Answer:
B) 10.6 cubic inches
Step-by-step explanation:
Vol = (1/3) base area × hight = (1/3)π×1.5²×4.5
1. You are given a margin of error as 3 percentage points and a confidence level of 99%. If the sample percentage from a recent poll is 35%, find the minimum sample size to estimate a population proportion.
a.496
b.2579
c.1677
d.248
2. You are given E = 0.020, a confidence level of 90% and a sample proportion of 85% recent survey. Find the minimum sample size to estimate a population proportion.
a.1225
b.259
c.5751
d.863
3. Given n = 875 and p^ = 0.45, find the margin of error E that corresponds to a 95% confidence level
a.0.001
b.0.016
c.0.044
d.0.033
Answer:
1677
Step-by-step explanation:
Answer:
Step-by-step explanation:
1) p=0.35 and q = 0.65
Std error =[tex]\sqrt{\frac{0.35*0.65}{n} }[/tex]
Margin of error = 2.58*std error = 3%
i.e. [tex]2.58*0.477/\sqrt{n}= 0.03\\n = 1683\\[/tex]
Approximately 1677
2) Same method as above
Margin of error = 1.645 * [tex]\sqrt{\frac{0.85(0.15)}{n} }[/tex]=0.02
Hence n = 863
3) Margin of error = 1.96*[tex]\sqrt{\frac{0.45(0.55)}{875} }[/tex]
=0.0329
=0.033
(option d)
Which system of equations does this graph represent?
A. y = x^2 − 6
y = −x − 4
B. y = x^2 + 6
y = x + 4
C. y = x^2 + 4
y = −x + 4
D. y = x^2 − 6
y = x − 4
Answer:
Option D
y = x^2 − 6
y = x − 4
Step-by-step explanation:
we know that
The y-intercept of the quadratic equation is the point (0,-6) (see the graph)
Could be option A or option D
The y-intercept of the linear equation is the point (0,-4) and the x-intercept is the point (4,0)
Could be option D
therefore
The system of equations is the option D
Verify
[tex]y=x^{2}-6[/tex]
[tex]y=x-4[/tex]
using a graphing tool
see the attached figure
The system of equations is the option D
Answer:
5
Step-by-step explanation:
.
.
.
Nikhil gets paid a 5 percent commission on every pair of shoes that he sells. He earned $1.00 on the last pair of shoes that he sold. The expression that can be used to represent x, the price of the shoes, is What was the price of the shoes?
If 5 equals 1
then 100 will equal 20
the shoes are 20 dollars
Answer:
$20.00 is the correct answer
Step-by-step explanation:
I promise this is correct
Which function is represented by the table of values below?
Answer:
If im correct from the way this is set up, I believe it is C
Step-by-step explanation:
Answer:
Your answer would be A) y=-x+1
Step-by-step explanation:
Looking at each value in the table you can take x, make it a negative, then add 1 for it to equal y. Hope this helped and have a wonderful day!
Charlie can invest $8,000 at 8.5% interest for 15 days. How much interest will he earn on his investment if the interest is compounded daily?
Answer:
$27.99 interest.
Step-by-step explanation:
Use the formula for Compound interest = P(1 + r/n)^t . Here n = 365 (number of days in a year), r = annual rate as a decimal and t = the number of days, P = 8000.
Amount after 15 days = 8,000(1 + 0.085/365)^15
= $8027.99.
Final answer:
Charlie will earn interest on his $8,000 investment at an 8.5% annual rate, compounded daily, for 15 days. The interest can be calculated using the formula for compound interest and will likely result in slightly more interest earned than if it was calculated using simple interest.
Explanation:
Charlie can invest $8,000 at 8.5% interest for 15 days. To calculate the interest earned with daily compounding, we use the formula A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount ($8,000), r is the annual interest rate (8.5%), n is the number of times that interest is compounded per year (365, since it's daily), and t is the time the money is invested in years (15/365, because here t is 15 days).
By substituting the values into the formula we get: A = $8,000(1 + 0.085/365)365*(15/365). After computing this, we find the new amount that Charlie will have after the 15 days are over. The interest earned is then found by subtracting the principal ($8,000) from this new amount.
