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3 years ago

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Nathan wanted to go on a field trip to Europe. The total cost of the field trip was $3,960. Nathan wanted to make payments. Each

monthly payment would be $242 a month. How many months would he have to wait to pay off the total cost.

1 answer:

Alchen [17]3 years ago

3 0

The nearest whole number is 17. when you divide 3960 by 242, you get 16.363636.... but, he wouldn't have completely paid it off at 16 months, so it would be fully paid at 17 months

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Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :

$\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ$ .

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3 years ago

Kipish [7]

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3 years ago

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dion flips a coin 20 times and records if it comes up heads. if getting heads is a success, what is the probability of a success

kolbaska11 [484]

Answer:

$\frac{1}{2}$

Step-by-step explanation:

The probability of success (getting heads) on one roll DOESNT affect other rolls, so we need to find probability of getting a head in a roll.

Probability is defined as the number of favorable outcomes divided by the total number of outcomes.

<em>Here, favorable outcome is getting a head. So, on one roll, getting a head is 1. Also, the total number of outcomes is either a head or a tail. So total number of outcomes is 2.</em>

Thus,

P(Heads) = 1/2

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3 years ago

Can someone help me

True [87]

Answer:

Step-by-step explanation: dont work sorry

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3 years ago

can someone please help me find the surface area of the pyramid with an equilateral triangle for a base

ioda

To obtain the total surface we have to calculate the surface of the 4 triangles and add up the areas (remember that the area of a triangle is (b*h)/2 , b is the base, h is the height ).

We will caculate first the area of the base triangle for that we considerer the fact that it is an equilateral triangle with sides of lenght 6 cm, now we calculate the height, I am going to draw please wait a moment

using the pythagorean theorem we have that

$\begin{gathered} h^2=6^2cm^2-3^2\operatorname{cm}=27cm^2 \\ h=\text{ }\sqrt[]{27\text{ }}cm \end{gathered}$

Then, the area of the triangle is 6*h/2 = 3h = 15.59 cm^2.

Now we calculate the area of the other 3 triangles, notice that those triangles have the same base and height so we will calculate for one of them and multiply by 3. From the image we know that the height is 15cm and the base is 6 cm so the area is 45cm^2, and 45*3 cm^2 = 135cm^2.

Finally we add up all the areas:

$135cm^2+15.59cm^2=150.59cm^2$

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1 year ago