skyless

11.12.2021 •

Mathematics

Determine whether the ratios are proportion or not proportion write the answer on the blank _6. 2/25=10/125
_7. 9:27=3:18
_8. 3/12=21/84
_9. 5:8=20:32
_10. 2:5=27:45

in pic

Determine whether the ratios are proportion or not proportion write the answer on the blank

_6. 2

Solved

Show answers

Ответ:

autumn452392

05.10.2022

Mathematics

The value of $\frac{\mathrm{d} y}{\mathrm{d} x}$ at t = √2 is $\frac{1}{2 \times \sqrt{2}}$ .

Step-by-step explanation:

Given as :

x = t³ - 3 t

y = 3 t²

We have to calculate $\frac{\mathrm{d} y}{\mathrm{d} x}$ at t = √2

Now,

$\frac{\mathrm{d} x}{\mathrm{d} t}$ = $\frac{\mathrm{d} (t³ - 3 t)}{\mathrm{d} t}$

Or, $\frac{\mathrm{d} x}{\mathrm{d} t}$ = $\frac{\mathrm{d} t³}{\mathrm{d} t}$ - 3 $\frac{\mathrm{d} t}{\mathrm{d} t}$

Or, $\frac{\mathrm{d} x}{\mathrm{d} t}$ = 3 t² - 3 ......A

Again

$\frac{\mathrm{d} y}{\mathrm{d} t}$ = $\frac{\mathrm{d} (3 t²)}{\mathrm{d} t}$

Or, $\frac{\mathrm{d} y}{\mathrm{d} t}$ = 3 × 2 t

Or, $\frac{\mathrm{d} y}{\mathrm{d} t}$ = 6 t ......B

So,

$\frac{\mathrm{d} y}{\mathrm{d} x}$ = $\frac{\frac{\partial y}{\partial t}}{\frac{\partial x}{\partial t}}$

Or, $\frac{\mathrm{d} y}{\mathrm{d} x}$ = $\dfrac{3 t^{2} - 3 }{6 t}$

Or, $\frac{\mathrm{d} y}{\mathrm{d} x}$ = $\frac{3(t^{2}-1)}{6 t}$

Or, $\frac{\mathrm{d} y}{\mathrm{d} x}$ = $\frac{(t^{2}-1)}{2 t}$

Or, $\frac{\mathrm{d} y}{\mathrm{d} x}$ at t = √2

i.e $\frac{\mathrm{d} y}{\mathrm{d} x}$ = $\frac{(\sqrt{2}^{2}-1)}{2 \times \sqrt{2}}$

Or, $\frac{\mathrm{d} y}{\mathrm{d} x}$ = $\frac{(2-1)}{2 \times \sqrt{2}}$

Or, $\frac{\mathrm{d} y}{\mathrm{d} x}$ = $\frac{1}{2 \times \sqrt{2}}$

Hence, The value of $\frac{\mathrm{d} y}{\mathrm{d} x}$ at t = √2 is $\frac{1}{2 \times \sqrt{2}}$ . Answer

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice

Determine whether the ratios are proportion or not proportion write the answer on the blank _6. 2/25=10/125_7. 9:27=3:18_8. 3/12=21/84_9. 5:8=20:32_10. 2:5=27:45in pic