Question 1)
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles ..
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Answers
Answer:
The height of pole is 20√3 m each and distance of pole from the point on road is 60 m and 20 m respectively.
Step-by-step explanation:
Given:
Two poles of equal heights are standing on opposite side of the road which is 80 m wide facing each other. From a point on the road the angle of elevation of poles are 60° and 30° respectively.To Find:
The height of poles and the distance of that point on the road from the pole.Formula used:
tan60° = √3 tan30° = 1/√3Let the height of each pole be H metres.
Also, let's assume that distance of the point from one pole (as shown in figure) be x m.
According to question, we have
tan60° = H/(80-x)
H = (80-x)√3.... (1)
Also, tan30° = H/x
H = x/√3... (2)
Putting value of eq(2) in eq(1), we get
x/√3 = (80-x)√3
x = 3(80-x)
x = 240 - 3x
4x = 240
x = 60 m
Putting value of x in eq(2), we get
H = 60/√3 = 20√3 m
So, the height of pole is 20√3 m each and distance of pole from the point on road is 60 m and 20 m respectively.
Answer:
Height of Pole: 20√3 m
Distance Of Point From Poles: 20m and 60m
Step-by-step explanation:
The attached graph may help you understand my explanation better
The two poles are Ab and CD and are 80m apart
O is the point between them
The angle of elevation from O to A is 60°
The angle of elevation from O to D is 30°
Since the two poles are given to be of equal height,
AB = CD
In ΔAOB using the law of tangents
tan 60° = AB/BO
tan 60° = √3 and AB = x
So we get
√3 = x/BO
Multiplying both sides by BO we get
√3 · BO = x
or BO = x/√3
Looking at ΔCOD
tan 30° = DC/OC
tan 30° = 1/√3
1/√3 = x/OC
OC · ( 1/√3) = x
OC = x ÷ 1/√3
= x · √3/1
OC = √3x
We also know that BO + OC = 80
Plugging this information with values computed gives us
x/√3 + √3x = 80
Multiply by √3 on both sides
(x/√3) · √3 + (√3x) √3 = 80√3
(x/√3) · √3 = x since the √3 terms cancel out
(√3x) √3 = 3x
So we get
(x/√3) · √3 + (√3x) √3 = 80√3
=>
x + 3x = 80√3
4x = 80√3
x = (80√3)/4
x =20√ 3
So the height of each pole = 20√ 3 m ≈ 34.64 m
The distance OC can be found from the previous equation
OC = √3x
=> OC = √3 x 20√3 = 20 x 3 = 60m
Since BO + OC = 80 m
BO = 80 - 60 = 20 m
Answer:
Height of each pole = 20√3 m
The point is located 20 m from one pole and 60 m from the other pole
Related Questions
brian sells wholesome computer parts at a comission rate of 4% .what is his income last month if his total sales were 82,968.00
Answers
Brian's income last month t is $3,318.92
How to calculate the income ?The commission rate for the computer parts is 4%
The total sales for last month is 82,968.00
Brian income last month can be calculated as follows
Total sales × commission percentage
4/100 × 82,968
= 0.04 × 82,968
= 3,318.92
Hence Brian income for last month is $3,318.92
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Here is some information about a heating oil tank.
Top Outlet Tank
Height (h): 2550 mm
Diameter (d): 2100mm
Mass: 650kg
(b) Work out the volume, in cubic metres, of the tank.
Answers
The volume of the tank is 15315.35
What is volume?Volume is a measurement of three-dimensional space that is occupied. [1] Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up.
