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2 years ago

Find the perimeter of the polygon with the vertices U(-2,4), V(3,4) W(3,-4). Round your answer the nearest hundredths

Mathematics

1 answer:

Nastasia [14]2 years ago

6 0

Answer:

22.43

Step-by-step explanation:

three points ==> it's a triangle

so we will just have to calculate the length of each side

U & V has the same y-coordinate, which means UV is a horizontal line ==>

UV = 3 - (-2) = 5

V & W has the same x-coordinate, which means VW is a vertical line ==>

VW = 4 - (-4) = 8

UW is not a horizontal line nor a vertical line, so we will have to calculate it using distance formula

UW = sqrt { [3 - (-2)]^2 + [-4 - 4]^2 } = sqrt{25 + 64} = sqrt(89) ~~ 9.43

so the perimeter of the polygon is UV + VW + UW = 5 + 8 + 9.43 = 22.43

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For any circle, which ratio is equal to the number n? Select all that apply. Plsss help me!!

barxatty [35]

Answer:

Options A-C-F

Step-by-step explanation:

we know that

<em>The circumference of a circle is equal to</em>

$C=\pi D$ or $C=2\pi r$

where

D is the diameter and r is the radius

therefore

$\pi =\frac{C}{D}$ or $\pi =\frac{C}{2r}$

The number pi is the ratio circumference - diameter or is the ratio circumference - 2 times radius

<em>The area of the circle is equal to</em>

$A=\pi r^{2}$

therefore

The number pi is the ratio Area - radius squared

6 0

3 years ago

Which of the following is the equation for the graph shown?a. x^2/144+y^2/95=1b. x^2/144-y^2/95=1c. x^2/95+y^2/144=1d. x^2/95-y^

Andrews [41]

e follSOLUTION

Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the general equation of an ellipse

$\frac{\mleft(x-h\mright)^2}{a^2}+\frac{(y-h)^2}{b^2^{}}=1$

STEP 2: Identify the parameters

the length of the major axis is 2a

the length of the minor axis is 2b

$\begin{gathered} 2a=24,a=\frac{24}{2}=12 \\ 2b=20,b=\frac{20}{2}=10 \end{gathered}$

STEP 3: Get the equation of the ellipse

$\begin{gathered} By\text{ substitution,} \\ \frac{(x-h)^2}{a^2}+\frac{(y-h)^2}{b^2}=1 \\ \frac{(x-0)^2}{12^2}+\frac{(y-0)^2}{10^2}=1=\frac{x^2}{144}+\frac{y^2}{100}=1 \end{gathered}$

STEP 4: Pick the nearest equation from the options,

Hence, the equation of the ellipse in the image is given as:

$\frac{x^2}{144}+\frac{y^2}{95}=1$

OPTION A

8 0

1 year ago

Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 450 newtons stretches a sprin

vlada-n [284]

Answer:

The work done is 202.50Nm

Step-by-step explanation:

Given

$F =450N$

$x_1 = 30cm$

$x_2 = 60cm$

Required

The work done

First, we calculate the spring constant (k)

$F = kx_1$

$450N = k *30cm$

$k = \frac{450N}{30cm}$

$k =15N/cm$

So:

$F = kx_1$

$F(x) = 15x$

The work done using Hooke's law is:

$W =\int\limits^a_b {F(x)} \, dx$

This gives:

$W =\int\limits^{60}_{30} {15x} \, dx$

Rewrite as:

$W =15\int\limits^{60}_{30} {x} \, dx$

Integrate

$W =15 \frac{x^2}{2}|\limits^{60}_{30}$

This gives:

$W =15 *\frac{60^2 - 30^2}{2}$

$W =15 *\frac{2700}{2}$

$W =15 *1350$

$W =20250N-cm$

Convert to Nm

$W =\frac{20250Nm}{100}$

$W =202.50Nm$

7 0

3 years ago

When does the proportion form of newton's second law take the form of an equation?

Brrunno [24]

Newton's law of motion has three parts. The second of which states that the force needed to move an object is directly proportional to the acceleration of the motion. The proportion can be written as,
F = ka
where k is the constant of proportionality. This can be substituted with the mass of the object such that the equation would become.
F = ma
where F is force, m is mass, and a is acceleration.

8 0

3 years ago

What is the unit rate of 5/7 : 4/7?

allochka39001 [22]

9514 1404 393

Answer:

a = 5/4

Step-by-step explanation:

To make the second number in this ratio be 1, you need to multiply the whole ratio by 7/4:

(7/4)(5/7) : (7/4)(4/7) = 5/4 : 1 = a : 1

a = 5/4

6 0

3 years ago