(a) Check that y =1/2 x^2+x + 3 satisfies the differential equation dy/dx=x +1. (b) Check that y = sin t satisfies the differential equation d^2y/dt^2= -y.

Answer:

r=20

Step-by-step explanation:

r/20​​−5=−4

r/20​​=−4+5

r/20=1

r=1×20

r=20

Answer:

20

step by step

The laptop will be worth $594.48 in two years.

To find the value of the laptop in two years, we need to substitute the given values into the formula:

Value = P x (1 - r)ⁿ

In this case, the original value of the laptop is $700, and it depreciates at a rate of 0.08 per year (which is 8% expressed as a decimal). We want to find the value in two years, so t = 2.

Substituting the values into the formula:

Value = $700 x (1 - 0.08)²

Value = $700 x (0.92)²

Value ≈ $700 x 0.8464

Value ≈ $594.48

Therefore, the laptop will be worth $594.48 in two years.

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Answer:

Since we know that,

cos2x= cos²x-sin²x=(cosx-sinx)(cosx+sinx)

And, sin2x=2sinx.cosx

Therefore,

1-sin2x= cos²x+sin²x-2sinx.cosx

1-sin2x= (cosx-sinx)²

Then let

y=cos2x/(1-sin2x)

Answer:

5/6

Step-by-step explanation:

1/2=3/6

1/3=2/6

2/6+3/6=5/6

The size of the second application given the size of the first application and the expression ( x - 3.45 mb) for the size of the second application is 293.55 MB.

Answer:

I\A

Step-by-step explanation:

Answer is B

Step-by-step explanation:

When you roll 3 dice, if if you get the same number, you earn 10 $. if you get two numbers the same, you get 5 $. if the numbers are all different, you lose $2, the expected win is $1.25.

Given,

You  roll 3 dice.

In each dice there will be 6 outcomes

Total number of  outcomes = \(6^{3}=216\)

Conditions are

We can find the number of each cases by using the combination method

Number of cases all the outcomes are same =6

Number of cases you get two numbers same = \(6C_{2}\)×3!

=90

Number of cases the numbers are all different= 6×5×4

=120

Therefore the expected win = (6×10+90×5-120×2)÷216

=270÷216

= $1.25

Hence, when you roll 3 dice, if if you get the same number, you earn 10 $. if you get two numbers the same, you get 5 $. if the numbers are all different, you lose $2, the expected win is $1.25.

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Answer:

Kapdweswq DAWFDGEADAEF DAC E FEWAFWED EW DCQFFF

Step-by-step explanation:

Sfweqrwrrf wqwf q fewqfwqefw f wqfqwefqw

Answer:

45% or -45% decrease

Step-by-step explanation:

The number of dimes Joe has is 6.

Joe has dimes and nickels, the total amount is $1.45

We have to find the number of dimes Joe has.

Suppose the number of dimes is d, so we have the number of nickels is 2d + 5

Now from the question, we get an equation:

0.10d + 0.05( 2d+ 5) = $1.45

To know the value of d we need to solve the equation:

0.10d + 0.10d + 0.25 = 1.45

0.20d = 1.20

d = 120/20

   = 6

Hence we get the total number of dimes Joe has is 6.

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The length of the chord is approximately 7.62 inches.

Let's call the center of the circle point O, the radius of the circle 5 inches, the point where the chord intersects the radius point A, and the point where the chord intersects the circle point B.

Since the chord is perpendicular to the radius, we know that angle AOB is a right angle. Also, since OA is 5 inches and AB is 2 inches, we can use the Pythagorean theorem to find the length of OB

OB^2 = OA^2 + AB^2

OB^2 = 5^2 + 2^2

OB^2 = 25 + 4

OB^2 = 29

OB = sqrt(29) ≈ 5.39 inches

Now that we know the length of OB, we can use it to find the length of the chord. Let's call the length of the chord CD, where C and D are the points where the chord intersects the circle. Since OB is perpendicular to CD, we can use the Pythagorean theorem again to find the length of CD

CD^2 = 2OB^2

CD^2 = 2(29)

CD^2 = 58

CD = sqrt(58) ≈ 7.62 inches

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Answer:

im sorry i dont understand but u can probably aks my friend

Step-by-step explanation:

so all i can do is give u her ig if u need it let me know ok bye hope u can answer it

Answer: -4

Step-by-step explanation: Hello! :) To get started we need to use the equation 7x+3=4x-9, First, we need to subtract 4x from both sides to get 3x+3=-9, then we need to subtract 3 on both sides to get 3x=-12, Finally, we need to divide both sides by 3 to get x = -4. So x = -4.

Hope this helps!

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Given the following data set:

[13,13,13,15,15,16,16,17,17]​

Let's determine the median.

Step 1: Arrange the data points from smallest to largest.

The set is already arranged in ascending order.

[13,13,13,15,15,16,16,17,17]​

Step 2:

a.) If the number of data points is odd, the median is the middle data point in the list.

b.) If the number of data points is even, the median is the average of the two middle data points in the list.

