Robin files to San Francisco from Santa Barbara in 3 hours. She files back in 2 hours. If the wind is blowing from the north at a velocity of 40 mph going, but changed to 20 mph from the north returning, what was the airpeed of the Plane Cit's speed in still air)? [francisco is & worth of Santa Barbara]

The given differential equation is exact c is an arbitrary constant.

To determine if the given differential equation is exact, we can check if the partial derivatives of the coefficients with respect to x and y are equal. Let's do that:

∂/∂y (2x - 1) = 0

∂/∂x (3y + 7) = 0

Since both partial derivatives are zero, the differential equation is exact.

To solve the exact differential equation, we need to find a potential function F(x, y) such that ∂F/∂x = 2x - 1 and ∂F/∂y = 3y + 7.

Integrating the first equation with respect to x, we get:

F(x, y) = x² - x + g(y)

Here, g(y) is an arbitrary function of y.

Now, we can differentiate F(x, y) with respect to y:

∂F/∂y = d/dy (x² - x + g(y))
        = g'(y)

Comparing this with the second equation, we can see that g'(y) = 3y + 7.

Integrating g'(y) = 3y + 7 with respect to y, we get:

g(y) = (3/2)y² + 7y + c

Here, c is an arbitrary constant.

Therefore, the general solution to the given exact differential equation is: F(x, y) = x² - x + (3/2)y² + 7y + c where c is an arbitrary constant.

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Required length of the ST is 35 feet.

What is circle?

A circle is a geometrical shape in which all points on its boundary or circumference are equidistant from a fixed point called the center. It can also be defined as the locus of all points that are at a fixed distance from the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter.

First, we notice that since PS is a diameter, angle PXS is a right angle (90 degrees) since it subtends the diameter. Therefore, angle QXT = 180 - angle PXT - angle RXS = 180 - 125 - 97 = 38 degrees.

Since X is the center of the circle, PX = RX = SX = TX (the radius of the circle), and so triangle PXS is an isosceles triangle with PS = 28 feet as its base. We can find PX as follows:

cos(125/2) = (PS/2) / PX

PX = (PS/2) / cos(125/2) = 28 / cos(62.5) = 60.1 feet (rounded to one decimal place)

Now we can use the law of cosines to find ST:

ST² = PS² + PT² - 2(PS)(PT)cos(QXT)

ST² = 28² + 2(PX² - 14²) - 2(28)(PX)cos(38)

ST² = 784 + 2(3602 - 196) - 2(28)(3602 - 196)cos(38)

ST² = 784 + 6806 - 2(28)(3406)cos(38)

ST²= 784 + 6806 - 64687.5

ST² = 1245.5

ST ≈ 35.3 feet (rounded to the nearest ten)

Therefore, the length of ST is approximately 35 feet.

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Answer

35 (3 + x)

Step-by-step explanation:

Answer:

x = 19

Step-by-step explanation:

\(\sqrt[2]{x-3^3}\) = 64

\(\sqrt[2]{x-3^3}\) = 4³

multiply each side by the exponent 2/3 so the radical sign on left is removed

(\(\sqrt[2]{x-3^3}\))^2/3 = (4³)^2/3

x - 3 = 4²

x - 3 = 16

x = 19

Answer:

a. 20%

b. 40%

Step-by-step explanation:

a. 3km =3000m

600/3000×100=20%

b. 3200/8000×100=40%

Step-by-step explanation:

m(x + n) = n

mx + mn = n

mx = n - mn

x = (n - mn)/m

x(a + b) = b(c - x)

ax + bx = bc - bx

ax + bx + bx = bc

x(a + b + b) = bc

x(a + 2b) = bc

x = bc/(a + 2b)

mx = n(m + x)

mx = mn+ nx

mx - nx = mn

x(m - n) = mn

x = mn/(m-n)

Answer:

56.55

Step-by-step explanation:

To convolve signals \(x_1(t) = \exp(-at)u(t)\) and \(x_2(t) = \exp(-bt)u(t)\) graphically, slide one signal over the other, multiply overlapping areas, and sum them up to obtain the convolution \(y(t)\).

To convolve the signals \(x_1(t) = \exp(-at)u(t)\) and \(x_2(t) = \exp(-bt)u(t)\), we can use the graphical method. Graphically, convolution involves sliding one signal over the other and calculating the overlapping area at each time point. In this case, the exponential functions decay over time, so their overlap will decrease as we slide them.

