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3 years ago

12

Find area of shaded regions

1 answer:

vagabundo [1.1K]3 years ago

5 0

Answer:

1039.5 cm²

Step-by-step explanation:

Area (shaded) = 22/7 x 21 x 21 - 22/7 x 21/2 x 21/2

= 1386 - 346.5

= 1039.5 cm²

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F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2)<br><br> I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

<u>Given function</u>:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find <em>a</em>, compare the coefficients of x³:

$\implies a=3$

To find <em>b</em>, substitute the found value of <em>a</em> into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find <em>c</em>, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

<u>Zero Product Property</u>

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

3 0

1 year ago

Math help asap timed 24 points!

S_A_V [24]

3x+8.5 =2.5x + 14.5

subtract 2.5x from each side

.5x + 8.5 = 14.5

subtract 8.5 from each side

.5x =6

multiply by 2

x =12

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4 years ago

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butalik [34]

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4 years ago

How many ways are there to fill either the pitcher or catcher field position (but not both) from among the 25 players (leaving t

Artemon [7]

Using the permutation formula, it is found that there are 600 ways to fill the pitcher and catcher positions.

The order is important, as one player is the pitcher and the other is the catcher, hence the <em>permutation formula </em>is used to solve this question.

<h3>What is the permutation formula?</h3>

The number of possible permutations of x elements from a set of n elements is given by:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

2 players are taken from a set of 25, hence the number of ways is given by:

$P_{(25,2)} = \frac{25!}{23!} = 600$ .

More can be learned about the permutation formula at brainly.com/question/25925367

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