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3 years ago

Find parametric equations for the tangent line at the point (cos(3pi/6),sin(3pi/6), (3pi/6))

1 answer:

5 0

$r(t)=(\cos{t},\sin{t},t)
\\r'(t)=(-\sin{t},\cos{t},1)
\\t= \frac{3\pi}{6} = \frac{\pi}{2}
\\ r'(t)=(-\sin{\frac{\pi}{2}},\cos{\frac{\pi}{2}},1)
\\ r'(t)=(-1,0,1)
\\
\\x=0+t(-1)=-t
\\y=1+t\times 0=1
\\z= \frac{\pi}{2} +t$

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The radius of the base of a cylinder is increasing at a rate of 7 millimeters per hour. The height of the cylinder is fixed at 1

Ilya [14]

Answer:

The rate of change of the volume of the cylinder at that instant = $791.28\ mm^3/hr$

Step-by-step explanation:

Given:

Rate of increase of base of radius of base of cylinder = 7 mm/hr

Height of cylinder = 1.5 mm

Radius at a certain instant = 12 mm

To find rate of change of volume of cylinder at that instant.

Solution:

Let $r$ represent radius of base of cylinder at any instant.

Rate of increase of base of radius of base of cylinder can be given as:

$\frac{dr}{dt}=7\ mm/hr$

Volume of cylinder is given by:

$V=\pi\ r^2h$

Finding derivative of the Volume with respect to time.

$\frac{dV}{dt}=\pi\ h\ 2r\frac{dr}{dt}$

Plugging in the values given:

$\frac{dV}{dt}=\pi\ (1.5)\ 2(12)(7)$

$\frac{dV}{dt}=252\pi$

Using $\pi=3.14$

$\frac{dV}{dt}=252(3.14)$

$\frac{dV}{dt}=791.28\ mm^3/hr$ (Answer)

Thus rate of change of the volume of the cylinder at that instant = $791.28\ mm^3/hr$

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2 years ago

Nazerhy deposits $8,000 in a certificate of deposit. The annual interest rate is 6%, and the interest will be compounded monthly

Likurg_2 [28]

Answer:

$A=\$14,555.17$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=10\ years\\ P=\$8,000\\ r=6\%=6/100=0.06\\n=12$

substitute in the formula above

$A=8,000(1+\frac{0.06}{12})^{12*10}$

$A=8,000(1.005)^{120}$

$A=\$14,555.17$

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In total there will be 688 milliliters of compound used 258 from compound B and 430 milliliters of compound A so 688 in total.

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Effectus [21]

Answer:

4. D

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