The resulting convolution signal, denoted as \(y(t)\), is given by:

\[y(t) = \int_{-\infty}^{\infty} x_1(\tau) \cdot x_2(t-\tau) \, d\tau\]

The graphical approach involves plotting \(x_1(t)\) and \(x_2(t)\) on separate axes and then sliding one signal over the other. At each time point, we multiply the overlapping areas and sum them up to obtain \(y(t)\). The resulting graph will show the convolution of the two signals. Therefore, To convolve signals \(x_1(t) = \exp(-at)u(t)\) and \(x_2(t) = \exp(-bt)u(t)\) graphically, slide one signal over the other, multiply overlapping areas, and sum them up to obtain the convolution \(y(t)\).

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A circular park of radius 14 m has a road of 7 m width all around on its outside then the  area of the road is approximately 153.943 square meters.

The circular park has a radius of 14 m. This means that the diameter of the park is 2 x 14 = 28 m. The road around the park has a width of 7 m. This means that the total width of the park and the road is 28 + 7 + 7 = 42 m. The area of the circular park can be found using the formula for the area of a circle: Area of park =\(π x r^2 = π x 14^2 = 615.752 m^2\) (rounded to 3 decimal places)

The area of the park and the road can be found by calculating the area of the larger circle and subtracting the area of the park: Area of park and road =\(π x (r+7)^2 - π x r^2 = π x (14+7)^2 - π x 14^2 = π x 21^2 - π x 14^2 = π x (441 - 196) = π x 245 = 769.695 m^2\) (rounded to 3 decimal places)

To find the area of just the road, we need to subtract the area of the park from the area of the park and road: Area of road = Area of park and road - Area of park = 769.695 - 615.752 =\(153.943 m^2\) (rounded to 3 decimal places)

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Answer:

y= (2)(5)+12

 =10+12

 = 22

Answer:

22

Step-by-step explanation:

replace the variables with the given values:

y=(2)(5)+12

y=10+12

y=22

Answer: 7.5 i believe

Step-by-step explanation:

Answer:

Distributive property

Answer:

The distributive property

Step-by-step explanation:

In the equation, we can see that the 4 in 4(7x - 2) was distributed to the parentheses in the other side of the equation.

The 4 was multiplied to both 7x and -2, creating 28x - 8 on the other side of the equation.

So, this represents the distributive property.

This is my honest opinion

Science is not just facts. Science, to me, is full of theories and hypotheses that can be proved wrong. Yes, a majority of it is actually factual, but in the future it may or may not be true.

I hope it helps.

Answer:

4

Step-by-step explanation:

hope it helps ;)

Answer:

This weekend I played basketball

Step-by-step explanation:

I practiced my jumpshot

layups

etc

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

f(x) = x² - 10x + 22

Step-by-step explanation:

Let's assume the quadratic polynomial as:

f(x) = ax² + bx + c

Now we know that if one of the zeroes is 5 + √3, then the other zero must be 5 - √3 (because complex roots always come in conjugate pairs).

So the sum of the zeroes will be:

(5 + √3) + (5 - √3) = 10

10 = 2 * 5

The product of the zeroes will be:

(5 + √3) * (5 - √3) = 25 - 3 = 22

Now, using the sum and product of zeroes, we can write:

b/a = 10

c/a = 22

Solving for b and c, we get:

b = -10a

c = 22a

Substituting these values in f(x), we get:

f(x) = a(x - 5 - √3)(x - 5 + √3)

Expanding the right-hand side:

f(x) = a[(x - 5)² - (√3)²]

f(x) = a(x² - 10x + 22)

Comparing the coefficients of f(x) with ax² + bx + c, we get:

a = 1, b = -10, c = 22

Therefore, the quadratic polynomial is:

f(x) = x² - 10x + 22

Answer: See explanation

Step-by-step explanation:

x=-(2-2*the square root of 6)/5, about 0.58

or

x=-(2+2*the square root of 6)/5, about -1.38

The values of the x from equation  \(5x^2+4x-4=0\) are  x = 0.5798 and -1.38.

Given that:

Equation:  \(5x^2+4x-4=0\)

To find the values of x that satisfy the equation \(5x^2+4x-4=0\), use the quadratic formula:

\(x = \dfrac{ -b \± \sqrt{b^2 - 4ac}}{ 2a}\)

Compare the equation with \(ax^2 + bx + c = 0\).

Here, a = 5, b = 4, and c = -4.

