Find the missing side length when the perimeter is 20<br>

A hole is poked in a balloon so that every minute the balloon loses 3/10ft 3 of air. What is the total change in the number of c

GaryK [48]

5/9 minutes

amount lost=times times amout lost per unit of time
amount lost=5/9 times 3/10
amount lost=15/90
amount lost=5/30
amount lost=1/6

answer is 1/6 ft³ of air

6 0

4 years ago

Ami'yan runs every day for exercise at a rate of 1 kilometer every 15 minutes. How many meters does he run in 1 hour? - Thank yo

Alona [7]

Answer:

The total distance covered in 1 hour is 4000 meters.

Step-by-step explanation:

The distance Ami'yan runs is 15 minutes = 1 kilometer

Using the unit formula,

The distance ran in 1 minute = $(\frac{1}{15} ) \textrm{Kilometer}$

Now, 1 hour = 60 minutes

⇒The distance covered in 60 minutes = 60 x (Distance run in 1 minute)

= $60 \times \frac{1}{15} = 4$

So, the distance covered in 1 hour = 4 kilometer

1 kilometer = 1000 meters

⇒ 4 km = 4 x 1000 meters = 4000 m

Hence, the total distance covered in 1 hour = 4000 meters.

6 0

3 years ago

What can you say about the y-values of the two functions f(x)=-5^x +2 and g(x)=-5x^2+2?

Kryger [21]

Answer:

B) The maximum y-value of f(x) approaches 2

C) g(x) has the largest possible y-value

Step-by-step explanation:

f(x)=-5^x+2

f(x) is an exponential function.

Lim x→∞ f(x) = Lim x→∞ (-5^x+2) = -5^(∞)+2 = -∞+2→ Lim x→∞ f(x) = -∞

Lim x→ -∞ f(x) = Lim x→ -∞ (-5^x+2) = -5^(-∞)+2 = -1/5^∞+2 = -1/∞+2 = 0+2→

Lim x→ -∞ f(x) = 2

Then the maximun y-value of f(x) approaches 2

g(x)=-5x^2+2

g(x) is a quadratic function. The graph is a parabola

g(x)=ax^2+bx+c

a=-5<0, the parabola opens downward and has a maximum value at

x=-b/(2a)

b=0

c=2

x=-0/2(-5)

x=0/10

x=0

The maximum value is at x=0:

g(0)=-5(0)^2+2=-5(0)+2=0+2→g(0)=2

The maximum value of g(x) is 2

7 0

4 years ago

A hockey team's morning workout schedule consists of 15 minutes of warm-ups, 30 minutes of weight training, and 20 minutes of ae

borishaifa [10]

Hello! The ratio would be 15 minutes warm ups: 65 minutes total workout.

To simplify this: 3:13 ratio. (Divided 15 by 5 and 65 by 5)

6 0

3 years ago

Read 2 more answers

Find the smallest 4 digit number such that when divided by 35, 42 or 63 remainder is always 5

alex41 [277]

The smallest such number is 1055.

We want to find $x$ such that

$\begin{cases}x\equiv5\pmod{35}\\x\equiv5\pmod{42}\\x\equiv5\pmod{63}\end{cases}$

The moduli are not coprime, so we expand the system as follows in preparation for using the Chinese remainder theorem.

$x\equiv5\pmod{35}\implies\begin{cases}x\equiv5\equiv0\pmod5\\x\equiv5\pmod7\end{cases}$

$x\equiv5\pmod{42}\implies\begin{cases}x\equiv5\equiv1\pmod2\\x\equiv5\equiv2\pmod3\\x\equiv5\pmod7\end{cases}$

$x\equiv5\pmod{63}\implies\begin{cases}x\equiv5\equiv2\pmod 3\\x\equiv5\pmod7\end{cases}$

Taking everything together, we end up with the system

$\begin{cases}x\equiv1\pmod2\\x\equiv2\pmod3\\x\equiv0\pmod5\\x\equiv5\pmod7\end{cases}$

Now the moduli are coprime and we can apply the CRT.

We start with

$x=3\cdot5\cdot7+2\cdot5\cdot7+2\cdot3\cdot7+2\cdot3\cdot5$

Then taken modulo 2, 3, 5, and 7, all but the first, second, third, or last (respectively) terms will vanish.

Taken modulo 2, we end up with

$x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod2$

which means the first term is fine and doesn't require adjustment.

Taken modulo 3, we have

$x\equiv2\cdot5\cdot7\equiv70\equiv1\pmod3$

We want a remainder of 2, so we just need to multiply the second term by 2.

Taken modulo 5, we have

$x\equiv2\cdot3\cdot7\equiv42\equiv2\pmod5$

We want a remainder of 0, so we can just multiply this term by 0.

Taken modulo 7, we have

$x\equiv2\cdot3\cdot5\equiv30\equiv2\pmod7$

We want a remainder of 5, so we multiply by the inverse of 2 modulo 7, then by 5. Since $2\cdot4\equiv8\equiv1\pmod7$ , the inverse of 2 is 4.

So, we have to adjust $x$ to

$x=3\cdot5\cdot7+2^2\cdot5\cdot7+0+2^3\cdot3\cdot5^2=845$

and from the CRT we find

$x\equiv845\pmod2\cdot3\cdot5\cdot7\implies x\equiv5\pmod{210}$

so that the general solution $x=210n+5$ for all integers $n$ .

We want a 4 digit solution, so we want

$210n+5\ge1000\implies210n\ge995\implies n\ge\dfrac{995}{210}\approx4.7\implies n=5$

which gives $x=210\cdot5+5=1055$ .

5 0

3 years ago

Find the missing side length when the perimeter is 20​

Find the missing side length when the perimeter is 20