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ruslelena [56]
4 years ago
5

Can someone help me with factoring? 4x^3 + 43x^2 + 30x

Mathematics
1 answer:
Sergio039 [100]4 years ago
5 0
4x^{3}+43x^2+30x
First in factoring, you must find out what is common in the whole equation
x(4x^2+43x+30)
Now, make 2 sets of parentheses and "split up" the rest of the equation
Try to experiment which numbers work out
We are not subtracting anything so both parentheses are positive
x(4x+3)(x+10)
Therefore, the factored version of 4x^3+43^2+30x is
x(4x+3)(x+10)
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Use the tangent identity to
Lunna [17]

Answer:

tan(x)=\frac{44\sqrt{89}}{89}

Step-by-step explanation:

tan is defined as: tan(x)=\frac{opposite}{adjacent}

sin is defined as: sin(x)=\frac{opposite}{hypotenuse}

cos is defined as: cos(x)=\frac{adjacent}{hypotenuse}

We can also define tan as: tan(x)=\frac{sin(x)}{cos(x)}

because plugging in the definitions of sin and cos in we get: tan(x)=\frac{(\frac{opposite}{hypotenuse})}{(\frac{adjacent}{hypotenuse})}\\\\tan(x)=\frac{opposite}{hypotenuse}*\frac{hypotenuse}{adjacent}\\\\tan(x)=\frac{opposite}{adjacent}

which you'll notice is the original definition of tan(x)

So using this definition of tan(x) we can use the givens sin(x) and cos(x) to find tan(x)

sin(x)=\frac{44}{45}\\\\cos(x)=\frac{\sqrt{89}}{45}\\\\tan(x)=\frac{sin(x)}{cos(x)}

plugging in sin(x) and cos(x) we get:

tan(x)=\frac{\frac{44}{45}}{\frac{\sqrt{89}}{45}}\\\\tan(x)=\frac{44}{45}*\frac{45}{\sqrt{89}}\\\\tan(x)=\frac{44}{\sqrt{89}}

We usually don't like square roots in the denominator, and from here we want to rationalize the denominator which we do by removing the square root from the denominator.

We can do this by multiplying the fraction by: \frac{\sqrt{89}}{\sqrt{89}} which doesn't change the value of the fraction since it simplifies to 1, but it gets rid of the square root in the denominator

tan(x)=\frac{44}{\sqrt{89}}*\frac{\sqrt{89}}{\sqrt{89}}\\\\tan(x)=\frac{44\sqrt{89}}{89}

5 0
1 year ago
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blagie [28]
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3 years ago
Find the value of the variables. x and y​
Dmitriy789 [7]

Answer:

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x = 34·sin 60°

x = 29.4

sin 90° / 34 = sin 30° / y

y = 34·sin 30°

y = 17

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3 years ago
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