Plugging in the values to get,

\(x = \dfrac{-4 \± \sqrt{4^2 - 4 \times 5 \times (-4)}}{2 \times 5} \\x = \dfrac{-4 \± \sqrt{16 +80}}{10} \\x = \dfrac{-4 \± \sqrt{96}}{10}\\x = \dfrac{-4 \± {4\sqrt6}}{10}\)

So the solutions for x are calculates as:

Taking positive sign,

\(x = \dfrac{-4 + {4\sqrt6}}{10}\\x = \dfrac{-4 + {9.798}}{10}\\\)

x = 5.798/10

x = 0.5798

Taking negative sign,

\(x = \dfrac{-4 - {4\sqrt6}}{10}\\x = \dfrac{-4 - {9.798}}{10}\\\)

x = -13.798/10

x = -1.38

Hence, the exact solutions for the equation  \(5x^2 + 4x - 4 = 0\)  are x = 0.5798 and -1.38.

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Answer: x = 9

We know that 26 and 17 are in a fact family.

Let's see the fact family.

26 - 17 = 9.

So, the answer is 9.

Hope this helps you!

Answer:

x = 9

Step-by-step explanation:

-x = 17 - 26                       Take the numbers to one side and leave the letters                                                       on the other side

-x = -9                                    Subtract the numbers

x = 9                       since the x and the 9 are negative they become positive

                              (two negatives equals a positive only when multiplying or

                               dividing and in this case you are dividing the -1x to both

                               sides)

The factored form of the quadratic equation is given as follows:

y = 3(x + 0.6667)(x - 6).

The quadratic equation for this problem is defined as follows:

3x² - 16x - 7 = 5.

3x² - 16x - 12 = 0.

The coefficients are given as follows:

a = 3, b = -16, c = -12.

Hence the discriminant is of:

D = (-16)² - 4(3)(-12)

D = 400.

Then the roots are of:

Considering the leading coefficient of 3 and the roots, the factored form of the equation is given as follows:

y = 3(x + 0.6667)(x - 6).

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If total of 180 of these shapes with be strung on the necklace, the necklace contains 30 squares, 30 circles, and 30 triangles.

The sequence of shapes in the necklace follows a pattern of increasing the number of shapes in each group by one, starting with one shape of each type in the first group. This means that the necklace will contain 1+2+3=6 shapes in each group, and there are a total of 180 shapes.

To find the number of each shape in the necklace, we need to determine the number of groups in the necklace. Since there are 6 shapes in each group, we can divide the total number of shapes by 6 to get the number of groups:

180 shapes ÷ 6 shapes/group = 30 groups

This means that there are 30 groups of shapes in the necklace. Within each group, there is one square, one circle, and one triangle. Therefore, the total number of each shape in the necklace is:

1 square/group × 30 groups = 30 squares

1 circle/group × 30 groups = 30 circles

1 triangle/group × 30 groups = 30 triangles

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The simplified polynomial after standard form will be;

⇒ - 8x² - 43x - 36

What is an expression?

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

Given that;

The algebraic expression is;

''The expression (3x + 6)² is subtracted from x² - 7x.''

Now,

We can formulate as;

⇒ (x² - 7x) - (3x + 6)²

⇒ x² - 7x - (9x² + 36x + 36)

⇒ x² - 7x - 9x² - 36x - 36

⇒ - 8x² - 43x - 36

Thus, The simplified polynomial after standard form will be;

⇒ - 8x² - 43x - 36

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The equation of line is y = ( -7/3 )x - 2

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 3 , -5 )

Let the second point be Q ( 0 , -2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -5 + 2 ) / ( 3 )

m = -7/3

Now , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y + 2 = ( -7/3 )x

Subtracting 2 on both sides , we get

y = ( -7/3 )x - 2

Hence , the equation is y = ( -7/3 )x - 2

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Answer:

155 degrees

Step-by-step explanation:

Hi there!

The sum of the interior angles of a quadrilateral is always 360 degrees. To find the measure of the fourth angle, subtract 65, 95 and 45 from 360:

360-65-95-45

= 155

Therefore, the measure of the fourth angle is 155 degrees.

I hope this helps!

Answer:

155 degrees

Step-by-step explanation:

A quadrilateral has a total internal angle sum of 360 so we can set up an equation where x is the fourth angle

360=65+95+45+x

360=205+x

x=155

Total Surface Area = (Perimeter of the base × Length) + (2 × Base Area); or TSA = (S1 + S2 + S2)L + bh

Now, According to the question:

The surface area of a triangular prism is also known as the total surface area. Therefore, it is calculated using the formula, Total Surface Area = (Perimeter of the base × Length) + (2 × Base Area); or TSA = (S1 + S2 + S2)L + bh; where:

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Answer:

Step-by-step explanation:

7x^2 + 5x - 1 - 3x^2 + 4x - 2

4x^2 + 9x - 3