the angle of elevation of an object from a point 200 meters above a lake is 30 degrees and the angle of depression of it's image in the lake is 45 degrees. Find the height of the object above the lake.
Answers
Looking at the reflection of the object in the lake's surface is equivalent to observing the object at distance h below the lake's surface, or observing it from 200 m below the lake's surface. Considering the latter case, we have
(h+200)/d = tan(45°)
(h -200)/d = tan(30°)
Solving these for d and equating the results gives
(h+200)/tan(45°) = (h -200)/tan(30°)
Solving for h, we get
h(1/tan(30°) -1/tan(45°)) = 200(1/tan(45°) +1/tan(30°))
h = 200(tan(45°) +tan(30°))/(tan(45°) -tan(30°))
h ≈ 746.41
The object is about 746.4 meters above the lake.
Related Questions
Each gallon of shingle stain covers 120 square feet. How many gallons should you buy to cover 658 square feet?
Answers
5.483 gallons bought to cover 658 square feet.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Each gallon of shingle stain covers 120 square feet.
We have to find gallons should be bought to cover 658 square feet.
We have to perform division
= 658/120
= 5.483 gallons
Hence, 5.483 gallons bought to cover 658 square feet.
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What is the mode of the data set? 61, 92, 61, 89, 92, 61 Enter your answer in the box.
Answers
Hope that helped:)!!!!!!!
Answer:
61 is the Answer
Step-by-step explanation:
K12 for life
Jim is climbing a mountain that has a base 150 feet above sea level. If he climbs 233 feet then descends into a cave 64 feet, how far above sea level is Jim? A. 86feet, B. 169 feet, C. 214 feet, D. 319 feet.
Answers
1) Jim is climbing a mountain that has a base -----> 150 ft above sea level
2) He climbs 233 ft------------> 150 ft+233 ft----> 383 ft above sea level
3) He descends into a cave 64 ft------> 383 ft-64 ft----> 319 ft above sea level
the answer is
the option
D. 319 feet.
Josiah has 3 packs of toy animals. Each pack has the same number of animals. Josiah gives 6 animals to his sister stephanie. Then josiah has 9 animals left.how many animals were in each pack?
Answers
Total number of animals will be 3x
after Josiah gave 6 animals to his sister the remaining animals were:
3x-6=9
thus sloving for x we have:
3x-6=9
add 6 on both sides
3x-6+6=9+6
3x=15
divide both sides by 3
(3x)/3=15/3
x=5
Answer:
There were 5 animals in each pack
the height of triangle is 8 meters less than its base. if the area of the triangle is 212.5 square meters, find the length of its bas and heiight.
Answers
b = length of base in meters, then
h = (b-8) m
Area of a triangle, A = (1/2)bh
Therefore,
212.5 = (1/2)(b)(b-8) = (1/2)(b^2-8b)
425 = b^2-8b
b^2 - 8b -425 =0
Solving the resulting quadratic equation;
b = [8+/- Sqrt [8^2 - 4(1)(-425)]]/2(1) = 4+/- 21 = 4+21 = 25 m (ignore negative value as it is not applicable)
Then,
h = b-8 = 25 - 8 = 17 m
Therefore,
Base = 25 m
Height = 17 m
Final answer:
The base of the triangle is 25 meters, and the height is 17 meters. This was calculated using the area formula for a triangle and by solving the resulting quadratic equation by using the quadratic formula.
Explanation:
The area of a triangle is given by the formula 1/2 × base × height. Given that the area is 212.5 square meters and the height is 8 meters less than the base, let's call the base 'b' and the height will then be 'b - 8'. Using the area formula:
Area = 1/2 × base × height
212.5 = 1/2 × b × (b - 8)
Multiplying both sides by 2 to get rid of the 1/2 gives:
425 = b × (b - 8)
Now we have a quadratic equation in the form of:
b² - 8b - 425 = 0
We can solve this equation by factoring or using the quadratic formula. In this case, the equation doesn't factor neatly, so we use the quadratic formula:
b = (-(-8) ± √((-8)² - 4 × 1 × (-425)))/(2 × 1)
b = (8 ± √(64 + 1700))/2
b = (8 ± √(1764))/2
b = (8 ± 42)/2
Since the base cannot be negative, we take the positive root:
b = (8 + 42)/2
b = 25 meters
Therefore, the base of the triangle is 25 meters and the height is b - 8 = 25 - 8 = 17 meters.
