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2 years ago

What is the value of x? X=

Mathematics

1 answer:

brilliants [131]2 years ago

5 0

Answer:

x=7

step-by-step explanation:

$\frac{5}{40} = \frac{3}{2x + 10}$

5(2x+10) =3×40

10x + 50 = 120

10x =120-50= 70

x = 70/10= 7

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Use separation of variables to solve dy dx − tan x = y2 tan x with y(0) = √3. Find the value of c in radians, not degrees

a_sh-v [17]

Answer:

$y(x)=tan(-log(cos(x))+\frac{\pi }{3} )$

Step-by-step explanation:

Rewrite the equation as:

$\frac{dy(x)}{dx}-tan(x)=y(x)^{2} *tan(x)$

Isolating $\frac{dy}{dx}$

$\frac{dy}{dx} =tan(x)+tan(x)*y^{2}$

Factor:

$\frac{dy}{dx} =tan(x)*(1+y^{2} )$

Dividing both sides by $(1+y^{2} )$ and multiplying them by $dx$

$\frac{dy}{1+y^{2} } =tan(x)dx$

Integrate both sides:

$\int\ \frac{dy}{1+y^{2} } = \int\ tan(x) dx$

Evaluate the integrals:

$arctan(y)=-log(cos(x))+C_1$

Solving for y:

$y(x)=tan(-log(cos(x))+C_1)$

Evaluating the initial condition:

$y(0)=\sqrt{3} =tan(-log(cos(0))+C_1)=tan(-log(1)+C_1)=tan(0+C_1)$

$\sqrt{3} =tan(C_1)\\arctan(\sqrt{3} )=C_1\\60=C_1$

Converting 60 degrees to radians:

$60degrees*\frac{\pi }{180degrees} =\frac{\pi }{3}$

Replacing $C_1$ in the diferential equation solution:

$y(x)=tan(-log(cos(x))+\frac{\pi }{3} )$

3 0

2 years ago

(x2 + 4x2 + x3 + x) + (x3 + x + 5x + 5)

yuradex [85]

Answer:

2x³+5x²+7x+5

Step-by-step explanation:

(x² + 4x² + x³ + x) + (x³ + x + 5x + 5)

(5x²+x³+x)+(x³+6x+5)

2x³+5x²+7x+5

3 0

3 years ago

A bird is 4 meters from the ground. The bird is 74 cm higher from the ground than a squirrel that is sitting in a tree. How far

Igoryamba

The squirrel is 3.16 meters away from the ground, or 316 centimeters.

4 0

2 years ago

Accidents on highways are one of the main causes of death or injury in developing countries and the weather conditions have an i

pashok25 [27]

Answer:

0.105 = 10.5% probability that an accident results in a death.

Step-by-step explanation:

What is the probability that an accident results in a death?

5% of 60%(sunny)

25% of 20%(foggy)

12.5% of 20%(rainy)

$p = 0.05*0.6 + 0.25*0.2 + 0.125*0.2 = 0.105$

0.105 = 10.5% probability that an accident results in a death.

6 0

2 years ago

5. The students are trying to determine the distance between two particular

natali 33 [55]

Answer:

The actual distance between the cities is 211.67 cm.

Step-by-step explanation:

Given:

The map key indicates that 4.5 cm is equivalent to 75 cm.

Now, to find the actual distance between the cities if the cities are 12.7 cm apart on the map.

Let the actual distance be $x$ .

So, we set a proportion to find the actual distance:

4.5:12.7 = 75:x.

Changing into fractions.

$\frac{4.5}{12.7} =\frac{75}{x}$

By cross multiplication we get:

$4.5x=952.5$

Dividing both sides by 4.5 we get:

$x=211.67$

Therefore, the actual distance between the cities is 211.67 cm.

8 0

2 years ago