There are 9 data in the set, it is odd. The middle data is the 5th data.

[13,13,13,15,15,16,16,17,17]​

The 5th data is 15.

Therefore, the median of the given set of data is 15.

Answer:

16x+6

Step-by-step explanation:

5x+2+3x+1+5x+2+3x+1 =

16x+6

Answer:

16x + 2

Step-by-step explanation:

\(\boxed{\begin{minipage}{4 cm}\underline{Perimeter of a rectangle}\\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\\phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}\)

Given expressions:

To write an expression for the perimeter of the rectangle, substitute the given expressions for the width and length into the perimeter formula:

\(\begin{aligned}\implies \textsf{Perimeter} &=2\left(5x+2+3x-1 \right)\\ &= 2(5x+3x+2-1)\\&=2(8x+1)\\&=16x+2\end{aligned}\)

Answer:

5 x n

Step-by-step explanation:

This is the answer because:

1) 5 times a number n is just 5 times n

Hope this helps!

Answer:

c = 14

Step-by-step explanation:

hope this helps

Answer:

x=-2

Step-by-step explanation:

Divide 14 by -7, then plug in the result(-2) in place of x.  Run this new equation(-7*-2=14) through your calculator to be sure it's correct.

The vector with a magnitude of 7 and a direction of 160° has a horizontal component of approximately -6.5779 and a vertical component of approximately 2.3940.

To find the horizontal and vertical components of a vector given its magnitude and direction, we can use trigonometry. Let's break down the steps:

Determine the horizontal component:

The horizontal component represents the projection of the vector onto the x-axis. To find this component, we can use the cosine function. The formula for the horizontal component (Cx) is:

Cx = magnitude × cos(direction)

In this case, the magnitude of the vector is given as 7, and the direction is 160°. So we can calculate the horizontal component as follows:

Cx = 7 × cos(160°)

Using a calculator or software, the cosine of 160° is approximately -0.9397. Thus, the horizontal component is:

Cx = 7 × (-0.9397) ≈ -6.5779

So, the horizontal component of the vector is approximately -6.5779.

Determine the vertical component:

The vertical component represents the projection of the vector onto the y-axis. To find this component, we can use the sine function. The formula for the vertical component (Cy) is:

Cy = magnitude × sin(direction)

Using the same values as before, we can calculate the vertical component:

Cy = 7 × sin(160°)

The sine of 160° is approximately 0.3420. Thus, the vertical component is:

Cy = 7 × 0.3420 ≈ 2.3940

Therefore, the vertical component of the vector is approximately 2.3940.

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multiply everything by 3

x=81x+6

-80x=6

x=6/-80

x=3/-40

Answer:

x= -3/40

x= -0.075

Step-by-step explanation:

The required elevation after filling the bush by 34 feet is 134 feet.

Given that,
Parin digs a hole at a rate of 56 feet every 15 minutes. After digging for 45 minutes, Parin places a bush in the hole that fills exactly 34 feet of the hole. Relative to ground level, what is the elevation of the hole after placing the bush in the hole is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The total depth of the digging = 56 × 45 / 15
                                                  = 168 feet
Now, 34 feet dig is filled by bush, so the remaining elevation of the depth, = 168 - 34 = 134

Thus, the required elevation after filling the bush by 34 feet is 134 feet.

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Answer: The expected value of V can be calculated as the sum of the products of the possible values of V and their corresponding probabilities. Let's consider the three possible scenarios:

Using the utility function, we can see that the expected value of V is:

E[V] = 0 * 0.2 + (1/2) * (0.8 * 9/10) + 10 * (0.8 * 1/10)

E[V] = 0 + 0.36 + 0.8

E[V] = 1.16

Therefore, the expected value of V is 1.16. However, since V represents the number of healthy vacation days, it must be a non-negative integer. So, the closest integer to 1.16 is 1. Therefore, the answer is c. 2.

Answer:

4.35

Step-by-step explanation:

-4.35. Step-by-step explanation: You multiply three eights times .4 which gives you .15, then you subtract that from 4.5 which gives you 4.35

Answer:

x=7

Step-by-step explanation:

x(x-2) (x+4) =385

distribute the x and solve

The value of x is 8 in.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

Length = x + 4

Width = x

Height = x - 2

The volume of the rectangular prism = 385 in³

The volume of the rectangular prism = length x width x height

Now,

length x width x height = 385

(x + 4) x (x - 2) = 385

(x + 4) (x² - 2x) = 385

x³ - 2x² + 4x² - 8x = 385

x³ + 2x² - 8x = 385

This is a cubic polynomial.

f(x) = x³ + 2x² - 8x - 385

f(x) = a³ + bx² + cx + d = 0

Using the calculator we get,

Roots:

x = -3.20181 + 5.96339 i (rejected)

x = -3.20181 - 5.96339 i (rejected)

x = 8.40362 = 8

Thus,

The value of x is 8 in.

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17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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