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3 years ago

Healthy Gym

Mathematics

2 answers:

ehidna [41]3 years ago

8 0

Answer:

$c=2d+5$

Step-by-step explanation:

Let

d ------> the number of days

c -----> the cost

we know that

The cost is equal to the number of days multiplied by $2 per day plus the initial fee of $5

The linear equation in slope-intercept form is

$c=md+b$

where

m is the slope

b is the c-intercept (value of c when the value of d is equal to zero)

in this problem we have

m=$2 per day

b=$5

substitute

$c=2d+5$

Juliette [100K]3 years ago

3 0

Answer:

c = d + 15

Step-by-step explanation:

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Komok [63]

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3 years ago

The circumference of a circle is 7pi ft. Find its diameter in feet

Mumz [18]

Answer:

The diameter is 7 ft.

Step-by-step explanation:

Circumference= Diameter*pi

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4 years ago

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A photographic negative is 3 cm by 2 cm. A similar print from the negative is 9cm long on its shorter side. What is the length o

lbvjy [14]

Answer:

13.5 cm

Step-by-step explanation:

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4 years ago

15. If x=a Sin2t (I+Cos2t) and y=b Cos 2t (1-Cos2t) then find dy/dx at =22/7*4

Sav [38]

By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}$

It looks like we're given

$\begin{cases}x=a\sin(2t)(1+\cos(2t))\\y=b\cos(2t)(1-\cos(2t))\end{cases}$

where a and b are presumably constant.

Recall that

$\cos^2t=\dfrac{1+\cos(2t)}2$

$\sin^2t=\dfrac{1-\cos(2t)}2$

so that

$\begin{cases}x=2a\sin(2t)\cos^2t\\y=2b\cos(2t)\sin^2t\end{cases}$

Then we have

$\dfrac{\mathrm dx}{\mathrm dt}=4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t$

$\dfrac{\mathrm dy}{\mathrm dt}=-4b\sin(2t)\sin^2t+4b\cos(2t)\sin t\cos t$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4b\cos(2t)\sin t\cos t-4b\sin(2t)\sin^2}{4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t}$

$\implies\boxed{\dfrac{\mathrm dy}{\mathrm dx}=\dfrac ba\tan t}$

where the last reduction follows from dividing through everything by $\cos(2t)\cos^2t$ and simplifying.

I'm not sure at which point you're supposed to evaluate the derivative (22/7*4, as in 88/7? or something else?), so I'll leave that to you.

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3 years ago