A surveyor is trying to find the height of a hill. He/she takes a ‘sight’ on the top of the hill and find that the angle of elevation is 40°. He/she move a distance of 150 metres on level ground directly away from the hill and takes a second ‘sight’. From this point, the angle of elevation is 22°. Find the height of the hill, correct to 1 d.p.
Answers
Answer:
The height of the hill is 116.9 meters.
Step-by-step explanation:
The diagram depicting this problem is drawn and attached below.
From Triangle ABC
[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]
From Triangle XBC
[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]
Therefore:
[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]
Therefore, the height of the hill
[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]
The height of the hill is 116.9 meters.
Related Questions
Emily and George had a farm with a new barn.
True
False
Answers
Answer:
true
Step-by-step explanation:
it is so because they are brother and sister
And in the chapter there is that they had farm with a new barn
if in your book lesson there is that they had no farm with a new barn then there will be false
Now did you understood?
Answer:
True
Step-by-step explanation:
The vector matrix[ 27 ]is dilated by a factor of 1.5 and then reflected across the X axis if the resulting matrix is a B then a equals an VE
Answers
Correct question:
The vector matrix [ [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex] is dilated by a factor of 1.5 and then reflected across the x axis. If the resulting matrix is [a/b] then a=??? and b=???
Answer:
a = 3
b = 10.5
Step-by-step explanation:
Given:
Vector matrix = [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex]
Dilation factor = 1.5
Since the vector matrix is dilated by 1.5, we have:
[tex] \left[\begin{array}{ccc}1.5 * 2\\1.5 * 7\end{array}\right] [/tex]
= [tex] \left[\begin{array}{ccc}3\\10.5\end{array}\right] [/tex]
Here, we are told the vector is reflected on the x axis.
Therefore,
a = 3
b = 10.5
Answer:
a = 3
b = -10.5
Step-by-step explanation:
got a 100% on PLATO
The curvature of a plane parametric curve x = f(t), y = g(t) is $ \kappa = \dfrac{|\dot{x} \ddot{y} - \dot{y} \ddot{x}|}{[\dot{x}^2 + \dot{y}^2]^{3/2}}$ where the dots indicate derivatives with respect to t. Use the above formula to find the curvature. x = 6et cos(t), y = 6et sin(t)
Answers
Answer:
The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].
Step-by-step explanation:
The equation of the curvature is:
[tex]\kappa = \frac{|\dot {x}\cdot \ddot {y}-\dot{y}\cdot \ddot{x}|}{[\dot{x}^{2}+\dot{y}^{2}]^{\frac{3}{2} }}[/tex]
The parametric componentes of the curve are:
[tex]x = 6\cdot e^{t} \cdot \cos t[/tex] and [tex]y = 6\cdot e^{t}\cdot \sin t[/tex]
The first and second derivative associated to each component are determined by differentiation rules:
First derivative
[tex]\dot{x} = 6\cdot e^{t}\cdot \cos t - 6\cdot e^{t}\cdot \sin t[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot \sin t + 6\cdot e^{t} \cdot \cos t[/tex]
[tex]\dot x = 6\cdot e^{t} \cdot (\cos t - \sin t)[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t)[/tex]
Second derivative
[tex]\ddot{x} = 6\cdot e^{t}\cdot (\cos t-\sin t)+6\cdot e^{t} \cdot (-\sin t -\cos t)[/tex]
[tex]\ddot x = -12\cdot e^{t}\cdot \sin t[/tex]
