Solve. Okay here is 20 letters brainy

Mathematics

1 answer:

juin [17]3 years ago

6 0

Answer:

-12

Step-by-step explanation:

4 1/2 - 5 1/8 = -0.625

7.5 x -0.625 = -12

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A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min

sesenic [268]

$A'(t)=(\text{flow rate in})(\text{inflow concentration})-(\text{flow rate out})(\text{outflow concentration})$
$\implies A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\left(2+\sin\dfrac t4\right)\dfrac{\text{lb}}{\text{gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}$
$A'(t)+\dfrac1{100}A(t)=6+3\sin\dfrac t4$

We're given that $A(0)=30$ . Multiply both sides by the integrating factor $e^{t/100}$ , then

$e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$\left(e^{t/100}A(t)\right)'=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$e^{t/100}A(t)=600e^{t/100}-\dfrac{150}{313}e^{t/100}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+C$
$A(t)=600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+Ce^{-t/100}$

Given that $A(0)=30$ , we have

$30=600-\dfrac{150}{313}\cdot25+C\implies C=-\dfrac{174660}{313}\approx-558.02$

so the amount of salt in the tank at time $t$ is

$A(t)\approx600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)-558.02e^{-t/100}$

3 0

3 years ago

What is the sum of the interior angles, each interior angle, the central angle, and each exterior angle of a pentagon, a hexagon

WITCHER [35]

Sum of Interior Angles: Formula: (n-2) * 180
-Pentagon: 540°
-Hexagon: 720°
-Octagon: 900°
-Nonagon: 1260°
-Decagon: 1440°
-Dodecagon: 1800°

Each interior Angle: Formula: [(n-2)*180] / n
-Pentagon: 108°
-Hexagon: 120°
-Octagon: 135°
-Nonagon: 140°
-Decagon: 144°
-Dodecagon: 150°

The sum of the exterior angles of each polygon stated above is equal to 360 degrees. Using the formula: (180-interior angle) * n

The central angle is formed by making a circle in the middle and divide it by the number of sides. Therefore, CA = 360 /n
-Pentagon: 72°
-Hexagon: 60°
-Octagon: 45°
-Nonagon: 40°
-Decagon: 36°
-Dodecagon: 30°

3 0

3 years ago

In 47,201 what digit tells the number of thousand

Rudiy27

Answer: The 7

Step-by-step explanation:

5 0

2 years ago

Write this number in word form 84,052

DENIUS [597]

Eighty-four thousand fifty-two

3 0