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3 years ago

Solve for x 6(x-3)=8(x-4)

Mathematics

2 answers:

Sveta_85 [38]3 years ago

6 0

Answer:

7=x

Step-by-step explanation:

6(x-3)=8(x-4)

Distribute

6x -18 = 8x-32

Subtract 6x from each side

6x-18 -6x = 8x-32-8x

-18 = 2x-32

Add 32 to each side

-18+32 = 2x-32+32

14 = 2x

Divide by 2

14/2 =2x/2

7=x

SpyIntel [72]3 years ago

6 0

$\sf\purple{x= 7}$

$\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}$

$➺\:6(x - 3) = 8(x - 4)$

$➺ \: 6x - 18 = 8x - 32$

$➺ \: 6x - 8x = - 32 + 18$

$➺ \: - 2x = - 14$

$➺ \: x = \frac{ - 14}{ - 2}$

$➺ \: x = 7$

Therefore, the value of $x$ is 7.

$\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}$

$➺ \: 6(x - 3) = 8(x - 4)$

$➺ \: 6(7 - 3) = 8(7 - 4)$

$➺ \: 6 \times 4 = 8 \times 3$

$➺ \: 24 = 24$

➺ L. H. S. = R. H. S.

Hence verified.

$\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}$

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brilliants [131]

Answer:

The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Step-by-step explanation:

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$\int dx={\displaystyle\int\limits}\dfrac{10000\sec^2\left(u\right)\sqrt{100000000\tan^2\left(u\right)+100000000}}{7}\,\mathrm{d}u$

$={\dfrac{100000000}{7}}}{\displaystyle\int}\sec^3\left(u\right)\,\mathrm{d}u\\\\=\dfrac{50000000\ln\left(\tan\left(u\right)+\sec\left(u\right)\right)}{7}+\dfrac{50000000\sec\left(u\right)\tan\left(u\right)}{7}\\\\=\dfrac{50000000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+5000x\sqrt{\dfrac{49x^2}{100000000}+1}$

Plug in the solved integrals in Arc Length and solve as follows:

$\text{Arc Length}=\dfrac{5000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+\dfrac{x\sqrt{\frac{49x^2}{100000000}+1}}{2}|_{limits^{605}_{-605}}\\\\$

$=1245.253707795227\\\\\approx 1245.25$

Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

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