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Delvig [45]
1 year ago
10

Question Progress Homework Progres 23/2 Solve the quadratic equation 3x + x-5 = 0 Give your answers to 2 decimal places.​

Mathematics
1 answer:
kykrilka [37]1 year ago
3 0

The value of x is 1.14 or x = -1.47

We find the value of x in the quadratic equation 3x^2 +x-5=0

Using the formula: (-b ± √ (b²- 4 a c)) / (2a)

Where the value of a = 3, b = 1 and c = -5

Substituting the above values (a = 3, b = 1 and c = -5)

in the formula:

(-1 ± √ (1²- 4 3 (-5))) / (2*3)

= (-1 ± √ (1+60)) / (6)

= (-1 ± √ (61)) / (6)

= (-1 ± 7.81) / (6)

= (-1 + 7.81) / (6) or (-1 -7.81) / (6)

= (6.81) / (6) or (-8.81) / (6)

=1.135 or -1.468

Hence the value of x= 1.14 or -1.47

LEARN MORE ABOUT QUADRATIC EQUATIONS HERE: brainly.com/question/1214333

#SPJ9

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A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t
andreyandreev [35.5K]

Answer:

  • r = 2.632 cm
  • h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

  V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

  r² = 3V/(πh)

The lateral surface area of the cone is ...

  A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

  T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

  T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

  dT/dh = -18V²/h³ +3πV

This will be zero when ...

  3πV = 18V²/h³

  h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

  h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

  r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

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The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

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Interestingly, the ratio of h to r is √2.

8 0
3 years ago
A geometric sequence is a sequence of numbers where the next term equals to
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C

Step-by-step explanation:

Let the first term be a and the common ratio be r.

ATQ, ar^4=24 and ar^6=144, r=sqrt(6) and a=24/(sqrt(6))^2=24/36=2/3

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Which polynomial can be simplified to a difference of squares
Mrrafil [7]
<h2>Hello!</h2>

The answer is:

The polynomial that can be simplified to a difference of squares is the second polynomial:

16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}=(4-1)(4+1)

<h2>Why?</h2>

To solve this problem, we need to look for which of the given quadratic terms given for the different polynomials can be a result of squaring (elevating by two).

So,

Discarding, we have:

The quadratic terms of the given polynomials are:

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Fourth=24a^{2}

We have that the coefficients of the quadratic terms that can be obtained by squaring are:

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The other two coefficients are not perfect squares since they can not be obtained by square rooting whole numbers.

So, the first and the fourth polynomial are discarded and cannot be simplified to a difference of squares at least using whole numbers.

Therefore, we need to work with the second and the third polynomial.

For the second polynomial, we have:

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So, the second polynomial can be simplified to a difference of squares.

For the third polynomial, we have:

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So, the third polynomial cannot be simplified to a difference of squares since it's a sum of squares.

Hence, the polynomial that can be simplified to a difference of squares is the second polynomial:

16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}

7 0
3 years ago
Read 2 more answers
Read the question and type your response in the box provided. Your response will be saved automatically.
gayaneshka [121]

Answer:

h=32 cm

Step-by-step explanation:

12*2=24

+8=32

6 0
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