54x9=756<br> explain the error

One side of a right triangle is known to be 12 cm long and the opposite angle is measured as 30°, with a possible error of ±1°.

vladimir1956 [14]

Answer:

estimated error=±0.725

Step-by-step explanation:

Side of the triangle= 12cm

Opposite of triangle x= 30

h= hypotenose side

Error= =±1

From trigonometry

Sin(x)=opposite/hypotenose

hypotenose=opposite/sin(x)

h=12/sin(x)

h=12Csc(x)

dh=-12Csc(x)Cot(x) dx...............eqn(1)

dx is the possible error in angle measurements

So we need to convert to radius

dx=±1°× (π/180)

=±1°(π/180)

Substitute x and dx into equation (1)

dh= - 12Csc30°Cot30°×[±(π/180)]

= -12(2)(√3)(±(π/180)

==±0.725

Therefore, estimated error=±0.725

3 0

2 years ago

Please, I'm confuse!

Ivahew [28]

OK. You asked for it. Here we go.
First, let's gather up the tools we might use ...
some things that we know about triangles:

-- Every triangle: Area = (1/2) x (length of the base) x (the height)

-- Isosceles triangle: It has two sides that are the same length.

-- Right triangle: It has one right angle in it.
The sides that meet at the right angle are called the "legs".
They form a corner there, like this    _|   .
-------------------------------------------
Now we can start using these tools to hack away at the problem.
Farmer Ted has an isosceles right triangle garden.
The problem asks us to figure out how long the legs are.

Before he changes anything, it looks like this   _|   and both of
those sides are the same length. Call it 'x' until we figure out
what it really is.

Notice that one of them is the base of the triangle, and the other one
is the height. So the area of this triangle is

                           (1/2) (x) (x) or (1/2) x² .

-------------------------------

Farmer Ted is never satisfied. Suddenly, one day without warning, he
comes along and makes the garden bigger. He makes one of the legs
7 ft longer, and he makes the other one 5 ft longer.

Now the length of one leg is (x + 7) and the other one is (x + 5) .
They're still the base and height of the triangle, so the area of the
bigger garden is
                           (1/2) (x + 7) (x + 5).

The problem says that this area is 55 square feet more than the original
area, so look out, here comes the <em>equation </em>:

                       new area         =      old area + bigger

                (1/2) (x + 7) (x + 5) =      (1/2) x² + 55

Locked in the mysterious shadowy crevices of this equation is
everything we need in order to figure out the original length of the legs ...
what we called 'x'.

At this point, we can forget about Farmer Ted, forget about the garden,
and just go back to our laboratory with this equation and solve it to find 'x'.

Let's take it slow and easy, one little step at a time:

                             <u>(1/2) (x + 7) (x + 5) = (1/2) x² + 55</u>

Multiply each side by 2 :       (x + 7) (x + 5) =   x² + 110

Expand (FOIL) the left side:     x² + 12x + 35 =   x² + 110

Subtract x² from each side:          12x + 35 =   110

Subtract 35 from each side:          12x   =      75

Divide each side by 12 :                         <em>x = 6.25 feet</em>

==============================================

OK. That's a very nice number. How do we know whether it's correct ?
Let's check it out, and see if it fits the story:

Original area = (1/2 x base x height) = (0.5 x 6.25 x 6.25) = 19.53125 sq ft

One new leg = (6.25 + 7) =   13.25 ft
Other new leg = (6.25 + 5) = 11.25 ft

New area = (1/2 x base x height) = (0.5 x 13.25 x 11.25) = 74.53125 sq ft

How much bigger is the new area ?

   74.53125 - 19.53125 = <em>55 sq ft </em> yay !

When we start with legs that are 6.25-ft and go through the whole story,
the new area is exactly what the problem says it was. So 6.25-ft is the
correct original length of the legs, before Farmer Ted messed with it.

7 0

2 years ago

Erik's disabled sailboat is floating stationary 3 miles east and 2 miles north of Kingston. A ferry leaves Kingston heading towa

sergij07 [2.7K]

Answer:

Step-by-step explanation:

Let's suppose that Ballard is an origin with coordinates (0;0)

Ballard is 8 miles south and 1 mile west of Edmonds ⇒ Edmonds is 1 mile east and 8 miles north of Ballard.