Given that,
Top Outlet Tank
Height (h): 2550 mm
Diameter (d): 2100mm
radius (r) : 2.1/2
Mass: 650kg
The volume, in cubic metres, of the tank is
volume of tank = 2π + π[tex]r^{2} h[/tex]
= 2π(1100) + π(2.1/2)(2550)
= 2(3.14)1100+ (3.14)(2.1/2)(2550)
= 6908+ 8407.35
= 15315.35
Therefore, the volume of the tank is 15315.35
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a dog walks due east 180 feet at a corner after turning through an angle of 81.5 the dog walks 329 feet to the second corner. then the dog walked back to the starting point. what is the area of the triangle formed by his path
Answers
The area of the triangle formed by his path is mathematically given as
Area = 29284.886 ft^2
This is further explained below.
What is the area?Generally, the equation for the defining cosine rule is mathematically given as
[tex]b^2 = a^2 + c^2 - 2ac cos B[/tex]
where
b = side B of the triangle
a = side A of the triangle
c = side C of the triangle
Therefore
[tex]b^2 = 180^2 + 329^2 - 2(180 * 329)cos 81.5[/tex]
b^2 = 32400 + 108241 - 17506.55
b = 350.91 ft
We calculate the area of the triangle using heron's formula.
Area = [tex]\sqrt{(p(p - a)(p - b)(p - c))}[/tex]
b = side B of the triangle
a = side A of the triangle
c = side C of the triangle
p = path
Where
p = (a + b + c)/2
p= (180 + 350.91 + 329)/2
p= 429.955 ft
Area = [tex]\sqrt{(429.955(429.955 - 180)(429.955 - 350.91)(429.955 - 329)}[/tex]
Area = 29284.886 ft^2
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When an integer is subtracted from 5 times the next consecutive odd integer,the difference is 22.find the value of the greater integer
Answers
The value of the greatest integers will be 5.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
'' An integer is subtracted from 5 times the next consecutive odd integer, the difference is 22''.
Now,
Write the mathematical expression for an algebraic expression as;
Let an integer = 2x + 1
Then, The next consecutive odd integer = 2x + 3
So, We can formulate;
5 (2x + 3) - (2x + 1) = 22
Solve for x as;
5 (2x + 3) - (2x + 1) = 22
10x + 15 - 2x - 1 = 22
8x + 14 = 22
Subtract 14 both sides, we get;
8x + 14 - 14 = 22 - 14
8x = 8
Divide by 8,
x = 8/8
x = 1
Since, The greatest integers = 2x + 3
Substitute x = 1, we get;
The greatest integers = 2x + 3
The greatest integers = 2 × 1 + 3
The greatest integers = 2 + 3
The greatest integers = 5
Therefore, The value of the greatest integers will be 5.
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Simplify 3(2x-5) - (1-3x)
6x-15 - 1 - 3x
6x - 16
Why is this wrong
Answers
Answer:
6X-15-1-3X=3X-16
6-3=3
Find and interpret the slope. The number of cubic feet of watery In a reservoir x hours after the water starts flowing into the reservoir Is a linear function. The points (40,2,000) and (60, 3,000) are on the line of the function. The slope ls which means that the amount of water in the reservoir is increasing at a rate of cubic feet each hour.what is the y- intercept? what is the x- intercept?
Answers
The slope of a line (m) given two points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with (40,2,000) and (60, 3,000):
[tex]m=\frac{3000-2000}{60-40}=\frac{1000}{20}=50[/tex]The slope ls 50 cubic feet/hour which means that the amount of water in the reservoir is increasing at a rate of 50 cubic feet each hour.
Slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-intercept. Replacing with m = 50 and point (40, 2000), e get:
200050()40
2000
2000 - 2000 = b
0 = b
Then the y-intercept is point (0, 0) which is also the x-intercept
The equation is:
y = 50x
Which is a correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” when n = 4?
The correct expression is StartFraction n cubed Over 16 EndFraction minus 2 + 8.
The correct expression is 2 minus StartFraction n cubed Over 16 EndFraction + 8.
One of the steps to determining the value when n = 4 is 1 minus 2 + 8.
One of the steps to determining the value when n = 4 is 2 minus 1 + 8.
The value when n = 4 is 6.
The value when n = 4 is 7.
