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dolphi86 [110]
3 years ago
11

Find an equation for the line through (-6, 3) and parallel to y = 3x + 1.

Mathematics
1 answer:
Anika [276]3 years ago
7 0

Since this line is parallel to y = 3x + 1 their slopes are equal. The slope is equal to 3. The line is also passing the point (-3,4).

This is the format of the line parallel to y = 3x + 1

y = 3x+ b

This line passes through point (-3, 4)

Replacing the values of y and x coming from the coordinates of (-3, 4)

4 = 3 * (-3) + b

Solving for the y-intercept b

4 = -9 + b

b = 4 + 9

b = 13

Knowing the slope as equal to 3 and the y-intercept as 13 the equation of the line is

y = 3x+13

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Between 0 degrees Celsius and 30 degrees Celsius, the volume V (in cubic centimeters) of 1 kg of water at a temperature T is giv
Ira Lisetskai [31]

Answer:

T = 3.967 C

Step-by-step explanation:

Density = mass / volume

Use the mass = 1kg and volume as the equation given V, we will come up with the following equation

D = 1 / 999.87−0.06426T+0.0085043T^2−0.0000679T^3

   = (999.87−0.06426T+0.0085043T^2−0.0000679T^3)^-1

Find the first derivative of D with respect to temperature T

dD/dT = \dfrac{70000000\left(291T^2-24298T+91800\right)}{\left(679T^3-85043T^2+642600T-9998700000\right)^2}

Let dD/dT = 0 to find the critical value we will get

\dfrac{70000000\left(291T^2-24298T+91800\right)}  = 0

Using formula of quadratic, we get the roots:

T =  79.53 and T = 3.967

Since the temperature is only between 0 and 30, pick T = 3.967

Find 2nd derivative to check whether the equation will have maximum value:

-\dfrac{140000000\left(395178T^4-65993368T^3+3286558821T^2+2886200857800T-121415215620000\right)}{\left(679T^3-85043T^2+642600T-9998700000\right)^3}

Substituting the value with T=3.967,

d2D/dT2 = -1.54 x 10^(-8)    a negative value. Hence It is a maximum value

Substitute T =3.967 into equation V, we get V = 0.001 i.e. the volume when the the density is the highest is at 0.001 m3 with density of

D = 1/0.001 = 1000 kg/m3

Therefore T = 3.967 C

3 0
3 years ago
Hi, Please i need help with this question. Workings would be deeply appreciated .
kupik [55]

Answer:

k = ⅕  

Step-by-step explanation:

The slope-intercept equation for a straight line is

y = mx + b, where

m = the slope and

b = the y-intercept

Data:

(3,4)     = a point on the line

(3k,0)   = x-intercept

(0,-5k) = y-intercept

Calculations:

1. Slope

m = (y₂ - y₁)/(x₂ - x₁) = (-5k - 0)/(0 - 3k) = -5/(-3) = ⁵/₃

This makes the equation

y = ⁵/₃x - 5k

2. k

Insert the value of the known point: (3,4)

4 = (⁵/₃)(3) - 5k

4 = 5 - 5k

-1 = -5k

k = ⅕

The figure below shows your graph passing through (3,4) with intercepts 3k and -5k on the x- and y-axes respectively .

 

8 0
3 years ago
URGENT PLEASE HELP!!!
Naily [24]
15.7 feet
and you are welcome
7 0
3 years ago
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Which of the following expressions has 3 terms?<br><br> A 8x + y - z<br> B xyz<br> C y3 + 1
Alja [10]
Since C only has two and although it may look like B has three terms, when the letters are joined together like that they are basically just become one big term, so your answer would be A.
5 0
3 years ago
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Anybody body willing to help i have to do 1-3 and 14-17 for all of my hw
Ymorist [56]

I will help, what is your book called?

6 0
2 years ago
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