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3 years ago

SOMEONE SMART PLEASE HELP ME!! a rectangle's area is 336 mm Its height is 16 mm. What is its bases?

Mathematics

1 answer:

Brums [2.3K]3 years ago

8 0

Answer:

The base of the rectangle is 21 mm.

Step-by-step explanation:

Given that a rectangle's area is 336 mm, and its height is 16 mm, to determine what is the measure of its base, the following calculation must be performed, knowing that the area of a rectangle arises from multiplying its base by its height:

16 x X = 336

X = 336/16

X = 21

Therefore, the base of the rectangle is 21 mm.

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Find all the solutions of the given equations in the interval [0,2pi) tan^3x=tanx and cos 3x=-cos3x

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$\tan^3x=\tan x$
$\tan^3x-\tan x=0$
$\tan x(\tan^2x-1)=0$
$\tan x(\tan x-1)(\tan x+1)=0$
$\begin{cases}\tan x=0\\\tan x-1=0\\\tan x+1=0\end{cases}$

$\tan x=\dfrac{\sin x}{\cos x}=0\implies \sin x=0\implies x=0,\pi$

$\tan x-1=0\iff\tan x=1\implies x=\dfrac\pi4,\dfrac{5\pi}4$

$\tan x+1=0\iff\tan x=-1\implies x=\dfrac{3\pi}4,\dfrac{7\pi}4$

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$\cos3x=-\cos3x$
$2\cos3x=0$
$\cos3x=0\implies 3x=\dfrac\pi2,3x=\dfrac{3\pi}2\implies x=\dfrac\pi6,x=\dfrac\pi2$

This doesn't account for all the solutions, however; there are some values of $x$ that push $3x$ outside the interval $[0,2\pi)$ , so let's take a few more:

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$3x=\dfrac{9\pi}2\implies x=\dfrac{9\pi}6$
$3x=\dfrac{11\pi}2\implies x=\dfrac{11\pi}6$

We can stop there, since the next candidate gives

$3x=\dfrac{13\pi}2\implies x=\dfrac{13\pi}6>2\pi$

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3 years ago

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3 years ago

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4 years ago

Ron's recycle shop had an old paper-shredding machine. Business was good, so he bought a new paper-shredding machine. The old ma

levacccp [35]

Answer: 1 hour 20 minutes

Step-by-step explanation:

Given : The old machine could shred a truckload of paper in 4 hours.

Rate of work done by old machine = $\dfrac{1}{4}$

The new machine could shred the same truckload in 2 hours.

Rate of work done by new machine = $\dfrac{1}{2}$

Let 't' be the time taken by both of them working together , then we have the following equation:-

$\dfrac{1}{t}=\dfrac{1}{4}+\dfrac{1}{2}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1+2}{4}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{3}{4}\\\\\Rightarrow t=\dfrac{4}{3}=1\dfrac{1}{3}\ \text{ hours}$

Since 1 hour = 60 minutes

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4 years ago

How do u solve this need answers

Ket [755]

By splitting the shape into a semi-circle and rectangle, we can see that we have a semi-circle with a diameter of 14 cm and a rectangle with dimensions of 28 cm by 15 cm. To find the area of the entire shape, we can add the areas of the two shapes up.

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$\dfrac{\pi (14)^2}{2} = \dfrac{196\pi}{2} = 98 \pi \,\,\textrm{cm}^2$

The formula for the area of a rectangle is $lw$ , where $l$ is the length of the rectangle and $w$ is the width. In this case, the area would be:

$(28)(15) = 420 \,\,\textrm{cm}^2$

Thus, the area of the total shape is:

$98 \pi \,\,\textrm{cm}^2+ 420 \,\,\textrm{cm}^2 \approx \boxed{727.88 \,\,\textrm{cm}^2}$

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3 years ago

SOMEONE SMART PLEASE HELP ME!! a rectangle's area is 336 mm Its height is 16 mm. What is its bases?​

SOMEONE SMART PLEASE HELP ME!! a rectangle's area is 336 mm Its height is 16 mm. What is its bases?