Note that compound interest, especially when compounded frequently, can lead to greater earnings than simple interest. This difference is more pronounced with larger amounts and over longer periods, as shown by the reference provided where compound interest for a $100 investment over three years was $0.76 more than with simple interest.
Which choice is equivalent to the quotient shown here for acceptable values of x?
Answer: OPTION D
Step-by-step explanation:
You need to remember this property:
[tex]\frac{\sqrt{x} }{\sqrt{y} }=\sqrt{\frac{x}{y} }[/tex]
And remember that:
[tex]\frac{a}{a}=1[/tex]
Then, the first step is rewrite the expression:
[tex]\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^2}}[/tex] [tex]=\sqrt{\frac{30(x-1)}{5(x-1)^2}} }[/tex]
Now, to find the corresponding equivalent expression, you need to simplify the expression.
Therefore, the equivalent expression is the following:
[tex]\sqrt{\frac{6}{(x-1)}} }[/tex]
Finally, you can observe that this matches with the option D.
Answer:
Choice D
Step-by-step explanation:
The division of the two radicals can be re-written in the following format;
[tex]\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^{2} } }[/tex]
Using the properties of radicals division, the expression can further be written as;
[tex]\sqrt{\frac{30(x-1)}{5(x-1)^{2} } }[/tex]
We simplify the terms under the radical sign to obtain;
[tex]\sqrt{\frac{6}{x-1} }[/tex]
Choice D is thus the correct solution
What is the term a_5?
Answer:
34Step-by-step explanation:
[tex]\text{We have the recursive form of sequence:}\\\\a_1=50\\a_n=a_{n-1}+(-4)=a_{n-1}-4\\\\a_2=a_{2-1}-4=a_1-4\to a_2=50-4=46\\a_3=a_{3-1}-4=a_2-4\to a_3=46-4=42\\a_4=a_{4-1}-4=a_3-4\to a_4=42-4=38\\a_5=a_{5-1}-4=a_4-4\to a_5=38-4=34[/tex]
Nick buys 2 shirts and 4 hats for a total of 44.00.If the hats cost 5.00 each, how much does each shirt cost?
If he bought 4 hats for $5 each and he spent a total of $44, he spent $44 - $20 in shirts.
44 - 20 = 24
2 shirts for $24 is 1 for 12
$12 for each shirt
Hope it helps :)
Answer:
1 shirt= $12
Step-by-step explanation
we can make an equation where S= shirts, and H for hats. this would look like 2S+4H=44. now we get the info H=5(dollars). we plug it in to get 2S+4 x 5=44. now we simplify to get 2S+20=44. we subtract 20 from both sides to simplify further to get 2S=24. now we can divide this by 2 on each side to get S=11, and since S is the shirts, it says one shirt is =to 11, or 1 shirt= $12
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
When Mrs. Myles gave a test, the scores were normally distributed with a mean of 72 and a standard deviation of 8. This means that 95% of her students scored between which two scores?
Answer:
C.
Step-by-step explanation:
Answer: c) 56 and 88
Step-by-step explanation:
95% is 2 standard deviations above and below the mean.
72 ± 2(8)
= 72 ± 16
= 56 and 88
PLEASE HELP SHOW YOUR WORKING OUT Branliest
Answer:
The equation of this line is therefore y = 2x + 3.
Step-by-step explanation:
this line passes thru the points (0, 3) and (3, 9). As we move from (0, 3) to (3, 9), x increases by 3 and y increases by 6. Thus, the slope of this line is
m = rise / run = 6/3, or m = 2. Inserting the known info (m = 2, x = 0, y = 3) into y = mx + b, we get: 3 = 2(0) + b, so we see that b = 3.
The equation of this line is therefore y = 2x + 3.
Select ALL the correct answers.!!!!
Observe the expression below and select the true statement(s)
3y(7 + 2x) + 9xy - 10
1. The "(7 + 2x)" in the first term is a factor.
2. The "9" in the second term is a coefficient,
3. The "3" in the first term is a factor
4.The "10" in the third term is a coefficient
5. The "2" in the first term is a constant,
6. The "x in the second term is an exponent
Answer: The true statements are:
The "(7 + 2x)" in the first term is a factor.
The "9" in the second term is a coefficient.
The "3y" in the first term is a factor.
Step-by-step explanation:
Answer:
Option 1 and 2.
