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Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If a fu

natta225 [31]

Answer:

See Explanation

Step-by-step explanation:

If a Function is differentiable at a point c, it is also continuous at that point.

but be careful, to not assume that the inverse statement is true if a fuction is Continuous it doest not mean it is necessarily differentiable, it must satisfy the two conditions.

the function must have one and only one tangent at x=c
the fore mentioned tangent cannot be a vertical line.

And

If function is differentiable at a point x, then function must also be continuous at x. but The converse does not hold, a continuous function need not be differentiable.

For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.

5 0

3 years ago

Where r is the radius of the cylinder and h is the height of the cylinder.

AnnyKZ [126]

<h3>Given:-</h3>

radius = 7 inches
height = 9 inches

$\\ \\$

Surface area of cylinder

$\\ \\$

we know:-

$\bigstar \boxed{ \rm Surface \: Area \: of \: Cylinder=2\pi rh+2\pi {r}^{2} }$

$\\ \\$

So:-

⇢SA of cylinder=2πrh+2πr²

$\\$

⇢SA of cylinder = 2πr(h+r)

$\\$

⇢SA of cylinder = 2 × π × 7(7 + 9)

$\\$

⇢SA of cylinder = 2 × π × 7 (16)

$\\$

⇢SA of cylinder = 2 × π × 112

$\\$

⇢SA of cylinder = 2 × 112 × π

$\\$

⇢SA of cylinder = 224π inches ²

$\\$

.°. Surface Area of cylinder is 224π inches².

3 0

2 years ago

What is the sum? 8+(-12) -20 -4 4 20

matrenka [14]

Answer:

-4

Step-by-step explanation:

5 0

3 years ago

- Use the functions f(x) = 4x + 3 and g(x) = 2x2 + 2 to answer parts (a)-(c).

mario62 [17]

9514 1404 393

Answer:

a) f(x)

b) g(x)

c) for all values of x > 1, g(x) has a greater rate of change

Step-by-step explanation:

a) The rate of change of f(x) is the x-coefficient: 4. The average rate of change of g(x) on an interval can be found by dividing the change by the interval width. Here, the width of the interval of interest is 1-0 = 1, so the average rate of change is g(1) -g(0) = 4-2 = 2.

On the interval [0, 1], f(x) has the greater rate of change.

__

b) The interval [2, 3] also has a width of 1, so the rate of change of g(x) on that interval is g(3) -g(2) = 20 -10 = 10. This value is greater than 4, so ...

on the interval [2, 3], g(x) has the greater rate of change.

__

c) Part (b) demonstrates that g(x) will have a greater rate of change on some intervals. In fact, for any interval whose center is greater than x=1, g(x) will have a greater rate of change than f(x).

_____

In calculus terms, the rate of change of g(x) is g'(x) = 4x. This will be greater than 4 for any x > 1. The graph shows the rate of change is 4 at x=1, and is higher for x > 1. The average rate of change will be greater than 4 on any interval whose center is greater than x=1.

We can figure the average rate of change on the interval [a, b] as ...

m = (g(b) -g(a))/(b -a)

m = ((2b² +2) -(2a² +2))/(b -a) = 2(b² -a²)/(b-a) = 2(b+a)

For the average rate of change to exceed 4, the sum of the ends of the interval must exceed 2, which is to say the midpoint must exceed 1.

5 0

3 years ago

Work out 69% of 102.16m Give your answer rounded to two Decimal Place

Mnenie [13.5K]

Answer:

70.49

Step-by-step explanation:

Finding the percent of a number is the same as multiplying the number by the percent in decimal form. In other words, diving the percent by (100) and then multiplying the reuslt by the number one wants to find the percent of.

69% of 102.16

= (69 / 100) * 102.16

= 0.69 * 102.16

= 70.4914

~ 70.49

6 0

3 years ago

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