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sweet [91]
3 years ago
8

The function f(x) is a quartic function and the zeros of f(x) are -3,-1,4, and 6. Assume the leading coefficient of f(x) is 1. W

rite the equation of the quartic polynomial in standard form.
Mathematics
1 answer:
bekas [8.4K]3 years ago
4 0

Answer:

f(x) = x⁴-6x³-13x²+66x+72

Step-by-step explanation:

Factors are: (x+3)(x+1)(x-4)(x-6)

[(x+3)(x+1)][(x-4)(x-6)]

[x²+3x+x+3][x²-4x-6x+24]

(x²+4x+3)(x²-10x+24)

x⁴+4x³+3x²-10x³-40x²-30x+24x²+96x+72

f(x) = x⁴-6x³-13x²+66x+72

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Find the length x to the nearest whole number. A right triangle has a vertical leg of length x units, a base leg with a length o
wel

Complete Question

The diagram for this question is shown on the first uploaded image

Answer:

The value of x is  x = 274 \ unites

Step-by-step explanation:

From the question we are told that

       The length of the vertical length is  x

      The length of the base leg is L = 330 + d units

      The length of the bisecting line segment is h

       The base angle is \theta  = 28^o

       The angle between d and line segment is  \theta_1 =  56^o

For the first angle

         Tan \theta_1 =  \frac{x}{d}

=>     d =  \frac{x}{Tan \theta _1}

 For the whole big triangle

      Tan \theta = \frac{x}{330 + d}

=>     d = \frac{x}{Tan \theta }  -330

So equating the both d

        \frac{x}{Tan \theta _1} =    \frac{x}{Tan \theta }  -330

Substitute values

        \frac{x}{Tan (56)} =    \frac{x}{Tan (28) }  -330

      0.6745 x =    1.880x  -330

       1.20549 x = 330

       x = 274 \ unites

     

   

5 0
3 years ago
A long solenoid with radius r = 7 cm and n = 3,170 turns/m carries a current i = 6. 7 a. What is the magnitude of the magnetic f
kondaur [170]

The magnitude of the magnetic field in the central area inside the solenoid, in T is 0.0267 T

<h3>Magnetic field inside solenoid</h3>

The magnetic field inside the central area of the solenoid is given by B = μ₀ni where

  • μ₀ = permeability of free space = 4π × 10⁻⁷ Tm/A,
  • n = number of turns per unit length = 3,170 turns/m and
  • i = current in solenoid = 6.7 A

Since B = μ₀ni

Substituting the values of the variables into the equation, we have

B = μ₀ni

B = 4π × 10⁻⁷ Tm/A × 3,170 turns/m × 6.7 A

B = 4π × 10⁻⁷ Tm/A × 21239 A-turns/m

B = 84956π × 10⁻⁷ T

B = 266897.15 × 10⁻⁷ T

B = 0.026689715 T

B ≅ 0.0267 T

So, the magnitude of the magnetic field in the central area inside the solenoid, in T is 0.0267 T

Learn more about magnetic field inside a solenoid here:

brainly.com/question/25562052

6 0
2 years ago
Membership to a music club costs $70. Members pay $5 per music lesson and nonmembers pay $10 per
Snezhnost [94]

Answer:

a member would have to take 14 lessons versus a non-member which would only have to take 7

3 0
3 years ago
Our current equation is:
inessss [21]

Answer:

C

Step-by-step explanation:

subtracting 289 from both sides, will make one side will be equal to zero.

thus we can then easily solve for b.

can this answer get the brainliest tag?

8 0
3 years ago
Cuál es el resultado de |-15| x (-5)​
notka56 [123]

Answer:

\frac{15}{x^5}

Step-by-step explanation:

\left|-15\right|x^{-5}

Step 1: Apply exponent rule: \:a^{-b}=\frac{1}{a^b}

=\left|-15\right|\frac{1}{x^5}

Step 2: Multiply fractions: a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}

=\frac{1\cdot \left|-15\right|}{x^5}

Step 3: Simplify

=\frac{15}{x^5}

The result is =\frac{15}{x^5}

<u>Spanish/Espanól</u>

Respuesta:

\frac{15}{x^5}

Explicación paso a paso:

\left|-15\right|x^{-5}

Paso 1: aplique la regla del exponente: \:a^{-b}=\frac{1}{a^b}

=\left|-15\right|\frac{1}{x^5}

Paso 2: multiplica fracciones: a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}

=\frac{1\cdot \left|-15\right|}{x^5}

Paso 3: simplifica

=\frac{15}{x^5}

El resultado es =\frac{15}{x^5}

7 0
3 years ago
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