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3 years ago

14

Each gridline represents one mile. If Ryan drove from home to the soccer field and then from the soccer field to the library, tr

aveling in a straight line to each destination, he would have traveled ___ miles by the time he reached the library.

1 answer:

romanna [79]3 years ago

3 0

Answer:

13 miles

Step-by-step explanation:

Given that he traveled in a straight line to each destination. Then,

i. distance from his home to soccer field = $\sqrt{x^{2} + y^{2} }$

= $\sqrt{4^{2} + 3^{2}}$

= $\sqrt{16 + 9}$

= $\sqrt{25}$ = 5 miles

ii. The distance from soccer field to the library = 8 miles.

So that we can say that;

Ryan's total distance from home to the library = 5 + 8

= 13 miles

Thus, Ryan would have traveled 13 miles by the time he reached the library.

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If f(1) = 0, what are all the roots of the function f(x)=x^3+3x^2-x-3? Use the Remainder Theorem.

Sophie [7]

There's no if about it,

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

has a zero $f(1)=0$ so $x-1$ is a factor. That's the special case of the Remainder Theorem; since $f(1)=0$ we'll get a remainder of zero when we divide $f(x)$ by $x-1.$

At this point we can just divide or we can try more little numbers in the function. It doesn't take too long to discover $f(-1)=0$ too, so $x+1$ is a factor too by the remainder theorem. I can find the third zero as well; but let's say that's out of range for most folks.

So far we have

$x^3+3x^2-x-3 = (x-1)(x+1)(x-r)$

where $r$ is the zero we haven't guessed yet. Again we could divide $f(x)$ by $(x-1)(x+1)=x^2-1$ but just looking at the constant term we must have

$-3 = -1 (1)(-r) = r$

so

$x^3+3x^2-x-3 = (x-1)(x+1)(x+3)$

We check $f(-3)=(-3)^3+3(-3)^2 -(-3)-3 = 0 \quad\checkmark$

We usually talk about the zeros of a function and the roots of an equation; here we have a function $f(x)$ whose zeros are

$x=1, x=-1, x=-3$

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2 years ago

Read 2 more answers

CALCULUS: For an object whose velocity in ft/sec is given by v(t) = sin(t), what is its distance, in feet, travelled on the inte

rodikova [14]

The linked answer is wrong because that integral gives you the net displacement of the object, not the total distance.

To get the distance, you have to integrate the speed (as opposed to velocity), which involves integrating the absolute value of the velocity function.

$\mathrm{distance} = \displaystyle\int_1^5 |\sin(t)| \,\mathrm dt$

By definition of absolute value,

$|\sin(t)|=\begin{cases}\sin(t)&\text{for }\sin(t)\ge0\\-\sin(t)&\text{for }\sin(t)$

Over this particular integration interval,

• sin(<em>t</em> ) ≥ 0 for 1 ≤ <em>t</em> < <em>π</em>, and

• sin(<em>t</em> ) < 0 for <em>π</em> < <em>t</em> ≤ 5

so you end up splitting the integral at <em>t</em> = <em>π</em> as

$\mathrm{distance} = \displaystyle\int_1^\pi \sin(t)\,\mathrm dt + \int_\pi^5 (-\sin(t))\,\mathrm dt$

Now compute the distance:

$\mathrm{distance} = -\cos(t)\bigg|_1^\pi + \cos(t)\bigg|_\pi^5$

$\mathrm{distance} = -(\cos(\pi) - \cos(1)) + (\cos(5) - \cos(\pi))$

$\mathrm{distance} = -2\cos(\pi) + \cos(1) + \cos(5) \approx 2.82$

making B the correct answer.

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2 years ago

Dexter has four different coins in his pocket. He randomly selects a coin from his pocket, replaces it, and selects another coin

skad [1K]

Answer:

Step-by-step explanation:

So what is the probability of the selecting the first coin? There are total of 4 different coins, so the probability of getting a dime is 1 out of 4, then he replace it, then again the probability stays the same, he still has 1 out 4 chance of getting a dime. So then it's just 1/4*1/4=1/16 :)

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3 years ago

Here are descriptions for how two dot patterns are growing,

Arisa [49]

The steps in the patterns A and B form a sequence

The attached diagram represents dots in patterns A and B

<h3>How to draw the diagrams</h3>

For pattern A, we have:

Step 2 = 10 dots

Increment of 3 dots in each step

This means that:

Step 0 = 4 dots

Step 1 = 7 dots

Step 2 = 10 dots

Step 3 = 13 dots

For pattern A, we have the following rule

$T_n =2n^2 + 1$

When n = 0 to 3, we have:

$T_0 =2(0)^2 + 1 =1$

Step 0 = 1 dot

$T_1 =2(1)^2 + 1 =3$

Step 1 = 3 dots

$T_2 =2(2)^2 + 1 =9$

Step 2 = 9 dots

$T_3 =2(3)^2 + 1 =19$

Step 3 = 19 dots

Next, we draw the diagrams of both patterns (see attachment)

Read more about patterns at:

brainly.com/question/15590116

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2 years ago

The equation of a parabola is y=x^2-10x+27. Write the equation in vertex form

azamat

Answer:

$\large \boxed{y = (x - 5)^{2} + 2 }$

Step-by-step explanation:

y = x² - 10x + 27

y = ax² + bx + c

This is the general form of the equation for a parabola.

We must convert it to the vertex form

y = (x - h)² + k, where (h,k) are the coordinates of the vertex.

We can do this by completing the square.

$\begin{array}{rcll}y & = & x^{2} - 10x + 27 & \\y - 27 & = & x^{2} - 10x & \text{Subtracted 27 from each side}\\y - 27&= & x^{2} - 10x + 25 - 25 & \text{Added and subtracted (b/2)}^{2}\\y - 27&= & (x - 5)^{2} - 25 & \text{Wrote the first three terms as the square of a binomial}\\y& = & \mathbf{(x - 5)^{2} + 2} & \text{Added 27 to each side}\\\end{array}\\\text{The vertex form of the parabola is $\large \boxed{\mathbf{y = (x - 5)^{2} + 2 }}$}$ The figure below shows that your parabola has its vertex at (5,2).

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3 years ago