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3 years ago

5

The first two terms of a sequence are A1 equals 3 and A2 equals -12. Let A3 be the third term when the sequence is arithmetic an

d let it B3 you search someone the sequence is geometric.

1 answer:

Alex Ar [27]3 years ago

4 0

Answer:

e

Step-by-step explanation:

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A cardboard box without a lid is to have a volume of 19,652 cm3. Find the dimensions that minimize the amount of cardboard used.

Effectus [21]

Answer:

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

Step-by-step explanation:

Let the dimension of the cardboard box be x cm by y cm by z cm.

The surface area of the cardboard box without lid is

f(x,y,z)= xy+2xz+2yz.....(1)

Given that the volume of the cardboard is 19,652 cm³.

Therefore xyz =19,652

$\Rightarrow z=\frac{19652}{xy}$ ......(2)

putting the value of z in the equation (1)

$f(x,y)=xy+2x(\frac{19652}{xy})+2y(\frac{19652}{xy})$

$\Rightarrow f(x,y)=xy+\frac{39304}{y})+\frac{39304}{x}$

The partial derivatives are

$f_x=y-\frac{39304}{x^2}$

$f_y=x-\frac{39304}{y^2}$

To find the dimension of the box set the partial derivatives $f_x=0$ and $f_y=0$ .Therefore $y-\frac{39304}{x^2}=0$

$\Rightarrow y=\frac{39304}{x^2}$ .......(3)

and $x-\frac{39304}{y^2}=0$

$\Rightarrow x=\frac{39304}{y^2}$ .......(4)

Now putting the x in equation (3)

$y =\frac {39304}{(\frac{39304}{y^2})^2}$

$\Rightarrow y=\frac{y^4}{39304}$

$\Rightarrow y^3= 39304$

⇒y=34 cm

Then $\Rightarrow x=\frac{39304}{34^2}$ =34 cm.

Putting the value of x and y in the equation (2)

$z=\frac{19652}{34 \times 24}$

=17 cm.

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

4 0

3 years ago

72 ounces in 6 steaks

Alona [7]

The unit rate is the total ounces divided by the total number of steaks:

72 ounces / 6 steaks = 12 ounces per steak.

3 0

3 years ago

Which of the following numbers are greater than or equal to 4/7<br> A. 2/5<br> B. 0.57<br> C. 2/3

Bumek [7]

Answer:

B.

Step-by-step explanation:

If you were to divide 4 by 7, you would get a decimal that would be rounded up to that value. 2/3 is roughly .66 and 2/5 is .4.

6 0

3 years ago

What’s the answer to this please? Thank u!

masya89 [10]

Answer:

I think the answer is C.

Step-by-step explanation:

Have a good day ;-).

6 0

2 years ago

If the mean of 10 numbers is 45, what is their sum?

Yakvenalex [24]

55hhjgsgjhsfjbnjccdbgjhsdsghjkdss

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3 years ago