What is the approximate radius of a sphere with a volume of 900 cm^3?

0 A pigeon can fly at a speed of 84 kilometers per hour. How long does it take the pigeon to fly 7 kilometers

QveST [7]

The miles per hour is 84 kilometers per 60 minutes (7:5 ratio) so if we take seven kilometers times the ratio 5/7 we get 5 minutes

7 0

3 years ago

the density of a certain material is such that weighs 6900 grams for every 4.5 quarts of volume express this density in pounds p

dlinn [17]

Answer:

$d=101.4\ \text{pounds}/\text{feet}^3$

Step-by-step explanation:

Given that,

Mass of material, m = 6900 grams

Volume of the material, V = 4.5 quarts

We need to find the density in pounds per cubic foot

We know that,

1 pound = 453.59 grams

⇒ 6900 grams = 15.21 pounds

Also, 1 cubic foot = 29.92 quarts

4.5 quart = 0.15 feet³

Density = mass/volume

Or

$d=\dfrac{15.21\ \text{pounds}}{0.15\ \text{feet}^3}\\\\d=101.4\ \text{pounds}/\text{feet}^3$

Hence, the density of the material is $101.4\ \text{pounds}/\text{feet}^3$

3 0

3 years ago

‘write an equation of the line that passes through each pair of points’ (1,2) and (4,8)

Levart [38]

Hi there!

Step-by-step explanation:

$Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}$

$\frac{8-2}{4-1}=\frac{6}{3}=2$

So therefore, the slope is 2.

Final answer is 2.

*The answer must have a positive sign.*

I hope this helps you!

Have a nice day! :)

-Charlie

:D

8 0

3 years ago

Does there exist a di↵erentiable function g : [0, 1] R such that g'(x) = f(x) for all x 2 [0, 1]? Justify your answer

agasfer [191]

Answer:

No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Step-by-step explanation:

Assuming: the function is $f(x)=x^{2}$ in [0,1]

And rewriting it for the sake of clarity:

Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer

1) A function is considered to be differentiable if, and only if both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:

$g'(0)=g'(1)$

2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]

The limit to the left

$g(x)=x^{2}\\g'(x)=2x\\ g'(0)=2(0) \Rightarrow g'(0)=0$

$g(x)=x^{2}\\g'(x)=2x\\ g'(1)=2(1) \Rightarrow g'(1)=2$

g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)

3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Because this is the same as to calculate the limit from the left and right side, of g(x).

$f'(c)=\lim_{x\rightarrow c}\left [\frac{f(b)-f(a)}{b-a} \right ]\\\\g'(0)=\lim_{x\rightarrow 0}\left [\frac{g(b)-g(a)}{b-a} \right ]\\\\g'(1)=\lim_{x\rightarrow 1}\left [\frac{g(b)-g(a)}{b-a} \right ]$

This is what the Bilateral Theorem says:

$\lim_{x\rightarrow c^{-}}f(x)=L\Leftrightarrow \lim_{x\rightarrow c^{+}}f(x)=L\:and\:\lim_{x\rightarrow c^{-}}f(x)=L$

4 0

3 years ago

Maria has a collection of 40 baseball cards, of which x cards are damaged. The value of each undamaged card is 5 dollars and the

hodyreva [135]

(40 - x) represents A. the number of undamaged cards

Step-by-step explanation:

Step 1; Maria has a total of 40 cards out of which x number of cards are damaged so 40 - x cards are undamaged. The value of an undamaged card is 5 dollars whereas every damaged card has a value of 3 dollars.

Step 2; We need to determine what each term in equation 5(40−x)+3x represents. The equation will give us how much total value Maria's card collection has.

The first term 5 (40 - x) signifies the total value of the undamaged cards in the deck where (40 - x) equals the total number of undamaged cards.

The second term represents the total value of the undamaged cards.

So the second factor of the first term i.e (40 - x) represents the amount of undamaged cards in her collection.

7 0

3 years ago