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3 years ago

What is the equation of the line through (1,4) and (2,2)? y= _x + __

Mathematics

1 answer:

aivan3 [116]3 years ago

6 0

Answer:

y = -2x + 6

Step-by-step explanation:

y = mx + c

m = (2-4)/(2-1) = -2/1

m = -2

y = -2x + c

When x = 1, y = 4

4 = -2(1) + c

c = 4 + 2 = 6

y = -2x + 6

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A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling water. How long will it tak

IgorC [24]

Answer

According to newton law of cooling

$\dfrac{d T}{dt} = k (T - T_a)$

and

$T = Ce^{kt} + T_a$

now At Ta = 100

T₀ = 10 °C

T₁ = 12° C

$T(0) = Ce^{0} + T_a$

10 = C + 100

C = -90

now,

$12 = -90e^k + 100$

$e^k = \dfrac{88}{90}$

$k = ln{\dfrac{88}{90}}$

at time equal to t

T(t) = 70

$T(t) = -90 (\dfrac{88}{90})^t + 100$

$70 = -90(\dfrac{88}{90})^t + 100$

$(\dfrac{88}{90})^t = \dfrac{1}{3}$

$t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{3})$

t = 48.88 s

hence, after 48.88 s the temperature of the body will be 70°C

b) time taken to reach 98°C

$T(t) = -90 (\dfrac{88}{90})^t + 100$

$98 = -90(\dfrac{88}{90})^t + 100$

$(\dfrac{88}{90})^t = \dfrac{1}{45}$

$t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{45})$

t = 390 s

hence, after 390 s the temperature of the body will be 98°C

5 0

3 years ago

Which of the following relations describes a function?

PtichkaEL [24]

Howdy! My name is Christian and I’ll try and help you with this question!

Date: 9/29/20 Time: 9:08 am CST

Answer:

{ (1, 3), (2, 3), (3, 3), (4, 3) }

Explanation:

This is because for each x value, the number on the left of the set, there is no other x values of the same number, ( 1, 2, 3, 4)

Hope this helps you with your question!

Sincerely,

Christian

8 0

4 years ago

Ben, sean, alexis and samantha divide a $47 so that ben and sean together got $27, ben and alexis got $25, and ben and samantha

ELEN [110]

Answer:

$11

Step-by-step explanation:

Let Ben has b,

sean has s

alexis has a

samantha has s

Money.

We need to write the words into equations and solve as we can.

b + s + a + s = 47

b + s = 27

b + a = 25

b + s = 23

We need to find a.

Let's put 2nd equation in first, to get:

27 + a + s = 47

a + s = 20 ---------- 5th equation

Now let's solve 4th equation for b and put it into 3rd equation:

b + s = 23

b = 23 - s

Putting in 3rd equation:

23 - s + a = 25

a - s = 2 ---------------6th equation

Now, add up 5th and 6th equation to get a:

a + s = 20

a - s = 2

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

2a = 22

a = 22/2 = 11

Alexis got $11

8 0

3 years ago

Please show your work. Convert decimals into fractions in simplest form

Hoochie [10]

Answer:

1. 0.5 = 5/10 ÷ 5 = 1/2

2. 0.7 = 7/10

3. 0.33 = 33/100 ÷ 33 = 1/3

4. 0.875 = (875/1000) ÷ 125 = 7/8

5 0

3 years ago

( 23 pts )Please answer this math question.

marishachu [46]

Answer:

Step-by-step explanation:

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4 0

3 years ago