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3 years ago

Between which two natural numbers is 37 ?

Mathematics

1 answer:

Andru [333]3 years ago

6 0

Answer:

Step-by-step explanation:

The answer is b.

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The sum of 6 times a position number and 1 is the same as the sauare of 1 less than the number

stepan [7]

If the number is x, then:
6x+1= (x-1)^2

Now we just need to simplify it
6x+1=(x-1)*(x-1)
6x+1=x^2-2x+1
8x=x^2
8=x

The number is 8.

To check the answer
6*8+1=7^2
49=49
correct :)

5 0

3 years ago

Express the fractions 3/4 ,7/16 and 5/8 with the lowest common denominator

xxTIMURxx [149]

3/4, 7/16, 5/8.....LCD = 16

3/4 = 12/16
7/16
5/8 = 10/16

4 0

3 years ago

The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

6 0

3 years ago

A rectangular prism has a length of 1/1/4 yards, a width of 2/1/2 yards, and a height of 4 yards. Enter the volume of the prism

dmitriy555 [2]

Prism volume = lbh

= 10*8*12

= 960cm^3

Note: I'm assuming the hole was cut right through it...

Hole volume = lbh

= 2*3*12

= 72cm^3

Final volume = 960 - 72 = 888cm^3

7 0

3 years ago

What is the median of this set of data? 362,187,211,298,331,250,347,199

AVprozaik [17]

Answer:

250

Step-by-step explanation:

Line it up least to greatest

187,199,211,250,298,347,362

Cut each one off at each ends until middle

250

6 0

3 years ago