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beks73 [17]
1 year ago
10

Ivy is running errands for her mother. She bikes along straight paths to the supermarket, the bank, and then back home.Find the

distance between Ivy's house and the supermarket and the distance between the supermarket and the bank. Each distance is rounded to the nearest meter.
Mathematics
1 answer:
chubhunter [2.5K]1 year ago
5 0

The distance between Ivy's house and the supermarket and the distance between the supermarket and the bank:
H&S = 1,014 M; and S&B = 854m. This is resolved using the Sine Theorem.

<h3>What is the calculation backing the above solution?</h3>

Notice that the Angles of a Triangle add up to 180° That is

∠A + ∠B  + ∠C = 180°

Thus,

∠C = 180° - 32° - 109°

= 39°

Recall the Sine Theorem which indicates;

a/SinA = b/SinB = c/SinC

thus given that

AC = 1,523m

We have

AC/SinB = BC/SinA


BC = AC/SinB * SinA

= 1523/Sin109° * Sin32°

BC =854m

Therefore

AC/SinB = AB/SinC
Thus,

AB = AC/SinB * SinC

= 1523/Sin109° * Sin39°
AB ≈ 1,014m

Learn more about the Sine Theorem at;
brainly.com/question/27174058
#SPJ1

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Please someone help me to prove this. ​
morpeh [17]

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities:   sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

<u />

<u>Proof LHS → RHS</u>

LHS:                                  2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle:    2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]  

Expand:        2[(1/2)cos²2A  + cos2A·sin2A + (1/2)sin²2A]

Distribute:              cos²2A   + 2cos2A·sin2A + sin²2A  

Pythagorean Identity:    1 + 2cos2A·sin2A

Double Angle:                1 + sin4A

LHS = RHS:  1 + sin4A = 1 + sin4A   \checkmark

6 0
3 years ago
The figure undergoes a 90° rotation counterclockwise, followed by a reflection across a vertical line.
ollegr [7]

I am almost confident it is B

8 0
3 years ago
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The population of Watesville decreases at a rate of 1.6% per year. If the population was 62,500 in 2014, what will it be in 2020
yKpoI14uk [10]

Answer:

56,735 people

Step-by-step explanation:

We can set up an equation to model this:

The equation for exponential decay is y = C(1 - r)^t, where C is the original amount, r is rate of change, and t is time.

We can plug in the corresponding values and solve:

y = 62500(1 - 0.016)^6

y = 62500(0.984)^6

y = (62500)(0.9077)

y = 56,734.94, which we can round to 56,735 people

8 0
3 years ago
If f(n) = n 2 - n, then f(-4) is _____.
stich3 [128]

Answer:

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Step-by-step explanation:

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7 0
3 years ago
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Determine the value of r so that line through. -2,5 and 6,r has a slope of -3,2
Mademuasel [1]

Answer:

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Step-by-step explanation:

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3 0
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