The value when n = 4 is 9.
The value when n = 4 is 10.
Answers
The correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” is "StartFraction n cubed Over 16 EndFraction minus 2 + 8"
The correct answer option is option a
The value of the expression when n = 4 is 10. option D
How to write algebraic expressionThe unknown number = nQuotient means divisionquotient of a number cubed and sixteen
= n³ / 16
two less than the quotient of a number cubed and sixteen
= (n³ / 16 - 2)
two less than the quotient of a number cubed and sixteen, increased by eight”
= (n³ / 16 - 2) + 8
If n = 4
(n³ / 16 - 2) + 8
= (4³ / 16 - 2) + 8
= (64/16 - 2) + 8
= (4 - 2) + 8
= 2 + 8
= 10
In conclusion, the expression can be written as "StartFraction n cubed Over 16 EndFraction minus 2 + 8"
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Evaluate c/2 -3 + 6/d when c=14 and d=3
with an explanation if possible :))
Answers
Answer:
c/2-3+6/d
=
14/2-3+6/3
= (Order of Operations)
7-3+2
=
6
Step-by-step explanation:
See explanation above
Is 9 11/13 bigger than 9.79
Answers
[tex]9\frac{11}{13}[/tex] is bigger than 9.79
The mixed fraction = [tex]9\frac{11}{13}[/tex]
The mixed fraction is the fraction that expressed with its quotient and remainder. The mixed fraction is the combination of a whole number and a simple fraction
Simple fraction is the fraction that has whole numbers as the numerator and denominator.
The decimal number is a number that has whole and the fractional parts are separated by a decimal point
First we have to convert the mixed fraction into simple fraction
[tex]9\frac{11}{13}[/tex] = 128/13
Next we have to convert the simple fraction into decimal form
Divide 128 by 13
The result will be
128/13 = 9.85
Hence, [tex]9\frac{11}{13}[/tex] is bigger than 9.79
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Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 into the form (x − p)2 = q?
[p and q are integers]
Step 1 x2 + 10x + 24 − 1 = 0 − 1
Step 2 x2 + 10x + 23 = −1
Step 3 (x + 5)2 = −1
Step 1 x2 + 10x + 24 − 2 = 0 − 2
Step 2 x2 + 10x + 22 = −2
Step 3 (x + 5)2 = −2
Step 1 x2 + 10x + 24 + 2 = 0 + 2
Step 2 x2 + 10x + 26 = 2
Step 3 (x + 5)2 = 2
Step 1 x2 + 10x + 24 + 1 = 0 + 1
Step 2 x2 + 10x + 25 = 1
Step 3 (x + 5)2 = 1
Answers
The correct steps to transform equation x² + 10x + 24 = 0 into the form (x - p)² = q are:
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
In this question, we have been given an equation x² + 10x + 24 = 0
We need to transform given equation x² + 10x + 24 = 0 into the form (x - p)² = q
x² + 10x + 24 = 0 .............(Given equation)
x² + 10x + 24 + 1 = 0 + 1 ............(Add 1 to each side)
x² + 10x + 25 = 1
x² + 2(5)x + 5² = 1
(x + 5)² = 1
Therefore, the correct steps to transform equation x² + 10x + 24 = 0 into the form (x - p)² = q are:
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
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Solve one sixth times quantity x plus 18 end quantity equals negative 5.
x = −48
x = −138
x = 12
x = 18
pls hurry
Answers
Answer:
(a) -48
Step-by-step explanation:
You want the solution to the equation 1/6(x +18) = -5.
2 Step equationThe first step to solving this can be to multiply both sides by 6, eliminating the fraction:
x +18 = -30
The second step can be to isolate the variable by subtracting 18 from both sides.
x = -48
The solution is x = -48.
__
Additional comment
Sometimes you may want to simplify the equation before you start the solution process. Here, you can also start by eliminating parentheses:
1/6x +3 = -5
Now, subtracting 3 gives ...
