A 30m high pole was standing at a point of the length side of a rectangle garden. If the angles of elevation of that pole form end points of that length are found 60 degree and 30 degree,find the length of that garden.
Answers
Answer:
Length of the garden = 69.28 meters.
Step-by-step explanation:
See the attached diagram.
Let CD is the pole with a height of 30 m and the elevation of the top of the pole from the endpoints of the length A and B are 60° and 30° respectively.
So, ∠ DAC = 60° and ∠ DBC = 30°
Now, Δ ACD is a right triangle and [tex]\tan 60 = \frac{CD}{AC}[/tex]
⇒ [tex]AC = \frac{CD}{\tan 60} = \frac{30}{\tan 60} = 17.32[/tex] meters.
Now, from Δ BCD which is a right triangle, [tex]\tan 30 = \frac{CD}{CB}[/tex]
⇒ [tex]CB = \frac{30}{\tan 30} = 51.96[/tex] meters.
Hence, AB = AC + CB = 17.32 + 51.96 = 69.28 meters. (Answer)
Answer:
The length of the rectangle garden is 20 [tex]\sqrt{3}[/tex] i.e 34.64 meters .
Step-by-step explanation:
Given as :
The height of the pole = H = 30 m
The two angles of elevation as 60° and 30°
Let The length of the rectangle garden = L m
Now, From figure
The measure from pole ground to first elevation 60° = x m
The measure from pole ground to second elevation 30° = (L + x ) m
Now, from triangle BOC
Tan Ф = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]
I.e Tan 60° = [tex]\dfrac{\textrm 30}{\textrm x}[/tex]
Or, [tex]\sqrt{3}[/tex] = [tex]\dfrac{\textrm 30}{\textrm x}[/tex]
or, x = [tex]\frac{30}{\sqrt{3} }[/tex]
I.e x = 10[tex]\sqrt{3}[/tex] meter ...1
Again From triangle BAC
Tan Ф = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]
I.e Tan 30° = [tex]\dfrac{\textrm 30}{\textrm L + x}[/tex]
Or, [tex]\frac{1}{\sqrt{3} }[/tex] = [tex]\dfrac{\textrm 30}{\textrm L + x}[/tex]
Or, L + x = 30 × [tex]\sqrt{3}[/tex] ....2
Put the value of x from 1 into 2
i.e L + 10[tex]\sqrt{3}[/tex] meter = 30 × [tex]\sqrt{3}[/tex]
or, L = 30 [tex]\sqrt{3}[/tex] - 10 [tex]\sqrt{3}[/tex]
Or, L = 20 [tex]\sqrt{3}[/tex] = 34.64 meters
I.e length of garden is 20 [tex]\sqrt{3}[/tex]
Hence The length of the rectangle garden is 20 [tex]\sqrt{3}[/tex] i.e 34.64 meters . answer
Related Questions
III.
a small appliance manufacturer finds that if the firm produces and sells x blenders
monthly, the total monthly profit P (in dollars) is given by
P(x) = 8x + 0.3x2 - 0.0013x3 - 372.
ne owner wants to produce no more than 225 blenders/month in order to maintain quality
(SLO #1, 2, 6)
a. Find the y-intercept and explain what it means in this context.
Answers
Answer:
The y-intercept is - 372 and it means that if the manufacturers do not produce and sell any blenders they will have a loss of $ 372.Explanation:
The polynomial that represents the function is:
[tex]P(x)=8x+0.3x^2-0.0013x^3-372[/tex]Where the variable, x, represents the number of blenders produced and sold monthly, and P(x) is the monthly profit in dollars obtained for the sale of x blenders.
As for the question, the y-intercept is the point on the graph where the function crosses the y-axis, i.e. where the input of the function is x = 0.
Therefore, the y-intercept is the value of the function for x = 0, P(0), and it is found by substituting 0 for x in the polynomial function, which is shown next:
[tex]P(0)=8(0)+0.3(0)^2-0.0013(0)^3-372=-372[/tex]The meaning of this value is that the firm loses $372 when it does not produce and sell any blenders.
