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2 years ago

RSTUV - EABCD. Find AE.

Mathematics

1 answer:

larisa86 [58]2 years ago

3 0

9514 1404 393

Answer:

AE = 3

Step-by-step explanation:

First of all, we need to find corresponding sides that are defined in both figures. The table below shows the given values.

From the table, we can write the proportion ...

EA/RS = BC/TU . . . corresponding sides are proportional

EA/6 = 4/8 . . . . . . . substitute given lengths

EA = 6(4/8) = 3

The length of AE is 3 units.

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A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer. Find the rate of change of the an

lubasha [3.4K]

The rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground is 1/20 degree/sec.

<h3>What is angle of elevation?</h3>

It is described as a relationship between an oblique line from the observer's eye to an item above his eye and the horizontal plane. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.

Calculation for the rate of change of angle of elevation-

According to the question,

A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer.

The balloon is 100 feet above the ground.

Let the height of the balloon be 'h' ft.

Then tanØ = h/100

h = 100tanØ

Differentiate the above equation with respect to time.

dh/dt = 100 sec² Ø (dØ/dt)

We know dh/dt = 10 ft/sec.

when h = 100

tanØ = 100/100 = 1/1

tanØ = Perpendicular/Base

On comparing above two equations,

Perpendicular = 1; Base = 1.

By Pythagoras the hypotenuse is,

H² = P² + B²

= 1² + 1²

= 2

H = √2

Now, calculate the value of cosØ.

cosØ = B/H = 1/√2

Squaring both side

cos² Ø = 1/2

sec² Ø = 1/cos² Ø

sec² Ø = 2

The main equation was,

dh/dt = 100 sec² Ø (dØ/dt)

Substitute the values,

dØ/dt = (dh/dt )/100 sec² Ø

= (10)/(100×2)

dØ/dt = 1/20 degree/sec.

Therefore, the rate of change of the angle of elevation of the balloon from the observer is 1/20 degree/sec.

To know more about the angle of elevation, here

brainly.com/question/9817377

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8 0

1 year ago

Find the values of x, y, and z.

SashulF [63]

The three inside angles of a triangle need to equal 180 degrees.

This means X = 180 - 43 - 59 = 78 degrees.

X and Z make a straight line that also needs to equal 180 degrees,

so Z = 180 - 78 = 102 degrees.

Y = 180 - 102 - 13 = 65 degrees.

5 0

2 years ago

Let w be the set of all points in r3 that lie in the xz-plane. is w a subspace of r3?

hichkok12 [17]

It might be helpful to remember that the definitions of R2 and R3 are not geometric at all. R2 is the set of all ordered pairs of real numbers, whereas R3 is the set of all ordered triples of real numbers. W is a subspace fo R3, and so it still consists of elements which are triples, not pairs. The fact that R2 and W can be visualized with the same geometric picture, namely the xy plane, is one way to see in a concrete way the isomorphism which the second poster refered to.

7 0

3 years ago

The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each f

Rom4ik [11]

Answer:

The area of the figure will be 5π/2 in².
The perimeter will be 3π + 2 in

Step-by-step explanation:

This figure is a combination of two semi-circles.

One having diameter of 2 inches i.e. AD
Other having diameter of 4 inches i.e. AC

$\pi ={\frac {C}{d}}$

${{{C}}}=\displaystyle \pi.d$

Perimeter of the big figure could be computed by cutting the perimeters of each circle in half, and then combing them together.

Area could be computed using the same way.

Calculating the Perimeter:

As the circumference of the smaller circle is 2π in. Cutting it half would yield the circumference of the smaller semi-circle i.e. π.

As the circumference of the bigger circle is 4π in. Cutting it half would yield the circumference of the bigger semi-circle i.e. 2π.

As the length of the segment DC is 2 in.

So, the total perimeter would be: π + 2π + 2 = 3π + 2 in

Calculating the Area

Area could be computed using the same way as we did during measuring perimeter.

As the area of circle is

$A={\displaystyle \pi.r^{2}$

As we are dealing with semi-circles. So, cutting the diameters of two semi-circles in half can let us find the radii of them.

So,

Smaller semi-circle has 1 in radius
Larger semi-circle has 2 in radius

Areas would have to be cut in half as well, as we are dealing with semi-circles.

So,

For smaller:

$A_{small} =\frac{1}{2} {\displaystyle \pi.r^{2}$

$A_{small} =\frac{1}{2} {\displaystyle \pi.(1)^{2}$

$A_{small} =\frac{1}{2} {\displaystyle \pi$

Hence, the area of smaller will be: π/2 in²

For larger:

$A_{larger} =\frac{1}{2} {\displaystyle \pi.r^{2}$

$A_{larger} =\frac{1}{2} {\displaystyle \pi.(2)^{2}$

$A_{larger} =2 \pi^{}$

Hence, the area of larger will be: 2π in²

Combining them together:

$\frac{1}{2} {\displaystyle \pi^{} + 2 {\displaystyle \pi^{}=\frac{5}{2} {\displaystyle \pi^{}$

Therefore,

The area of the figure will be 5π/2 in².
The perimeter will be 3π + 2 in

Keywords: radius, area, perimeter, semi-circle, circle, diameter, circumference of circle

Learn more about circle measurements from brainly.com/question/3855576

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3 0

3 years ago

Read 2 more answers

2 easy math questions!!!!!! Show work! Multiple choice!

elena55 [62]

Greetings!

Question Seven:
To find the slope given two points, we can use the slope formula:
$m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Input the points: (-11,5) (-6,1)
$m= \frac{1-5}{-6-(-11)}$

Simplify the equation:
$m= \frac{-4}{5}$

A parallel slope would be identical to this slope.

Therefore, the answer is B:
$\boxed{m_{2}= \frac{-4}{5}}$

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

Question Eight:
This question essentially asks you to rearrange the equation into slope y-intercept form:
$y=mx+b$

Rearrange the equation:
$8x+7y=51$

$7y=-8x-51$

$y=\frac{-8x-51}{7}$

$y=\frac{-8}{7}x-\frac{51}{7}$

The slope (rate of change) is $\frac{-8}{7}$

Therefore the answer is F:
$\boxed{m=\frac{-8}{7} }$

I hope this helped!
-Benjamin

4 0

3 years ago

Read 2 more answers