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3 years ago

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A 500-foot weather

1 answer:

Archy [21]3 years ago

3 0

<h3>Answer: 293 feet</h3>

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

Explanation:

See the attached image below. The information that the tower is 500 ft is never used. Focus solely on triangle ABD (ignore point C).

AB = 200

AD = x = unknown

angle ABD = angle B = 47 degrees

Use the cosine rule to help find x

---------

cos(angle) = adjacent/hypotenuse

cos(B) = AB/BD

cos(47) = 200/x

x*cos(47) = 200

x = 200/cos(47)

x = 293.255837127926

Rounding to the nearest foot, we get 293 feet as the answer.

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Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below. 18.75 93.75 581.25 145.3125

Savatey [412]

we have that

$300 + 150 + 75 +...$

Let

$a1=300\\ a2=150\\ a3=75$

we know that

$\frac{a2}{a1} =\frac{150}{300} \\\\ \frac{a2}{a1}=0.5 \\ \\ a2=a1*0.50$

$\frac{a3}{a2} =\frac{75}{150} \\\\ \frac{a3}{a2}=0.5 \\ \\ a3=a2*0.50$

so

$a(n+1)=an*0.50$

Is a geometric sequence

Find the value of $a4$

$a(4)=a3*0.50$

$a(4)=75*0.50$

$a(4)=37.5$

Find the value of $a5$

$a(5)=a4*0.50$

$a(5)=37.5*0.50$

$a(5)=18.75$

Find $S5$

$S5=a1+a2+a3+a4+a5\\ S5=300+150+75+37.5+18.75\\ S5=581.25$

therefore

the answer is

$581.25$

Alternative Method

Applying the formula

$S_n=\frac{a_1 (1-r^n)}{1-r} \\\\a_1=300 \\ r=\frac{1}{2}\\\\ S_5=\frac{300(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}\\\\=\frac{300(1-\frac{1}{32})}{\frac{1}{2}}\\\\=\frac{300 \times \frac{31}{32}}{\frac{1}{2}}\\\\=\frac{75 \times \frac{31}{8}}{\frac{1}{2}}\\\\=\frac{\frac{2325}{8}}{\frac{1}{2}}\\\\=\frac{2325}{8} \times 2\\\\=\frac{2325}{4}\\\\=581 \frac{1}{4}\\\\=581.25$

therefore

the answer is

$581.25$

6 0

3 years ago

Read 2 more answers

What is the final cost of a $21,000 car with a sales tax of 7%?

fomenos

21,000 + 0.07(21,000) = 21,000 + 1,470 = 22,470

8 0

3 years ago

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I need help writing the first 5 terms of the sequence!

Angelina_Jolie [31]

The first five terms of the sequence are 1, 4, 7, 10, 13.

Solution:

Given data:

$a_{1}=1$

$a_{n}=a_{n-1}+3$

General term of the arithmetic sequence.

$a_{n}=a_{n-1}+d$ , where d is the common difference.

d = 3

$a_{n}=a_{n-1}+3$

Put n = 2 in $a_{n}=a_{n-1}+3$ , we get

$a_{2}=a_1+3$

$a_{2}=1+3$

$a_2=4$

Put n = 3 in $a_{n}=a_{n-1}+3$ , we get

$a_{3}=a_2+3$

$a_{3}=4+3$

$a_3=7$

Put n = 4 in $a_{n}=a_{n-1}+3$ , we get

$a_{4}=a_3+3$

$a_{4}=7+3$

$a_4=10$

Put n = 5 in $a_{n}=a_{n-1}+3$ , we get

$a_{5}=a_4+3$

$a_{5}=10+3$

$a_5=13$

The first five terms of the sequence are 1, 4, 7, 10, 13.

3 0

3 years ago

Can someone help me with this answer plsss

solniwko [45]

Answer: 44 ft

Step-by-step explanation:

if you add up the right square it adds up to 16 4+4+4+4 all sides are equal since its a square.

The left rectangle is

8+8=16

6+6=12

16+12=28

Now you add the square on the right to the square on the left which is

28+16= 44 ft

4 0

2 years ago

1. $200 is deposited into an account that earns 6% simple interest

katen-ka-za [31]

Answer:

$260

Step-by-step explanation:

0.06 x 200 = 12

12 x 5 = 60

200 + 60 = 260

3 0

3 years ago