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3 years ago

15

Carpeting costs $20 per square yard. You carpet a room that has a width of 15 feet for $800. What is the length of the room in f

eet?

1 answer:

mixer [17]3 years ago

3 0

800/$20 per square yard= 40 sq yards
15ft=5 yards
40 sq yds/5 yards= 8 yards or 24 feet
length= 24 feet or 8 yards

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In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track

Aloiza [94]

Answer:

Approximately $0.31\; \rm m$ , assuming that $g = 9.81\; \rm N \cdot kg^{-1}$ .

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

$\begin{aligned}\text{KE} &= \frac{1}{2}\, m \cdot v^{2} \\ &= \frac{1}{2} \times 14\; \rm kg \times (3.0\; \rm m\cdot s^{-1})^{2} \\ &= 63\; \rm J\end{aligned}$ .

Weight of the slide:

$\begin{aligned}W &= m \cdot g \\ &= 14\; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \\ &\approx 137\; \rm N\end{aligned}$ .

Normal force between the sled and the slope:

$\begin{aligned}F_{\rm N} &= W\cdot \cos(22^{\circ}) \\ &\approx 137\; \rm N \times \cos(22^{\circ}) \\ &\approx 127\; \rm N\end{aligned}$ .

Calculate the kinetic friction between the sled and the slope:

$\begin{aligned} f &= \mu_{k} \cdot F_{\rm N} \\ &\approx 0.20\times 127\; \rm N \\ &\approx 25.5\; \rm N\end{aligned}$ .

Assume that the sled and its passenger has reached a height of $h$ meters relative to the base of the slope.

Gain in gravitational potential energy:

$\begin{aligned}\text{GPE} &= m \cdot g \cdot (h\; {\rm m}) \\ &\approx 14\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times h\; {\rm m} \\ & \approx (137\, h)\; {\rm J} \end{aligned}$ .

Distance travelled along the slope:

$\begin{aligned}x &= \frac{h}{\sin(22^{\circ})} \\ &\approx \frac{h\; \rm m}{0.375}\end{aligned}$ .

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

$\begin{aligned} & - (-x)\, f \\ = \; & x \cdot f \\ \approx \; & \frac{h\; {\rm m}}{0.375}\times 25.5\; {\rm N} \\ \approx\; & (68.1\, h)\; {\rm J}\end{aligned}$ .

In other words, the sled and its passenger would have lost (approximately) $((137 + 68.1)\, h)\; {\rm J}$ of energy when it is at a height of $h\; {\rm m}$ .

The initial amount of energy that the sled and its passenger possessed was $\text{KE} = 63\; {\rm J}$ . All that much energy would have been converted when the sled is at its maximum height. Therefore, when $h\; {\rm m}$ is the maximum height of the sled, the following equation would hold.

$((137 + 68.1)\, h)\; {\rm J} = 63\; {\rm J}$ .

Solve for $h$ :

$(137 + 68.1)\, h = 63$ .

$\begin{aligned} h &= \frac{63}{137 + 68.1} \approx 0.31\; \rm m\end{aligned}$ .

Therefore, the maximum height that this sled would reach would be approximately $0.31\; \rm m$ .

7 0

3 years ago

20 POINTS HELPPPPP

kiruha [24]

For this case we have the following expression:

$\frac {216 ^ {n-2}} {(\frac {1} {36}) ^ {3n}} = 216$

We multiply both sides by: $(\frac {1} {36}) ^ {3n}$

$216 ^ {n-2} = 216 * (\frac {1} {36}) ^ {3n}$

We divide both sides by 216:

$\frac {216 ^ {n-2}} {216} = (\frac {1} {36}) ^ {3n}$

To divide powers of the same base, we place the same base and subtract the exponents:

$216 ^ {n-2-1} = (\frac {1} {36}) ^ {3n}\\216 ^ {n-3} = (\frac {1} {36}) ^ {3n}$

Rewriting:

$(6 ^ 3) ^ {n-3} = (\frac {1} {6 ^ 2}) ^ {3n}\\6 ^ {3n-9} = \frac {1} {6 ^ {6n}}\\6^{ 3n-9} * 6^{ 6n} = 1$

To multiply powers of the same base, we place the same base and add the exponents:

$6^{ 3n-9 + 6n} = 1\\6^{ 9n-9} = 1$

We know that any number raised to zero is 1, $a ^ 0 = 1.$

So, for equality to be true:

$9n-9 = 0\\9n = 9\\n = \frac {9} {9}\\n = 1$

Answer:

$n = 1$

3 0

3 years ago

Read 2 more answers

Which measurement is equivalent to 850 mg?

stepladder [879]

Answer:

0.00187393

Hope this helps! :)

Please mark me the Brainliest!

6 0

3 years ago

ALGEBRA II HELP :/

elena-14-01-66 [18.8K]

Answer:

18

Step-by-step explanation:

f(x) = x³+4x²-8x-6

P(a) <=> P(x)

-2 | 1 4 -8 -6

|

| -2 -4 24

----------------------------

1 2 -12 18

4 0

3 years ago

Find the next term is in the explicit and recursive rule for the in term of the sequence. NO LINKS!!!

BARSIC [14]

9514 1404 393

Answer:

5) 729, an=3^n, a[1]=3; a[n]=3·a[n-1]

6) 1792, an=7(4^(n-1)), a[1]=7; a[n]=4·a[n-1]

Step-by-step explanation:

The next term of a geometric sequence is the last term multiplied by the common ratio. (This is the basis of the recursive formula.)

The Explicit Rule is ...

$a_n=a_1\cdot r^{n-1}$

for first term a₁ and common ratio r.

The Recursive Rule is ...

a[1] = a₁

a[n] = r·a[n-1]

__

5. First term is a₁ = 3; common ratio is r = 9/3 = 3.

Next term: 243×3 = 729

Explicit rule: an = 3·3^(n-1) = 3^n

Recursive rule: a[1] = 3; a[n] = 3·a[n-1]

__

6. First term is a₁ = 7; common ratio is r = 28/7 = 4.

Next term: 448×4 = 1792

Explicit rule: an = 7·4^(n-1)

Recursive rule: a[1] = 7; a[n] = 4·a[n-1]

7 0

3 years ago