Triangles ABC and DEF are similar triangles. What are the lengths of the unknown sides?


A)

DF = 39 cm; DE = 15 cm

B)

DF = 48 cm; DE = 52 cm

C)

DF = 65 cm; DE = 25 cm

D)

DF = 52 cm; DE = 48 cm

Triangles ABC And DEF Are Similar Triangles. What Are The Lengths Of The Unknown Sides?A) DF = 39 Cm;

Answers

Answer 1

Answer:

D)

DF = 52

AB = 48

Step-by-step explanation:

Use the two lengths of sides already given.

Divide to find the scale factor:

20 / 5 = 4

Scale factor: 4

Now multiply to find the unknown sides:

13 × 4  = 52

12 × 4 = 48

DF = 52

AB = 48

Hope this helped.


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Answer:

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Answer:

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Answers

Answer:

The third side is increasing at an approximate rate of about 0.444 meters per minute.

Step-by-step explanation:

We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.

Let the angle between the two given sides be θ and let the third side be c.

Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.

First, convert the degrees into radians:

[tex]\displaystyle 2^\circ \cdot \frac{\pi \text{ rad}}{180^\circ} = \frac{\pi}{90}\text{ rad}[/tex]

Hence, dθ/dt = π/90.

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[tex]\displaystyle c^2 = a^2 + b^2 - 2ab\cos \theta[/tex]

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[tex]\displaystyle c^2 = (13)^2 + (19)^2 - 2(13)(19)\cos \theta[/tex]

Simplify:

[tex]\displaystyle c^2 = 530 - 494\cos \theta[/tex]

Take the derivative of both sides with respect to t:

[tex]\displaystyle \frac{d}{dt}\left[c^2\right] = \frac{d}{dt}\left[ 530 - 494\cos \theta\right][/tex]

Implicitly differentiate:

[tex]\displaystyle 2c\frac{dc}{dt} = 494\sin\theta \frac{d\theta}{dt}[/tex]

We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find c:

[tex]\displaystyle \begin{aligned} c &= \sqrt{530 - 494\cos \theta}\\ \\ &=\sqrt{530 -494\cos \frac{\pi}{3} \\ \\ &= \sqrt{530 - 494\left(\frac{1}{2}\right)} \\ \\&= \sqrt{283\end{aligned}[/tex]

Substitute:

[tex]\displaystyle 2\left(\sqrt{283}\right) \frac{dc}{dt} = 494\sin\left(\frac{\pi}{3}\right)\left(\frac{\pi}{90}\right)[/tex]

Solve for dc/dt:

[tex]\displaystyle \frac{dc}{dt} = \frac{494\sin \dfrac{\pi}{3} \cdot \dfrac{\pi}{90}}{2\sqrt{283}}[/tex]

Evaluate. Hence:

[tex]\displaystyle \begin{aligned} \frac{dc}{dt} &= \frac{494\left(\dfrac{\sqrt{3}}{2} \right)\cdot \dfrac{\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{\dfrac{247\sqrt{3}\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{247\sqrt{3}\pi}{180\sqrt{283}} \\ \\ &\approx 0.444\text{ m/min}\end{aligned}[/tex]

The third side is increasing at an approximate rate of about 0.444 meters per minute.

9514 1404 393

Answer:

  0.444 m/min

Step-by-step explanation:

I find this kind of question to be answered easily by a graphing calculator.

The length of the third side can be found using the law of cosines. If the angle of interest is C, the two given sides 'a' and 'b', then the third side is ...

  c = √(a² +b² -2ab·cos(C))

Since C is a function of time, its value in degrees can be written ...

  C = 60° +2t° . . . . . where t is in minutes, and t=0 is the time of interest

Using a=13, and b=19, the length of the third side is ...

  c(t) = √(13² +19² -2·13·19·cos(60° +2t°))

Most graphing calculators are able to compute a numerical value of the derivative of a function. Here, we use the Desmos calculator for that. (Angles are set to degrees.) It tells us the rate of change of side 'c' is ...

  0.443855627418 m/min ≈ 0.444 m/min

_____

Additional comment

At that time, the length of the third side is about 16.823 m.

__

c(t) reduces to √(530 -494cos(π/90·t +π/3))

Then the derivative is ...

  [tex]c'(t)=\dfrac{494\sin{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}\right)}\cdot\dfrac{\pi}{90}}{2\sqrt{530-494\cos{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}}}\right)}}}\\\\c'(0)=\dfrac{247\pi\sqrt{3}}{180\sqrt{283}}\approx0.443855...\ \text{m/min}[/tex]

Did any one know this?

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Five students want to play dodgeball and they all want to be a team captain. To be fair, the gym coach decides to place the names of all five students into a hat, mix well, and select two names at random without replacement. The names chosen will be the team captains. Each outcome in the sample space for the random selection of two team captains is equally likely. What is the probability of each outcome in the sample space?
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WARNING! PEOPLE HAVE BEEN PUTTING THE FOLLOWING WRONG ANSWERS:
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Answer:

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The manager of a juice bottling factory is considering installing a new juice bottling machine which she hopes will reduce the amount of variation in the volumes of juice dispensed into 8-fluid-ounce bottles. Random samples of 10 bottles filled by the old machine and 9 bottles filled by the new machine yielded the following volumes of juice (in fluid ounces).

Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9
New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1

Required:
Use a 0.05 significance level to test the claim that the volumes of juice filled by the old machine vary more than the volumes of juice filled by the new machine

Answers

Answer:

Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine

Step-by-step explanation:

Given the data:

Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9

New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1

To test if volume filled by old machine varies more than volume filled by new machine :

Hypothesis :

H0 : s1² = s2²

H1 : s1² > s2²

Using calculator :

Sample size, n and variance of each machine is :

Old machine :

s1² = 0.37889

n = 10

New machine :

s2² = 0.006111

n = 9

Using the Ftest :

Ftest statistic = larger sample variance / smaller sample variance

Ftest statistic = 0.37889 / 0.006111

Ftest statistic = 62.001

Decision region :

Reject H0 ; If Test statistic > Critical value

The FCritical value at 0.05

DFnumerator = 10 - 1 = 9

DFdenominator = 9 - 1 = 8

Fcritical(0.05, 9, 8) = 3.388

Since 62 > 3.388 ; Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

you cannot add some simple numbers ? you don't know how to use a calculator ?

to solve this yourself is way shorter than putting this in here.

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