[tex]\ddot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t) + 6\cdot e^{t}\cdot (\cos t - \sin t)[/tex]
[tex]\ddot{y} = 12\cdot e^{t}\cdot \cos t[/tex]
Now, each term is replaced in the the curvature equation:
[tex]\kappa = \frac{|6\cdot e^{t}\cdot (\cos t - \sin t)\cdot 12\cdot e^{t}\cdot \cos t-6\cdot e^{t}\cdot (\sin t + \cos t)\cdot (-12\cdot e^{t}\cdot \sin t)|}{\left\{\left[6\cdot e^{t}\cdot (\cos t - \sin t)\right]^{2}+\right[6\cdot e^{t}\cdot (\sin t + \cos t)\left]^{2}\right\}^{\frac{3}{2}}} }[/tex]
And the resulting expression is simplified by algebraic and trigonometric means:
[tex]\kappa = \frac{72\cdot e^{2\cdot t}\cdot \cos^{2}t-72\cdot e^{2\cdot t}\cdot \sin t\cdot \cos t + 72\cdot e^{2\cdot t}\cdot \sin^{2}t+72\cdot e^{2\cdot t}\cdot \sin t \cdot \cos t}{[36\cdot e^{2\cdot t}\cdot (\cos^{2}t -2\cdot \cos t \cdot \sin t +\sin^{2}t)+36\cdot e^{2\cdot t}\cdot (\sin^{2}t+2\cdot \cos t \cdot \sin t +\cos^{2} t)]^{\frac{3}{2} }}[/tex]
[tex]\kappa = \frac{72\cdot e^{2\cdot t}}{[72\cdot e^{2\cdot t}]^{\frac{3}{2} } }[/tex]
[tex]\kappa = [72\cdot e^{2\cdot t}]^{-\frac{1}{2} }[/tex]
[tex]\kappa = 72^{-\frac{1}{2} }\cdot e^{-t}[/tex]
[tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex]
The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].
Please help!!!!! I'm on a timerrrrrrrrrrrrrr!
Answers
Step-by-step explanation:
6
[tex]6 \sqrt{6} [/tex]
Answer:
6√6is the exact answer
The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.
(i) 6.9
mPQ = 1
(ii) 6.99
mPQ = 2
(iii) 6.999
mPQ = 3
(iv) 6.9999
mPQ = 4
(v) 7.1
mPQ = 5
(vi) 7.01
mPQ = 6
(vii) 7.001
mPQ = 7
(viii) 7.000
mPQ = 8
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at
P(7, −2).
m = 9
(c) Using the slope from part (b), find an equation of the tangent line to the curve at
P(7, −2).
Answers
The equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
For each given value of x, we substitute the coordinates of P and Q into the slope formula to find the slope mPQ.
(i) For x = 6.9:
mPQ = (2/(6 - 6.9) - (-2)) / (6.9 - 7)
= 2.22
(ii) For x = 6.99:
mPQ = (2/(6 - 6.99) - (-2)) / (6.99 - 7)
= 2.020
(iii) For x = 6.999:
mPQ = (2/(6 - 6.999) - (-2)) / (6.999 - 7)
= 2.002002
(iv) For x = 6.9999:
mPQ = (2/(6 - 6.9999) - (-2)) / (6.9999 - 7)
= 2.000200
(v) For x = 7.1:
mPQ = (2/(6 - 7.1) - (-2)) / (7.1 - 7)
= 1.818182
(vi) For x = 7.01:
mPQ = (2/(6 - 7.01) - (-2)) / (7.01 - 7)
= 1.980198
(vii) For x = 7.001:
mPQ = (2/(6 - 7.001) - (-2)) / (7.001 - 7)
= 1.998002
(viii) For x = 7.0001:
mPQ = (2/(6 - 7.0001) - (-2)) / (7.0001 - 7)
= 1.999800
By observing the pattern in the calculated slopes, we can see that as x approaches 7, the slope of the secant line PQ approaches 2.
Using the point-slope form, we have:
y - y₁ = m(x - x₁)
Substituting the values of P(7, -2), we have:
y - (-2) = 2(x - 7)
y = 2x -16
Therefore, the equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
Learn more about the equation of the tangent line here:
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What is PI times 4? HELP ASAP
Answers
Answer:
12.566370614359172953850573533118
Step-by-step explanation:
Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface that lies above the disk x2 + y2 ≤ 81
Answers
Answer:
A(s) = 255.8857
Step-by-step explanation:
Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface z = e^-x^2-y^2 that lies above the disk x2 + y2 ≤ 81.
