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4 years ago

Quiz

Mathematics

1 answer:

valina [46]4 years ago

4 0

Answer:

Step-by-step explanation:

As we know that in an hour there are 3600 seconds so

1.8 x 3600 = 6480

6480 / 1609 = 4.02 miles / hr

4.02 - 2.5 = 1.5( by substracting the speed)

so correct option is D which is

Talia swims about 1.5 miles per hour faster than Alina

hope it helps

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This is due tonight pls

Anettt [7]

Answer:

I think it's A.3

Step-by-step explanation:

if you didvide the 7.8 by 2.6 then you will get 3, therfore you will have to multiply the original (2.6) times 3 in order to get the scaled image (7.8).

7 0

3 years ago

Read 2 more answers

A rectangular box with a volume of 684 ftcubed is to be constructed with a square base and top. The cost per square foot for the

SCORPION-xisa [38]

Answer:

The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.

Minimum cost=2046.16 cents

Step-by-step explanation:

Given that a rectangular box with a volume of 684 ft³.

The base and the top of the rectangular box is square in shape

Let the length and width of the rectangular box be x.

[since the base is square in shape, length=width]

and the height of the rectangular box be h.

The volume of rectangular box is = Length ×width × height

=(x²h) ft³

$x^2h=684\Rightarrow h=\frac{684}{x^2}$ (1)

The area of the base and top of rectangular box is = x² ft²

The surface area of the sides= 2(length+width) height

=2(x+x)h

=4xh ft²

The total cost to construct the rectangular box is

=[(x²×20)+(x²×15)+(4xh×1.5)] cents

=(20x²+15x²+6xh) cents

=(25x²+6xh) cents

Total cost= C(x).

C(x) is in cents.

∴C(x)=25x²+6xh

Putting $h=\frac{684}{x^2}$

$C(x)=25x^2+6x\times\frac{684}{x^2} \Rightarrow C(x)=25x^2+\frac{4104}{x}$

Differentiating with respect to x

$C'(x)=50x-\frac{4104}{x^2}$

To find minimum cost, we set C'(x)=0

$\therefore50x-\frac{4104}{x^2}=0\\\Rightarrow50x=\frac{4104}{x^2}\\\Rightarrow x^3=\frac{4104}{50}\Rightarrow x\approx 4.345$ ft.

Putting the value x in equation (1) we get

$h=\frac{684}{(4.345)^2}$

≈36.23 ft.

The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.

Minimum cost C(x)=[25(4.345)²+10(4.345)(36.23)] cents

=2046.16 cents

5 0

3 years ago

Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more

dalvyx [7]

The power series is

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence

The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.

Its radius of convergence is 0.5

Let,

f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....

The power series expansion (geometric series),

valid for I2xI < 1 , IxI < 0.5

so, radius of convergence = 0.5

The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5

Now, g(x) = ln(1-2x)

= -2 $\int\limits^a_b {(1/1-2x)} \, dx = -2 \int\limits^a_b {f(x)} \, dx$