9 cm ÷ 10 = how many mm

Answers

Answer 1
Answer: 9 cm = 90 mm

90 mm / 10 = 9 mm

Hope this helps! 

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Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 9t + 9 cot(t/2), [π/4, 7π/4]

Answers

Final answer:

The absolute maximum and minimum of a function on a given interval can be found by calculating the function's critical points and evaluating the function at these points and the interval endpoints, then comparing these values.

Explanation:

In order to find the absolute maximum and absolute minimum values of a function on a given interval, you must first find the critical points of the function within the interval. Critical points occur where the derivative of the function is equal to zero or is undefined. In this case, the derivative of f(t) = 9t + 9 cot(t/2) is f'(t) = 9 - (9/2) csc2(t/2). Set this to zero and solve for t to find the critical points. Additionally, the endpoints of the interval, π/4 and 7π/4, could be the absolute maximum or minimum, so these should be evaluated as well. Once you have found the values of the function at these points and the endpoints, compare them to determine the absolute maximum and minimum values.

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Final answer:

To find the absolute maximum and minimum values of a function, we find the critical points and endpoints. Evaluating the function at these points gives the maximum and minimum values.

Explanation:

To find the absolute maximum and absolute minimum values of a function on a given interval, we need to find the critical points and endpoints of the interval.

To find the critical points of f, we need to find where the derivative of f is equal to zero or undefined. The derivative of f(t) = 9t + 9cot(t/2) is f'(t) = 9 - 9csc^2(t/2).

Setting f'(t) = 0, we have 9 - 9csc^2(t/2) = 0. Solving this equation, we get csc^2(t/2) = 1, which means sin^2(t/2) = 1. This gives us sin(t/2) = ±1. The critical points occur when t/2 = π/2 or t/2 = 3π/2. Solving for t, we get t = π or t = 3π as the critical points.

The endpoints of the interval are π/4 and 7π/4.

Now we evaluate the function f at the critical points and endpoints:

  • f(π/4) = 9(π/4) + 9cot(π/8) ≈ 6.566
  • f(π) = 9π + 9cot(π/2) = 9π
  • f(3π) = 9(3π) + 9cot(3π/2) = 27π
  • f(7π/4) = 9(7π/4) + 9cot(7π/8) ≈ 46.607

From these evaluations, we can see that the absolute maximum value occurs at t = 7π/4 and is approximately 46.607, while the absolute minimum value occurs at t = π/4 and is approximately 6.566.

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Every week, Hector works 20 hours and earns $210.00. He earns a constant amount of money per hour.Part A
Write an equation that can be used to determine the number of hours, h, Hector works given the number of weeks, W.
Enter your equation in the space provided

Part B
Write an equation that can be used to determine Hector's earnings, in dollars, m, for h hours of work.
Enter your equation in the space provided.

Answers

Answer:

A). h = 20 w

B). m = 10.5h

Step-by-step explanation:

Part (A).

Let the total number of hours Hector worked = h

And total number of weeks worked by Hector = w

Therefore, number of hours Hector worked in a week = (h)/(w)

Since, total number of hours worked in a week = 20

Equation will be,

20 = (h)/(w)

h = 20w

Part (B).

Per hour earning of Hector = \frac{\text{Total earning}}{\text{Number of hours worked}}=(210)/(20)

(m)/(h)=10.5

m = 10.5h

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Answers

easy, the degree of the function equals the number of roots it has
degree is the highest placeholder exponent

we have
7x^0
5x^4
-3x^2
which is highest?

4th

means 4 roots
means
(x-r1)(x-r2)(x-r3)(x-r4) where r1,r2,r3,r4 are the roots



4 roots

X^3+13x^2+32x+20
please help me factorizing above equation

Answers

x^3+13x^2+32x+20=x^3+x^2+12x^2+ 12x+20x+20 =\n\n=x^2(x+1)+12x(x + 1 )+20(x+1 )=(x+1)(x^2+12x+20)=\n\n=(x+1)[(x^2+10x+2x+20)]=(x+1)[x(x +10)+2(x+10))]=\n\n=(x+1) (x +2) (x+10)


1) which expression is the GCF of the terms of the polynomial?16x^3+28^5y
A)4x^3
B)4x^5y
C)8x^5
D)112x^5y

Answers

First, the statement seems to have an error. The right polynomial must be 16x^3 + 28x^5y.

With that said, we have to find the greatest common divisor of the coefficients and take the common letter with its minimum exponent.

Greatest common divisor of 16 and 28 is determined by facoring both numbers and taking the common factors raised to the minimum power.

16 = 2^4
28 = 2^2 * 7

So, the common factor with the minimum power is 2^2 =4

The common letter with its minimum power is x^3.

So the GCF is 4x^3, i.e. option A)

Bertha and Vernon are competing in a diving competition. Bertha's dive ended -24 m from the starting platform. Vernon's dive ended -4 m from the starting platform. How many times farther was the end of Bertha's dive than the end of Vernon's dive?A. 

-6

 B. 

6

 C. 

20

 D. 

-20

help help help

Answers

Answer:

B. Bertha's dive ended 6 times farther than Vernon's dive.

Step-by-step explanation:

We have that,

Bertha's dive ended -24 m from that starting point.

Vernon's dive ended -4 m from that starting point.

So, we get that,

Bertha's end point = 6 × Vernon's end point

i.e. -24 = 6 × (-4)

So, we see that,

Bertha's dive ended 6 times farther than Vernon's dive.