Solve the equation. Show your work. 45 = 3 b + 69
Answers
Subtract 69 from both sides.
-24 = 3b
Divide both sides by 3.
-8 = b
b = -8
Together, two people earn $28,000. One earns $2,000 more than the other. How much is the smaller income?
$30k
$26k
$14k
$13k
Answers
2x+$2,000=$28,000
2x=$28,000-$2,000
2x=$26,000
x=26,000 divided by 2
x=$13,000
P1+2= P2 . -------Equation 2 . I abbreviate the thousands of $
Using substitution
P1+(P1+2)=28
2P1 +2=28
P1=13
then substitute into equation 2 we get
13+2=p2
P2=15
Therefore one is $15,000
and the other is 13,000
Smaller is 13,000!!!
1/7-3(3/7n-2/7) in simplest form
Answers
=1/7 -9/7n +6/7
=(n-9+6n) /7n
=(7n-9) /7n
=1-9/7n
1/7-3(3/7n-2/7) in simplest form
[tex]\frac{1}{7} -3(\frac{3}{7}n-\frac{2}{7}) \\\\ Using \;Distributive \;property \\\\ =\frac{1}{7} -(3)\frac{3}{7}n-(-3)\frac{2}{7} \\\\ Multiplication \\\\ =\frac{1}{7} -\frac{3*3}{7}n+\frac{3*2}{7} \\\\ =\frac{1}{7} -\frac{9}{7}n+\frac{6}{7} \\\\ Combining \;terms \;with \;common \;denominator \\\\ =\frac{1-9n+6}{7} \\\\ Combining \;like \;terms \\\\ =\frac{7-9n}{7} \\\\ Simplification \\\\ =\frac{7}{7} -\frac{9n}{7} \\\\ =1 -\frac{9n}{7}[/tex]
Hence, final answer is [tex]\frac{7-9n}{7}[/tex] or [tex]1 -\frac{9n}{7}[/tex].
Line a and line b are parallel. Which is a true statement about the lines? A. the lines contain the same points B. the lines have the same y-intercept C. the lines have the same graph D. the lines have the same slope
Answers
How can you find the perimeter of the rhombus? Find 1/2 (QS)(RT). Find 1/2(QT)(TS). Use the distance formula to find QT, then multiply by 4. Use the distance formula to find QT and QR, add the distances, then multiply by 4.
Answers
Yes C is correct which would be
Use the distance formula to find QT, then multiply by 4.
The perimeter of the rhombus can be found by C. use the distance formula to find QT and then multiply by 4.
What is Rhombus?A rhombus is a two dimensional shape which consists of four equal sides with opposite side being parallel and opposite angles being equal.
Perimeter of a straight sided figures or objects is the total length of it's boundary.
Actual perimeter = QR + RS + ST + TQ
That is add all the sides.
Now since the polygon is rhombus, all the sides are of equal length.
So, it is enough to find any side length of the rhombus and then multiply by 4.
The length of a side can be found using the distance formula.
So the correct way is use the distance formula to find QT and then multiply by 4.
Hence the correct option is C.
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Your question is incomplete. The complete question is as given below.
a company that manufactures and ships canned vegetables is designing boxes in the shape of rectangular prisms to meet specific requirements. The vegetables are packed into cans that are 3 inches in diameter and 5 inches in height. Company regulations state that boxes must be filled in with two layers of 12 cans each, and be completely closed with no overlapping material. What is the smallest amount of cardboard needed to meet the company's requirements
Answers
Therefore, you need to understand how the cans are positioned in order to find the dimensions of the boxes: two layers of cans mean that the height is
h = 2 · 5 = 10 in
The other two dimensions depend on how many rows of how many cans you decide to place, the possibilities are 1×12, 2×6, 3×4, 4×3, 6×2, 12×1.
The smallest box possible will be the one in which the cans are placed 3×4 (or 4×3), therefore the dimensions will be:
a = 3 · 3 = 9in
b = 3 · 4 = 12in
Now, you can calculate the total surface area:
A = 2·(a·b + a·h + b·h)
= 2·(9·12 + 9·10 + 12·10)
= 2·(108 + 90 + 120)
= 2·318
= 636in²
Hence, the smallest amount of carboard needed for the boxes is 636 square inches.
