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vekshin1
3 years ago
14

How do you factor by grouping if the question is 2p^3+5p^2+6p+15?​

Mathematics
1 answer:
Inga [223]3 years ago
5 0

Answer:

(2p + 5)(p² + 3)

Step-by-step explanation:

2p³ + 5p² + 6p + 15

take out factor p²

p² × (2p + 5) + 6p + 15

p² × (2p + 5) + 3 (2p + 5)

= (2p + 5)(p² + 3)

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Max spends three times as long on his math homework than he does on his science homework
iren [92.7K]
Answer: Max is a very intelligent boy.
6 0
3 years ago
Read 2 more answers
A rectangular storage container with a lid is to have a volume of 2 m3. The length of its base is twice the width. Material for
Scilla [17]

Answer:

Dimensions are 2 m by 1 meter by 1 meter,

Minimum cost is $ 18.

Step-by-step explanation:

Let w be the width ( in meters ) of the container,

Since, the length is twice of the width,

So, length of the container = 2w,

Now, if h be the height of the container,

Volume = length × width × height

2 = 2w × w × h

1 = w² × h

\implies h=\frac{1}{w^2}

Since, the area of the base = l × w = 2w × w = 2w²,

Area of the lid = l × w = 2w²,

While the area of the sides = 2hw + 2hl

= 2h( w + l)

= 2\times \frac{1}{w^2}(w+2w)

=\frac{6w}{w^2}

=\frac{6}{w}  

Since, Material for the base costs $1 per m². Material for the sides and lid costs $2 per m²,

So, the total cost,

C(w) = 1\times 2w^2+2\times 2w^2 + 2\times \frac{6}{w}

=2w^2+4w^2+\frac{12}{w}

=6w^2+\frac{12}{w}

Differentiating with respect to w,

C'(w) = 12w -\frac{12}{w^2}

Again differentiating with respect to w,

C''(w) = 12 + \frac{24}{w^3}

For maxima or minima,

C'(w) = 0

\implies 12w -\frac{12}{w^2}=0

\implies 12w^3 - 12=0

w^3-1=0\implies w = 1

For w = 1, C''(w) = positive,

Hence, for width 1 m the cost is minimum,

Therefore, the minimum cost is C(1) = 6(1)²+12 = $ 18,

And, the dimension for which the cost is minimum is,

2 m by 1 meter by 1 meter.

7 0
3 years ago
The three numbers are in the ratio 2 : 3 : 4 and the sum of their cubes 12375
larisa86 [58]
Let us take each number as x = 2x , 3x,  4x 
(2x)³+(3x)³+(4x)³=12375
8x³+27x³+64x³=12375
99x³=12375
x³=12375/99 
  =125
x =∛125
x=5
2x=2×5=10
3x=3×5=15
4x=4×5=20

therefore, the three numbers are 10,15 and 20 .....

Hope it helps !!
7 0
3 years ago
Help help help plssssss
Novay_Z [31]

Answer:

SA = 108π cm²

Step-by-step explanation:

The surface area (SA) of a sphere is calculated as

SA = 4πr² ( r is the radius )

Thus the SA of a hemisphere is

SA = \frac{1}{2} × 4πr² = 2πr²

The area of the circular base = πr²

Then total SA is

SA = 2πr² + πr² = 3πr² = 3π × 6² = 3π × 36 = 108π cm²

5 0
3 years ago
Find the height of a cuboid whose volume is 540cu.cm and base area is 90sq.cm
grandymaker [24]

Answer:

6 cm

Step-by-step explanation:

Vcuboid  = lwh

⇒ h = Vcuboid ÷ lw

∴  h = 540 cm³ ÷ 90 cm²

⇒ h = 6 cm

6 0
2 years ago
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