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3 years ago

Define the term reference angle and give the equations to find reference angles.

Mathematics

1 answer:

EleoNora [17]3 years ago

6 0

Answer:

the measure of the smallest, positive, acute angle t formed by the terminal side of the angle t and the horizontal axis.

90° to 180°: reference angle = 180° - angle, 180° to 270°: reference angle = angle - 180, 270° to 360°: reference angle = 360° - angle.

if your given angle is 110°, then its reference angle is 180° – 110° = 70°. When the terminal side is in the third quadrant (angles from 180° to 270°) your reference angle is your given angle minus 180°. So, if your given angle is 214°, then its reference angle is 214° – 180° = 34°.

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a dental company has rolls of floss that are 1872 in long they want to put the distance in the yard on their label what is the d

statuscvo [17]

Copy and paste ur answer onto internet it will tell u

4 0

3 years ago

Given: AB tangent at D, AD = OD = 4 Find: Area of the shaded region

MrMuchimi

Answer:

1.72

Step-by-step explanation:

AB tangent at D, AD = OD = 4

so triangle OAD is right angle with side of 4 and 4.

area of OAD = 1/2 * 4 * 4 = 8

Angle AOD = DAO = 45 deg.

so circular sector OCD area = area of circle O * 45/360

= pi * 4 * 4 * 45/360

= 2pi

Shade area ACD = trigangle OAD - circular sector OCD

= 8 - 2pi

= 1.72

4 0

3 years ago

The length of a chord is equal to its distance to the center of the circle. A second chord in the same circle is twice as long a

Rama09 [41]

Answer:

The distance from the center of the circle to the longer chord is twice smaller than the distance from the center to the shorter chord.

Step-by-step explanation:

The length of the chord AB is the same as the distance OC from the center to the cord. Let OC=2x, then CA=x. By the Pythagorean theorem, the radius r of the circle is

$r^2=OC^2+AC^2,\\ \\r^2=(2x)^2+x^2=5x^2,\\ \\r=\sqrt{5}x.$

The length of the arc ED is 4x.

Consider right triangle EFO. In this triangle, EF=2x, EO=r, then the distance OF is

$OF^2=OE^2-EF^2,\\ \\OF^2=5x^2-(2x)^2=x^2,\\ \\OF=x.$

The distance from the center of the circle to the longer chord is twice smaller than the distance from the center to the shorter chord.

5 0

4 years ago

A bridge underpass in the shape of an elliptical arch, that is, half of an ellipse, is 40 feet wide and 13 feet high. An eight f

Liula [17]

Answer:

the truck should not be higher than 12.934 ft

Step-by-step explanation:

if the bridge underpass is half of an ellipse , then the arch function will be B(x,y) such that

x²/a² + y²/b² = 1 , for x≥0 and y≥0 and y=0 for x≤0

where x= width , y= height

for

a= length of the bridge underpass = 40 ft

b= height of the bridge underpass = 13 ft

x²/(40 ft)² + y²/(13 ft)² = 1

that represents all the points of the arch

the maximum height is reached when the truck touches the arch, then

for a point x= 4 ft wide , since 8 foot wide represents 4 foot to the left (x=-4) and 4 foot to the right (x=4)

then

(4 ft)²/(40 ft)² + y²/(13 ft)² = 1

1/100 - y²/(13 ft)² = 1

y/13 ft = √(1-1/100) = 3/10*√11

y= 3/10*√11 * 13 ft = 12.934 ft

y= 12.934 ft

then the truck should not be higher than 12.934 ft

7 0

3 years ago

Please show work if you do, ( and get it right) I will make you brainliest!!!

DerKrebs [107]

Answer:

The percentage increase in bird population in the second years is 4% .

Step-by-step explanation:

Given as :

During two years, the population of birds of an island became 7 times more than before.

The the percentage increase in first year = = $r_1$ =40%

Let The percentage increase in second year = $r_2$ = r%

So, According to question

The initial population of bird = x

The increase population of bird =7 times before = 7 x

Now,

The increase population of bird = initial population of bird × (1+ $\dfrac{r_1}{100}$ ) × (1+ $\dfrac{r_2}{100}$ )

Or, 7 x = x × (1+ $\dfrac{40}{100}$ ) × (1+ $\dfrac{r}{100}$ )

Or, $\dfrac{7 x}{x}$ = 1.4 × (1+ $\dfrac{r}{100}$ )

Or, 7 = 1.4 × (1+ $\dfrac{r}{100}$ )

Or, $\dfrac{7 }{1.4}$ = (1+ $\dfrac{r}{100}$ )

Or, 5 = (1+ $\dfrac{r}{100}$ )

Or, (1+ $\dfrac{r}{100}$ ) = 5

Or, $\dfrac{r}{100}$ = 5 - 1

Or, $\dfrac{r}{100}$ = 4

∴ r = 4 × 100

I.e r = 400

so, The percentage increase = r% = 4

Hence The percentage increase in bird population in the second years is 4% . Answer

3 0

3 years ago