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3 years ago

(5 points) A street light is at the top of a 18 ft pole. A 5 ft tall girl walks along a straight path

Mathematics

1 answer:

qwelly [4]3 years ago

3 0

Answer:

2.31 ft/sec

Step-by-step explanation:

In the picture attached, a representation of the problem is shown, where w(t) is the walking distance (as a function of time) and s(t) is the position of the tip of her shadow (as a function of time).

We want to find the derivative of s(t).

From triangles similarity:

s(t)/5 = [w(t) + s(t)]/18

18s(t) = 5w(t) + 5s(t)

13s(t) = 5w(t)

w(t) = 13/5*s(t)

We know that her speed is 6 ft/sec, that is:

d(w(t))/dt = 6 ft/sec

From the previous relationship:

d(w(t))/dt = 13/5*d(s(t))/t

Replacing:

6 = 13/5*d(s(t))/t

d(s(t))/t = 5*6/13

d(s(t))/t ≈ 2.31 ft/sec

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Which of the following is a solution to the following system of inequalities?

iren2701 [21]

Option D: $(0,3)$ is the solution to the inequalities.

Explanation:

From the given graph, we can see that the equation of the inequalities are

$y>-x+1$ and $y\leq 2 x+3$

To determine the coordinate that satisfies the inequality, let us substitute the coordinates in both of the inequalities $y>-x+1$ and $$y$

Thus, we have,

Option A: $(1,-1)$

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$ , we get,

$y>-x+1\implies-1>0$ is not true.

$$y\leq 2 x+3 \implies -1\leq 5$ is true.

Since, only one equation satisfies the condition, the coordinate $(1,-1)$ is not a solution.

Hence, Option A is not the correct answer.

Option B: $(-4,0)$

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$ , we get,

$y>-x+1\implies0>5$ is not true.

$$y\leq 2 x+3 \implies 0\leq -5$ is not true.

Since, both the equations does not satisfy the condition, the coordinate $(-4,0)$ is not a solution.

Hence, Option B is not the correct answer.

Option C: $(3,-2)$

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$ , we get,

$y>-x+1\implies-2>-2$ is not true.

$$y\leq 2 x+3 \implies -2\leq 9$ is true.

Since, only one equation satisfies the condition, the coordinate $(3,-2)$ is not a solution.

Hence, Option C is not the correct answer.

Option D: $(0,3)$

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$ , we get,

$y>-x+1\implies3>1$ is true.

$$y\leq 2 x+3 \implies 3\leq 3$ is true.

Since, both equation satisfies the condition, the coordinate $(0,3)$ is a solution.

Hence, Option D is the correct answer.

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3 years ago

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kvv77 [185]

Are there any multiple choice answers?

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4 years ago

Anna wants to factor the polynomial p(x)=5x^4+40x. She knows that the sum of cubes formula is a^3+b^3=(a+b)(a^2−ab+b^2).

Artemon [7]

Answer:

Part A: Option 2, A: Anna’s answer is incorrect. She correctly factored out 5x, but incorrectly identified a and b, so her answer cannot be correct.

Part B: Option 3, B: 5x(x+2)(x^2−2x+4)

Step-by-step explanation:

p(x) = 5x^4 + 40x

p(x) = 5x(x^3 + 8)

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Part B: Option 3, B: 5x(x+2)(x^2−2x+4)

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3 years ago

Write a double fact you can use to find the sum 5+4, 6+7, 8+9

Rina8888 [55]

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3 years ago

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Vilka [71]

Answer:

x = -3

Step-by-step explanation:

4x - 5 + 2(x - 3) = 12x + 7

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