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3 years ago

After a storm, a tree lies as shown. What was the original height of the tree? (Round to the nearest whole foot.)

Mathematics

1 answer:

Andreyy893 years ago

3 0

Using the Law of Sines, sina/A=sinb/B=sinc/C (although there are other ways considering that this is a 30, 60, 90 degree triangle with a basic identity) we can say:

97/sin60=x/sin30=y/sin90

x=97sin30/sin60 and y=97sin90/sin60

The total height of the tree is h=x+y so

h=97sin30/sin60 + 97sin90/sin60

h≈168.01 ft (to the nearest hundredth of a foot)

h≈168 ft (to nearest foot)

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Betsy started a business 2 years ago. She had 8 customers in the first year. She added 18

Tatiana [17]

Answer:

Betsy isn't correct. Betsy's calculations are wrong as she made her calculations by multiplying the base number of customers by 3 and then summing it all up for the 4 years under review instead of a continuous multiplication by 3.

26 × 3 × 4 is different from 26 × 3⁴

- If Betsy meets her target for the next 4 years, she will have 2106 customers in 4 years time.

Step-by-step explanation:

- Betsy started her business 2 years ago.

- In the first year, Betsy has 8 customers.

- In the second year, Betsy added 18 customers,

- So, her customers are now 8+18 = 26

- Betsy's goal is that in each of the next 4 years, she will have three times as many customers as the year before.

If the base number of customers is truly 26 this year,

Next year, Betsy would have 26 × 3 = 78 customers.

In 2 years, she would have 78 × 3 = 234

Thus indicating that in t years from now, the number of her customers will be

N(t) = N₀ × 3ᵗ

where

N(t) = number of customers t time from now

N₀ = number of customers at the moment = 26

t = number of years from now.

N(t) = 26 × 3ᵗ

In 4 years from now, Betsy will have

N(t=4) = 26 × 3⁴ = 2,106

So, it is evident that Betsy's calculations are wrong as she made her calculations by multiplying the base number of customers by 3 and then summing it all up for the 4 years under review instead of a continuous multiplication by 3.

26 × 3 × 4 is different from 26 × 3⁴

- If Betsy meets her target for the next 4 years, she will have 2106 customers in 4 years time.

Hope this Helps!!!

5 0

3 years ago

What are the verter and x-intercepts of the graph of the function given below?<br> y=x2-2x-35

horsena [70]

For x intercepts, plug in 0 for y.

0 = (x^2) - 2x - 35

*factoring* = (x-7)(x+5)

x intercepts = 7,-5

As for the vertex, you can use the equation -b/2a for the x-coordinate of the vertex

so,

x = -b/2a = -(-2)/2 = 1

then just find the y value by plugging it back in to the equation.

y = ((1)^2) - 2(1) - 35

= -36

so, vertex is at (1,-36)

5 0

3 years ago

"Statewide Insurers receives 1,600 applications per month Currently, there are 160 applications in the Reception area and 240 ap

Inessa05 [86]

Answer:

It takes 5 days to process an application.

Step-by-step explanation:

We have that number of requests per month would be equal 1600

Now, the applications in hand would be:

160 + 240 = 400

They tell us that everything must be in a number of 20 business days, therefore, the number of applications in one day would be:

1600/20 = 80

Which means that the time needed to finish an application is:

400/80 = 5 days

It takes 5 days to process an application.

4 0

3 years ago

Find the surface area of a sphere with a volume of 36π in3.

swat32

First use known volume to solve for radius:
$V=\frac{4}{3}\pi r^{3}$
$r=\sqrt[3]{\frac{3V}{4\pi}}$
$r=\sqrt[3]{\frac{3(36\pi)}{4\pi}}$
$r=\sqrt[3]{27}$
$r=3$

Then use the radius to get the surface area:
$A_{surf}=4 \pi r^{2}$
$A_{surf}=4 \pi 3^{2}$
$A_{surf}=4 \pi 9$
$A_{surf}=36\pi\approx113.09$

6 0

3 years ago

Four times a number, added to the sum of the number and three

BlackZzzverrR [31]

Answer:

Yup! Great Job!

Step-by-step explanation:

3 0

3 years ago