.125 as a fraction .

Explain how you would round the number 33 and 89 estimate their sum

Brrunno [24]

I am assuming that we have to round the numbers to the nearest tens.
When rounding off numbers, if the number is more than half, then you round it up for example, if the number is 15 and you want to round it off, you round it up to 20. But if the number is 14 you round is down to 10

Therefore, 33 would be rounded off to 30 as 3 is less than 5 in the ones place if you get what I mean.

As for 89, you would round it up to 90 as the 9 in the ones place is more than 5.

Therefore the sum of 90 and 10 is 100.

Hope this helps!

8 0

3 years ago

Find the absolute maximum and minimum values of the following function on the given interval. If there are multiple points in a

Bond [772]

$f(x)=3\sin x+3\cos x\implies f'(x)=3\cos x-3\sin x$

$f$ has critical points where $f'=0$ :

$3\cos x-3\sin x=0\implies\cos x=\sin x\implies\tan x=1\implies x=\pm\dfrac\pi4+2n\pi$

where $n$ is any integer. We get solutions in the interval $\left[0,\frac\pi3\right]$ for $n=0$ , for which $x=\frac\pi4$ .

At this critical point, we have $f\left(\frac\pi4\right)=3\sqrt2\approx4.243$ .

At the endpoints of the given interval, we have $f(0)=3$ and $f\left(\frac\pi3\right)=\frac{3+3\sqrt3}2\approx4.098$ .

So we have the extreme values

$\max\limits_{x\in\left[0,\frac\pi3\right]}f=3\sqrt2$

$\min\limits_{x\in\left[0,\frac\pi3\right]}f=3$

8 0

3 years ago

Mia found the area of a polygon The area is 32 square cm.

solniwko [45]

Answer:

Only the isosceles trapezoid has an area of 32 cm².

Step-by-step explanation:

Let's calculate the area of each polygon.

For the two triangles we have:

$A_{t} = \frac{bh}{2} = \frac{2 cm*4 cm}{2} = 4 cm^{2}$

This polygon does not have an area of 32 cm².

For the rectangle we have:

$A_{r} = bh = 6 cm*4 cm = 24 cm^{2}$

This polygon does not have an area of 32 cm².

For the rectangle trapezoid we have:

$A_{rt} = A_{t} + A_{r} = (4 + 24) cm^{2} = 28 cm^{2}$

So, this polygon does not have an area of 32 cm².

Finally, for the isosceles trapezoid:

$A_{it} = A_{t}*2 + A_{r} = (4*2 + 24) cm^{2} = 32 cm^{2}$

This polygon does have an area of 32 cm².

Therefore, only the isosceles trapezoid has an area of 32 cm².

I hope it helps you!

8 0

3 years ago

A motorcycle zoomed along the freeway, traveling 10 meters in 1/3 of a second . How fast was it going ?

Aleks04 [339]

Answer:

30m/sec

Step-by-step explanation:

v=s/t

given s= 10m

t=1/3 sec

v= 10/(1/3)=10×3/1= 30 m/s

8 0

4 years ago

Read 2 more answers

Show that cos(3x) = cos3(x) − 3 sin2(x)cos(x). (Hint: Use cos(2x) = cos2(x) − sin2(x) and the cosine sum

otez555 [7]

<u>Step-by-step explanation:</u>

To prove:

$\cos 3x=\cos^3x-3\sin^2 x\cos x$

Identities used:

$\cos(A+B)=\cos A\cos B+\sin A\sin B$ ......(1)

$\sin 2A=2\sin A\cos A$ ........(2)

$\cos 2A=\cos^2A-\sin^2 A$ .......(3)

Taking the LHS:

$\Rightarrow \cos 3x=\cos (x+2x)$

Using identity 1:

$\Rightarrow \cos (x+2x)=\cos x\cos 2x-\sin x\sin 2x$

Using identities 2 and 3:

$\Rightarrow \cos x(\cos ^2x-\sin^2 x)-\sin x(2\sin x\cos x)\\\\\Rightarrow \cos^3x-\sin^2x\cos x-2\sin^2 x\cos x\\\\\Rightarrow \cos^3x-3\sin^2x\cos x$

As, LHS = RHS

Hence proved

4 0

3 years ago