If 5 hours = 40 $

This question is from the similarity chapter. It would be really kind of you if you would answer this question.

katen-ka-za [31]

Answer:

a) 1650 m

b) 1677.05 m

Step-by-step explanation:

Hi there!

1) Determine what is required for the answers

For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.

For part B, we're asked to solve for the length of the road, or the length of AB.

2) Prove similarity

In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).

How do we know they're similar?

Angles AYX and ACB are corresponding and they both measure 90 degrees
Both triangles share angle A

Therefore, the two triangles are similar because of AA~ (angle-angle similarity).

3) Solve for part A

Recall that we need to find the length of AC.

First, set up a proportion. XY corresponds to BC and AY corresponds to AC:

$\frac{XY}{BC}=\frac{AY}{AC}$

Plug in known values

$\frac{2}{300}=\frac{11}{AC}$

Cross-multiply

$2AC=11*300\\2AC=3300\\AC=1650$

Therefore, the road will rise 300 m over a horizontal distance of 1650 m.

4) Solve for part B

To find the length of AB, we can use the Pythagorean theorem:

$a^2+b^2=c^2$ where c is the hypotenuse of a right triangle and a and b are the other sides

Plug in 300 and 1650 as the legs (we are solving for the longest side)

$300^2+1650^2=c^2\\300^2+1650^2=c^2\\2812500=c^2\\1677.05=c$

Therefore, the length of the road is approximately 1677.05 m.

I hope this helps!

3 0

3 years ago

A musical instrument has a pitch of 220 hertz when the wavelength is 3 feet. When the wavelength is 4 feet, the pitch is 165 her

earnstyle [38]

We know that
Inverse Variation is a relationship between two variables in which the product is a constant
so
let
x------> a pitch of a musical instrument
y------> the wavelength
x*y=k

find the value of k

for x=220 hertz y=3 ft
x*y=k
220*3=k
k=660

for x=165 hertz y=4 ft
x*y=k
165*4=660
k=660

the answer part a) is
the type of variation between pitch and wavelength is an inverse variation

part b) What is the pitch when the wavelength is 5 feet?
x=?
y=5 ft
k=660
x*y=k------> solve for x
x=k/y----------> x=660/5-----> x=132 hertz

the answer Part b) is
132 hertz

4 0

3 years ago

I WILL LITERALLY GIVE OUT 50 POINTS FOR THIS!!!!

kaheart [24]

Answer: B) -3

Step-by-step explanation:

X<-11/3 if u divide -11/3 = is about -3.6666

3 0

3 years ago

Read 2 more answers

You are drawing two cards, without replacement, from a standard deck of 52 cards. What is the

Serga [27]

Answer:

Dear student,

Answer to your query is provided below

Probability of drawing a 2 at first is (4/52) = (1/13)

Probability of drawing a face card in second try without replacement = 12/51

Step-by-step explanation:

Total no. Of cards = 52

Total no. Of cards of 2 = 4

Prob. Of drawing 2 = 4/52

Total no. Of face card = 12

Total no.of cards left in deck = 51

Prob. Of drawing face card = 12/51

5 0

3 years ago

The Clark family and the Lee family each used their sprinklers last summer. The water output rate for the Clark family's sprinkl

SpyIntel [72]

Each where used for 25 hours

6 0

3 years ago

Read 2 more answers