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ElenaW [278]
3 years ago
5

What is the value of the discriminant for the quadratic equation 0= 2x^2 + x - 3 discriminant = b^2 - 4ac

Mathematics
1 answer:
kvv77 [185]3 years ago
8 0
\Delta=1^2-4\cdot2\cdot(-3)=1+24=25
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You are creating identical picnic basket using 30 sandwiches and 42 apples. What is the greatest number of basket that you can f
UNO [17]

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Step-by-step explanation:

30: 1, 2, 3, 5, 6, 10, 15, 30

42: 1, 2, 3, 6, 7, 14, 21, 42

greatest number of fill using all of the food is 6

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4 years ago
Of the 2254 students at a liberal arts​ college, 257 are fifth year students. Among a sample of 321 of the students from this​ c
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Answer:ifk

Step-by-step explanation:

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3 years ago
Use the chain rule to find the indicated partial derivatives. z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s , ∂z ∂t , ∂z ∂u when
mafiozo [28]
By the chain rule,

\dfrac{\partial z}{\partial s}=\dfrac{\partial z}{\partial x}\cdot\dfrac{\partial x}{\partial s}+\dfrac{\partial z}{\partial y}\cdot\dfrac{\partial y}{\partial s}

\dfrac{\partial z}{\partial s}=(4x^3+2xy)(1)+(x^2)(tu^2)

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3 0
4 years ago
A very large tank initially contains 100L of pure water. Starting at time t = 0 a solution with a salt concentration of 0.8kg/L
Scorpion4ik [409]

Answer:

1. \dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}

2. y(40) = 110.873 \ kg

Step-by-step explanation:

Given that:

A very large tank initially contains 100 L of pure water.

Starting at time t = 0 a solution with a salt concentration of 0.8kg/L is added at a rate of 5L/min.

. The solution is kept thoroughly mixed and is drained from the tank at a rate of 3L/min.

As 5L/min is entering and 3L/min is drained out, there is a 2L increase per minute. Therefore, the amount of water at any given time t = (100 +2t) L

t = (50 + t ) L

Since it is given that we should  consider y(t) to be the  amount of salt (in kilograms) in the tank after t minutes.

Then , the differential equation that  y satisfies can be computed as follows:

\dfrac{dy}{dt}=rate_{in} - rate_{out}

\dfrac{dy}{dt}=(0.8)(5) -\dfrac{y(t)}{100+2t} \times3

\dfrac{dy}{dt}=(0.8)(5) -\dfrac{3y}{100+2t}

\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}

How much salt is in the tank after 40 minutes?

So,

suppose : e^{\int \dfrac{3}{100+2t} \ dt} = (t+50)^{3/2}

Then ,

( t + 50)^{3/2} y' + \dfrac{3}{2}(t+50)^{1/2} y = 4(t+50)^{3/2}

( t + 50)^{1.5} y' + \dfrac{3}{2}(t+50)^{0.5} y = 4(t+50)^{3/2}

[y\ (t + 50)^{1.5}]' = 4(t+ 50)^{1.5}

Taking the integral on both sides; we have:

[y(t + 50)^{1.5}] = 1.6 (t + 50)^{2.5} + C

y = 1.6 (t+50)+C(t+50)^{-1.5}

y(0) = 0 = 1.6(0+50) + C ( 0 + 50)^{-1.5}

0 = 1.6(50) + C ( 50)^{-1.5}

C= -1.6(50)^{2.5}

y(40) = 1.6 (40 + 50)^1  - 1.6 (50)^{2.5}(50+40)^{-1.5}

y(40) = 144  - 1.6 \times 17677.66953 (90)^{-1.5}

y(40) = 144  - 1.6 \times 17677.66953 \times 0.001171213948

y(40) = 144  - 33.12693299

y(40) = 110.873 \ kg

6 0
4 years ago
What is 2(x + 2) + (x + 5)
balandron [24]

Answer:

3x+9

Step-by-step explanation:

6 0
3 years ago
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