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3 years ago

What is the factored form of 6x2 11x – 10? (2x )( x – ).

Mathematics

1 answer:

Marina CMI [18]3 years ago

4 0

Answer:

$(2x+5)(3x-2)$

Step-by-step explanation:

Use slide-and-divide method

$6x^2+11x-10\\\\x^2+11x-60\\\\(x+15)(x-4)\\\\(2x+5)(3x-2)$

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Solve for theta in the interval 0<theta<2pi. cos(theta)sin(theta)-0.5 cos(theta)=0

riadik2000 [5.3K]

CosOsinO - 0.5 cosO = 0

cosO(sinO - 0.5) = 0

so cosO = 0 , sin O = 0.5

cosO = 0 gives O = pi/2 , 3pi/2
sinO = 0.5 gives O = pi/6, 5pi/6.

4 0

3 years ago

Read 2 more answers

A rectangular storage container with an open top is to have a volume of 10 m3 . then length of its base is twice the width. mate

katrin [286]

Answer:

The cost of materials for the cheapest such container is $163.54.

Step-by-step explanation:

A rectangular storage container with an open top is to have a volume of 10 m³.

The volume of the rectangle is

$\text{Volume} =\text{Length} \times \text{Width} \times \text{Height}$

Length of its base is twice the width.

Let Width be 'w'.

Length is l=2w.

Height be 'h'.

$10 =2w\times w\times h$

$10=2w^2h$

The height in terms of width is represented as,

$h=\frac{10}{2w^2}$

$h=\frac{5}{w^2}$

According to question,

The cost is 10 times the area of the base and 6 times the total area of the sides.

i.e. Cost is given by,

$C=10(L\times W)+6(2\times L\times H+2\times W\times H)$

$C=10(2w\times w)+6(2\times 2w\times \frac{5}{w^2}+2\times w\times \frac{5}{w^2})$

$C=20w^2+\frac{120}{w}+\frac{60}{w}$

$C(w)=20w^2+\frac{180}{w}$

To get the minimum value,

Differentiate the cost w.r.t 'w',

$C'(w)=20\frac{d(w^2)}{dw}+180\frac{d(w^{-1})}{dw}$

$C'(w)=20\times 2w-180 w^{-2}$

$C'(w)=40w-\frac{180}{w^2}$

To find critical points put derivate =0,

$40w-\frac{180}{w^2}=0$

$40w=\frac{180}{w^2}$

$w^3=\frac{180}{40}$

$w=\sqrt[3]{4.5}$

$w=1.65$

We find the second derivative to minimize,

$C''(w)=40\frac{d(w)}{dw}-180\frac{d(w^{-2})}{dw}$

$C''(w)=40+360(w^{-3})$

$C''(w)>0$

As $C''(w)>0$ it is the minimum cost.

The cost is minimum at w=1.65.

Substitute the values in the cost function,

$C(1.65)=20(1.65)^2+\frac{180}{1.65}$

$C(1.65)=54.45+109.09$

$C(1.65)=163.54$

Therefore, the cost of materials for the cheapest such container is $163.54.

7 0

3 years ago

Nothing to worry about

Darya [45]

Answer:

Your're my bestie

Crislie Mea

5 0

3 years ago

Read 2 more answers

Is this right? I feel like I’m wrong.

Arisa [49]

Answer:

no I believe you are correct

Hope This Helps! Have A Nice Day!!

4 0

4 years ago

Read 2 more answers

Stephen, Gavin and Jim share some sweets in the ratio 4:1:2. Stephen gets 30 more sweets than Jim. How many sweets are there alt

Kamila [148]

Answer:

105 sweets

Step-by-step explanation:

There are 4 + 1 + 2 = 7 parts in total

Stephen gets 4 parts (or 4x)

Jim gets gets 2 parts (or 2x)

Given,

Stephen gets 30 more than Jim, we can write:

Stephen = Jim + 30

4x = 2x + 30

We can solve for "x":

$4x = 2x + 30\\4x-2x=30\\2x=30\\x=15$

There are 7 parts of sweets altogether (or 7x), we know x so:

There are:

7 * 15 = 105 sweets altogether

7 0

3 years ago