Given that:
[tex]Z = e^{-x^2-y^2}[/tex]
By applying rule; the partial derivatives with respect to x and y
[tex]\dfrac{\partial z }{\partial x}= -2xe^{-x^2-y^2}[/tex]
[tex]\dfrac{\partial z }{\partial y}= -2ye^{-x^2-y^2}[/tex]
The integral over the general region D with respect to x and y is :
[tex]A(s) = \int \int _D \sqrt{1+(\dfrac{\partial z}{\partial x} )^2 +(\dfrac{\partial z}{\partial y} )^2 }\ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(-2xe^{-x^2-y^2})^2 +(-2ye^{-x^2-y^2})^2 } \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+4x^2({e^{-x^2-y^2})^2 +4y^2({e^{-x^2-y^2}})^2 }} \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)({e^{-x^2-y^2})^2 }} \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)e^{-2}({{x^2+y^2}) }} \ dA[/tex]
By relating the equation to cylindrical coordinates
[tex]A(s) = \int \int_D \sqrt{1+4r^2 e^{-2r^2} }. rdA[/tex]
The bounds for integration for the circle within the cylinder [tex]x^2+y^2 =81[/tex] is r =9
[tex]A(s) = \int \limits ^{2 \pi}_{0} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }. dr d\theta[/tex]
[tex]A(s) = {2 \pi} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }\ dr[/tex]
Using integral calculator to estimate the integral,we have:
A(s) = 255.8857
a.) The perimeter of a rectangular field is 354 m. If the length of the field is 95m, what is its width? b.) The area of a rectangular painting is 8439 cm^2. If the width of the painting is 87cm, what is its length?
Answers
Answer:
a) 82
b) 97
Step-by-step explanation:
a) 354 - (95+95)
354 - 190
164
164 ÷ 2 = 82
(82+82+95+95=254)
b) 8439 cm^2 = 87x
8439 cm^2 ÷ 87 = 87x ÷ 87
97 = x
Which expression represents the phrase 4 times the sum of 9 and 6
A. 4x (9+6)
B.4x 9+6
C.9+ 6x4
D. 9+ (6x4)
Answers
Answer:
The answer is option A
4 x ( 9 + 6)
Hope this helps you
Find the amount in an account where $500 is invested at 2.5% compounded continuously for period of 10 years
Answers
Hi
500 *1.025^10 ≈ 640.04
About 16.6% of Americans can speak Spanish. We obtain a random sample of seventy-five Americans and determine the proportion in the sample who speak Spanish. Find the probability that 25% or more in the sample speak Spanish.
Answers
Answer:
The probability that 25% or more in the sample speak Spanish is 76%.
Step-by-step explanation:
Sample of 75 Americans
If 25% or more in the sample speak Spanish, it can be deduced that 24% do not speak Spanish.
The proportion of those who do not speak Spanish is 18 (24% of 75)
Therefore, the proportion of those who speak Spanish is 57 (75 - 19)
This implies that 57/75 x 100 = 76% of the sample speak Spanish.
This 76% of the sample who speak Spanish is equal to the 25% or more who do speak Spanish in the sample.
Probability is the chance that an event may occur from many other events that could have occurred. It is an educated guess or estimate of something or one event happening when all the events in the set are given an equal chance.
What is the greatest common factor of the polynomial below 12x^2-9x
Answers
Answer:
the greatest common factor of this is 3
Please answer this correctly
Answers
Answer:
[tex] \frac{1}{6} [/tex]
Step-by-step explanation:
the ways of choosing 2 cards out of 4, is calculator by
[tex] \binom{4}{2} = 6[/tex]
so, 6 ways to select 2 cards.
but in only one way we can have 2 even cards. thus, the answer is
[tex] \frac{1}{6} [/tex]
Which graph represents the function?
Answers
the answer is the bottom left option
There are 12 teams, each representing a different country, in a women’s Olympic basketball tournament. In how many ways is it possible for the gold, silver, and bronze medals to be awarded? Use the formula for permutations to find your answer.
Answers
Answer:
1320 ways
Step-by-step explanation:
To solve we need to use permutations and factorials. If we wanted to find where they would all place 1-12, we would do 12!
