3 = 12

Factored expression:

\(12(\frac{24k}{12} + \frac{36q}{12} - \frac{12}{12}) = 12(2k + 3q - 1)\)

The factored expression is 12(2k + 3q - 1)

Answer:

It becomes 2 times or double.

The value of expression is ,

10) 6

11) 18

12) 2

13) 4

14) \(\frac{1}{4}\)

15) \(\frac{1}{3}\)

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression

10) 7+x+(-3)

Put x=2 then

=> 7+2-3

=> 7-1 = 6

11) 4\(x^2\)+2

put x=2 then

=> \(4*2^2+2\)

=> 4*4+2

=> 16+2=18

12) Ix+10I

put x=-12 then

=> I-12+10I

=> I-2I = 2

13) |2x + 1|

put x= 3/2 then

=> I2*\(\frac{3}{2}\)+1I

=> I3+1I

=> I4I = 4

14)(x - 3)/4

put x=4 then

=> \(\frac{4-3}{4}\)

=> \(\frac{1}{4}\)

15) (5 - x)/6

put x=3 then

=> \(\frac{5-3}{6}\)

=> \(\frac{2}{6}\) = \(\frac{1}{3}\)

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The first number is 8.33 percent more than the second number.

Let m be the first number, n be the second number and p be the third number.

Two numbers are respectively twenty percent and ten percent more than a third number.

m = (100 + 20)% of p

m = 120 percent of p

m = 120 % of p

m = (120 / 100) × p

m = 1.2 p

And the second number would be,

n = (100 + 10)% of p

n = 110 percent of p

n = (110 / 100) × p

n = 1.1 p

We need to find by how much number the first number more than the second.

Consider the difference,

1.2 p - 1.1p = 0.1 p

So the required percentage noting but the difference is what percent of the first number.

(0.1 p / 1.2 p) × 100 = 8.33%

Therefore, the first number is 8.33 percent more than the second number.

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Answer:

17abc

Step-by-step explanation:

To find the greatest common factor between 17abc and 51a²bc, let's start by breaking down any composite number here into prime factors. 17 is prime, but 51 is composite; its prime factorization is 3 · 17. Now, let's fully expand each term:

\(17\cdot a\cdot b\cdot c\\3\cdot17\cdot a\cdot a\cdot b\cdot c\)

The greatest common factor is the product of all the factors these terms have in common. Here, we can see that they have

in common. Multiplying these together, the greatest common factor is 17abc.

The rectangular equation that represents the parametric equation \(x=t^{\frac{1}{2} }\) and y = 4t is:

\(y=4x^2\) for \(x\geq0\)

Note the given representations:

\(x=t^{\frac{1}{2} }\)

\(y=4t\)

Make t the subject of the formula from the expression \(x=t^{\frac{1}{2} }\)

\(x^2=t^{\frac{1}{2}\times2\\\\x^2=t\\t=x^2\)

Substitute \(t=x^2\) into y = 4t

\(y=4x^2\)

Therefore, the rectangular equation that represents the parametric equation \(x=t^{\frac{1}{2} }\) and y = 4t is:

\(y=4x^2\) for \(x\geq0\)

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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The description of the  change in distance over time is;

He ran further away from home, then sped up and went further. He then

slowed down, still going further from home. He then turned

around and headed home.

A distance-time graph is defined as a graph that shows how far an object has travelled in a given time. It is a simple line graph that denotes distance versus time findings on the graph. Distance is plotted on the y-axis. Time is plotted on the x-axis.

From the attached graph, we see that Wesley ran further away from home, and then he sped up and went further in the journey. He then

slowed down, and still going further from home. Finally, he turned

around and headed home.

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Answer:

There are 39 different choices

Step-by-step explanation:

Add the the flavors of ice cream the cones and the scoops.

31+2=33

1+2+3=6

33+6=39

Hope this helps

Answer:

1863/275=6.7745recurring

Step-by-step explanation:

Dont u have a calculator

The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

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A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  =  $272,090

      A) - Calculate the Percentage of the Value Remaining After the Decrease

       B) - Calculate the NEW VALUE of the house

A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE

      100%  -  9%  =  91%

        0.91

B) - Calculate the NEW VALUE of the house:

NEW VALUE  =  OLD VALUE  *  REMAINING PERCENTAGE

NEW VALUE  =  299,000  *  0.91

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  = $272,090

I hope it helps!

The exact values of the given trigonometric functions are:

cos(330) = \(\sqrt{3}/2\) or 0.866

sin(330) = 1/2 or 0.5

To find the trigonometric values of cos(330) and sin(330) exactly, we can use the unit circle and the properties of the trigonometric functions.

In the unit circle, the angle of  330 degrees is equivalent to -30 degrees or \(-\pi/6\) radians. Since cosine is an even function, we know that \(cos(-\theta) = cos(\theta)\), so we can find cos(-30).

Using the special triangles and the reference angle of 30 degrees, we can determine the exact values:

cos(-30) = cos(30) = \(\sqrt{3}/2\)

Similarly, the sine of -30 degrees is the same as the sine of 30 degrees:

sin(-30) = sin(30) = 1/2

Therefore, the exact values are:

cos(330) = cos(-30)= cos(30) = \(\sqrt{3}/2\) or 0.866

sin(330) = sin(-30)= sin(30)= 1/2 or 0.5

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To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

x+y=20

.10x+.25y=3.80

Step-by-step explanation:

The value of x, considering the similar triangles in this problem, is given as follows:

x = 3.6.

Similar triangles are triangles that share these two features listed as follows:

The proportional relationship for the side lengths in this problem is given as follows:

3/20 = x/24

Applying cross multiplication, the value of x is obtained as follows:

20x = 72

x = 72/20

x = 3.6.

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Answer:

C

Step-by-step explanation:

\(\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)} \\ \\ \frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{2x+1}\)

The denominator cannot equal 0, so:

\(2x+1 \neq 0 \implies x \neq -\frac{1}{2}\)

Answer:

5

Step-by-step explanation:

2(x+6)=22

(x+6)=11

x=5