Step-by-step explanation:
Given : Expression [tex]3y(7 + 2x) + 9xy - 10[/tex]
To find : Observe the expression below and select the true statement(s)?
Solution :
Using definition mentioned below :
Term is defined as a single numbers, variables, or the product of a number and variable. Factor is defined as one part of a product.Coefficient is defined as a number multiplied by a variable.Constant is defined as the term without variable.Exponent is defined as the power.We can say that statements which are true are
1) The "(7 + 2x)" in the first term is a factor.
2) The "9" in the second term is a coefficient.
Rest are false.
Therefore, option 1 and 2 is correct.
PLEASE HELP THANK YOU SO MUCH
https://brainly.com/question/11525341
The graph of this system of equations is used to solve 4x2-3+6=2x4-9x3+2x What represents the solution set?
y intercepts of the graph
x intercepts of the graph
y coordinates of the intersection points
x coordinates of the intersection points
ANSWER
x coordinates of the intersection points
EXPLANATION
The given system of equations is:
[tex]y = 4 {x}^{2} - 3x + 6[/tex]
[tex]y = 2 {x}^{4} - 9 {x}^{3} + 2x[/tex]
We want to use the graph of these functions to solve
[tex] 4 {x}^{2} - 3x + 6 = 2 {x}^{4} - 9 {x}^{3} + 2x [/tex]
The point of the intersection of the graph gives the solution to the simultaneous equation above.
Hence the x-coordinates of the intersection points gives the solution set of
[tex]4 {x}^{2} - 3x + 6 = 2 {x}^{4} - 9 {x}^{3} + 2x [/tex]
The last choice is correct.
Answer: It's D
Step-by-step explanation:
A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square prism.
The company wants to use the package that has the least amount of wasted space. The company should choose
a.)the prism because it has approximately 11.6 in.3 less wasted space than the cylinder.
b.)the prism because it has approximately 14.1 in.3 less wasted space than the cylinder.
c.)the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
d.)the cylinder because it has approximately 14.1 in.3 less wasted space than the prism.
Answer:
Option c.) the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
Step-by-step explanation:
step 1
Find the volume of one ball
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=1.5\ in[/tex]
[tex]V=\frac{4}{3}(3.14)(1.5)^{3}=14.13\ in^{3}[/tex]
therefore
The volume of two balls is
[tex](2)*14.13=28.26\ in^{3}[/tex]
step 2
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=1.5\ in[/tex]
[tex]h=1.5*4=6\ in[/tex]
substitute
[tex]V=(3.14)(1.5)^{2}(6)=42.39\ in^{3}[/tex]
therefore
The wasted space with the cylinder is equal to
[tex]42.39\ in^{3}-28.26\ in^{3}=14.13\ in^{3}[/tex]
step 3
Find the volume of the square prism
The volume of the square prism is equal to
[tex]V=b^{2}h[/tex]
we have
[tex]b=1.5*2=3\ in[/tex]
[tex]h=1.5*4=6\ in[/tex]
substitute
[tex]V=(3)^{2}(6)=54\ in^{3}[/tex]
therefore
The wasted space with the prism is equal to
[tex]54\ in^{3}-28.26\ in^{3}=25.74\ in^{3}[/tex]
step 4
Find the difference of the wasted space
[tex]25.74\ in^{3}-14.13\ in^{3}=11.61\ in^{3}[/tex]
Answer:
C. the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
Step-by-step explanation:
if you find the volumes of both shapes and subtract the volumes of the two balls and then subtract the two remaining values you get a difference of 11.6 inches. This makes the cylinder smaller and therefore uses less space.
Please help me please
Answer:
1.44π m²
Step-by-step explanation:
The area (A) of the circle is calculated as
A = πr² ← r is the radius
here the diameter is 2.4 and the radius is half the diameter, thus
r = 1.2, so
A = π × 1.2² = 1.44π m²
Use technology or a z-score table to answer the question.
The lengths of green beans for sale at a supermarket are normally distributed with a mean of 11.2 centimeters and a standard deviation of 2.1 centimeters. Consider a bag of 150 green beans.
How many green beans will be 13 centimeters or shorter?