If x+3=5, what is the value of 2(x+4)?
Answers
So the equation would be 2(2+4)
2 multiplied by 2 would be 4 and 2 multiplied by 4 would be 8
You would be left with
4+8 which equals 12
x equals 2, and substituting x=2 into the equation 2(x+4) gives us the result 12.
Explanation:To determine the value of 2(x+4), we begin by solving the equation x+3=5. Subtracting 3 from both sides yields x=2. Substituting this into 2(x+4), we get 2(2+4), which simplifies to 2(6). Multiplying, we find the result to be 12. The process involves solving for x by isolating it in the initial equation, then substituting this value into the expression we seek to evaluate. In this case, x=2, making 2(x+4) equal to 2 times the sum of 2 and 4, resulting in 12. This algebraic approach allows us to systematically find the desired value based on the given information.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ11
The coordinates of the vertices of triangle 1 are A(6,6), B(12,9), C(9,6).
The coordinates of the vertices of triangle 2 are A′(2,2), B′(4,3), C′(3,2).
What transformation was performed on triangle 1 to create triangle 2?
Answers
Answer:
A
Step-by-step explanation:
The transformation performed on triangle 1 to create triangle 2 is a translation by the vector (-4, -4), which means each point was moved 4 units to the left and 4 units down.
Explanation:The transformation used can be determined by observing the differences between corresponding coordinates in the two triangles. If we subtract the coordinates of A′(2,2) from A(6,6), for instance, we get a change of -4 in the x-direction and -4 in the y-direction. Similarly, subtracting B′(4,3) from B(12,9) and C′(3,2) from C(9,6) results in changes of -8 and -6 in the x-direction and -6 and -4 in the y-direction, respectively.
This means that every point on triangle 1 was moved 4 units to the left and 4 units down to create triangle 2. Thus, the transformation that took place is called a translation by the vector (-4, -4).
Learn more about Translation here:https://brainly.com/question/38241586
#SPJ2
guys what is the answer 3/8+4/5
Answers
Answer:
the answer would be 47/40
Answer:
1 ⁷/40
find lcm of the denominators (the bottom numbers) 8&5
lcm is 40
ask your self how many times can 40 be divided by 8? 5 times good job .
so you multiply top & bottom of 3/8 by 5
3×5=15 8×5=40
we now get a new fraction 15/40
ask your self how many times can 40 be divided by 5? 8 times very good !
so you multiply top & bottom of tht fraction by 8
4×8=32 5×8=40
new fractions are 15/40 & 32/40
we did all of that to get fractions with the same denominator because fractions with like denominators are easy to add you add the top numbers & keep the bottom.
15+32=47
47/40 now this fraction can be simplified to a mixed number
ask yourself how many times can 40 go into 47 ? one time
40×1 =40 & there are 7 remainders & you just keep the denominator the same .
1 ⁷/40
What’s the answer ?
Answers
Answer:
C. Parallel
D. Segment
F. Ray
Explaination:
Answers A, E, & G (line, point, & plane) are undefined terms.
The figure below is a rhombus.
z = [ ? 10
Answers
Answer:
27
Step-by-step explanation:
x=90 because it's a rhombus
Answer:
27 degrees
Step-by-step explanation:
one property of a rhombus is that the diagonals makes an 90 degree angle. so x= 90 degrees. the angle above x is also 90 degrees as well and since angles in a triangle add up to 180, we do 180-63-90, to get z which is 27 degrees
Solve the following
2.87 x 7.8 =
Answers
Answer:
22.386
Step-by-step explanation:
Help with geometry, Find the value of x. Round the length to the nearest tenth.
Answers
Answer:
it is 9.8 yards wide or 1.8 which is 9.8- 18 = x-6
solve for x.
Answers
Answer:
x=-12
Step-by-step explanation:
-18=x-6
-18+6=x--6+6
-12=x
First, do the opposite, so add 6 to both sides.
-18 + 6 = x
Now that x is alone, solve -18 + 6.
-18 + 6 = -12
Therefore..
