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2 years ago

6

A segment with endpoints X (6, 2) and Y (- 1, - 3) is rotated 90º about the origin. What are the coordinates of X Prime and Y Pr

ime?

1 answer:

Minchanka [31]2 years ago

8 0

The line XY is shown in the diagram below
Coordinate X (-6, 2) rotated 90° through the origin, then coordinate X' is (2, 6)
Coordinate Y (-1, -3) rotated 90° through the origin, then coordinate Y' is (-3, -1)

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Apples cost $2.99 per pound at Natural Grocers. If Landon purchases 3.6 pounds of apples, then how much will he spend? Round you

Mashutka [201]

$10.8 rounding it to the nearest dollar is $10

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2 years ago

Find the range of the following set of data:12,2,14,80,100

Leviafan [203]

Answer: 98

Step-by-step explanation: Subtract the biggest number from the smallest. 100-2=98

8 0

1 year ago

Read 2 more answers

For the scientific notation, write the standard form: 5.61 x 102

Alekssandra [29.7K]

<em>I believe the exponential form above is 5.61 x </em> $10^{2}$

Answer:

561

Step-by-step explanation:

A<em> "scientific notation"</em> is being used in order to express large numbers in its <u>simplest form</u>. This is commonly used in careers that use Mathematics very often like<em> engineers</em> or<em> scientists </em>because it makes their computation easier.

The<em> "standard form"</em> refers to the standard or traditional way of writing the numbers.

In order to get the standard form above, you have to check the <em>"power of the number 10." </em>The exponent above is 2. This means that you have to move the decimal point of 5.61 to the<em> right twice.</em> So, the answer is 561.

4 0

2 years ago

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 $\theta$ :

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

3 0

2 years ago

Find the sum of the geometric series 40 + 40(1.005) + 40(1.005)^2 + ⋯ + 40(1.005)^11.

KiRa [710]

Answer:

The sum is 493.4

Step-by-step explanation:

In order to find the value of the sum, you have to apply the geometric series formula, which is:

$\sum_{i=1}^{n} ar^{i-1} = \frac{a(1-r^{n})}{1-r}$

where i is the starting point, n is the number of terms, a is the first term and r is the common ratio.

The finite geometric series converges to the expression in the right side of the equation. Therefore, you don't need to calculate all the terms. You can use the expression directly.

In this case:

a=40

b= 1.005

n=12 (because the first term is 40 and the last term is 40(1.005)^11 )

Replacing in the formula:

$\frac{a(1-r^{n})}{1-r} = \frac{40(1-1.005^{12})}{1-1.005}$

Solving it:

The sum is 493.4

4 0

2 years ago