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9 months ago

Find the number of DEGREES rotated in a circle of radius 6 inches if an arc is created with a length of 11(pi) inches

Mathematics

1 answer:

artcher [175]9 months ago

3 0

Radius = 6 inches

Arc lenght = 11pi inches

Degrees ?

Arc lenght = radius x angle in radians

A = r * a

Solving for a:

a = A/r = 11pi/6 = 5.759586532 radians

5.759586532 to degrees ==> a = 330 degrees

Answer:

330 degrees

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Write the exact value of, or estimate, the side length of a square with an area of 100 square units.

timofeeve [1]

Answer:

l =10 units, 9.7 units, 5.5 units

Step-by-step explanation:

Area = length x breadth

Area of a square = l^2

100= l^2

√100 =√l^2

l=10 units

95=l^2

√95 = √l^2

l= 9.7 units

30=l^2

√30=√l^2

l= 5.5 units

6 0

2 years ago

Item 16<br> Solve the equation.<br><br> −49f=−3

weqwewe [10]

I think the answer is either 3/49 or about 0.061
hope this helps.

4 0

2 years ago

WILL GIVE BRAINLIST ASAP PLZ HELP!!!

tamaranim1 [39]

Answer:

Step-by-step explanation:

I answered cause like you're my bsf on this page so yea...

5 0

2 years ago

Read 2 more answers

Find the minimum value of the function f(x)=x^2+5x-6

mash [69]

<h3><u>Explanation</u></h3>

Method 1 (Formula)

$\begin{cases}h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{2a} \end{cases}$

The vertex of Parabola is the maximum/minimum point depending on the value of a.

Find Vertex

<u>h-value</u>

$h = - \frac{5}{2(1)} \\ h = - \frac{5}{2}$

<u>k-value</u>

$k = \frac{4(1)( - 6) - {(5)}^{2} }{4(1)} \\ k = \frac{ - 24 - 25}{4} \\ k = \frac{ - 49}{4} \\ k = - \frac{49}{4}$

The minimum value is the value of k. Therefore the minimum value is - 49/4 at x = -5/2.

Method 2 (Derivative)

This is Calculus method. We simply differentiate the function then substitute y' = 0.

Differentiate Function

$f'(x) = 2 {x}^{2 - 1} + {5x}^{1 - 1} - 0 \\ f'(x) = 2x + 5$

Substitute f'(x) = 0

$0 = 2x + 5 \\ - 5 = 2x \\ - \frac{5}{2} = x$

Substitute x = -5/2 in the original equation.

$f(x) = {( - \frac{5}{2} )}^{2} + 5( - \frac{5}{2} ) - 6 \\ f(x) = \frac{25}{4} - \frac{25}{2} - 6 \\ f(x) = \frac{25}{4} - \frac{50}{4} - \frac{24}{4} \\ f(x) = \frac{25}{4} - \frac{74}{4} \\ f(x) = - \frac{49}{4}$

<h3><u>Answer</u><u /></h3>

<u> $\sf{the \: \: minimum \: \: value \: \: is \: \: - \frac{49}{4} \: \: at \: \: x = - \frac{5}{2} }$ </u>

4 0

3 years ago

The ratio of the number of mystery books to the number of science fiction books is 4:3. The ratio of the number of science ficti

vladimir1956 [14]

Given is the number of science fiction books = 48

Let the number of mystery books be = x

Let the number of biographies be = y

Ratio of the number of mystery books to the number of science fiction books is 4:3 so $\frac{4}{3}= \frac{x}{48}$

= $3x=48\times4$

$x=64$

Ratio of the number of science fiction books to the number of biographies is 4:5 so $\frac{4}{5}=\frac{48}{y}$

= $4y=5\times48$

$y=60$

Hence there are 48 science fiction books, 64 mystery books and 60 biographies.

So total number of books are = $48+64+60=172$

7 0

2 years ago