X = -12
STATE THE DOMAIN OF EACH OF THE FOLLOWING RELATIONS.
1.7) {(x, y): x = root y}
Domain ………
1.8) {(r, s): s = (2r -5)/13r }
Domain ………
1.9) {(a, b): ab = 12}
Domain ………
Answers
Step-by-step explanation:
1.7) x = √y
The square root must be non-negative, so the domain is x ≥ 0, or in interval notation, [0, ∞).
1.8) s = (2r − 5) / (3r)
The denominator can't be 0, so r can't be 0. So the domain is r ≠ 0, or in interval notation, (-∞, 0) (0, ∞).
1.9) ab = 12
Solve for b: b = 12/a
The denominator can't be 0, so a can't be 0. So the domain is a ≠ 0, or in interval notation, (-∞, 0) (0, ∞).
Gina recently got an 10% raise on her salary. If Gina used to make $25 per hour, what is her new salary?
Answers
Answer:
Her new salary is $27.5.
Step-by-step explanation:
25*0.10=2.5
2.5+25=27.5
In which type of triangle is the orthocenter on the perimeter of the triangle?
a right triangle
an acute triangle
an obtuse triangle
an equilateral triangle
Answers
Answer:
its a right triangle
Step-by-step explanation:
i just took the test
Answer: Yes, I can confirm it is right triangle!
10 5/12- 12 7/12 = in simplest form
Answers
Answer:
-13/6 or (in mixed number form) -2 1/6
Step-by-step explanation:
Rewriting our equation with parts separated
=10+512−12−712
Solving the whole number parts
10−12=−2
Solving the fraction parts
512−712=−212
Reducing the fraction part, 2/12,
−212=−16
Combining the whole and fraction parts
−2−16=−216
Another way to do it:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
125/12−151/12
Applying the fractions formula for subtraction,
=(125×12)−(151×12) / 12×12
=1500 − 1812/ 144
=−312/144
Simplifying -312/144, the answer is
=−2 1/6
Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of
of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to
skip crocheting some days so she can volunteer in other ways.
Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.
How many days can Darcie skip to still meet her goal?
Answers
Answer:
I believe it's 15 days
Answer:
The maximum number of days that she can skip crocheting is s = 57
Step-by-step explanation:
Darcie wants to crochet a minimum of 3 blankets.
She can crochet at a rate of a blanket per day, so she makes 1 blanket in one day.
She has a total of 60 days to work.
If X is the number of days that she works, we can write it as:
X ≥ 3
This means that she works at least 3 days, so she makes at least 3 blankets.
X < 60
This means that she not can work 60 days or more, in this way she has at least one day to do another volunteer job.
then
3 ≤ X < 60
then we have:
1 ≤ s ≤ 60 - 3 = 57
where s is the days that she can skip, where the less or equal sign is used because we have a bigger or equal sign previously.
The maximum number of days that she can skip
The maximum number of days that she can skip crocheting is when the right equality is true, so s = 57.
Describe the pattern 0.13, 0.65, 3.25, 16.25
Answers
Let n be the current term and n+1 be the next term
Then the pattern is: n+1 = n * 5
Step-by-step explanation:
Given series is:
0.13, 0.65, 3.25, 16.25
We can find the ratio between consecutive numbers to find the pattern
So,
[tex]Ratio = \frac{0.65}{0.13}\\=5[/tex]
We can see that multiplying the previous term with 5 gives us the next term
0.13 * 5 = 0.65
0.65 * 5 = 3.25
3.25 * 5 = 16.25
Let n be the current term and n+1 be the next term
Then the pattern is: n+1 = n * 5
Keywords: Pattern, Sequence
Learn more about series at:
brainly.com/question/2150928brainly.com/question/2154850#LearnwithBrainly
|4*(6-10)| algebra
--------------
Answers
Answer:
16
Step-by-step explanation:
6-10=-4
4*-4=-16
abs(-16)=16
Answer:
|4(6-10)|
|4(-4)|
|-16|=16
Step-by-step explanation:
do parentheses firstdo multiplicationthe answer is 16 because the distance of a number from zero is positive not negative.
what is 2x + 1 = 15 if x =8
Answers
Answer:
17
Step-by-step explanation:
17=15
so this is not equal
Which expression is equivalent to (x^6×x^10/×^-3)^2 and why?
