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3 years ago

14

Kailynn has been on a roll, and solving 5 math problems every 2.5 minutes. At this rae, how many problem will she solve in 30 mi

nutes.

1 answer:

d1i1m1o1n [39]3 years ago

4 0

Answer:

60 math problems.

Step-by-step explanation:

30/2.5=12

12*5=60

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A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la

SOVA2 [1]

Answer:

$8\pi\text{ square cm}$

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

$S=2\pi rh$

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

$4^2 = (2r)^2 + h^2$ ( see in the below diagram ),

$16 = 4r^2 + h^2$

$16 - 4r^2 = h^2$

$\implies h=\sqrt{16-4r^2}$

Thus, the surface area of the cylinder,

$S=2\pi r(\sqrt{16-4r^2})$

Differentiating with respect to r,

$\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})$

$=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})$

$=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})$

Again differentiating with respect to r,

$\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})$

For maximum or minimum,

$\frac{dS}{dt}=0$

$2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0$

$-8r^2 + 16 = 0$

$8r^2 = 16$

$r^2 = 2$

$\implies r = \sqrt{2}$

Since, for r = √2,

$\frac{d^2S}{dt^2}=negative$

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

$S = 2\pi (\sqrt{2})(\sqrt{16-8})$

$=2\pi (\sqrt{2})(\sqrt{8})$

$=2\pi \sqrt{16}$

$=8\pi\text{ square cm}$

4 0

3 years ago

H(t)=-10t+6<br> H(_____)=-44<br> Help me please.

alexira [117]

Answer:

-10t +6=-44

-10t=-44-6

-10t=-50

-50\-10

=5

8 0

3 years ago

In a certain class of students, there are 11 boys from Wilmette, 7 girls from Wilmette, 5 boys from Winnetka, 4 girls from

attashe74 [19]

Answer:

.571

Step-by-step explanation:

We need to find the total number of boys

11+5+4 = 20

And the total number of students

11+7+5+4+4+4 = 35

The Probability that the student is a boy is boy/total

P (boy) = boy/total

= 20/35

=4/7

=.571428571

to 3 decimal places

=.571

6 0

3 years ago

Help me please! will mark brainliest if ur correct!

Zina [86]

Answer:

i think it's c

Step-by-step explanation:

ok so i think i get it, volume is width*length*depth so dividing the known volume by its width gives you the length*depth.

after that set up a porportion:

(L*W)of known/92 = x/46

solve for x gives you the length*depth of the unknown volume, times that but the 46 width.. i got 60

i think that's right but im not a teacher or anything

5 0

3 years ago

Choose the equation that matches the line<br> PLZ HELP

Mars2501 [29]

Answer:

D.

Step-by-step explanation:

You would want this one because it says that y intercept and it gives the slope.

Hope this helps.

3 0

2 years ago