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3 years ago

Please explain your answer step by step

Mathematics

1 answer:

shepuryov [24]3 years ago

7 0

Answer:

Step-by-step explanation:A = 30 given

C = 90 given

B = 180 -30-90 = 60 triangle angles add up to 180

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Suppose a tank contains 400 gallons of salt water. If pure water flows into the tank at the rate of 7 gallons per minute and the

Strike441 [17]

Answer:

Step-by-step explanation:

This is a differential equation problem most easily solved with an exponential decay equation of the form

$y=Ce^{kt}$ . We know that the initial amount of salt in the tank is 28 pounds, so

C = 28. Now we just need to find k.

The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is $\frac{dy}{dt}$ . Thus, the change in the concentration of salt is found in

$\frac{dy}{dt}=$ inflow of salt - outflow of salt

Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:

$3(\frac{y}{400})$

Therefore,

$\frac{dy}{dt}=0-3(\frac{y}{400})$ or just

$\frac{dy}{dt}=-\frac{3y}{400}$ and in terms of time,

$-\frac{3t}{400}$

Thus, our equation is

$y=28e^{-\frac{3t}{400}$ and filling in 16 for the number of minutes in t:

y = 24.834 pounds of salt

6 0

3 years ago

Twenty-one students in Michael classroom are wearing jeans. There are 25 students in his class. Michael says that 80% of his cla

amid [387]

No because 21 divided by 25 is .84 which is 84 percent

6 0

3 years ago

Calculate the length of AB using Sine rule

vovikov84 [41]

Answer:

Approximately $22.2\; \rm m$ .

Step-by-step explanation:

By sine rule, the length of each side of a triangle is proportional to the sine value of the angle opposite to that side. For example, in this triangle $\triangle ABC$ , angle $\angle A$ is opposite to side $BC$ , while $\angle C$ is opposite to side $AB$ . By sine rule, $\displaystyle \frac{BC}{\sin{\angle A}} = \frac{AB}{\sin \angle C}$ .

It is already given that $BC = 22.4\; \rm m$ and $\angle A = 58^\circ$ . The catch is that the value of $\angle C$ needs to be calculated from $\angle A$ and $\angle B$ .

The sum of the three internal angles of a triangle is $180^\circ$ . In $\triangle ABC$ , that means $\angle A + \angle B + \angle C = 180^\circ$ . Hence,

$\begin{aligned}\angle C &= 180^\circ - \angle A - \angle B \\ &= 180^\circ - 58^\circ - 65^\circ \\ &= 57^\circ\end{aligned}$ .

Apply the sine rule:

$\begin{aligned} & \frac{BC}{\sin{\angle A}} = \frac{AB}{\sin \angle C} \\ \implies & AB = \frac{BC}{\sin{\angle A}} \cdot \sin \angle C \end{aligned}$ .

$\begin{aligned}AB &= \frac{BC}{\sin{\angle A}} \cdot \sin \angle C \\ &= \frac{22.4\; \rm m}{\sin 58^\circ} \times \sin 57^\circ \\ &\approx 22.2\; \rm m\end{aligned}$ .

5 0

3 years ago

I NEED HELP ASAP 30 POINTS - GEOMETRY

uranmaximum [27]

Answer:

Center = (-3, 7)

radius = 5

Step-by-step explanation:

x² + y² + 6x – 14y + 33 = 0

Put the equation in standard form:

(x - h)² + (y - k)² = r²

(h, k) is the center

r is the radius

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

Regroup

x² + 6x + y² - 14y = -33

Complete the square for x

(x + 3)² + (y - 7)² = -33 + 3² + (-7)²

(x + 3)² + (y - 7)² = 25

Center = (h, k) = (-3, 7)

radius = √25 = 5

8 0

3 years ago

Alice, Ben, and Calvin are waiting at a taxi stand, since taxis are the only ride service in this town. Although they haven’t me

mr_godi [17]

Answer: $17.78; 26.67; 35.56

Step-by-step explanation:

Given the following information.:

Price of cab = $2 per mile , irrespective of the number of passengers.

Alice's destination = 20 miles

Ben's destination = 30 miles

Calvin's destination = 40 miles

If the three share a cab, the cab fee will be (cost per mile * number of miles of the farthest destination).

($2 * 40) = $80

Let price = a, for 20 miles

Ben's mile = 30 miles = 1.5 times Alice's miles, then Ben's pay = (1.5a)

Calvin's mile = 40 miles = 2 times Alice's miles, then Calvin's pay = (2a)

Thus,

a + 1.5a + 2a = $80

4.5a = $80

a = $80 / 4. 5

a = $17.78

Ben's pay = 1.5a = $26.67

Calvin's pay = 2a = $35.56

8 0

3 years ago