Answer:
636
Step-by-step explanation:
trust
Concerned about graffiti, mayors of nine suburban communities instituted a citizen community watch program. community monthly incidents after monthly incidents before burr oak 2 7 elgin corners 3 2 elm grove 6 2 greenburg 4 3 huntley 5 11 north lyman 3 9 south lyman 3 5 pin oak 5 7 victorville 2 3 click here for the excel data file (a) choose the appropriate hypotheses to see whether the number of graffiti incidents declined. assume μd is the mean difference in graffiti incidents before and after.
Answers
After it, the mean and standard deviation of the differences should also be calculated. Then, we state the null and alternative hypotheses.
The null hypothesis is [tex]H_{0}: \mu_d=0[/tex]
The alternative hypothesis is [tex]H_a: \mu_d\ \textgreater \ 0[/tex]
These are the required hypotheses to see whether the number of graffiti incidents declined.
The null hypothesis H₀ represents what is believed true if the data don't prove the opposite.
The alternative hypothesis H₁ is the conclusion we want to deduce from the test.
If we call d the difference in graffiti before (B) and after (A) (pay attention to the order) d = B - A.
We want to prove that the incidents are declined, therefore B should be greater than A and d would be positive.
Therefore:
H₀ : μd ≤ 0
H₁ : μd > 0
The Fermi process gives you an exact answer. You will be exactly right every time you figure it this way.
True
or
False
Answers
The Fermi Process is a fast way to calculate an estimate (usually done with mental math or math you can do on the back of an envelope or napkin). It's unlikely you'll get the exact answer, though you should be fairly close. To make the math more simple, rounding is done.
Answer:
The correct answer is False
Step-by-step explanation:
I already took this test. I got it right.
Hope this helps! ;)
The Length of a rectangle is 5 times the width. The area is 125 square centimeters. What is the length?
Answers
length = 5x
Area = width*length
125=x*5x
5x²=125
x²=25
x=5
width= x = 5 cm
Length =5x=5*5=25 cm
Length=25 cm
What is the value of x? sin49°=cosx Enter your answer in the box.
Answers
if sin A=cos B
then
angle A and angle B are complementary angles
A+B=90°
in this problem
sin49°=cosx
so
49°+x=90-------> x=90-49--------> x=41°
the answer is
x=41°
Answer:
[tex]x=41^o[/tex]
Step-by-step explanation:
We have been given an equation [tex]sin(49^o)=cos(x)[/tex] and we are asked to find the value of x.
Since we know that trigonometric ratios are applied to right triangles and we also know that [tex]sin(a)=cos(b)[/tex], where a and b are the angles other than 90 degree angle.
As one angle of our triangle is given 49 degrees, so to find the value of angle x we need to subtract 49 degrees from 90 degree angle as 49 degree angle and x will be equal to 90 degrees.
[tex]x=90^o-49^o[/tex]
[tex]x=41^o[/tex]
Therefore, the value of x is 41 degrees.
YOU HAVE TO KNOW FOR SURE THE ANSWER. (: 15 points?!
Which fraction is equivalent to 95%
A. 0.95/10
B. 0.95/100
C. 95/10
D. 95/100
Answers
Answer:
D)
Step-by-step explanation:
Percent means "per hundred" or "out of one hundred." While B) is out of one hundred, turn it into a percent, and the percentage would be .95%. A) and C) are not out of 100, so those answers are not applicable. The only answer left is D), which is correct, because 95/100 is equivalent to 95%.
What is the range of the function in interval notation?
Answers
The range is negative infinity to positive infinity.
In interval notation it is
[tex] (-\infty, \infty) [/tex]
By accident, 4 burned out bulbs have been mixed in with 20 good ones. ken is replacing old bulbs in his house. if he selects two bulbs at random from the box of 24, what is the probability they both work?
Answers
next, there are 23 left, including 19 good ones. So the probability is 19/23.
Multiply 19/23 and 5/6 to get 95/138, which is out answer.
