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4 years ago

Is the absolute value of x -1 differentiable at x?

1 answer:

Pie4 years ago

7 0

$f(x)=|x-1|$

is differentiable everywhere except at $x=1.$ There the derivative limit from the left gives -1 and from the right +1, different, so no derivative at $x=1.$

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Substitution for math

ASHA 777 [7]

Explanation:

The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.

8 0

3 years ago

You pull a sled across a horizontal frictionless patch of snow. If your pulling force is in the same direction as the sled's dis

nexus9112 [7]

Answer:

The kinetic energy of the sled is going to increase by 18.75%

Step-by-step explanation:

The work W realized by a Force F is given by:

$W=F_x*x$

Where x is the displacement and $F_x$ is the component of the force that is parallel to the displacement.

Additionally, the work is equal to the change in the kinetic energy

$W=K_f-K_i$

If your pulling force is in the same direction as the sled's displacement, we can said that: $F=F_x$

And if increases the kinetic energy of the sled by 27%, we can said that:

$K_f-K_i=0.27K_i$

So, we can formulate the following equation:

$W=F*x\\W=0.27K_i\\\\F*x=0.27K_i$ (1)

On the other hand, if the pulling force acted at an angle of 46° above the horizontal, the work is:

$W=F_x*x=Fcos(46)*x=F*x*cos(46)$ (2)

Then, replacing (1) in (2), we get:

$W=F*x*cos(46)=0.27K_i*cos(46) = 0.1875K_i$

Finally, the kinetic energy increase by 18.75% because:

$W=K_f-K_i\\W=0.1875K_i\\\\K_f-K_i=0.1875K_i$

5 0

3 years ago

Find the area of this trapezoid. All length measures are in centimeters.

Lena [83]

we know that
The area of a trapezoid is given by the formula
Area=h*(b1+b2)/2
where
<span>b1, b2 are the lengths of each base
h is the altitude (height)
</span>Remember that the bases are the two parallel sides of the trapezoid. The altitude (or height) of a trapezoid is the perpendicular<span> distance between the two bases

</span> therefore
[area of trapezoid]=(11+5)*4/2--------> 64/2------> 32 cm²

the answer is 32 cm²

7 0

4 years ago

Someone help me please

gogolik [260]

x/5 = 6/15
15x = 30
x = 2

answer
x = 2 ft

y/10 = 6/15
15y = 60
y = 4

answer
y = 4 ft

3 0

3 years ago

Read 2 more answers

Given

arlik [135]

Answer:

a = 3, b = - 7

Step-by-step explanation:

Substitute x = 2 into the equation and equate to 5, that is

a(2)² + b = 5

4a + b = 5 → (1)

Substitute x = 3 into the equation and equate to 20

a(3)² + b = 20

9a + b = 20 → (2)

Subtract (1) from (2) term by term to eliminate b

(9a - 4a) + (b - b) = (20 - 5), that is

5a = 15 ( divide both sides by 5 )

a = 3

Substitute a = 3 into either of the 2 equations and solve for b

Substituting in (1)

4(3) + b = 5

12 + b = 5 ( subtract 12 from both sides )

b = - 7

3 0

4 years ago