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3 years ago

Solve each equation using the quadratic formula. Find the solutions. 4x^2 - 8x + 1 = 0

Mathematics

2 answers:

AfilCa [17]3 years ago

7 0

Answer:

Solution is : x = 1 ± 0.5√3

Step-by-step explanation:

We have given quadratic equation:

4x² - 8x + 1 = 0

We need to find solution using quadratic formula.

i.e x = $\frac{-b+(-)\sqrt{b^{2}-4ac } }{2a}$

Compare from general quadratic equation ax² + bx + c=0

Here a= 4 , b = -8 and c = 1

∴ x = -(-8)±√((-8)²-4·4·1) / 2·4

x = (8 ±√48 )/8

x = 1 ± 0.5√3 , This is the answer

kkurt [141]3 years ago

6 0

Answer:

1±√3/2

Step-by-step explanation:

Given quadratic equation is :

4x²-8x+1=0

Quadratic formula is :

x=(-b±√b²-4ac)/2a

ax²+bx+c=0 is standard quadratic equation.

Comparing given equation with standard equation,we get

a=4 , b=-8 and c=1

Putting above values in quadratic formula,we get

x=(-(-8)±√(-8)²-4(4)(1))/2(4)

x=(8±√64-16)/8

x=(8±√48)/8

x=(8±√16×3)/8

x=(8±4√3)/8

x=4(2±√3)/8

x=(2±√3)/2

x=1±√3/2 is the solution of given quadratic equation.

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A rectangle has area x3 + 3x2 - 18x in.2 and width x + 6 in. What is the length in inches?

Viefleur [7K]

Answer:

HOPE THIS HELPS

Step-by-step explanation:

The area = length * Width.

We know the width = X+6 inches and Area = x^3+3x^2–18x.

This problem can be solved just by dividing the area by width and we get a quotient as X^2–3x.

So the length is x^2–3x inches.

7 0

3 years ago

Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ

atroni [7]

Answer: $y=Ce^(^3^t^{^9}^)$

Step-by-step explanation:

Beginning with the first differential equation:

$\frac{dy}{dt} =27t^8y$

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

$\frac{1}{y} \frac{dy}{dt} =27t^8$

Multiply both sides by 'dt' to get:

$\frac{1}{y}dy =27t^8dt$

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

$\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt$

$ln(y)=27(\frac{1}{9} t^9)+C$

$ln(y)=3t^9+C$

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

$e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)$

$y=e^(^3^t^{^9} ^+^C^)$

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

$y=e^(^3^t^{^9}^)e^C$

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

$y=Ce^(^3^t^{^9}^)$

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

$\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8$

Now check if the derivative equals the right side of the original differential equation:

$(Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)$

$Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)$

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

7 0

2 years ago

A die is tossed. find the odds against rolling a number greater than 1

masya89 [10]

Answer:

5/6

Step-by-step explanation:

cuz there's 6 sides and there are 5 more sides than the 1

6 0

2 years ago

Read 2 more answers

Is this linear or exponential? or neither

Brrunno [24]

Answer:

Exponential

Step-by-step explanation:

3 0

3 years ago

Please help. Will give brainliet

kykrilka [37]

Answer:

It is D

Step-by-step explanation:

Because,

The sign ">" should have an underline and the point starts at 4, not 3. If it is not correct, I am sorry.

8 0

3 years ago