1/6x = -8
Finally, multiplying by 6, we have ...
x = -48
<95141404393>
4. Given Segment AC such that point B is between A and C. If AC = 2x + 21, AB = x + 9, and BC = 3x - 4. a. What is the value of x b. How long is AC
Answers
On solving the given statement, the length of AC equals 37.
What is meant by line segment?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that lie inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
According to the given statement,
AC = 2x + 21
AB = x + 9
BC = 3x - 4
As B is the mid point of the segment AC,
⇒ AB + BC = AC
⇒ x + 9 + 3x - 4 = 2x + 21
⇒ 4x + 5 = 2x + 21
⇒ 2x = 16
⇒ x = 8
Length of AC = 2 (8) + 21
= 16 + 21
= 37
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The marked of a jacket at a dealer's shop is Rs. 2400 The dealer allows a discount of 15% to the retailer. As the company's policy the marked price of the retailer should be the same as decler's marked price. What SP should the retailer fix for the Jacket ? What would it's final price beif 10% VAT is imposed? What would be the actual gain of retailer ? If 10% discount is allowed.
Answers
Answer:
Step-by-step explanation:
Given,
The marked price of a jacket at dealer shop is Rs. 2400
The dealer allows a discount of 15% to the retailer.
The marked price of the retailer should be same as the dealer's marked price.
To find,
1. SP the retailer should fix for the jacket
2. Its final price if 10% VAT is imposed
3. The actual gain of the retailer if 10% discount is allowed
Solution,
The SP rate for the jacket without VAT 2400
Let 10% VAT on jacket price 2400 be x
x= 2400÷10
x= 240
So, the final price including 10% VAT = 2640 (2400+240)
As the dealer allowed discount of 15% to the retailer, the retailer gain profit is 15% on the jacket price i.e., 2400
Let y be the gain of the retailer
y= 15/100 × 2400
y= 360
Therefore,
SP the retailer should fix for the jacket is 2400
final price if 10% VAT is imposed is 2640
the actual gain of the retailer is 360
Given the function f(x) = 3x + 1 and the linear function g(x), which function has a greater slope?
Answers
The function that has the greater slope is the function g(x) that is represented by the graph.
How to Determine the Slope of a Function?The slope (m) of a function using two points on a graph can be calculated as:
Slope of the line (m) = change in y/change in x
If we are given the equation of the line using function notation as .f(x) = mx + b, the slope of the function is represented in the equation as "m". The value of "m" is the slope of the function given.
Given the function, .f(x) = 3x + 1, the value that represents "m" which is 3. Therefore, the slope of the function .f(x) = 3x + 1 is: 3.
Find the slope of the function of the graph using two points on the line, say (2, 3) and (3, 7):
Slope of the function (m) = change in y / change in x = (7 - 3)/(3 - 2)
Slope of the function (m) = 4/1
Slope of the function (m) = 4
The larger the value of the slope, the greater the slope of the function.
Therefore, the function g(x) that is represented by the graph has a greater slope.
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Answer: B
Step-by-step explanation:
Simple
Thanks for all the help
Answers
Answer:
x=4.4
Step-by-step explanation:
To get from 4 to 10 what happens?
Well, we multiply 4 by 2.5.
That should be the same for x.
