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3 years ago

A cube with the side length of 4 inches has a volume of _____ cubic inches.

Mathematics

1 answer:

fenix001 [56]3 years ago

7 0

Answer:

64 cubic inches

Step-by-step explanation:

$volume \: of \: cube \\ = {4}^{3} \\ = 64 \: {inche}^{3} \\$

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Simplify your answer as much as possible. 3/x-4/7

Natasha2012 [34]

Answer:

That is ur answer. I was unable to type that so I use took a screenshooton my phone .

Step-by-step explanation:

5 0

3 years ago

Sven starts walking due south at 6 feet per second from a point 140 feet north of an intersection. At the same time Rudyard star

Vsevolod [243]

Answer:

a) y= y₀+vy*t , x= x₀+vx*t

b) they are closest at t= 29.23 s

c) r min = 63.79 ft

Step-by-step explanation:

a) denoting v as velocities and "₀" as initial conditions , then the position of Sven is given by the coordinate (0,y) where

y= y₀+vy*t

and the position of Rudyard is given by the coordinate (x,0) where

x= x₀+vx*t

b) the distance r between Sven and Rudyard is given by

r²=x²+y²

the distance will be minimum when the derivative of r with respect to the time is 0 . Then taking the derivative of the equation above

2*r*dr/dt = 2*x*dx/dt + 2*y*dy/dt

since dx/dt= vx and dy/dt= vy , then

r*dr/dt = x*vx+ y*vy

dr/dt = (x*vx+ y*vy)/r

assuming that r cannot be 0 , then

dr/dt =0 → x*vx+ y*vy = 0

(x₀+vx*t)*vx + (y₀+vy*t)*vy = 0

-(x₀*vx + y₀*vy) = (vx²+vy²)*t

t= -(x₀*vx + y₀*vy)/(vx²+vy²)

replacing values

t= -(x₀*vx + y₀*vy)/(vx²+vy²) = -[ 140 ft*(-6ft/s) + (-170 ft)*4 ft/s]/[ (-6ft/s)²+ (4 ft/s)²] = 29.23 s

then they are closest at t= 29.23 s

and the minimum distance will be

x = x₀ + vx*t = 140 ft+(-6ft/s)*29.23 s = -35.38 ft

y= y₀+vy*t = (-170 ft)+ 4 ft/s*29.23 s = -53.08 ft

r min = √(x²+y²)= 63.79 ft

r min = 63.79 ft

Note

to prove our assumption that r is not 0 , then x and y should be 0 at the same time. thus

0= y₀+vy*t → t = (-y₀)/vy = -140 ft/(-6ft/s) = 26.33 s

0= x₀+vx*t → t= (-x₀)/vx = -(-170 ft)/4 ft/s = 42.5 s

then r is never 0

8 0

3 years ago

Sara has $150 in her savings account. The amount in her account increases by %6 every year. If she does not put more money into

strojnjashka [21]

Answer:

$159

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

$y=a(1+r)^x$

where

y is the balance in the saving account

x is the number of years

a is the initial amount

r is the percent rate of change

we have

$a=\$150\\r=6\%=6/100=0.06$

substitute

$y=150(1+0.06)^x$

$y=150(1.06)^x$

For x= 1 year

substitute

$y=150(1.06)^1=\$159$

3 0

4 years ago

Please put the correct answer thank you :)

MatroZZZ [7]

Answer:

The answer to your question is: letter D

Step-by-step explanation:

Data

f(x) = x³ - 9x

g(x) = x² - 2x - 3

Process

$\frac{x^{3}- 9x }{x^{2} - 2x - 3}$

Factor both numerator and denominator

$\frac{x(x^{2}-9) }{x^{2} - 2x - 3} = \frac{x(x + 3)(x-3)}{(x - 3)(x + 1)}$

Simplification

$\frac{x(x + 3)}{(x + 1)}$

7 0

3 years ago

How much fencing is needed to enclose a circular pond with diameter 12.5 feet? A. 37.5 feet B. 19.625feet C. 98.5feet D. 39.25fe

Dima020 [189]

Answer:

c=pi x d

3.14x12.5

d is the answer

Step-by-step explanation:

3 0

4 years ago