Giải phương trình vi phân cấp 2

Answer:

(B) [tex]\sqrt{221}[/tex] yards

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem to find the length of x.

The Pythagorean Theorem states that [tex]a^2 + b^2 = c^2[/tex], where a and b are our legs and c is the hypotenuse.

We need to find c, and we already know a and b, so let's substitute.

[tex]10^2 + 11^2 = c^2\\\\100+121=c^2\\\\221=c^2\\\\c=\sqrt{221}[/tex]

Hope this helped!

Answer:

$89.1

Step-by-step explanation:

The original price is 99. The sale price is 99-99*(10/100)=89.1

Explanation:

Let [tex]f(x) = \sqrt{25x}[/tex] and [tex]g(x) = \frac{x^2}{25}[/tex]. The differential volume dV of the cylindrical shells is given by

[tex]dV = 2\pi x[f(x) - g(x)]dx[/tex]

Integrating this expression, we get

[tex]\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx[/tex]

To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:

[tex]\sqrt{25x} = \dfrac{x^2}{25}[/tex]

We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:

[tex]25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1[/tex]

or

[tex]x^3 =(25)^3 \Rightarrow x = \pm25[/tex]

Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is

[tex]\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx[/tex]

[tex]\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx[/tex]

[tex]\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}[/tex]

[tex]\:\:\:\:=4\pi(3125) - \pi(7812.5) = 14726.2[/tex]

Hi there! :)

Answer:

[tex]\huge\boxed{2(14x - 41y)}[/tex]

(75x - 67y) - (47x + 15y)

Distribute the '-' sign with the terms inside of the parenthesis:

75x - 67y - (47x - (15y))

75x - 67y - 47x - 15y

Combine like terms:

28x - 82y

Distribute out the greatest common factor:

2(14x - 41y)

30,20 and 10

30 + 20 + 1/3×30 = 60

50 + 10 = 60

60 = 60

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Answer:

32 years old

Step-by-step explanation:

The husband is 32 years old as the wife is 3 years younger than the husband. The son is 3 years older than the daughter. Their family altogether total age today is 68 years while 4 years ago their age total was 54 years. The difference is 14 years. If we divide the difference into 4 then the age can not be whole number which means daughter is born after 2 years. She is now 2 years older. Son is 3 years older than the daughter which means he is 5 years old. The husband then must be 32 years old and wife is 3 years younger which means she is 29 years old now.

32 + 29 + 5 + 2 = 68 years.

Classica aplicação de regra de 3:

é dito que: 1 milha = 1,6km

Logo, eis a regra de 3:

  milha           km

     1   --------    1,6

     X  --------   240

1,6X = 240.1

X = 240/1,6

Logo 240km equivalem a 150milhas

Answer:

given

f(x).4x+5

fog(x).8x+13

now

fog(x):8x+13

4x+5(g(x)):: 8x+13

g(x):: 8x+13/4x+5

Answer:

g(x) = 2x + 2

Step-by-step explanation:

One is given the following information:

One is asked to find the following:

Remember, (f o g (x)) is another way of representing a composite function. A more visual way of representing this composite function is the following (f(g(x)). In essence, one substitutes the function (g(x)) into the function (f(x)) in places of the varaible (x). Thus, represent this in the form of an equation:

f(g(x)) = 8x + 13

Substitute the given infromation into the equation:

4(g(x)) + 5 = 8x + 13

Solve for (g(x)) in terms of (x). Remember to treat (g(x)) as a single parameter:

4(g(x)) + 5 = 8x + 13

Inverse operations,

4(g(x)) + 5 = 8x + 13

4(g(x)) = 8x + 8

g(x) = (8x + 8) ÷ 4

g(x) = 2x + 2

Answer:

[tex]\displaystyle y=\frac{1}{2}x-2[/tex]

The point-slope form is represented with the formula:

[tex]y-y_1=m(x-x_1)[/tex]

We are given a point [tex](x_1, y_1)[/tex] and a slope: [tex]\displaystyle \frac{1}{2}[/tex].