Thus, 2.5x=11
x=4.4
Find the distance between each pair of points round to nearest tenth if needed
Answers
Answer: 10) √85 units 12) 4 units
Step-by-step explanation:
[tex]\boxed {l=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}}[/tex]
10) (8,5) (-1,3)
[tex]x_1=8\ \ \ \ x_2=-1\ \ \ \ y_1=5\ \ \ \ \ y_2=3\\\\l=\sqrt{(-1-8)^2+(3-5)^2} \\\\l=\sqrt{(-9)^2+(-2)^2} \\\\l=\sqrt{81+4}\\\\l=\sqrt{85}\ units[/tex]
12) (-6,-10) (-2,-10)
[tex]x_1=-6\ \ \ \ \ x_2=-2\ \ \ \ \ y_1=-10\ \ \ \ y_2=-10\\\\l=\sqrt{(-2-(-6)^2+(-10-(-10))^2} \\\\l=\sqrt{(-2+6)^2+(-10+10)^2}\\\\l=\sqrt{4^2+0^2} \\\\l=\sqrt{4^2} \\\\l=4\ units[/tex]
Please answer the question in the photo
Answers
Answer:
i got
Step-by-step explanation:
seventy-nine
so
you now know
42° + b + 22° + b - 42° = 180 °
you can simplify this to
64° + 2b - 42° = 180°
you can then take away 64 from both sides
2b - 42° = 116°
then you add the - 42 to both sides
which leaves you with
2b = 158
you divide it by two on both sides
which makes
b = 79
you can check this by doing
79 + 22 = 101
79 - 42 = 37
and then adding it
101 + 37 + 42 = 180
you’re welcome
i need help ASAP!!!!!!!!!!!!
Answers
Answer:
420 mark Brainliest
Step-by-step explanation:
distance is going up by 60 and the points are moving 2 for time so at 12 it will be 360 then 14 will be 420 so the answer is 420
micah is 111 of 282828 students in a class. micah's teacher is going to randomly select 333 students from their class to visit a classroom of younger students. what is the probability micah is included in the group of students chosen?
Answers
0.71% is the probability micah is included in the group of students chosen.
Describe probability using an example?
By dividing the number of favorable outcomes by the total number of possible outcomes, probability—the likelihood that an event will occur—is determined.The simplest example is a coin flip. When you flip a coin there are only two possible outcomes, the result is either heads or tails.the probability micah is included in the group of students chosen =
3/28 = 10.71%
The probability of her getting picked is unlikely.
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The complete question is -
Micah is 1 of 28 students in a class. Micah's teacher is going to randomly select 3 students from their class to visit a classroom of younger students. What is the probability Micah is included in the group of students chosen?
4/6 - 3/6p=16/6 what is p
20 points
Answers
Answer:
-4
Step-by-step explanation:
4/6 - 3/6p=16/6
Multiply each side by 6
4 - 3p = 16
Subtract 4 from both sides
-3p = 12
Divide both sides by -3
p = -4
Answer:
-4
Step-by-step explanation:
Solving for 'p':[tex]\sf \dfrac{4}{6}-\dfrac{3}{6}p=\dfrac{16}{6}[/tex]
To find the value of 'p', isolate 'p',
[tex]\sf \dfrac{-3}{6}p=\dfrac{16}{6}-\dfrac{4}{6}\\\\[/tex]
[tex]\sf = \dfrac{12}{6}[/tex]
= 2
[tex]\sf p = 2* \dfrac{6}{-3}\\\\ p = 2 *(-2)\\\\p = -4[/tex]
What is the Process for performing the transformation on a coordinate plane using rigid transformations
Answers
Flipping and Stretching is the Process for performing the transformation on a coordinate plane using rigid transformations.
A rigid transformation of a geometric object preserves distance between each pair of points of the object. In other words, rigid transformations preserve the shape and size of an object. For example, a rigid transformation of a triangle preserves both the measure of the angles and the lengths of the sides of the triangle. Think of rigid transformations of a shape as being like taking a cardboard cutout of the shape. The shape can be moved around, rotated, and flipped from one side to the other, but the shape itself does not change.
There are rules associated with rigid transformations. A rigid transformation is some function F from a set X to itself such that F preserves the distances between two points. Let d(x ,y) be the distance between two points. Then, to write the definition in mathematical notation, if d(x ,y) = d(F(x),F(y)) for all points x and y, then F is a rigid transformation.