Hey can you please help me posted picture of question
Answers
Of the six faces numbered 1 to 6, there is only one five. The probability therefore of rolling a die and getting a five is equal to 1/6. This approach is the theoretical. Hence, the answer to this item is the first option, A Theoretical.
So basically if you think about it the answer is Empirical.
The probability that it will snow on Friday is 70%, and the probability that it will snow on Saturday is 50%.
What is the probability that it will snow on both days? Express your answer as a decimal rounded to the nearest hundredth.
What is the probability that it will not snow on either day? Express your answer as a decimal rounded to the nearest hundredth.
Answers
P(Snow Saturday) = 0.3, P(No snow Saturday) = 1-0.3 = 0.7
Then,
P(Snow Friday) and P(Snow Saturday) = 0.7*0.3 = 0.21
P(No snow Friday) and P(No snow Saturday) = 0.3*0.7 = 0.21
Suppose that a large number of samples are taken from a population. Which of the following sample sizes will be most likely to result in the sample proportion distribution having the largest standard deviation?
Answers
If you use a large enough statistical sample size, you can apply the Central Limit Theorem (CLT) to a sample proportion for categorical data to find its sampling distribution. The population proportion, p, is the proportion of individuals in the population who have a certain characteristic of interest (for example, the proportion of all Americans who are registered voters, or the proportion of all teenagers who own cellphones). The sample proportion, denoted
Answer:
Whatever the lowest value answer choice is will be the correct answer.
Step-by-step explanation:
Say your answer choices are
A. 56
B. 42
C. 70
D. 84
The correct answer would be 42
HELP ASAP! Which figure shows how a shape can be rotated about an axis to form the given object?
Answers
Answer:
Option D.
Step-by-step explanation:
To find the answer we will analyse each options.
Option A.
If we rotate a semicircle by a vertical axis then an sphere will be formed. Therefore this option is not correct.
Option B.
In this rotation we will get a hollow sphere, so this option is also not correct.
Option C.
By rotation of a strip we will find the shape similar to the given object but there will not be a hole at the center. Therefore, the option is not correct.
Option D.
When we rotate this strip with a distance from vertical axis, we will find the same shape as given in the picture.
Option D is the correct option.
hey can you please help me posted picture of question
Answers
Addition of a number to the function results in vertical translation in upward direction. So here, adding 5 to F(x) will result in 5 units upward translation of F(x).
So, G(x) is the graph of F(x) shifted 5 units up.
So the correct answer is option B
simplify: -7/3 - (-61/6)
Answers
Final Answer: 47/6
Answer is=47/6[/tex]
Hope it helped you.
-Charlie
The area of a rectangle is 53.3 in2. If the width is 6.5 in, what is the perimeter of the rectangle?
Answers
A = LW
53.3 in² = L×(6.5 in)
(53.3 in²)/(6.5 in) = L = 8.2 in
The perimeter is twice the sum of length and width.
P = 2(L +W)
P = 2(8.2 in +6.5 in) = 29.4 in
The perimeter of the rectangle is 29.4 inches.
l × w
6.5 is our width you already know but 53.3 isn't the length so really
you are trying to solve for l, so l × 6.5 = 53.3
when you get that answer you should get 8.2
Now .. you already have the width and the length so you hook in 6.5(w) + 6.5(w)+ 8.2 (l)+ 8.2(l)
6.5 + 6.5 gives you 13 and
8.2 + 8.2 gives you 16.4
Adding both up you get the final answer/ perimeter 29.4 inches
Y=-6x-5 x and y intercept form
Answers
y intercept = -5
Now solve for x.
y = -6x - 5
-6x = y + 5
x = -1/6y - 5/6
x intercept = -5/6
Hey can you please help me posted picture of question
Answers
1) F(x) is narrower than G(x)
This implies G(x) is multiplied by a number greater than 1
2) F(x) is above G(x) by 1 unit
This implies vertical shift of , so a 1 is added to G(x).
Among the given options, only option B fulfills these two criteria.
So the answer is option B
Q#2 Graph the relation in the table.Then use the vertical-line test.Is the relation a function
Answers
x y
-1 3
1 -1
2 2
1 3
We observe that the graph shown in the question shows a scattering of points that do not obey any behavior of known function.
Therefore, the table does not represent any function.
Answer:
The table does not represent a function.