Answer:
121
Step-by-step explanation:
First, we find the z-score for 13 cm:
z = (x - μ) / σ
z = (13 - 11.2) / 2.1
z = 0.86
Next, we use a calculator or a z-score table to find P(x<0.857).
P(x<0.86) = 0.8051
So the number of green beans in a bag of 150 less than or equal to 13 cm is:
0.8051 * 150
121
The number of green beans that is 13 centimeters or shorter will be 121. Then the correct option is C.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
The z-score is given as,
z = (13 - 11.2) / 2.1
z = 1.8 / 2.1
z = 0.587
The number of green beans that is 13 centimeters or shorter will be given as,
⇒ 150 x P(z ≤ 0.587)
⇒ 150 x 0.8023
⇒ 121
Thus, the correct option is C.
More about the z-score link is given below.
https://brainly.com/question/15016913
#SPJ3
Find the equation of the cosine graphed.
Answer:
C) y = -cos(x) +2
Step-by-step explanation:
The centerline is 2, so 2 is added. That leaves out choices A and B.
There is a minimum (not a maximum) at x=0, so the multiplier is negative, eliminating choice D.
The correct equation is that of C: y = -cos(x) +2.
Which quotient will be negative?
24 ÷ 6
-35 ÷ 7
-54 ÷ (-6)
3 ÷ (-1)
Answer:
-35/7
3/-1
Step-by-step explanation:
If you divide a positive number by a positive number
the outcome will be positive
If you divide a positive number by a negative number the outcome will be negative
If you divide a negative number by a negative number the outcome will be positive
If you have any questions do not hesitate to ask
:)
3/-1 is also a solution
What is the length of a diagonal of a cube with a side length of 10 cm? 200 cm 210cm 300 cm 320cm
Answer:
The length of the diagonal of the cube = √(3 × 10²) = √300 cm
Step-by-step explanation:
* Lets revise the properties of the cube
- It has six equal faces all of them are squares
- It has 12 vertices
- The diagonal of the cube is the line joining two vertices in opposite
faces (look to the attached figure)
- To find the length of the diagonal do that:
# Find the diagonal of the base using Pythagoras theorem
∵ The length of the side of the cube is L
∵ The base is a square
∴ The length of the diagonal d = √(L² + L²) = √(2L²)
- Now use the diagonal of the base and a side of a side face to find the
diagonal of the cube by Pythagoras theorem
∵ d = √(2L²)
∵ The length of the side of the square = L
∴ The length of the diagonal of the cube = √[d² + L²]
∵ d² = [√(2L²)]² = 2L² ⇒ power 2 canceled the square root
∴ The length of the diagonal of the cube = √[2L² + L²] = √(3L²)
* Now lets solve the problem
∵ The length of the side of the square = 10 cm
∴ The length of the diagonal of the cube = √(3 × 10²) = √300 cm
- Note: you can find the length of the diagonal of any cube using
this rule Diagonal = √(3L²)
Answer:
its c on endeguity
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
If s(x) = 2x^2 + 3x - 4, and t(x) = x + 4 then s(x) · t(x) =
Answer:
A) 2x³+11x²+8x-16
Step-by-step explanation:
When you multiply s(x) by t(x) you get something like this:
[tex]s(x) \times t(x) = (2 {x}^{2} + 3x - 4) \times (x + 4) \\ = 2 {x}^{3} + 3 {x}^{2} - 4x + 8 {x}^{2} + 12x - 16 \\ = 2 {x}^{3} + 11 {x}^{2} + 8x - 16[/tex]
Answer: A) 2x³ + 11x² + 8x - 16
Step-by-step explanation:
s(x) · t(x) = (x + 4)(2x² + 3x - 4)
= x(2x² + 3x - 4) + 4(2x² + 3x - 4)
= 2x³ + 3x² - 4x + 8x² + 12x - 16
= 2x³ + (3x² + 8x²) + (- 4x + 12x) - 16
= 2x³ + 11x² + 8x - 16
Define the following terms. Be sure to write the definitions in your own words and use complete sentences, proper grammar, and spelling.
Mean :
Median:
Mode:
Range:
Outlier:
Answer: Here...
