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Stolb23 [73]
2 years ago
15

Find All Real Square Roots Of 144

Mathematics
1 answer:
HACTEHA [7]2 years ago
6 0

Answer:

plus or minus 12

hope that help

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What is (27/8)^-2/3 ?
Paraphin [41]

Answer:

Step-by-step explanation:

7 0
2 years ago
What is the ratio of the width of the yard to the area of the yard in 10 feet long by 7 feet wide
dezoksy [38]

Area = (length) x (width)

Area = (10-ft) x (7-ft) = 70 ft²

(Width) / (Area) = (7-ft) / (70 ft²)  =  1 / 10-ft .
4 0
3 years ago
Use the Midpoint Rule with n = 5 to estimate the volume V obtained by rotating about the y-axis the region under the curve y = 1
velikii [3]

Using the shell method, the volume is given exactly by the definite integral,

2\pi\displaystyle\int_0^1x(1+9x^3)\,\mathrm dx

Splitting up the interval [0, 1] into 5 subintervals gives the partition,

[0, 1/5], [1/5, 2/5], [2/5, 3/5], [3/5, 4/5], [4/5, 5]

with left and right endpoints, respectively, for the i-th subinterval

\ell_i=\dfrac{i-1}5

r_i=\dfrac i5

where 1\le i\le5. The midpoint of each subinterval is

m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}{10}

Then the Riemann sum approximating the integral above is

2\pi\displaystyle\sum_{i=1}^5m_i(1+9{m_i}^3)\frac{1-0}5

\dfrac{2\pi}5\displaystyle\sum_{i=1}^5\left(\frac{2i-1}{10}+9\left(\frac{2i-1}{10}\right)^4\right)

\dfrac{2\pi}{5\cdot10^4}\displaystyle\sum_{i=1}^5\left(16i^4-32i^3+24i^2+1992i-999\right)=\frac{112,021\pi}{25,000}\approx\boxed{14.08}

(compare to the actual value of the integral of about 14.45)

3 0
3 years ago
Pentagon ABCDE and pentagon A″B″C″D″E″ are shown on the coordinate plane below:
erastova [34]

The transformations that are applied to pentagon ABCDE to create A"B"C"D"E" are:

1) Translation (x, y) → (x + 8, y + 2)

2) Reflection across the x-axis (x, y) → (x, -y)

So, the overall transformation given in the graph is (x, y) → {(x + 8), -(y + 2)}.

<h3>What are the transformation rules?</h3>

The transformation rules are:

  • Reflection across x-axis: (x, y) → (x, -y)
  • Reflection across y-axis: (x, y) → (-x, y)
  • Translation: (x, y) → (x + a, y + b)
  • Dilation: (x, y) → (kx, ky)

<h3>Calculation:</h3>

The pentagons in the graph have vertices as

For the pentagon ABCDE: A(-4, 5), B(-6, 4), C(-5, 1), D(-2, 2), and (-2, 4)

For the pentagon A"B"C"D"E": A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), and E"(6, -6)

Consider the vertices A(-4, 5) from the pentagon ABCDE and A"(4, -7) from the pentagon A"B"C"D"E".

Applying the Translation rule for the pentagon ABCDE:

The rule is (x, y) → (x + a, y + b)

So, the variation is

-4 + a = 4

⇒ a = 4 + 4 = 8

5 + b = 7

⇒ b = 7 - 5 = 2

So, the pentagon ABCDE is translated by (x + 8, y + 2).

Applying the Reflection rule for the translated pentagon:

The translated pentagon has vertices (x + 8, y + 2).

When applying the reflection across the x-axis,

(x + 8, y + 2) → {(x + 8), -(y + 2)}

Therefore, the complete transformation of the pentagon ABCDE to the pentagon A"B"C"D"E" is (x, y) → {(x + 8), -(y + 2)}

Verification:

A(-4, 5) → ((-4 + 8), -(5 + 2)) = (4, -7)A"

B(-6, 4) → ((-6 + 8), -(4 + 2)) = (2, -6)B"

C(-5, 1) → ((-5 + 8), -(1 + 2)) = (3, -3)C"

D(-2, 2) → ((-2 + 8), -(2 + 2)) = (6, -4)D"

E(-2, 4) → ((-2 + 8), -(4 + 2)) = (6, -6)E"

Learn more about transformation rules here:

brainly.com/question/4289712

#SPJ1

5 0
1 year ago
What separates the portion of a number that is greater than 1 from the portion of the number that less than 1
konstantin123 [22]

Answer:

1/2 -2/1

Step-by-step explanation:

122

8mar12

212323

123345wqesfef

7 0
3 years ago
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