All categories

3 years ago

Subtract and simplify 1/6m - (- 5/8m + 1/3)

Mathematics

1 answer:

ratelena [41]3 years ago

4 0

Answer:

19/24m-1/3

Step-by-step explanation:

1/6m-(-5/8m+1/3)=1/6m+5/8m-1/3=4/24m+15/24m-1/3=19/24m-1/3

You might be interested in

Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12cm3/s . if the radius of the funnel is 8

Bezzdna [24]

Answer:

h ≅ 16.29 cm

$\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}$

Step-by-step explanation:

From the conical funnel;

Let the adjacent line at the base of the cone be radius (r) and the opposite ( vertical length) be the height (h)

Then;

$tan \theta= \dfrac{r}{h}$

$tan \theta= \dfrac{8}{16}$

$tan \theta= \dfrac{1}{2}$

∴

$\dfrac{r}{h} = \dfrac{1}{2}$

$r = \dfrac{h}{2}$

The volume (V) of the cone is expressed as:

$V = \dfrac{1}{3}\pi r ^2 h$

$V = \dfrac{1}{3}\pi (\dfrac{h}{2})^2 h$

$V = \dfrac{\pi h^3}{3\times 4}$

$\dfrac{dv}{dt} = \dfrac{3 \pi h^2}{3 \times 4} \dfrac{dh}{dt}$

$\dfrac{dv}{dt} = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}$

Given that:

$\dfrac{dv}{dt} = 12 \pi$

Then:

$-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}$

$- \int 48 \ dt = \int h^2 \ dh$

$\dfrac{h^3}{3}= -48 t + c$

$At \ t = 0 \ ; h = 0$

∴

$\dfrac{0^3}{3} = -48(0) + c$

c = 0

So;

$\dfrac{h^3}{3}= -48 t + 0$

$\dfrac{h^3}{3}= -48 t$

t = 30

$\implies h = (-48(30))^{1/3}$

h = 16.2865

h ≅ 16.29 cm

Thus;

from $-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}$

$\dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} } =\dfrac{dh}{dt}$

$\dfrac{dh}{dt} = \dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} }$

$\dfrac{dh}{dt}=\dfrac{-12 \times 4} { {16.29^2} }$

$\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}$

7 0

3 years ago

What is the domain of the function f(x)=x+3

PolarNik [594]

There are no restrictions on the values x can and can’t be, so in this case, your domain would be the set of all real numbers.

3 0

3 years ago

What is the true solution to 2 In e in5x = 2 In 15?

just olya [345]

Answer:

x = 3

Step-by-step explanation:

Using the rules of logarithms

ln x = ln y ⇒ x = y

ln e = 1

Given

2 ln e ln 5x = 2 ln 15 ( divide both sides by 2 )

ln e ln 5x = ln 15

ln 5x = ln 15, hence

5x = 15 ( divide both sides by 5 )

x = 3

5 0

3 years ago

Read 2 more answers

PLEASE HELP ME

VladimirAG [237]

The value of x is 11.

Solution:

JH is a midsegment of the triangle KLM.

LM = 22

JH = x

To find the value of x.

<u>Mid-segment theorem:</u>

<em>The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side.</em>

By the mid-segment theorem,

JH = Half of LM

$$x=\frac{1}{2} LM$

$$x=\frac{1}{2} \times 22$

x = 11

The value of x is 11.

7 0

3 years ago

Omar wrote 3 + ( 4 × 6 ) to represent the phrase "3 more then the product of 4 and 6." Did Omar need to use a grouping symbol? E

valentina_108 [34]

The order of operations is PEMDAS (parenthesis, exponents, multiplication/division, addition/subtraction). This means that you do multiplication before adding, so 3 + 4*6 is the same thing as 3 + (4*6). Because of this, Omar did not need to use a grouping symbol.

8 0

3 years ago

Read 2 more answers