Evaluate and simplify

Radius is 21 5/8 incercepted by 5Pi/6? What is arc lenght?

vesna_86 [32]

9514 1404 393

Answer:

(18 1/48)π ≈ 56.61 units

Step-by-step explanation:

Arc length is the product of radius and intercepted arc in radians:

s = rθ

s = (21 5/8)(5π/6) = (18 1/48)π ≈ 56.61 . . . units

7 0

3 years ago

Zack spent $150 for 3tickets what was the ratio of money to tickets

Tcecarenko [31]

$50 each.................... hope it helped

4 0

3 years ago

Now convert 3/8 to a decimal number by completing the long division. Remember to add 0s to the dividend as you work. Divide thro

VMariaS [17]

Answer:

you feel happy with the process on the long division page you can skip the first bit.

divide step 1 4 ÷ 25 = 0 remainder 4 The first number of the dividend is divided by the divisor.

divide step 2 The whole number result is placed at the top. Any remainders are ignored at this point.

divide step 3 25 × 0 = 0 The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.

divide step 4 4 − 0 = 4 Now we take away the bottom number from the top number.

divide step 5 Bring down the next number of the dividend.

divide step 6 43 ÷ 25 = 1 remainder 18 Divide this number by the divisor.

divide step 7 The whole number result is placed at the top. Any remainders are ignored at this point.

divide step 8 25 × 1 = 25 The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.

divide step 9 43 − 25 = 18 Now we take away the bottom number from the top number.

divide step 10 Bring down the next number of the dividend.

divide step 11 185 ÷ 25 = 7 remainder 10 Divide this number by the divisor.

divide step 12 The whole number result is placed at the top. Any remainders are ignored at this point.

divide step 13 25 × 7 = 175 The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.

divide step 14 185 − 175 = 10 Now we take away the bottom number from the top number.

divide step 15 Now we have reached the end of the whole numbers we add a decimal place and the first zero. Notice the decimal point which has appeared on the answer line and by the dividend. It does not appear anywhere else.

divide step 16 Bring down the next number of the dividend.

divide step 17 100 ÷ 25 = 4 remainder 0 Divide this number by the divisor.

divide step 18 The whole number result is placed at the top. Any remainders are ignored at this point.

divide step 19 25 × 4 = 100 The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.

divide step 20 100 − 100 = 0 Now we take away the bottom number from the top number.

divide step 21

The subtraction has given zero. We stop when this happens. The answer is 17.4

As long as the subtraction gives a number above zero the long division can carry on to as many decimal places as we wish.

Answer: 435 ÷ 25 = 17.4 FOLLOW ME

6 0

3 years ago

What is the common difference for this arithmetic sequence -6,-1,4,9,14 A.6 B.5 C.3 D.4

lawyer [7]

The common difference is B. 5 because the numbers are increasing by 5.

4 0

3 years ago

Read 2 more answers

Math pls help!! answers?

statuscvo [17]

Answer: Choice B) Infinitely many solutions

one solution: x = 8, y = -7/2, z = 0
another solution: x = -12, y = 13/2, z = 10

=======================================================

Explanation:

Here's the starting original augmented matrix.

$\left[\begin{array}{ccc|c} 1 & 0 & 2 & 8\\5 & 1 & 9 & 73/2\\-4 & 0 & -8 & -32\\\end{array}\right]$

We'll multiply everything in row 3 (abbreviated R3) by the value -1/4 or -0.25, which will make that -4 in the first column turn into a 1.

We use this notation to indicate what's going on: $(-1/4)*R3 \to R3$

That notation says "multiply everything in R3 by -1/4, then replace the old R3 with the new corresponding values".

So we have this next step:

$\left[\begin{array}{ccc|c} 1 & 0 & 2 & 8\\5 & 1 & 9 & 73/2\\1 & 0 & 2 & 8\\\end{array}\right]\begin{array}{l} \ \\\ \\(-1/4)*R3 \to R3\\\end{array}$

Notice that the new R3 is perfectly identical to R1.

So we can subtract rows R1 and R3, and replace R3 with the result of nothing but 0's

$\left[\begin{array}{ccc|c} 1 & 0 & 2 & 8\\5 & 1 & 9 & 73/2\\0 & 0 & 0 & 0\\\end{array}\right]\begin{array}{l} \ \\\ \\R3-R1 \to R3\\\end{array}$

Whenever you get an entire row of 0's, it always means there are infinitely many solutions.

-------------------

Now let's handle the second row. That 5 needs to turn into a 0. We can multiply R1 by 5, and subtract that from R2.

So we need to compute 5*R1-R2 and have that replace R2.

$\left[\begin{array}{ccc|c} 1 & 0 & 2 & 8\\0 & 1 & -1 & -7/2\\0 & 0 & 0 & 0\\\end{array}\right]\begin{array}{l} \ \\5*R1-R2 \to R2\ \\\ \\\end{array}$

Notice that in the third column of R2, we have 9-5*2 = 9-10 = -1. So we have -1 replace the 9. In the fourth column of R2, we have 73/2 - 5*8 = -7/2. So the -7/2 replaces the 73/2.

--------------------

At this point, the augmented matrix is in RREF form. RREF stands for Reduced Row Echelon Form. It seems a bit odd that the "F" of "RREF" stands for "form" even though we say "form" right after "RREF", but I digress.

Because the matrix is in RREF form, this means R1 and R2 lead to these equations:

$R1 : 1x+0y+2z = 8\\ R2: 0z+1y-1z = -7/2$

which simplify to

$R1: x+2z = 8\\R2: y-z = -7/2$

Let's get the z terms to each side like so:

$x+2z = 8\\x = -2z+8\\\text{ and }\\y-z = -7/2\\y = z-7/2\\$

Therefore, all of the solutions are of the form $(x,y,z) = (-2z+8, z-7/2, z)$ where z is any real number.

If z is allowed to be any real number, then we can simply pick any number we want to replace it. We consider z to be the "free variable", in that it's free to be whatever it wants. The values of x and y will depend on what we pick for z.

So the concept of "infinitely many solutions" doesn't exactly mean we can pick just any triple for x,y,z (admittedly it would be nice to randomly pick any 3 numbers off the top of my head and be done right away). Instead, we can pick anything we want for z, and whatever we picked, will directly determine x and y. The x and y are locked into place so to speak.

Let's say we picked z = 0.

That would lead to...

$x = -2z+8\\x = -2(0)+8\\x = 8\\\text{ and }\\y = z-7/2\\y = 0-7/2\\y = -7/2\\$

So z = 0 would lead to x = 8 and y = -7/2

Rearranging the items in alphabetical order gets us:

x = 8, y = -7/2, z = 0

We have one solution of (x,y,z) = (8, -7/2, 0)

Now let's say we picked z = 10

$x = -2z+8\\x = -2(10)+8\\x = -12\\\text{ and }\\y = z-7/2\\y = 10-7/2\\y = 13/2\\$

So we have x = -12, y = -13/2, z = 10

Another solution is (x,y,z) = (-12, 13/2, 10)

There's nothing special about z = 0 or z = 10. You can pick any two real numbers you want for z. Just be sure to recalculate the x and y values of course.

To verify each solution, you'll need to plug them back into the original equations formed by the original augmented matrix. After simplifying, you should get the same thing on both sides.

8 0

2 years ago