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VashaNatasha [74]
3 years ago
7

Match each value with the smallest number set that it belongs to.

Mathematics
1 answer:
SOVA2 [1]3 years ago
4 0
The first one is one because anything to the power of zero is one.
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Find the length of the following curve. If you have a​ grapher, you may want to graph the curve to see what it looks like.
stepladder [879]

The length of the curve y = \frac{1}{27}(9x^2 + 6)^\frac 32 from x = 3 to x = 6 is 192 units

<h3>How to determine the length of the curve?</h3>

The curve is given as:

y = \frac{1}{27}(9x^2 + 6)^\frac 32 from x = 3 to x = 6

Start by differentiating the curve function

y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x

Evaluate

y' = x(9x^2 + 6)^\frac 12

The length of the curve is calculated using:

L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx

This gives

L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx

Expand

L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx

This gives

L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx

Express as a perfect square

L =\int\limits^6_3 {\sqrt{(3x^2 + 1)^2}\ dx

Evaluate the exponent

L =\int\limits^6_3 {3x^2 + 1} \ dx

Differentiate

L = x^3 + x|\limits^6_3

Expand

L = (6³ + 6) - (3³ + 3)

Evaluate

L = 192

Hence, the length of the curve is 192 units

Read more about curve lengths at:

brainly.com/question/14015568

#SPJ1

7 0
2 years ago
A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18 \pi18π18, pi
Whitepunk [10]

Answer:

A=81\pi $ m^2

Step-by-step explanation:

Circumference of the column =18\pi $ meters

Circumference of a circle=2\pi r

Therefore:

2\pi r =18\pi $ meters\\2r=18\\r=18 \div 2\\$Radius, r=9 meters

Area of a Circle =\pi r^2

Since radius of the cross section of the column =9 meters

Area of the cross section of the column

=\pi *9^2\\=81\pi $ m^2

5 0
3 years ago
Suppose that the local sales tax rate is 5 %
bazaltina [42]

Answer:

A: Tax paid us $1370

B: Total cost= car cost + taxes

$27,400+ $1370

=$28,770

Step-by-step explanation:

4 0
2 years ago
I don't understand this problem...like how to combine the k terms or how to get the answer. ​
creativ13 [48]

Answer:

-6 k +5

Step-by-step explanation:

-2k -4k +5

Think of k is apples

-2 apples -4 apples

-6 apples

-6 k +5

3 0
3 years ago
Read 2 more answers
Need help , due tomorrow. Plz give all correct answers for brainliest answer
velikii [3]
1, 2, 3, 5, and 7 are all functions. 4, 6, 8, and 9 are not functions.
4 0
3 years ago
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