Answers
Answer:
The solution for the given expression is [tex]x^{38}[/tex] , i.e option C
Step-by-step explanation:
Given expression as :
[tex](\dfrac{x^{6}\times x^{10}}{x^{-3}})^{2}[/tex]
Now, From the common radix method
∵ In multiplication of radix , if the radix is same , then power is added
I.e [tex]x^{6}\times x^{10[/tex] = [tex]x^{6+10}[/tex]
Or , [tex]x^{6}\times x^{10[/tex] = [tex]x^{16}[/tex]
Now, The expression can be written as
[tex](\frac{x^{16}}{x^{-3}})^{2}[/tex]
And In Division of radix , if the radix is same , then power is subtracted
So, [tex]\frac{x^{16}}{x^{-3}}[/tex]
Or, [tex]x^{16 - (-)3}[/tex]
Or, [tex]x^{16 + 3}[/tex]
or, [tex]x^{19}[/tex]
∴ The expression is now
[tex](x^{19})[/tex]²
Now, again this is written as
[tex]x^{19}[/tex] × [tex]x^{19}[/tex]
I.e here again the radix is same and in multiple for, so, power is added
∴ [tex]x^{19}[/tex] × [tex]x^{19}[/tex] = [tex]x^{19+19}[/tex]
I.e [tex]x^{19}[/tex] × [tex]x^{19}[/tex] = [tex]x^{38}[/tex]
Hence The solution for the given expression is [tex]x^{38}[/tex] , i.e option C . Answer
Choose the equation that represents the line passing through the point (2, - 5) with a slope of −3.
y = −3x − 13
y = −3x + 11
y = −3x + 13
y = −3x + 1
Answers
Answer:
y = -3x + 1
Step by step (I hope I don't confuse you):
1. First, look for the equation that has a slope of -3. In this case, it's all of them because they all have -3 before the x value.
2. Then look for what's given:
The y of (2, -5) is negative. If the x is 2, that means that the slope has moved down 3 units twice. (-3 is the slope. -3 x 2 is -6.)3. Now see what equation will have -5 when you subtract 6 from it's y intercept.
y = 3x + 11. 11 - 6 is 5, not -5. this one is wrong.y = 3x - 13. -13 - 6 is -19, also incorrect.y = 3x + 1. 1 - 6 is -5, so this is the correct answer.Hope you found this helpful.
The equation of line is y= -3x + 1.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
point (2, - 5) with a slope of −3.
Using slope- intercept form
y = mx + c
-5 = (-3) (2) + c
-5 = -6 + c
c = -5 + 6
c= 1
So, the equation of line is y= -3x + 1
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
according to the blueprint, the floor area of the stage in the new auditorium at your college must be rectangular and equal to 1200 square feet. The width of the stagr is key to all of the theatre priductions. therefore, in this situation, the stages depth is a function of its width.
Answers
Answer:
[tex]d = \frac{1200}{w}[/tex]
Step-by-step explanation:
According to the blueprint, the floor area of the stage in the new auditorium at my college must be rectangular and equal to 1200 sq. feet.
If the width of the stage is w feet and depth of the stage is equal to d feet, then being a rectangle, we can write
[tex]d \times w = 1200[/tex]
Therefore, the equation that represents the depth d as a function of width w is given by [tex]d = \frac{1200}{w}[/tex] (Answer)
Answer:
the correct answer d=1200[tex]d=1200/w[/tex]
Step-by-step explanation:
simplify numeric expression 4x(1.5+1.5)+5.75
Answers
Answer:
17.75
Step-by-step explanation:
4(1.5+1.5)+5.75
4(3)+5.75=12+5.75=17.75
Gary’s pet gorilla eats all the time. He eats 5/6 pound of food in 1/4 of an hour. How much food does he eat in an hour
Answers
Answer:
5/16
Step-by-step explanation:
1/4 x 5/4= 5/16
(just multiply it, straight across.)
