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2 years ago

explain why the polynomial of least degree that goes through exactly four distinct zeros must have a degrre of 4

1 answer:

6 0

Generally four, but polynomials may have repeated roots. “Could” contain four different binomial, but they just happen to be the same.

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two points on the same side of a tree are 65 feet apart. the angles of elevation of the top the tree are 21 19 from one point an

zloy xaker [14]

The question is find the height of the tree, given that at two points 65 feet apart on the same side of the tree and in line with it, the angles of elevaton of the top of the tree are 21° 19' and 16°20'.

1) Convert the angles to decimal form:

19' * 1°/60' = 0.32° => 21° 19' = 21.32°

20' * 1°/60' = 0.33° => 16° 20' = 16.33°

2) Deduce the trigonometric ratios from the verbal information.

You can form a triangle with

- horizontal leg x + 65 feet
- elevation angle 16.33°
- vertical leg height of the tree, h

=> trigonometric ratio: tan (16.33) = h /( x + 65) => h = (x+65) * tan(16.33)

You can form a second triangle with:

- horizontal leg x
- elevation angle 21.32°
- vertical leg height of the tree, h

=> trigonometric ratio: tan(21.32) = h / x => h = x * tan(21.32)

Now equal the two expressions for h:

(x+65)*tan(16.33) = x*tan(21.32)

=> x*tan(16.33) + 65*tan(16.33) = x*tan(21.32)
=> x*tan(21.32) - x*tan(16.33) = 65*tan(16.33)
=> x = 65*tan(16.33) / [ tan(21.32) - tan(16.33) ] = 195.73 feet

=> h = 195.73 * tan(21.32) = 76.39 feet.

Answer: 76.39 feet

5 0

3 years ago

What is the value of r? Round your final answer to the nearest whole number.

vaieri [72.5K]

Answer:

r = 13

Step-by-step explanation:

Hypotenuse is the side opposite to 90 degree angle, so hypotenuse is r.

Also, with respect to the angle given, the side "12" is the opposite.

So we have opposite side to angle and we need hypotenuse. Which trigonometric ratio related opposite with hypotenuse? It is SINE.

So we can write:

$Sin(67.4)=\frac{Opposite}{Hypotenuse}=\frac{12}{r}\\rSin(67.4)=12\\r=\frac{12}{Sin(67.4)}\\r=12.99$

Rounded to nearest whole number, r = 13

8 0

3 years ago

Read 2 more answers

Please help!! Very urgent..thank you!!

erastova [34]

Answer : 4 times

Here it's given that ,

The height and base of the butterfly sitting on the stem (red butterfly) is two times greater than the height and base of the butterfly sitting on the flower .

And we need to find out how many times the area of red winged butterfly is greater than that of sitting on the flower (blue butterfly) .

Let us take ,

base of blue butterfly be b
height of blue butterfly be h
Area be A .

Then ,

base of red butterfly will be 2b .
height of red butterfly will be 2h .
Area be A' .

We know that ,

→ area of the triangle = 1/2 × base × height

So that ,

→ A/A' = (1/2 * b * h) ÷ (1/2 *2b *2h)

→ A/A' = bh/4bh

→ A/A' = 1/4

→ A' = 4A

Henceforth the area of blue butterfly is 4 times greater than that of red winged butterfly .

I hope this helps.

6 0

2 years ago

a fabric store sells pieces of material for $5 each Ali bought two white pieces and 8 blue pieces she also bought a pack of butt

Murrr4er [49]

The term (2 + 8) is described as the total amount of pieces of fabric. It makes it easier to put this term this way so you wouldn't have to do (8 x 5) + (2 x 5) and do the distributive property.

8 0

3 years ago

Read 2 more answers

How many degrees does each angle of an equilateral triangle measure? 45o, 60o, 90o, 100o

LiRa [457]

A triangle has 3 angles.

The sum of the measures of the angles of a triangle is 180.

In an equilateral triangle, all angles have the same measure.

180/3 = 60

Answer: 60 degrees.

7 0

2 years ago