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3 years ago

13

A 21-foot ladder is leaning against a building. The base of the ladder is 7 feet from the base of the building.

1 answer:

vodka [1.7K]3 years ago

3 0

X - <span>the measure of the angle that the ladder makes with the ground

</span> $\cos{x}= \frac{7}{21} 
\\
\\ \cos{x}= \frac{1}{3} 
\\
\\ x=\arccos{\frac{1}{3} } \approx 71^o$ <span>
</span>

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Cory is hiking up a hill with a constant slope. The double number line shows that after Cory hikes 3 \text{ km}3 km3, start text

Andrews [41]

Answer:

The answer is "3 km ".

Step-by-step explanation:

Distance in (km): $3 \to 1$

Elevation value in (m): $120 \to 40$

$\to \frac{3}{1} = 3 \ km \\\\\to \frac{120}{40} =\frac{12}{4} = 3 \ km$

3 0

3 years ago

Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions th

trasher [3.6K]

Answer:

(a) 100 fishes

(b) t = 10: 483 fishes

t = 20: 999 fishes

t = 30: 1168 fishes

(c)

$P(\infty) = 1200$

Step-by-step explanation:

Given

$P(t) =\frac{d}{1+ke^-{ct}}$

$d = 1200\\k = 11\\c=0.2$

Solving (a): Fishes at t = 0

This gives:

$P(0) =\frac{1200}{1+11*e^-{0.2*0}}$

$P(0) =\frac{1200}{1+11*e^-{0}}$

$P(0) =\frac{1200}{1+11*1}$

$P(0) =\frac{1200}{1+11}$

$P(0) =\frac{1200}{12}$

$P(0) = 100$

Solving (a): Fishes at t = 10, 20, 30

$t = 10$

$P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483$

$t = 20$

$P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999$

$t = 30$

$P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168$

Solving (c): $\lim_{t \to \infty} P(t)$

In (b) above.

Notice that as t increases from 10 to 20 to 30, the values of $e^{-ct}$ decreases

This implies that:

${t \to \infty} = {e^{-ct} \to 0}$

So:

The value of P(t) for large values is:

$P(\infty) = \frac{1200}{1 + 11 * 0}$

$P(\infty) = \frac{1200}{1 + 0}$

$P(\infty) = \frac{1200}{1}$

$P(\infty) = 1200$

5 0

3 years ago

I’m one day, 18 people each withdrew 1000$ from an atm machine. What was the overall change in the amount of money in the atm ma

labwork [276]

Let M = amount of money in ATM at the beginning

M - 18(100) = M - 1800

The change is a decrease of $1,800

4 0

3 years ago

A store is having a sale on walnuts and chocolate chips. For 9 pounds of walnuts and 7 pounds of chocolate chips, the total cost

vfiekz [6]

Answer:

Walnuts = $1.75 per pound

Choc chips = $3.75 per pound

Step-by-step explanation:

In photo, is working out.

6 0

4 years ago

Plzz help i hav a test after i need the answer quick plzz.

Katen [24]

Answer:Oop

Step-by-step explanation:

5 0

3 years ago