5/6 • 4
The reason why I did this is because it gives us how much Gary eats in 1/4 of an hour so you need to find the amount he eats in 1 full hour.
Then you get...
20/6
Which simplifies to:
3 2/6 = 3 1/3
Final Answer:
3 1/3 lbs
Can someone help me with this????? The question is attached in the image
Answers
Answer:
See explanation
Step-by-step explanation:
Since [tex]\overline{CB}[/tex] is parallel to [tex]\overline {ED},[/tex] then
angles EDF and CBF are congruent as alternate interior angles when parallel lines [tex]\overline{CB}[/tex] is parallel to [tex]\overline {ED}[/tex] intersect by transversal DB;angles DEF and BCF are congruent as alternate interior angles when parallel lines [tex]\overline{CB}[/tex] is parallel to [tex]\overline {ED}[/tex] intersect by transversal CE.Consider triangles CBF and EDF. In these triangles:
[tex]\angle EDF\cong \angle CBF[/tex] (proven);[tex]\angle FED\cong \angle FCB[/tex] (proven);[tex]\overline{CB}\cong \overline {ED}[/tex] (given).Thus, triangles CBF and EDF are congruent by ASA postulate.
Which of the following numbers would you subtract from each side of the equation x + 12 = 17 + 3 to get the variable by itself?
17
12
3
1/12
Answers
Answer:
you will subtract 17 from both sides to get the variable by itself.
Step-by-step explanation:
x+12=17+3.
subtract 12 from both sides
How do I graph and find slope intercept for for x+y=0
Answers
Answer:
y = -x + 0
slope intercept: 0
Step-by-step explanation:
You would start at the origin, since your slope intercept is 0. The slope, -1 (since -x is the same as -1x), is telling us the line will be negative, so the line you are graphing will be heading up one space at a time towards the left, up 1 and sideways 1. Rise over Run.
Fill in the missing term in the equation x/x^2-4x+4 - x/x^2-3x+2= ?/(x-2)^2(x-1)
Answers
Answer:3
Step-by-step explanation:
Explaination
write the numerical expression as a power. (4 x4 x 4 = )
Answers
Answer:
[tex] {4}^{3} [/tex]
Step-by-step explanation:
your are taking 4 and multiplying it by itself three times hence 4 to the third power
Answer:
4³
Step-by-step explanation:
A simple question:
Is a vector made like or ?
Answers
Answer:
A vector is a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.
Lashonda bought a desk on sale for $159.60. This price was 62% less than the original price. What was the original price?
Answers
p - 62%p = %=$159.60
p - 62p/100 = $159.60
100p - 62p = $15960
38p = $15960
p = $15960/38
p = $420
What is the area of a regular pentagon with a side of 10in?
Answers
Area of a regular pentagon with a side of 10in is 172
Step-by-step explanation:
Given:
Side of the regular pentagon = 10in
To Find:
Area of the regular pentagon=?
Solution:
We know that ,
[tex]Area of Pentagon = 5\times\text{ Area of triangle}[/tex]................(1)
Step 1: Finding the Area of the triangle
we know that in a right angle triangle, there are base, height and hypotenuse [tex]tan(\frac{\pi}{5}) =\frac{ height}{hypotenuse }[/tex]
So, from the above equation,
[tex]height=\frac{(base/2)}{tan(36^{\circ})}[/tex]
[tex]height=\frac{5}{tan(36)}=6.88[/tex]
area of right angle triangle
=> [tex]\frac{1}{2}\times base \times height[/tex]
=> [tex]=\frac{1}{2} \times 5\times 6.88[/tex]
=> 17.20
Area of the triangle =2 x area of right angle triangle
Area of the triangle =2 x 17.20
Area of the triangle= 34.40
Step 2: Finding the Area of the pentagon
Substituting the values in (1)
[tex]Area of Pentagon = 5\times 34.40 [/tex]
Area of Pentagon= 172