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3 years ago

|c- 24| = 7c :D :D :D

2 answers:

8 0

Start by making this absolute value equation into two equations; one positive and one negative equation. The two equations will be: c - 24 = 7c and c - 24 = -7c.

Start by solving the positive equation first: c - 24 = 7c. Add 24 to both sides and subtract 7c from both sides of the equation.

-6c = 24, now divide both sides by -6 to find your first c value.

c = -4

Solve the negative equation next: c - 24 = -7c. Add 24 to both sides and add 7c to both sides of the equation.

8c = 24, divide both sides by 8 to isolate c and find your second c value.

c = 3

Substitute to see if these values actually work with the given absolute value equation. Substitute -4 for c.

|c - 24| = 7c ==> |(-4) - 24| = 7(-4)

Solving this equation gives us 28 = -28, and this is a false statement so -4 cannot be part of the solutions. Now check 3 by substituting it for c.

|c - 24| = 7c ==> |(3) - 24| = 7(3)

Solving this equation we get 21 = 21, and this is a true statement so our only possible solution is c = 3.

Ivanshal [37]3 years ago

3 0

$c\geq0\\\\\\ |c- 24| = 7c\\\\c-24=7c \vee c-24=-7c\\\\6c=-24 \vee -8c=-24\\\\c=-4 \vee c=3\\\\-4\not \geq0\\\\\boxed{c=3}$

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X ÷ 4 + 5= 8 I need someone to do it and double check for me please.

kow [346]

= x/4 + 5 = 8

= x/4 = 8 - 5 ( transposing +5 from LHS to RHS changes +5 to -5 )

= x/4 = 3

= x = 3 × 4 ( transposing ÷4 from LHS to RHS changes ÷4 to ×4 l

= x = 12

Let us see whether the value of x is correct or not by placing 12 in the place of x .

= 12 ÷ 4 + 5 = 8

= 3 + 5 = 8

= 8 = 8

= LHS = RHS

Which means the value of x we found out is correct .

<h3>Therefore , x = 12 .</h3>

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3 years ago

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Sam and Janet are mountain biking. Sam rides his bike down into a valley, 8 feet below sea level. Janet rides her bike to the to

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3 years ago

A body moves s metres in a time t seconds so that s = t3 – 3t2 + 8. Find:

Lady bird [3.3K]

Using derivatives, it is found that:

i) $v(t) = 3t^2 - 6t$

ii) 9 m/s.

iii) $a(t) = 6t - 6$

iv) 6 m/s².

v) 1 second.

<h3>What is the role of derivatives in the relation between acceleration, velocity and position?</h3>

The velocity is the derivative of the position.

The acceleration is the derivative of the velocity.

In this problem, the position is:

$s(t) = t^3 - 3t^2 + 8$

item i:

Velocity is the <u>derivative of the position</u>, hence:

$v(t) = 3t^2 - 6t$

Item ii:

$v(3) = 3(3)^2 - 6(3) = 27 - 18 = 9$

The speed is of 9 m/s.

Item iii:

Derivative of the velocity, hence:

$a(t) = 6t - 6$

Item iv:

$a(2) = 6(2) - 6 = 6$

The acceleration is of 6 m/s².

Item v:

t for which a(t) = 0, hence:

$6t - 6 = 0$

$6t = 6$

$t = \frac{6}{6}$

$t = 1$

Hence 1 second.

You can learn more about derivatives at brainly.com/question/14800626

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2 years ago

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3 years ago

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A cup of coffee at 85 degrees Celsius is placed in a room at 25 degrees Celsius. Suppose that the coffee cools at a rate of 5 de

bezimeni [28]

Answer: k = - 6.6667

Step-by-step explanation:

this is quite very simple to begin. I would encourage you take other practice questions similar to help with understanding it.

let us begin.

Given that ;

dT/dt = k ( Tm - T) where Tm is the temp of the medium

dT/dt = 5 degrees Celsius per minute when T = 70

so we have that, 5 = k ( 25 - 70)

remember to convert 5 degree celsius per minute to seconds

we have that;

5*60(sec) = k ( 25 - 70)

k = 5*60 / ( 25 - 70)

k = - 6.6667

note K is negative because we consider it for cooling process (temp decreasing).

cheers i hope this helps!!!

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3 years ago