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3 years ago

Solve for x. 0.71= 1/2(9.8) x^2.

Mathematics

1 answer:

Fudgin [204]3 years ago

5 0

Answer: 0.38065

in simpler terms x=± 0.145 =±0.38065

Step-by-step explanation: -490x2+71 = 0

Subtract 71 from both sides of the equation :

-490x2 = -71

Multiply both sides of the equation by (-1) : 490x2 = 71

Divide both sides of the equation by 490:

x2 = 71/490 = 0.145

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 71/490

The equation has two real solutions

These solutions are x = ±√ 0.145 = ± 0.38065

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Is 9/27 irrational number

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3 years ago

4^6 • 4^-8 pls answer

Alex777 [14]

Answer:

$\boxed{4^{-2}}$

Step-by-step explanation:

$4^6 \times 4^{-8}$

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3 years ago

Read 2 more answers

The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65°E and the two towers are 30 kilometers apart. A

Novay_Z [31]

Answer:

The distance of fire from Pine Knob fire tower is 42.43 km

The distance of fire from Colt Station fire tower is 15.53 km

Step-by-step explanation:

Consider point A as Pine Knob fire tower and Point B as Colt Station fire tower. So the distance between both towers that is AB is 30 km.

Now both fire tower are located at a bearing of N65°E. That is at point A from north, Colt station fire tower is located at an angle of 65° towards east.

From ranger on Pine knob tower, fire spotted makes bearing of N80°E. That is at point A from north fire is located at an angle of 80° towards east.

Similarly, from ranger on Pine knob tower, fire spotted makes bearing of S70°E. That is at point B from south fire is located at an angle of 70° towards east.

Now calculate $\theta_{1}=\angle BAC$ and $\theta_{2}=\angle ABD$ as follows,

For $\theta_{1}=\angle BAC$

$\angle XAC=\angle XAB+\angle BAC$

$\therefore 80\degree=65\degree+\angle BAC$

$\therefore \angle BAC=15\degree$

For $\theta_{2}=\angle ABD$

By using alternate angle property,

$\ angle XAB =\angle ABD=65\degree$

Refer attachment 1.

From diagram consider the triangle ABC. To find the third angle that is \angle BAC can be calculated by using angle sum property of triangle.

$\angle BAC+\angle ABC+\angle BCA=180\degree$

$\therefore15\degree +135\degree +\angle BCA=180\degree$

$\therefore \angle BCA=30\degree$

Refer attachment 2.

Sine rule for the $\Delta ABC$ can be applied as follows,

$\ddfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

Substituting the values,

$\dfrac{\sin 15}{a}=\dfrac{\sin 135}{b}=\dfrac{\sin 30}{30}$

Now distance AC and BC can be calculated as follows,

For distance AC,

$\dfrac{\sin 135}{b}=\dfrac{\sin 30}{30}$

Cross multiplying,

$30\times\sin 135=b\times\sin 30$

$\dfrac{30\times \sin 135}{\sin 30}=b$

$b=42.43\:km$

The distance of fire from Pine Knob fire tower is 42.43 km

For distance BC,

$\dfrac{\sin 15}{a}=\dfrac{\sin 135}{42.43}$

Cross multiplying,

$42.43\times\sin 15=a\times\sin 135$

$\dfrac{42.43\times \sin 15}{\sin 135}=a$

$a=15.53\:km$

The distance of fire from Pine Knob fire tower is 15.53 km

6 0

3 years ago

Suppose that r1 and r2 are roots of ar2 + br + c = 0 and that r1 = r2; then exp(r1t) and exp(r2t) are solutions of the different

Nady [450]

The Correct Question is:

Suppose that r1 and r2 are roots of ar² + br + c = 0 and that r1 = r2; then e^(r1t) and e^(r2t) are solutions of the differential equation

ay'' + by' + cy = 0.

Show that

φ (t; r1, r2) = [e^(r2t) - e^(r1t )]/(r2 - r1)

is a solution of the differential equation.

Answer:

φ (t; r1, r2) is a solution of the differential equation, and it shown.

Step-by-step explanation:

Given the differential equation

ay'' + by' + cy = 0

and r1 and r2 are the roots of its auxiliary equation.

We want to show that

φ (t; r1, r2) = [e^(r2t) - e^(r1t )]/(r2 - r1)

satisfies the given differential equation, that is

aφ'' + bφ' + cφ = 0 .....................(*)

Where φ = φ (t; r1, r2)

We now differentiate φ twice in succession, with respect to t.

φ' = [r2e^(r2t) - r1e^(r1t )]/(r2 - r1)

φ'' = [r2²e^(r2t) - r1²e^(r1t )]/(r2 - r1)

Using these in (*)

We have

a[r2e^(r2t) - r1e^(r1t )]/(r2 - r1) + [r2²e^(r2t) - r1²e^(r1t )]/(r2 - r1) + c[e^(r2t) - e^(r1t )]/(r2 - r1)

= [(ar2² + br2 + c)e^(r2t) - (ar1² + br1 + c)e^(r1t)]/(r1 - r2)

We know that r1 and r2 are the roots of the auxiliary equation

ar² + br + c = 0

and r1 = r2

This implies that

ar1² + br1 + c = ar2² + br2 + c = 0

And hence,

[(ar2² + br2 + c)e^(r2t) - (ar1² + br1 + c)e^(r1t)]/(r1 - r2) = 0

Therefore,

aφ'' + bφ' + cφ = 0

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3 years ago

What is the number 255 written as a percent?

DochEvi [55]

<span>255 as a percent = 25500%
</span>

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3 years ago

Read 2 more answers

Solve for x. 0.71= 1/2(9.8) x^2. ​

Solve for x. 0.71= 1/2(9.8) x^2.