From the top of a vertical cliff 50 m high, the angle of depression of an object that is level with the base of the cliff is 70°. How far is the object from the base of the cliff?
Answers
Answer:
The distance of the object from the base of cliff is 18.24 meters
Step-by-step explanation:
Given as :
The height of the vertical cliff = h = 50 meters
The distance of the object from the base of cliff = x meters
Let The angle of depression of object that level with cliff base = Ф = 70°
Now, from figure
Tan angle = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]
I.e TanФ = [tex]\dfrac{\textrm AB}{\textrm OA}[/tex]
Or, TanФ = [tex]\dfrac{\textrm h}{\textrm x}[/tex]
Or, Tan 70° = [tex]\dfrac{\textrm 50 meters}{\textrm x meters}[/tex]
Or, 2.74 = [tex]\dfrac{\textrm 50}{\textrm x}[/tex]
∴ x = [tex]\dfrac{\textrm 50}{\textrm 2.74}[/tex]
I,e x = 18.24 meters
So, The distance of the object from the base of cliff = x = 18.24 meters
Hence,The distance of the object from the base of cliff is 18.24 meters Answer
We can determine the distance of the object from the base of the cliff using trigonometry. Specifically, we form an equation using the tangent of the given angle and the known height, solve for the distance, and then substitute the known values to obtain the specific distance.
Explanation:The subject matter of this question falls in the field of trigonometry as it involves calculating distance using a known height and angle of depression. The object is level with the base of the cliff, and therefore forms a right triangle with the cliff and the sight line from the top of the cliff.
We can use the tangent function to solve this problem. In trigonometry, the tangent of an angle in a right triangle is the opposite side (height) over the adjacent side (distance we're looking for). Given the angle of depression (70°) and the height of the cliff (50 m), we can set up the following equation:
tangent(70°) = height/distance
Moving terms around gives:
distance = height / tangent(70°)
Substituting for height and tangent(70°) we get:
distance = 50 m / tan(70°)
Solving the above equation will give us the distance of the object from the base of the cliff.
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Related Questions
a 20.00 pair of jeans is discounted 20%. What is the final price of the jeans?
Answers
Consider matrix A.
A=[1 1
[1 1
(2 by 2 box)
Does the inverse of matrix A exist?
1The inverse of a square matrix exists only when
a. all entries are the same sign
b. no two entries are equal
c. the determinate does not equal zero
2The inverse of matrix A
a.does not exist
b. does exist
Answers
Answer:
1. Inverse of matrix A exist If and Only If
c. the determinate does not equal zero
2. The inverse of matrix A
a.does not exist
Step-by-step explanation:
Given:
Consider matrix A. 2 by 2
A=[tex]\left[\begin{array}{cc}1&1\\1&1\end{array}\right][/tex]
To Find:
Does the inverse of matrix A exist?
Solution:
1. Inverse of matrix A exist If and Only If
c. the determinate does not equal zero
For the Given Matrix A We have
Det |A| = 1×1 -1×1
Det |A| = 0
2. The inverse of matrix A
a.does not exist
Answer:
The determinate does not equal zero and does not exist
Step-by-step explanation:
During the closing process, which of the following would likely occur?
Debit Revenue and Credit Income Summary
Debit Cash and Credit Income Summary
Debit Earned Income and Credit Income Summary
Debit Assets and Credit Income Summary
pls help i need to know soon
Answers
Answer:
The correct answer is A. Debit Revenue and Credit Income Summary
Step-by-step explanation:
Let's recall that at the end of the accounting year, closing entries transfer the balances from the temporary accounts to a permanent account with the purpose that those temporary accounts will begin the next accounting year with zero balances.
However, an intermediate account called Income summary is created and used in the closing stage of the accounting year to register all income and expense balances and determine the net result for the period (income or loss).
Upon saying that, usually revenue accounts have a credit balance. To make it zero we want to decrease the balance. We will debit the revenue account and credit the Income Summary account. This credit to income summary should be exactly the total revenue from the income statement.
The correct answer is A. Debit Revenue and Credit Income Summary
Answer:
Step-by-step explanation:
During the closing process, which of the following would likely occur?
Question options:
Debit Revenue and Credit Income Summary
Find the slope of the line that passes through the following points. (6 points, 2 points each)
A (10,4) and B(-2,-5)
C(-7.1) and D(7,8)
E(1, 1) and F/2.3)
Answers
Answer:
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-4)/(-2-10)
m=-9/-12
m=9/12
m=3/4
------------------------
m=(y2-y1)/(x2-x1)
m=(8-1)/(7-(-7))
m=7/(7+7)
m=7/14
m=1/2
-------------------------
m=(y2-y1)/(x2-x1)
m=(3-1)/(2-1)
m=2/1
m=2
Final answer:
The slope of a line between two points is found using the formula slope (m) = (y2 - y1) / (x2 - x1), with an example given for points A (10,4) and B (-2,-5), resulting in a slope of 3/4.