12! is the same as 12x11x10x9x8... etc
But in this problem, we are only looking for the top 3.
We can set up a formula
[tex]\frac{n!}{(n-r)!}[/tex]
N is the number of options that are available and r represents the amount we are choosing
In this case, we have 12 teams so n=12
We are looking for the top 3 so r=3
[tex]\frac{12!}{(12-3)!}[/tex]
[tex]\frac{12!}{9!}[/tex]
We expand the equation and cancel out
[tex]\frac{12x11x10x9x8x7x6x5x4x3x2}{9x8x7x6x5x4x3x2}[/tex]
Notice how both sides can cancel out every number 9 and below
That leaves us with 12x11x10
1320 ways
The possible ways for the gold, silver, and bronze medals to be awarded is 1320
What is permutation?A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
The word "permutation" also refers to the act or process of changing the linear order of an ordered set.
Given that, there are 12 teams, each representing a different country, in a women’s Olympic basketball tournament.
We need to find that, in how many ways is it possible for the gold, silver, and bronze medals to be awarded,
Using the concept of permutation, to find the number of ways
ⁿPₓ = n!/(n-x)!
= 12! / (12-3)!
= 12! / 9!
= 1320
Hence, the possible ways for the gold, silver, and bronze medals to be awarded is 1320
Learn more about permutation click;
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PLEASE ANSWER FAST, THANKS! :)
Answers
Answer:
Step-by-step explanation:
k = 3 ; 2k + 2 = 2*3 + 2 = 6 + 2 = 8
k = 4; 2k + 2 = 2*4 + 2 = 8 +2 = 10
k =5; 2k + 2 = 2*5 +2 = 10+2 = 12
k=6; 2k +2 = 2*6 + 2 = 12+2 = 14
k = 7 ; 2k + 2 = 2*7 +2 = 14 +2 = 16
k = 8 ; 2k + 2 = 2*8 + 2 = 16 +2 = 18
∑ (2k + 2) = 8 + 10 + 12 + 14 + 16 + 18 = 78
10) BRAINLIEST & 10+ Points!
Answers
Answer:
20Solution,
Complement of 70°
=90°-70°
=20°
hope this helps...
Good luck on your assignment..
Answer:
20°
Step-by-step explanation:
Complement of 70° is 90°-70°= 20°
To determine the complement, subtract the given angle from 90.
what is the gfc of 16 and 8
Answers
Answer:
Greatest common factor of 16 and 8 is 8 .....A bus can carry a maximum of 60 passengers. Each row accommodates the same number of passengers. If two rows are added then each row would accommodate one passenger less for the bus to carry maximum number of passengers. Determine number of rows in the bus and no. Of passengers per row
Answers
Answer:
10 rows with 6 passengers per row
Step-by-step explanation:
Let x be the number of rows and y the number of passengers per row.
Then we can interpret the story as the following two equations:
xy=60
(x+2)(y-1)=60
Solving these two equations:
y=60/x
(x+2)(60/x-1)=60 (substitute y)
60 - x + 120/x - 2 = 60 (multiply by -x)
x² + 2x - 120 = 0 (factor)
(x-10)(x+12) = 0
x = 10
y = 60/10 = 6
and indeed 10 * 6 = 60 and also 12 * 5 = 60
Solving by fractions
Answers
Answer: Step 3
Step-by-step explanation:
x = -9 or 1. She flipped the signs.
Hope it helps <3
━━━━━━━☆☆━━━━━━━
▹ Answer
Step 3
▹ Step-by-Step Explanation
Juliet flipped the signs. The final answer should be (-9, 1)
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Basic factoring. Please help!
Answers
Answer:
-1(3 - y)
Step-by-step explanation:
If you factor out a negative 1, you will get the opposite signs you already have, so -1(3 - y). To check, we can simply distribute again:
-3 + y
So our answer is 2nd Choice.
Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a function of x { x ( t ) = 5 √ t y ( t ) = 7 t + 4
Answers
Answer:
y(x) = (7/25)x^2 + 4
Step-by-step explanation:
Given:
x = 5*sqrt(t) .............(1)
y = 7*t+4 ..................(2)
solution:
square (1) on both sides
x^2 = 25t
solve for t
t = x^2 / 25 .........(3)
substitute (3) in (2)
y = 7*(x^2/25) +4
y= (7/25)x^2 + 4
I NEED HELP PLEASE, THANKS! :)
Answers
Answer:
Step-by-step explanation:
Step1 : Verify Sn is valid for n = 1
The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000586 mm. Assume a random sample of 59 sheets of metal resulted in an x¯ = .2905 mm. Calculate the 95 percent confidence interval for the true mean metal thickness.
Answers
Answer:
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.000586}{\sqrt{59}} = 0.0002[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm
The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
Perform the indicated operation.
Answers
Answer:
√75 = 5√3 and √12 = 2√3 so √75 + √12 = 5√3 + 2√3 = 7√3.
Answer:
[tex] 7\sqrt{3} [/tex]
Step-by-step explanation:
[tex] \sqrt{12} \: can \: be \: simplified \: as \: 2 \sqrt{3} \: and \: \sqrt{75} \: canbe \: simplified \: as \: 5 \sqrt{3} \\ after \: simplifying \: we \: can \: add \: them \: up \\ 2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} [/tex]
Translate the following statements into symbolic form using capital letters to representaffirmative English statement.
If Maria Cantwell promotes alternative energy,then if Patty Murray supports wilderness areas, then Dianne Feinstein's advocating gun control implies that Susan Collins does so,too.
Answers
Answer:
Step-by-step explanation:
There are two distinct statements but put together, it is:
- If Maria Cantwell (MC) promotes Alternative Energy (AE) and if Patty Murray (PM) supports Wilderness Areas (WA) then Dianne Feinstein (DF) advocating Gun Control (GC), implies that Susan Collins (SC) does so too.
For Susan Collins, she advocates gun control too.
So the symbolic or algebraic representation is:
(SC = DF): (MC ~ AE), (PM ~ WA)
OR
(GC = GC): (MC ~ AE), (PM ~ WA)
Where ":" represents "such that" or "given that"
" ~ " represents "support or promotion of"
It can now be read thus;
Susan Collins has same or equal interest as Dianne Feinstein, given that Maria Cantwell promotes alternative energy and Patty Murray supports Wilderness Areas.
In the parallelogram below, solve for x and y. (Give your answer as a decimal, when necessary)
Answers
Answer: x = 15, y = 12.5
Step-by-step explanation:
The sum of the three angle measures of a triangle equals 180ᴼ
Since these triangles are vertical, the measures are congruent.
45 + 60 = 105
180 - 105 = 75
So now we know that 5x = 75ᴼ and 6y = 75ᴼ.
To find x, divide 75 by 5
75 / 5 = 15
x = 15
To find y, divide 75 by 6
75 / 6 = 12.5
y = 12.5
CAN SOMEONE HELP ME ASAP
A. 5
B. 53‾√53
C. 10
D. 103√3
Answers
Answer:
n = 5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 30 = n/ 5 sqrt(3)
5 sqrt(3) tan 30 = n
5 sqrt(3) * 1/ sqrt(3) = n
5 = n
i-Ready
Sofia
The area of a rectangle is 7/9 square feet. The width of the rectangle is 2 1/3 feet. What is the length of the rectangle?
Answers
Answer:
1/3 feet.
Step-by-step explanation:
The length = area / width
= 7/9 / 2 1/3
= 7/9 / 7/3
= 7/9 * 3/7
= 3/9
= 1/3 feet,
Now divide 7/9 with 7/3
Answer: 1/3
Check: 1/3*7/3=7/9
Solve: -1/2+ c =31/4 c=8 c=7 c=33/4 c=29/4
Answers
Answer:
c = 29/4Step-by-step explanation:
[tex] - \frac{1}{2} + c = \frac{31 }{4} \\ \\ c = \frac{31}{4} + \frac{1}{2} = \frac{31 - 2}{4} \\ \\ c = \frac{29}{4} [/tex]
Hope this helps you