We are asked to solve this equation in slope-intercept form, which is:

[tex]y=mx+b[/tex]

Givens

[tex]x_1: 10\\\\y_1: 3\\\\\displaystyle m: \frac{1}{2}[/tex]

To solve:

1. Substitute the givens into the point-slope form equation:

[tex]y-y_1=m(x-x_1)\\\\\displaystyle y-3=\frac{1}{2}(x-10)[/tex]

2. Simplify by using the distributive property, which states:

[tex]a(b+c)=ab+ac[/tex]

[tex]\displaystyle y-3=\frac{1}{2}x-5[/tex]

3. Simplify further by combining like terms:

[tex]\displaystyle y-3+3=\frac{1}{2}x-5+3\\\\\displaystyle y=\frac{1}{2}x-2[/tex]

The final answer in slope-intercept form is:

[tex]\large \boxed{\displaystyle y=\frac{1}{2}x-2}[/tex]

Answer:

y = 1/2x - 2

Step-by-step explanation:

Step 1:

y = mx + b      Slope Intercept Form

Step 2:

y = 1/2x + b          Equation

Step 3:

3 = 1/2 ( 10 ) + b         Input x and y

Step 4:

3 = 5 + b         Multiply

Step 5:

3 - 5 = b      Subtract 5 on both sides

Step 6:

b = - 2

Answer:

y = 1/2x - 2

Hope This Helps :)

Answer:

[tex]40.97<\mu<43.03[/tex]

Step-by-step explanation:

Th formula for calculating the confidence interval of a population is expressed as shown;

CI = xbar ± Z*S/√n where;

xbar is the mean or average sample

Z is the z-score at 90% confidence

S is the standard deviation

n is the sample size

Given parameters

xbar = 42

Z at 90% CI = 1.645

S = 5

n = 64

Substituting the values into the formula will give;

CI = 42±(1.645*5/√64)

CI = 42±(1.645*5/8)

CI = 42±(1.645*0.625)

CI = 42±1.028125

CI = (42-1.028125, 42+1.028125)

CI = (40.971875, 43.028125)

Hence the 90% confidence interval for the population is approximately (40.97, 43.03) i.e [tex]40.97<\mu<43.03[/tex]

Subtracting 3 at the end of the equation shifts the graph down 3 units

Answer:

D

Step-by-step explanation:

area of a rectangle : length × width = 6×3 = 18

area of a circle : pi×r² = pi × (1.5)² = pi × (3/2)² = pi×9/4

the area of the shaded region is simply the area of the rectangle minus the area of the circle.

and so it is

18 - 9×pi/4

Answer:

14.(8.2)= 14.16 = 224

Step-by-step explanation:

the answer is the first one

Answer:

Step-by-step explanation:

Answer:

300%

Step-by-step explanation:

1 year = 12 months

percent = part/whole * 100%

percent = 12/4 * 100% = 300%

Answer:

please can u follow me I've started following you

Answer:

x < -4

Step-by-step explanation:

-3x > 12

-----   ----

-3      -3

12 ÷ -3 = -4

Which means:

x < -4

(The sign changes because the equation is divided by a negative number)

Hope this helped.

Answer:

x <-4

Step-by-step explanation:

-3x > 12

Divide each side by -3. remembering to flip the inequality

-3x/-3 > 12/-3

x <-4

Step-by-step explanation:

distance of (1,0) from the origin is,

√{(1-0)²+(0-0)²}

= √1

= 1

So the radius of the circle is 1,

now for the point (2/5,y) distance from origin should be the same since it's the radius

so,

√{(2/5-0)²+(y-0)²} = 1

or, √(4/25+y²)=1

or, 4/25+y²=1

or, y² = 1-4/25

or, y²=21/25

or, y=√(21/25)

or, y=√21/5

so, the simplest form of y is,

[tex] \frac{ \sqrt{21} }{5} [/tex]

Answer:

A) Maximum error = 170.32 cm³

B)Relative error = 0.0575

Step-by-step explanation:

A) Formula for circumference is: C = 2πr

Differentiating with respect to r, we have;

dC/dr = 2π

r is small, so we can write;

ΔC/Δr = 2π

So, Δr = ΔC/2π

We are told that ΔC = 0.5.

Thus; Δr = 0.5/2π = 0.25/π

Now, formula for Volume of a sphere is;

V(r) = (4/3)πr³

Differentiating with respect to r, we have;

dV/dr = 4πr²

Again, r is small, so we can write;

ΔS/Δr = 4πr²

ΔV = 4πr² × Δr

Rewriting, we have;

ΔV = ((2πr)²/π) × Δr

Since C = 2πr, we now have;

ΔV = (C²/π)Δr

ΔV will be maximum when Δr is maximum

Thus, ΔV = (C²/π) × 0.25/π

C = 82 cm

Thus;

ΔV = (82²/π) × 0.25/π

ΔV = 170.32 cm³

B) Formula for relative error = ΔV/V

Relative error = 170.32/((4/3)πr³)

Relative error = 170.32/((4/3)C³/8π³)

Relative errror = 170.32/((4/3)82³/8π³)

Relative error = 170.32/2963.744

Relative error = 0.0575

9514 1404 393

Answer:

  14 minutes

Step-by-step explanation:

Let t represent the time it took Suki to pick out her pumpkin. The given relation is ...