Step-by-step explanation:
Mean: The average of the numbers so add them up then divide by how many numbers you added
Median: The middle number of the numbers in numerical order
Mode: The number that is repeated the most often
Range: The smallest number subtracted from the larger number
Outlier: A data point or observation that is not with the others so basically the odd one out
Hope this helps Brainliest plz
Mrs thompson plans to carpet her bedroom which is in the shape of a rectangle. The room is 15 feet by 19 feet. How many square feet of carpet does she need
Answer:
I think it is 285 bc 15*19 is 285
Geometry help needed, thanks!!
Use a calculator to find the cos 48° to the nearest thousandth.
0.669
0.770
0.743
0.640
Find the value of x in the triangle below to the nearest hundredth. (Picture below)
7.73 cm
23.78 cm
8.12 cm
20.46 cm
Answer:
Part 1) 0.669
Part 2) x=23.78 cm
Step-by-step explanation:
Part 1) we have
cos(48°)
Using a calculator
cos(48°)=0.66913
Round to the nearest thousandth
0.66913=0.669
Part 2) we know that
In the right triangle of the figure
The cosine of angle of 18 degrees is equal to divide the adjacent side to the angle of 18 degrees by the hypotenuse of the right triangle
so
cos(18°)=x/25
x=(25)cos(18°)=23.78 cm
Answer:
Use a calculator to find the cos 48° to the nearest thousandth: A. 0.669
Find the value of x in the triangle below to the nearest hundredth.: B. 23.78 cm
Step-by-step explanation:
I just did these questions and these were the answers that were right for me. Hope this helps!
Osmium is a chemical element with a density of 22.6 grams per cubic centimeter. A piece of Osmium has a volume of 15.1 cubic centimeters. What is the mass of the piece of Osmium to the nearest tenth of a gram?
Answer:
341.3 g
Step-by-step explanation:
we know that
The density is equal to the ratio of the mass by the volume
D=m/V
Solve for the mass m
m=D*V
In this problem we have
D=22.6 g/cm³
V=15.1 cm³
substitute in the formula
m=22.6*(15.1)=341.26 g
Round to the nearest tenth of a gram
341.26 g=341.3 g
In EFGH find the measure of GFH !!!! PLEASE HELP!!!!
Need to graduate.
A. 30
B. 120
C. 60
D. 90
Answer:
C
Step-by-step explanation:
Since EF and GH are parallel lines then
∠EGF = ∠GFH = 60° ( Alternate angles )
Identify the volume and surface area of the sphere in terms of π. HELP PLEASE!!
Answer:
First choice V = 18,432π m^3; S = 2,304π m^2
Step-by-step explanation:
Start with the two formulas:
Volume of a circle:
[tex] V = \dfrac{4}{3} \pi r^3 [/tex]
Surface area of a circle:
[tex] S = 4 \pi r^2 [/tex]
Now use r = 24 m in each formula.
Volume:
[tex] V = \dfrac{4}{3} \pi (24~m)^3 [/tex]
[tex] V = \dfrac{4}{3} \pi (13,824~m^3) [/tex]
[tex] V = 18,432\pi~m^3 [/tex]
Surface area:
[tex] S = 4 \pi r^2 [/tex]
[tex] S = 4 \pi (24~m)^2 [/tex]
[tex] S = 4 \pi (576~m^2) [/tex]
[tex] S = 2,304\pi ~m^2 [/tex]
Answer: First choice V = 18,432π m^3; S = 2,304π m^2
Correct Option 2: The volume of the sphere is 972π cm³ and its surface area is 324π cm²
To determine the volume and surface area of a sphere, we use the formulas:
Volume: V = (4/3)πr³Surface Area: S = 4πr²Given the radius (r) of the sphere is 9 centimeters:
Volume: V = (4/3)π(9)³ = (4/3)π(729) = 972π cm³Surface Area: S = 4π(9)² = 4π(81) = 324π cm²Hence, the volume of the sphere is 972π cm³ and the surface area is 324π cm².
If you were to draw three different parallelograms each base of 6 units and a height of 4 units how would the areas compare
Answer:
They are all the same.
Step-by-step explanation:
The area of a parallelogram is computed by multiplying the base length by the height. All of these parallelograms will have an area of ...
A = (6 units)(4 units) = 24 units²
You can draw any number of parallelograms with these dimensions, and they will all have the same area.
Please help me out !!!!!!
