What is x in the expression (8x^2-2x-21)

Find the next three terms in the sequence. 3, 6, 12, 24,...

Sauron [17]

Answer:

48,96,192

Step-by-step explanation:

We see that each term is twice of the previous term. Using this principle, we get the next three terms, which are 48,96,192.

3 0

3 years ago

Giving Brainliest

Komok [63]

The dimensions of the region which enclose the maximal area will be: Length = 162 feet and Width = 108 feet.

Explanation

According to the below diagram, the total rectangular area is divided into two separate regions by a vertical segment.

Suppose, the length and width of the rectangular area are L and W respectively.

So, the length of that vertical segment will be equal to the width, W.

If the four walls of the rectangular area and the vertical segment are made up of fencing, then the total fence required feet.

Given that, the farmer has 648 feet of fencing. So, the equation will be .....

Now, the area of the rectangular area:

Substituting equation (1) into equation (2) , we will get ......

Taking derivative on the both sides of the above equation with respect to W, we will get ......

Now, A will be maximum when. So....

Plugging this into equation (1) ........

So, the dimensions of the region which enclose the maximal area will be: Length = 162 feet and Width = 108 feet.

Step-by-step explanation:

6 0

4 years ago

The sum of two numbers is 52, and the difference between the numbers is 2. Find the numbers.

geniusboy [140]

The difference between them is 2, so let the unknown numbers be x and (x+2).

Their sum is 52, so: 
52 = x + (x+2) 
52 = x + x + 2 
50 = x + x 
50 = 2x 
25 = x 

So your unknown numbers x and (x+2) are 25 and 27.

4 0

4 years ago

Figure 6 shows a semicircle PTS with center O and radius 8cm. QST is a sector of a circle with center S and R is the midpoint of

sveticcg [70]

(a) <TOR=pi/3 radians

To determine <TOR we use the fact that in the right-angled triangle ORT we know two sides:

|OT|=radius=8cm and |OR|=radius/2=4cm

and can use the sine:

$\sin \angle OTR=\frac{r/2}{r}=\frac{1}{2}\implies \angle OTR =\frac{\pi}{6}$

and since <TRO=pi/2, it must be that

$\angle TOR =\pi-\frac{\pi}{2}-\frac{\pi}{6}=\frac{\pi}{3}$

(b) The arc length is approximately 7.255 cm

In order to calculate the arc length QT, we need to first determine the length |ST| and the angle <OST.

Towards determining angle <OST:

$\angle SOT = \pi - \angle TOR = \pi - \frac{\pi}{3} = \frac{2}{3}\pi$

Next, draw a line connecting P and T. Realize that triangle PTS is right-angled with <PTS=pi/2. This follows from the Thales theorem. Since R is a midpoint between P and O, it follows that the triangles ORT and PRT are congruent. So the angles <PTR and <OTR are congruent. Knowing <PTS we can determine angle <OTS:

$\angle OTR \cong \angle PTR=\frac{\pi}{6}\implies\angle OTS=\angle PTS -\angle PTR -\angle OTR\\\angle OTS = \frac{\pi}{2}-\frac{\pi}{6}-\frac{\pi}{6}=\frac{\pi}{6}$

and so the angle <OST is

$\angle OST = \pi - \angle TOS - \angle OTS = \pi -\frac{2}{3}\pi - \frac{1}{6}\pi=\frac{\pi}{6}$

Towards determining |TS|:

Use cosine:

$\cos \angle OST =\frac{|RS|}{|ST|}\implies |ST|=\frac{\frac{3}{2}r}{\cos \frac{\pi}{6}}=\frac{12\cdot 2}{\sqrt{3}}=8\sqrt{3}cm$

Finally, we can determine the arc length QT:

$QT = {\angle OST}\cdot |ST|=\frac{\pi}{6}\cdot 8 \sqrt{3}=\frac{4\pi}{\sqrt{3}}\approx 7.255cm$

3 0

3 years ago

Which graph represents y=⌈x⌉ over the domain 3≤x≤6 ?

Nataly_w [17]

Im pretty sure the answer would be the fourth one. because a greater than or equal to. is a solid dot and just greater than is just a circle. and it get higher. so That is what im thinking the answer would be.
Hope this helps.

4 0

3 years ago

Read 2 more answers