By applying the vertical line test we find that the relation is not a function because there are two points which are (1,-1) , (1,3) have the same value of x with different values of y which contradicts with with the rule of function.
Question partpointssubmissions usedverify that the divergence theorem is true for the vector field f on the region
e. give the flux.f(x, y, z) = 3xi + xyj + 5xzk,e is the cube bounded by the planes x = 0, x = 2, y = 0, y = 2, z = 0, and z = 2.
Answers
By the divergence theorem, the flux across the boundary of the given region [tex]\mathcal E[/tex] is
[tex]\displaystyle\iint_{\partial\mathcal E}\mathbf f(x,y,z)\cdot\mathrm d\mathbf S=\iiint_{\mathcal E}\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV[/tex]
[tex]=\displaystyle\int_{z=0}^{z=2}\int_{y=0}^{y=2}\int_{x=0}^{x=2}(3+6x)\,\mathrm dx\,\mathrm dy\,\mathrm dz=72[/tex]
Find the area of the surface. the part of the surface z = 9 + 5x + 2y2 that lies above the triangle with vertices (0, 0), (0, 1), (2, 1).
Answers
The area of the surface is [tex]\rm \dfrac{1}{54}(53\sqrt{53} -17\sqrt{17} )[/tex] and this can be determined by doing the integration.
Given :
The part of the surface [tex]\rm z = 9+5x+2y^2[/tex] that lies above the triangle with vertices (0, 0), (0, 1), (2, 1).
The formula of the surface area is given by:
[tex]\rm A(S) = \int \int_D\sqrt{1+\left(\dfrac{\delta z}{\delta x}\right)^2 +\left(\dfrac{\delta z}{\delta y}\right)^2 }[/tex]
Now, the values of D varies from:
D = {(x,y): 0 [tex]\leq[/tex] y [tex]\leq[/tex] 1 , 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2y}
Now, the area of the surface is given by:
[tex]\rm A(S) = \int \int_D\sqrt{1+4^2+(6y)^2 }\;dA[/tex]
[tex]\rm A(S) = \int^1_0 \int^{2y}_0\sqrt{17+36y^2 }\;dx\;dy[/tex]
[tex]\rm A(S) = \int^1_02y\sqrt{17+36y^2 }\;dy[/tex]
Now, let [tex]u=17+36y^2[/tex]
[tex]du = 72y dy[/tex]
[tex]\rm \dfrac{du}{36}=2ydy[/tex]
Now, the integral becomes:
[tex]\rm A(S)= \dfrac{1}{36}\sqrt{u} \; du[/tex]
[tex]\rm A(S) = \dfrac{1}{54}\times u^{3/2}+C[/tex]
Now, substitute the value of u in the above expression.
[tex]\rm A(S) = \dfrac{1}{54}\times \left[\left[\sqrt{17+36y^2} \right]^{3/2}\right]^1_0[/tex]
Now, simplify the above expression.
[tex]\rm A(S) = \dfrac{1}{54}(53\sqrt{53} -17\sqrt{17} )[/tex]
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To calculate the surface area of the part of the surface z = 9 + 5x + 2y² lying over a triangle, the limits of the variables are determined by triangle vertices. Then, the double integral of the surface area formula, which integrates the square root of 1 plus the squares of the partial derivatives of the function over these limits, is computed.
Explanation:The problem presented is leading us to calculate the surface area of a part of z = 9 + 5x + 2y² that lies above a right triangle whose vertices are (0, 0), (0, 1), (2, 1). The first step in resolving this is to recognize the given formula of the surface, it is a quadratic surface in three-dimensional space, also known as a paraboloid.
The vertices of the triangle give as a hint to define the limits of the variables. Given that this triangle is defined in the xy plane, owing to the vertices of the triangle provided, the limits for x would range from 0 to 2, the limits of y would range from 0 to 1 (since for x = 0, y = 1 and for x = 2, y = 1).
Finally, the area S of a part of the surface z = f(x, y) that lies above the region D in the xy plane is defined by the double integral: S = ∫∫D √(1 + (fx)² + (fy)²) dA where fx and fy are partial derivatives of the function f(x, y) with respect to x and y respectively. The integral needs to be computed over the region D which is defined by triangle vertices.
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