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Ahat [919]
3 years ago
14

You are in a panic! You forgot to buy your little brother a birthday present. You start with $60 in your wallet. You buy him sev

eral toys, t, that are $5 each. You know have $45 leftover. How many toys did you buy your little brother for his birthday? (set up the equation)
Mathematics
1 answer:
MAVERICK [17]3 years ago
3 0

Answer: 3 toys

Step-by-step explanation:

equation will be 60 - 5 x t = 45

solving it we get

5 x t = 60 - 45 = 15

=> t = 15/5 = 3

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A tank contains 3,000 L of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 30 L/min. The solution is
Shalnov [3]

Answer:

Step-by-step explanation:

Volume of tank is 3000L.

Mass of salt is 15kg

Input rate of water is 30L/min

dV/dt=30L/min

Let y(t) be the amount of salt at any time

Then,

dy/dt = input rate - output rate.

The input rate is zero since only water is added and not salt solution

Now, output rate.

Concentrate on of the salt in the tank at any time (t) is given as

Since it holds initially holds 3000L of brine then the mass to volume rate is y(t)/3000

dy/dt= dV/dt × dM/dV

dy/dt=30×y/3000

dy/dt=y/100

Applying variable separation to solve the ODE

1/y dy=0.01dt

Integrate both side

∫ 1/y dy = ∫ 0.01dt

In(y)= 0.01t + A, .A is constant

Take exponential of both side

y=exp(0.01t+A)

y=exp(0.01t)exp(A)

exp(A) is another constant let say C

y(t)=Cexp(0.01t)

The initial condition given

At t=0 y=15kg

15=Cexp(0)

Therefore, C=15

Then, the solution becomes

y(t) = 15exp(0.01t)

At any time that is the mass.

5 0
3 years ago
Which value of y below is the solution to the system shown below. A) y=6 B) y=-1 C) y=-4 D) y=8
Grace [21]

Answer:

D

Step-by-step explanation:

given the 2 equations

x + 2y = 27 → (1)

2x + 3y = 46 → (2)

Rearrange (1) expressing x in terms of y by subtracting 2y from both sides

x = 27 - 2y ← substitute into (2)

2(27 - 2y) + 3y = 46

54 - 4y + 3y = 46

54 - y = 46 ( subtract 54 from both sides )

- y = - 8 ( multiply both sides by - 1 )

y = 8 → D

4 0
3 years ago
The angle of elevation from the top of a house to a jet flying 2 miles above the house is x radians. If d represents the horizon
alisha [4.7K]

Answer:

d = 2cot(x) or d = 2/tan(x)

Step-by-step explanation:

The vertical distance from the jet to the top of the house represents the opposite side to the 'x' angle, while the horizontal distance, d, represents the adjacent side. Since we do not know the hypotenuse, the tangent and cotangent functions are the preferable choices:

tan (x) = \frac{2}{d}\\d = \frac{2}{tan (x) }\\cot (x) = \frac{d}{2} \\d= 2cot(x)

Therefore, the distance 'd' can be expressed as d = 2cot(x) or d = 2/tan(x).

6 0
3 years ago
6 O
Elenna [48]

Answer:

2x -6

Step-by-step explanation:

2x is slope

-6 is y intercept

The function passes though -6

a slope of 2 means the function goes up 2 and over 1 unit for every 1 x unit

3 0
2 years ago
Read 2 more answers
Emma had 10 Balls in a bag. The balls were numbers 1 through 10. She wanted to test the probability of drawing a ball that is a
Goryan [66]

Answer:

  • 30%
  • Unlikely

Step-by-step explanation:

<u>The balls - multiples of 3 are:</u>

  • 3, 6 and 9

<u>The probability of a multiple of 3 is:</u>

  • 3 out of 10 or
  • P = 3/10 = 30%

30% probability is in the range 0%-50% so this event is unlikely

5 0
3 years ago
Read 2 more answers
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