Thus, coordinates of Edmonds (0+1; 0+8) (1;8)

Edmonds is 6 miles due east of Kingston. So, is 6 miles due of Edmonds

Thus, Kingston coordinates (1-6;8) (-5:8)

Sailboat is 3 miles east and 2 miles north of kingston

So, coordinates of sailboat are (-5+3; 8+2) (-2;10)

a)

Ferry leaves Kingston towards Edmonds at mph and Edmonds is 6 miles due east of Kingston.

Initial ferry coordinates as calculated above are equal to Kingston coordinates (-5;8)

After 20 minutes the ferry turns to south.

This distance travelled (20min) is d=9mph*20/60h=3 miles

So, ferry travelled 3 miles toward east in 20 min

Then, coordinates became (-5+3;8+0) (-2;8)

Thus, we have a line connecting two points (-5;8) and (-2;8)

Line connecting them has an equation:

y-8 = (8-8)/(-2+5) * (x+5)

y-8=0

y=8 - This is the equation for the first 20 minutes of travel

Then, ferry turns due south (-2;8) and has a vertiacl line

The equation of verical line is x=a, so the equation will be x=2

b) The sailboat has a radar scope that will detect any object within 3 miles of the sailboat.

region looks like a circular disc with a center (-2;10)

(x+2)^2+(y-10)^2=3^2

(x+2)^2+(y-10)^2 <9 (interior of the circular disc)

(x+2)^2+(y-10)^2 >9 (exterior)

The equation of the line joining the Kingston and Edmonds is y=8

the point of intersection:

(x+2)^2+(8-10)^2=9

(x+2)^2=5

x is approximately 0.24; -4.24

(0.24;8) (-4.24;8) - intersection points

c) The ferry exits the radar during the trid due south long x=-2

The points of intersection of the circle and the line x=-2:

(-2+2)^2+(y-10)^2=9

0+(y-10)^2=0

y is 7.13

(-2;7)

d) Takes south turn at (-2;8), then ferry travels 0.8 miles up to point (-2;7) where it exists the radar zone

Speed is 9mph

The time taken to cover 1 mile = t=1/9hr=1/9 *60=6.667min

So, it exists after 6.67 minutes

e) Ferry enters at (-4.24;8) and takes turn due to south at (-2;8)

The distance travelled is = [-4.24+2]=2.24 miles

The time taken to cover these miles is = t=2.24/9 *60=14.93 min

After turning to south ferry remains in radar for 6.7 min

So, it remains in radar zone for 14.93+6.7=21.63min

8 0

2 years ago

Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 m

VLD [36.1K]

<h2>Answer:</h2>

The average speed of car is:

0.75 miles per minutes.

The equation of line is:

$n=\dfrac{3}{4}t$

<h2>Step-by-step solution:</h2>

The table that describes the time and number of miles marked is given by:

Time Miles

0 0

4 3

8 6

Clearly we could observe that with the increase in time by every 4 minutes the number of mile increases by 3.

i.e. the average speed is calculated as the ratio of change in miles to the change in time.

Hence,

$Average\ Speed=\dfrac{3-0}{4-0}\\\\\\i.e.\\\\\\Average\ Speed=\dfrac{3}{4}=0.75$

Hence, the average speed=0.75 miles per minutes.

Also we will find the equation of the lines that related the miles and time by using the two-point formula.

i.e. any line passing through (a,b) and (c,d) is calculated by using the formula:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

Here (a,b)=(0,0) and (c,d)=(4,3)

i.e. the equation is given by:

$n-0=\dfrac{3-0}{4-0}\times (t-0)\\\\i.e.\\\\n=\dfrac{3}{4}t$

6 0

2 years ago

Read 2 more answers

A right triangle has legs of length 4x and 20x. What is an expression for the hypotenuse of the right triangle

kherson [118]

Answer:

$4x\sqrt{26}$ .

Step-by-step explanation:

Given information:

$Leg_1=4x$

$Leg_2=20x$

According to the Pythagoras theorem,

$(hypotenuse)^2=(Leg_1)^2+(leg_2)^2$

Using Pythagoras theorem, we get

$(hypotenuse)^2=(4x)^2+(20x)^2$

$(hypotenuse)^2=16x^2+400x^2$

$(hypotenuse)^2=416x^2$

Taking square root on both sides.

$hypotenuse=\sqrt{416x^2}$

$hypotenuse=4x\sqrt{26}$

Hence, the expression of the hypotenuse is $4x\sqrt{26}$ .

5 0

2 years ago

54x9=756 explain the error