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3 years ago

(x-4)/(2x+1)-3 can you help me with this question

Mathematics

1 answer:

lilavasa [31]3 years ago

4 0

Answer:

$\frac{(x - 4)}{(2x + 1)} - 3$ $=$ $\frac{-7x- 7}{3x + 1}$

Step-by-step explanation:

Given

$\frac{(x - 4)}{(2x + 1)} - 3$

Required

Solve

Express 3 as a fraction

$\frac{(x - 4)}{(2x + 1)} - \frac{3}{1}$

Take LCM

$\frac{x - 4 - 3(2x + 1)}{3x + 1}$

$\frac{x - 4 - 6x - 3}{3x + 1}$

Collect Like Terms

$\frac{x - 6x- 4 - 3}{3x + 1}$

Simplify like terms

$\frac{-7x- 7}{3x + 1}$

Hence:

$\frac{(x - 4)}{(2x + 1)} - 3$ $=$ $\frac{-7x- 7}{3x + 1}$

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Find the approximate perimeter of the trapezoid? PLSSS HELPPP

choli [55]

Answer:

Step-by-step explanation:

side 1 = |18-3|= 15

side 2 = |12-3| = 9

side 3 = |16-4| = 12

side 4: $\sqrt{(18-12)^2 + (4-16)^2} \\ \sqrt{36+144} \\ = \sqrt{180} \\ = 13,4$

perimeter = 15 + 9 + 12 + 13,4= 49,4 = 49

5 0

3 years ago

In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. Acc

Troyanec [42]

Answer:

Step-by-step explanation:

(a)

Consider the following:

$A=\frac{\pi}{4}=45°\\\\B=\frac{\pi}{3}=60°$

Use sine rule,

$\frac{b}{a}=\frac{\sinB}{\sin A}
\\\\=\frac{\sin{\frac{\pi}{3}}
}{\sin{\frac{\pi}{4}}}\\\\=\frac{[\frac{\sqrt{3}}{2}]}{\frac{1}{\sqrt{2}}}\\\\=\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{1}=\sqrt{\frac{3}{2}}$

Again consider,

$\frac{b}{a}=\frac{\sin{B}}{\sin{A}}
\\\\\sin{B}=\frac{b}{a}\times \sin{A}\\\\\sin{B}=\sqrt{\frac{3}{2}}\sin {A}\\\\B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

Thus, the angle B is function of A is, $B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

Now find $\frac{dB}{dA}$

Differentiate implicitly the function $\sin{B}=\sqrt{\frac{3}{2}}\sin{A}$ with respect to A to get,

$\cos {B}.\frac{dB}{dA}=\sqrt{\frac{3}{2}}\cos A\\\\\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos A}{\cos B}$

When $A=\frac{\pi}{4},B=\frac{\pi}{3}$ , the value of $\frac{dB}{dA}$ is,

$\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos {\frac{\pi}{4}}}{\cos {\frac{\pi}{3}}}\\\\=\sqrt{\frac{3}{2}}.\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}\\\\=\sqrt{3}$

In general, the linear approximation at x= a is,

$f(x)=f'(x).(x-a)+f(a)$

Here the function $f(A)=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

At $A=\frac{\pi}{4}$

$f(\frac{\pi}{4})=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{\frac{\pi}{4}}]\\\\=\sin^{-1}[\sqrt{\frac{3}{2}}.\frac{1}{\sqrt{2}}]\\\\\=\sin^{-1}(\frac{\sqrt{2}}{2})\\\\=\frac{\pi}{3}$