What angle do the minute and hour hands of a clock make at 9:00?

cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0

Dafna11 [192]

Answer:

Radius=2.09 cm

Height,h=14.57 cm

Step-by-step explanation:

We are given that

Volume of cylinderical shaped can=200 cubic cm.

Cost of sides of can=0.02 cents per square cm

Cost of top and bottom of the can =0.07 cents per square cm

Curved surface area of cylinder= $2\pi rh$

Area of circular base=Area of circular top= $\pi r^2$

Total cost,C(r)= $0.02\times 2\pi rh+2\pi r^2\times 0.07$

Volume of cylinder, $V=\pi r^2 h$

$200=\pi r^2 h$

$h=\frac{200}{\pi r^2}$

Substitute the value of h

$C(r)=0.02\times 2\pi r\times \frac{200}{\pi r^2}+2\pi r^2\times 0.07$

$C(r)=\frac{8}{r}+0.14\pi r^2$

Differentiate w.r.t r

$C'(r)=-\frac{8}{r^2}+0.28\pi r$

$C'(r)=0$

$-\frac{8}{r^2}+0.28\pi r=0$

$0.28\pi r=\frac{8}{r^2}$

$r^3=\frac{8}{0.28\pi}=9.095$

$r=(9.095)^{\frac{1}{3}}=2.09$

Again, differentiate w.r.t r

$C''(r)=\frac{16}{r^3}+0.28\pi$

Substitute the value of r

$C''(2.09)=\frac{16}{(2.09)^3}+0.28\pi=2.63>0$

Therefore,the product cost is minimum at r=2.09

h= $\frac{200}{\pi (2.09)^2}=14.57$

Radius of can,r=2.09 cm

Height of cone,h=14.57 cm

4 0

3 years ago

Help I need help please

s344n2d4d5 [400]

a) Negative correlation

Negative correlation corresponds to points that move down as you go from left to right on the scatter plot.

b) Positive correlation

Positive correlation corresponds to points that move up as you go from left to right on the scatter plot.

c) No correlation

Scattered points on the scatter plot make no relationship.

4 0

3 years ago

3 1/2 divided by 2 1/4

liberstina [14]

3 1/2 divided by 2 1/4 = 1.55555556

1.55555556 Rounded is 1.55

8 0

3 years ago

Write the equation of the line that passes through the points (-9, -8) and (–6,6).

sveta [45]

Answer:

Slope - intercept form $y = \frac{14}{3} x + 34$

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given points are ( -9 ,-8 ) and (-6,6)

slope of given two points

$m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} } = \frac{6-(-8)}{-6-(-9)} = \frac{14}{3}$

The equation of the straight line passing through the points and having slope

$y - y_{1} = m ( x - x_{1} )$

$y - (-8) = \frac{14}{3} ( x - (-9) )$

3 y + 2 4 = 14 x + 126

3 y = 14 x + 126 - 24

3 y = 14 x + 102

$y = \frac{14}{3} + \frac{102}{3}$

$y = \frac{14}{3} x + 34$

Slope - intercept form y= mx +C

Slope - intercept form $y = \frac{14}{3} x + 34$

6 0

2 years ago

egment AB falls on line 2x − 4y = 8. Segment CD falls on line 4x + 2y = 8. What is true about segments AB and CD?

jolli1 [7]

Answer:

The line segments AB and CD are perpendicular to each other.

Step-by-step explanation:

Segment AB falls on line 2x − 4y = 8.

Rearranging the equation into slope-intercept form we get, ............. (1)

Therefore, slope of the line segment AB is

Now, the segment CD falls on line 4x + 2y = 8.

Rearranging the equation into slope-intercept form we get, ............. (2)

Therefore, the slope of the line segment CD is, N = - 2

So, M × N =

Hence, we can conclude that the line segments AB and CD are perpendicular to each other

8 0

3 years ago