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steven had $5 that his mom gave him to buy lunch at school he spent $5 on his lunch. plot a point on the number line to show how much money steven has after he spent $5 on food
Answers
If Steven had $5 to buy lunch at school, and he spent all of the $5 on his lunch, then he will have $0 remaining, as plotted on the number line in the reference attachment hereby.
As per the question statement, Steven had $5 that his mom gave him to buy lunch at school and he spent all of the $5 on his lunch.
We are required to plot a point on the number line to depict how many dollars Steven has left with himself after spending on his lunch.
To solve this question, we simply need to subtract the amount Steven spent for his lunch, from the amount, his mother gave him to spend on lunch, and then plot the result of the said subtraction on the number line to obtain our desired answer.
Since, Steven had $5 to buy lunch at school, and he spent all of the $5 on his lunch, he has $(5 - 5) = $0 left with himself after spending on his lunch.
That is, we will have to plot 0 on the number line, which is shown in the reference attachment hereby.
Number Line: In elementary Mathematics, a number line is a graduated straight line that serves as visual representation of real numbers, marked at regular, equal intervals.To learn more about Number Line, click on the link below.
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True or false? If x>0, then x² > x.
Answers
Answer:
False
Step-by-step explanation:
It is false when x=1 because
[tex]1^{2} =1[/tex]
What 685,203 rounded to the nearest ten , hundred , thousand, ten ten thousand and, hundred thousand
Answers
Answer:
685200 is ten and hundred 685000 thousand 690000 ten thousand 700000 hundred thousand
Work out the value of (6.31 x 10^5) + (2.6 × 10^1)
Give your answer in standard form.
Answers
Answer: 16,406,000
Step-by-step explanation:
First, multiply 6.31 and 2.6 to get 16.406. Then, add 10^5 and 10^1 to get 10^6.
It should now look like this, 16.406 x 10^6
The number has to be between 10 and 1 so you need to make it smaller by moving the decimal point over once to the left. It should now be 1.6406. But, you can't leave the exponent at 10^6 so, you need to make it bigger since you made the number smaller.
Your answer should now look like this, 1.6406 x 10^7
Since it needs to be in standard form, move the decimal point 7 times to the right since it is a positive number.
So, your answer is: 16,406,000
Use the equation below to find a, if b=3 and h=4
Answers
Write an equation of the line passing through point P(-1,-4) that is parallel to
y = -6x + 8
Answers
The equation of the line passing through point P(-1,-4) that is parallel to y = -6x + 8 is y = -6x - 10.
What is a straight line?A straight line is made up of an infinite number of points connected at their ends.
Any straight line's slope, "m," is determined by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line y = -6x + 8
m = -6
The slope of the line passing point P (-1,-4)
M = -6
y - (-4) = -6(x - (-1))
y + 4 = -6(x + 1)
y = -6x - 10
Thus, the equation of the line passing through point P(-1,-4) that is parallel to y = -6x + 8 is y = -6x - 10.
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f(x)=x^2
g(x)=−x^2+7
h(x)=(x−6)2
p(x)=(x−2)2−9
q(x)=x^2+12
Answers
Answer:
Step-by-step explanation:
interval notation is (-∞,∞)
set-builder notation is {x|x ∈ R}
Look at the image for the problem, also round to the nearest hundredth if necessary.
Answers
ANSWER
[tex]V=3052.08ft^3[/tex]EXPLANATION
We want to find the volume of the sphere.
The volume of a sphere is given as:
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]where r = radius of the sphere.
Therefore, we have that the volume of the sphere is:
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot9^3 \\ V=3052.08ft^3 \end{gathered}[/tex]That is the volume of the sphere.
Find n(A) when
A = {14, 16, 18, 20, 22, 24}
Answers
n(A) is 6 when A = {14, 16, 18, 20, 22, 24}
What is set?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things. Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
Given Data
A = {14, 16, 18, 20, 22, 24}
We are aware that the cardinality, which is represented by the letter n, is the number of items in any set A.
n(A) = number of elements in set
n(A) = 6
n(A) is 6
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