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3 years ago

May I please get help.

Mathematics

1 answer:

Karo-lina-s [1.5K]3 years ago

3 0

Answer:

$y = -\frac{2}{3} +6$

Step-by-step explanation:

To be parallel to the original line, the slope has to be the same $(-\frac{2}{3})$ . For the line to go through the point (6,2) the y-intercept has to be 6.

The graph shows the original line (black) and new line that goes through the point (yellow).

Hope it helps!

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Finding Derivatives Implicity In Exercise,Find dy/dx implicity.<br> xey - 10x + 3y = 0

uranmaximum [27]

Answer:

$\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}$

Step-by-step explanation:

Given:

The implicit equation is given as:

$xe^y-10x+3y=0$

In implicit differentiation, we treat 'y' as a function of 'x' and differentiate both sides of the equation with respect to 'x' and then collect all the $\frac{dy}{dx}$ together and finally solve for $\frac{dy}{dx}$ .

So, differentiating both sides of the above equation with respect to 'x'. This gives,

$\frac{d}{dx}(xe^y-10x+3y)=\frac{d}{dx}(0)\\\\\frac{d}{dx}(xe^y)+\frac{d}{dx}(-10x)+\frac{d}{dx}(3y)=0\\\\\textrm{Using product rule, (uv)' = uv' + vu'}\\\\(x\cdot e^y\cdot \frac{dy}{dx}+e^y\cdot 1)-10\cdot1+3\frac{dy}{dx}=0\\\\\frac{dy}{dx}(xe^y)+e^y-10+\frac{dy}{dx}(3)=0\\\\\textrm{Grouping}\ \frac{dy}{dx}\textrm{ terms together}\\\\\frac{dy}{dx}(xe^y+3)+e^y-10=0\\\\\frac{dy}{dx}(xe^y+3)=10-e^y\\\\\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}$

Therefore, the derivative $\frac{dy}{dx}$ implicitly is:

$\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}$

5 0

3 years ago

You and a friend start riding bikes toward

Setler [38]

Answer:

1.5 hours

I traveled farther

2 miles

Step-by-step explanation:

$\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$

My speed

$\dfrac{2\dfrac{1}{6}}{\dfrac{1}{4}}=\dfrac{\dfrac{13}{6}}{\dfrac{1}{4}}=\dfrac{26}{3}\ \text{mph}$

Speed of my friend

$7\dfrac{1}{3}=\dfrac{22}{3}\ \text{mph}$

Time passed for both me and my friend will be equal if we start at the same time and the combined distance covered by both of us will be 24 miles. Let $t$ be the time taken to meet

$\text{Distance}=\text{Speed}\times\text{Time}$

$\dfrac{26}{3}t+\dfrac{22}{3}t=24\\\Rightarrow \dfrac{48}{3}t=24\\\Rightarrow 16t=24\\\Rightarrow t=\dfrac{24}{16}\\\Rightarrow t=1.5\ \text{hours}$

So, we meet each other after 1.5 hours.

Distance traveled by me

$\dfrac{26}{3}\times 1.5=13\ \text{miles}$

Distance traveled by my friend

$\dfrac{22}{3}\times 1.5=11\ \text{miles}$

So, I traveled farther by $13-11=2\ \text{miles}$ .

7 0

3 years ago

Pls help<br> 16x^2-64x=0

Slav-nsk [51]

the answer is above one

x=4

x=0

5 0

3 years ago

Situation:

Arturiano [62]

Answer:

t = 6162 years

Step-by-step explanation:

Apparently you are asked to use the constant k = 0.0001 instead of the most common 0.00012. We'll answer the problem using such number you typed, but make sure that there is no omission in your typing.

The equation to use is that for carbon decay:

$N(t)=N_0\,e^{-0.0001\,\,t}$

If the skull contains 54% of its original amount of C14, then that means that :

$N(t)=0.54 \,\,N_0$

we use this to solve for the time (t) in our equation:

$0.54\,\,N_0=N_0\,e^{-0.0001\,\,t}\\\frac{0.54\,\,N_0}{N_0}=e^{-0.0001\,\,t}\\0.54=e^{-0.0001\,\,t}\\ln(0.54)=-0.0001\,\,t\\t=\frac{ln(0.54)}{-0.0001} \\t=6161.86\,\,years$

which rounded to the nearest year as requested gives :

t = 6162 years

8 0

3 years ago

Company A has a sales position with a yearly salary of $42,000. Company B has a similar sales position with a slary of $39,000 p

Ugo [173]

Company A has a sales position with a yearly salary of $42,000. Company B has a similar sales position with a slary of $39,000 plus 1% conmission on yearly sales.

Let x be the amount of yearly sales

Company A has a sales position with a yearly salary of $42,000.

yearly salary = 42,000

Company B has a similar sales position with a salary of $39,000 plus 1% commission on yearly sales.

1% is 0.01

yearly salary = 39,000+ 0.01x

yearly sales is the salary at company A greater than the salary and conmission at company B

A > B

42000 > 39000+ 0.01x

We solve the inequality

39000+ 0.01x < 42000

Subtract 39000 on both sides

0.01x < 3000

divide by 0.01

x> 300,000

For yearly sales > $300,000, the salary at company A greater than the salary and commission at company B

8 0

3 years ago

May I please get help. ​

May I please get help.