  10t -13 = 127 . . . . . equation for minutes to carve

  10t = 140 . . . . . . . . add 13

  t = 14 . . . . . . . . . . divide by 10

It took Suki 14 minutes to pick out her pumpkin.

Answer:

The survey result doesn't indicate the change

Step-by-step explanation:

Previous study result is 50%

Survey result:

Comparing with previous result:

Since this result is within 5% level of significance, it can be concluded that the survey result doesn't indicate the change

Answer:

12.6 ft

Step-by-step explanation:

∡NMO = 59°

if MO bisect =>

=> ∡LMN = 2∡LMO =>

=> 5x - 22 = 2(x + 31)

5x - 22 = 2x + 62

5x - 2x = 62 + 22

3x = 84

x = 28°

∡LMO = ∡NMO => ∡NMO = x + 31

=> ∡NMO = 28 + 31 = 59°

Answer:

8:6

or

4:3

Step-by-step explanation:

Answer-7/3

Step-by-step explanation:

Answer:

El valor máximo de los platos a ordenar en el almuerzo es de $ 20.32.

Step-by-step explanation:

Sea [tex]c[/tex] el coste máximo que puede asumir el comensal, medido en pesos, el cual es representada por la siguiente suma:

[tex]c = c_{o} + c_{i} + c_{ii}[/tex]

Donde:

[tex]c_{o}[/tex] - Coste del consumo, medido en pesos.

[tex]c_{i}[/tex] - Coste del impuesto en el condado, medido en pesos.

[tex]c_{ii}[/tex] - Coste de la propina, medido en pesos.

Ahora, los costes por impuesto y por propina se determinan en función del coste de consumo:

Coste del impuesto en el condado

[tex]c_{i} = r_{i}\cdot c_{o}[/tex]

Donde [tex]r_{i}[/tex] es la razón entre el coste del impuesto en el condado y el coste del consumo, adimensional.

Coste de la propina

[tex]c_{ii} = r_{ii}\cdot (c_{o}+c_{i})[/tex]

[tex]c_{ii} = r_{ii}\cdot (c_{o}+r_{i}\cdot c_{o})[/tex]

[tex]c_{ii} = r_{ii}\cdot (1 + r_{i})\cdot c_{o}[/tex]

Donde [tex]r_{ii}[/tex] es la razón entre el coste de la propina y la suma de los costes de consumo y del impuesto del condado, adimensional.

Entonces, la suma completa queda representada por:

[tex]c = c_{o} + r_{i}\cdot c_{o}+r_{ii}\cdot (1+r_{i})\cdot c_{o}[/tex]

[tex]c = [1+r_{i}+r_{ii}\cdot (1+r_{i})]\cdot c_{o}[/tex]

A continuación, se despeja el coste de consumo (valor máximo de los platos):

[tex]c_{o} = \frac{c}{1 +r_{i}+r_{ii}\cdot (1+r_{i})}[/tex]

Si [tex]c = \$\,25[/tex], [tex]r_{i} = 0.07[/tex] y [tex]r_{ii} = 0.15[/tex], entonces:

[tex]c_{o} = \frac{\$\,25}{1+0.07+0.15\cdot (1+0.07)}[/tex]

[tex]c_{o} = \$\,20.32[/tex]

El valor máximo de los platos a ordenar en el almuerzo es de $ 20.32.

Answer:

NT = 14 units

Step-by-step explanation:

In this question we will apply the theorem of intersecting chords.

Two chords MY and TN are intersecting each other inside a circle at a point H.

Theorem states,

MH × HY = TH × HN

12(x) = 8(x + 2)

12x = 8x + 16

12x - 8x = 16

4x = 16

x = 4

Therefore, measure of chord NT = NH + HT

                                                       = 8 + (x + 2)

                                                       = x + 10

                                                       = 4 + 10

                                                       = 14 units

Answer:

y=-1/7x + 12/7

Step-by-step explanation:

Start by finding the slope

m=(1-0)/(-5-2)

m=-1/7

next plug the slope and the point (-5,1) into point slope formula

y-y1=m(x-x1)

y1=1

x1= -5

m=-1/7

y- 1 = -1/7(x - -5)

y-1=-1/7(x+5)

Distribute -1/7 first

y- 1=-1/7x + 5/7

Add 1 on both sides, but since its a fraction add 7/7

y=-1/7x + (5/7+7/7)

y=-1/7x+12/7

Answer:

Step-by-step explanation:

(-5,1) (2,0)

m=(y-y)/(x-x)

m = (0-1)/2- -5)

m = -1/7

(2,0)

y-0= -1/7 (x-2)

y = -1/7x + 2/7

Answer: Hello I have your Answer

It's A

Step-by-step explanation:

Your welcome