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3 years ago

Maybe Someone can help on thiss too

Mathematics

1 answer:

Rom4ik [11]3 years ago

3 0

Answer:

-6/7

Step-by-step explanation:

The slope of the line perpendicular to DE is the negative reciprocal of the slope of DE. The slope of DE is ...

(change in y)/(change in x) = (y2 -y1)/(x2 -x1) = (-3-4)/(1-7) = -7/-6 = 7/6

The inverse of that is 6/7, and the opposite of that inverse is -6/7.

The slope of the line perpendicular to DE is -6/7.

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Triangle ΔABC has side lengths of a = 18, <img src="https://tex.z-dn.net/?f=b%3D18%5Csqrt%7B3%7D" id="TexFormula1" title="b=18\s

ozzi

The measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

<h3 /><h3>What is the law of cosine?</h3>

When the three sides of a triangle is known, then to find any angle, the law of cosine is used.

It can be given as,

$\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle B=\cos^{-1}\left(\dfrac{a^2+c^2-b^2}{2ac}\right) \\\angle C=\cos^{-1}\left(\dfrac{a^2+b^2-c^2}{2ab}\right)$

Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.

Triangle ΔABC has side lengths of a = 18, b=18√3 and c = 36 inches.

Part A: Determine the measure of angle A

Put the value, in the cosine law, the measure of angle A.

$\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle A=\cos^{-1}\left(\dfrac{(18\sqrt{3})^2+36^2-18^2}{2(18\sqrt{3})(36)}\right) \\\angle A=0.5236\rm\; rad\\\angle A=30^o\rm\; degree\\$

Part B: Show how to use the unit circle to find tan A

Using the chart of unit circle, the value of tangent A can be found out. The tangent A is,

$\tan A=\tan 30^o\\\tan A=\dfrac{1}{\sqrt{3}}$

Part C: Calculate the area of ΔABC.

Use the following formula to find area of ΔABC.,

$A=\dfrac{ab.\sin C}{2}\\A=\dfrac{18\times18\sqrt{3}.\sin C}{2}\\A=280.6\rm\; in^2$

Thus, the measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

Learn more about the law of cosine here;

brainly.com/question/4372174

#SPJ1

7 0

2 years ago

A cylinder has diameter of 4ft and a height of 9ft. Explain whether halving the diameter has the same effect on the surface area

elena55 [62]

Answer:

See Below

Step-by-step explanation:

The surface area of cylinder is given by the formula:

$SA=2\pi r^2 + 2\pi r h$

Where

r is radius ( diameter is 4, so radius is 4/2 = 2)

h is height ( h = 9)

Lets find original surface are:

$SA=2\pi r^2 + 2\pi r h\\SA=2\pi (2)^2 + 2\pi (2) (9)\\SA=8\pi +36\pi\\SA=44\pi$

<u>Halving diameter:</u>

diameter would be 4/2 = 2, so radius would be 2/2 = 1

So, SA would be:

$SA=2\pi r^2 + 2\pi r h\\SA=2\pi (1)^2 + 2\pi (1) (9)\\SA=2\pi +18\pi\\SA=20\pi$

<u>Halving height:</u>

Height is 9, halving would make it 9/2 = 4.5

Now, calculating new SA:

$SA=2\pi r^2 + 2\pi r h\\SA=2\pi (2)^2 + 2\pi (2) (4.5)\\SA=8\pi + 18\pi\\SA= 26\pi$

Original SA is $44\pi$ ,

Halving diameter makes it $20\pi$

Halving height makes it $26\pi$

So, halving diameter does not have same effect as halving height.

5 0

3 years ago

My pigg y bank has only pennies and nicklels in it , and 2/7 of the coins are nickel If i remove 84 pennies then 1/3 of the reme

zubka84 [21]

Answer:

There are 105 pennies in the piggy bank.

There are 42 nickels in the piggy bank.

Step-by-step explanation:

there are:

p pennies in the piggy bank

n nickels in the piggy bank

Then we can define T, the total number of coins, as:

T = p + n

We know that 2/7 of the total number of coins are nickels.

This can be written as:

n = (2/7)*T = (2/7)*(n + p)

And if we remove 84 pennies, 1/3 of the remaining coins are pennies.

This can be written as:

p - 84 = (1/3)*(n + p - 84)

Then we have a system of two equations:

n = (2/7)*(n + p)

p - 84 = (1/3)*(n + p - 84)

Let's solve the system, to do it, we first need to isolate one of the variables in one of the equations.

We can isolate n in the first one, to get:

n = (2/7)*(n + p) = (2/7)*n + (2/7)*p

n - (2/7)*n = (2/7)*p

n*(5/7) = (2/7)*p

n = (7/5)*(2/7)*p = (2/5)*p

n = (2/5)*p

Now we can replace this in the other equation:

p - 84 = (1/3)*(n + p - 84)

p - 84 = (1/3)*( (2/5)*p + p - 84)

Let's solve this for p

p - 84 = (1/3)*( (7/5)*p - 84)

3*(p - 84) = (7/5)*p - 84

3p - 252 = (7/5)*p - 84

3*p - (7/5)*p = 252 - 84

(15/5)*p - (7/5)*p = 168

(8/5)*p = 168

p = (5/8)*168 = 105

There are 105 pennies in the piggy bank.

And we know that:

n = (2/5)*p = (2/5)*105 = 42

There are 42 nickels in the piggy bank.

4 0

3 years ago

Describe julius caesar as a child

lianna [129]

Answer:

You dare challenge me...

Step-by-step explanation:

Gaius Julius Caesar was a Roman general and statesman who played a critical role in the events that led to the demise of the Roman Republic and the rise of the Roman Empire. In 60 BC, Caesar, Crassus and Pompey formed the First Triumvirate, a political alliance that dominated Roman politics for several years.

8 0

3 years ago

The diameter of a circle is 8 inches. what is the circle's circumference

Svetradugi [14.3K]

Answer:

approx. 25.13

Step-by-step explanation:

C= 2πr

radius is half diameter

6 0

3 years ago

Read 2 more answers