Answer:
101.956 cm²
Step-by-step explanation:
The area (A) of a parallelogram is calculated using the formula
A = bh ( b is the base and h the perpendicular height )
here b = 14.2 and h = 7.18, hence
A = 14.2 × 7.18 = 101.956 cm²
Write the complex number in the form a + bi.
3(cos 60° + i sin 60°)
Answer:
The complex number in the form of a + b i is 3/2 + i √3/2
Step-by-step explanation:
* Lets revise the complex number in Cartesian form and polar form
- The complex number in the Cartesian form is a + bi
-The complex number in the polar form is r(cosФ + i sinФ)
* Lets revise how we can find one from the other
- r² = a² + b²
- tanФ = b/a
* Now lets solve the problem
∵ z = 3(cos 60° + i sin 60°)
∴ r = 3 and Ф = 60°
∵ cos 60° = 1/2
∵ sin 60 = √3/2
- Substitute these values in z
∴ z = 3(1/2 + i √3/2) ⇒ open the bracket
∴ z = 3/2 + i √3/2
* The complex number in the form of a + b i is 3/2 + i √3/2
Answer:
3/2 + (3sqrt(3))/2 i
Step-by-step explanation:
On the unit circle cosine and sine 60 degrees can be found in the first quadrant. With the correct measures. Once located, (1/2, sqrt(3)/2), multiply those numbers by 3. Don't forget to include i.
3(1/2 + sqrt(3)/2 * i)
= 3/2 + (3sqrt(3))/2 i
There is a lightning rod on top of a building. From a location 500 feet from the base of the building, the angle of elevation to the top of the building Is measured to be 36 degrees. From the same location, the angle of elevation to the top of the lightning rod is measured to be 38 degrees. Find the height of the lightning rod. Round to the nearest foot.
The answer is:
The height of the lightning rod is 27.4 feet.
Why?To solve the problem, we need to use the given information about the two points of observation, since both are related (both finish and start at the same horizontal distance) we need to write to equations in order to establish a relationship.
So, writing the equations we have:
We know that the angle of elevation from the base of the buildings is 36°
Also, we know that from the same location, the angle of elevation to the top of the lightning rod is 38°.
Using the information we have:
To the top of the building:
[tex]tan(\alpha )=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}\\\\tan(36\°)=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}[/tex]
To the top of the lightning rod:
[tex]tan(\alpha )=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}\\\\tan(38\°)=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}[/tex]
Now, isolating we have:
[tex]tan(36\°)=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}\\\\DistanceToTheTopOfTheBuilding=tan(36\°)*BuildingBase \\\\DistanceToTheTopOfTheBuilding=tan(36\°)*500feet=363.27feet[/tex]
Also, we have that:
[tex]tan(38\°)=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}\\\\DistanceToTheTopOfTheLightningRod=tan(38\°)*BuildingBase\\\\DistanceToTheTopOfTheLightningRod=tan(38\°)*500feet=390.64feet[/tex]
Therefore, if we want to calculate the height of the lightning rod, we need to do the following:
Let "x" the distance to the top of the building and "y" the distance to the top of the lightning rod, so:
[tex]LightningRodHeight=y-x=390.64feet-363.27feet=27.37feet[/tex]
Rounding to the nearest foot, we have:
[tex]LightningRodHeight=y-x=390.64feet-363.27feet=27.37feet=27.4feet[/tex]
Hence, the answer is:
The height of the lightning rod is 27.4 feet.
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To find the height of the lightning rod, create two right triangles using the tangent function and the given angles of elevation. Use the distance from the base to the location as the base of both triangles. Calculate the height of the building and the height of the lightning rod separately using trigonometry.
Explanation:To find the height of the lightning rod, we can use the concept of trigonometry and create a right triangle with the base of the triangle as the distance from the base of the building to the location, the height of the building as the vertical side of the triangle, and the angle of elevation to the top of the building as one of the acute angles. Using the tangent function, we can calculate the height of the building to be approximately 287 feet. Next, we can create another right triangle with the same base the height of the lightning rod as the vertical side, and the angle of elevation to the top of the lightning rod as one of the acute angles. Again, using the tangent function, we can calculate the height of the lightning rod to be approximately 310 feet. Therefore, the height of the lightning rod is approximately 310 feet.
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