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Harman [31]
3 years ago
11

For the function, f(x) = -3x + 5. If f(x) = -1, what is the value of x?

Mathematics
1 answer:
Citrus2011 [14]3 years ago
5 0

Answer:

x=2

Step-by-step explanation:

f(x) = -3x + 5.

f(x) =-1

-1 = -3x+5

Subtract 5 from each side

-1 -5 = -3x+5-5

-6 = -3x

Divide each side by -3

-6/-3 = -3x/-3

2 =x

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alukav5142 [94]

Answer:

168.56 in²

Step-by-step explanation:

The area will be found by subtracting the area of the circle from the area of the square.

The area of the square will be given by A = 28(28) = 784 in².

The area of the circle will be given by A = 3.14(14²) = 3.14(196) = 615.44 in².

The area of the shaded portion is given by

784-615.44 = 168.56 in²

4 0
3 years ago
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3 years ago
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riadik2000 [5.3K]

Let

S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n

where we assume |r| < 1. Multiplying on both sides by r gives

r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}

and subtracting this from S_n gives

(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}

As n → ∞, the exponential term will converge to 0, and the partial sums S_n will converge to

\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}

Now, we're given

a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a

a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}

We must have |r| < 1 since both sums converge, so

\dfrac{15}a = \dfrac1{1-r}

\dfrac{150}{a^2} = \dfrac1{1-r^2}

Solving for r by substitution, we have

\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)

\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}

Recalling the difference of squares identity, we have

\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}

We've already confirmed r ≠ 1, so we can simplify this to

\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15

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\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12

and so the sum we want is

ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

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serg [7]
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Answer:

Step-by-step explanation:

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

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Total area

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3 years ago
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