Explanation:
The slope of a line passing through two points (A and B) can be determined using the formula slope
(m) = (y2 - y1) / (x2 - x1).
This formula calculates the rate of change in the y-values with respect to the x-values, resulting in a description of the steepness of the line.
For example, let's find the slope for points A (10,4) and B (-2,-5). Applying the formula, we have:
m = (y2 - y1) / (x2 - x1) = (-5 - 4) / (-2 - 10) = (-9) / (-12) = 3/4
The slope between points A and B is 3/4. This process can be repeated for other pairs of points to find the respective slopes.
if w = -2 and V = -8 which of the following Expressions shown the values correctly substituted and for the valuables in the expression w^2 - v + 1
Answers
Answer:
13
Step-by-step explanation:
w^2=(-2)(-2)=4
4-(-8)+1=4+8+1=12+1=13
which ordered pair is a solution of the equation
Answers
Answer:
OPTION D: NEITHER
Step-by-step explanation:
The given equation is: 7x - 2y = - 5
To find a solution to this, we substitute the options and compare LHS and RHS.
OPTION A: (1, 5)
LHS = 7(1) - 2(5) = 7 - 10 = -3
RHS = - 5
LHS [tex]$ \ne $[/tex] RHS.
So, this option is eliminated.
OPTION B: (-1, 1)
LHS = 7(-1) - 2(1) = -7 - 2 = - 9
RHS = - 5
Again, LHS [tex]$ \ne $[/tex] RHS.
So, this Option is eliminated as well.
OPTION C: It says both A and B. Clearly, this is eliminated as well.
Therefore, the answer is: OPTION D: NEITHER.
NOTE: This is a two variable equation. So, we need a minimum of two equations to determine the solution. Since, only one equation is given here, we use the help of options.
A regular decagon has a radius of 14'. Determine the length of the apothem. Then determine the perimeter of the decagon
Answers
Answer:
Part 1) The length of the apothem is 13.32'
Part 2) The perimeter of the decagon is 86.5'
Step-by-step explanation:
we know that
A regular decagon has 10 equal sides and 10 equal interior angles
A regular decagon can be divided into 10 congruent isosceles triangle
(they are isosceles since their two sides are the radii of the polygon and the unknown side is the side of the polygon)
The vertex angle of each isosceles triangle is equal to
[tex]\frac{360^o}{10}=36^o[/tex]
To find out the side length of the decagon, we can use the law of cosines
so
[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]
where
c is the length side of decagon
a and b are the radii
we have
[tex]a=14'\\b=14'\\C=36^o[/tex]
substitute the values
[tex]c^2=14^2+14^2-2(14)(14)cos(36^o)[/tex]
[tex]c^2=392-(392)cos(36^o)[/tex]
[tex]c^2=392-(392)cos(36^o)[/tex]
[tex]c=8.65'[/tex]
To fin out the perimeter of decagon multiply the length side by 10
so
[tex]P=8.65(10)=86.5'[/tex]
To find out the apothem we can apply the Pythagorean Theorem in one isosceles triangle
see the attached figure to better understand the problem
[tex]r^2=a^2+(c/2)^2[/tex]
substitute the given values
[tex]14^2=a^2+(8.65/2)^2[/tex]
solve for a
[tex]a^2=14^2-(8.65/2)^2[/tex]
[tex]a=13.32'[/tex]
Explain how you would determine the density of solid common salt
Answers
Answer:
In order to determine the density of a solid , it is necessary to determine the mass and the volume
Step-by-step explanation:
Answer:
density of a solid?
Answer
Density of a solid
Mass/Volume
So (i) measure the mass, and (ii) measure the volume, and then take the quotient.
Of course, the mass is easy to measure. The volume is a little harder to assess, especially if it is an irregularly shaped solid, however, volume displacement of a liquid would be a quite feasible means.
Step-by-step explanation:
Density of salt is in the picture above please mark me brainliest
:)
4 1/4 = 16/blank + 1/4
Answers
Answer:
The “blank” is 4
Step-by-step explanation:
4 1/4= 16/x+ 1/4
We want to get rid of the 1/4. So we subtract it from both sides and get
4= 16/x
We know that if we put 16 divided by 4, you get 4.
This gives you 4= 16/4.
This is your final answer.
Help asap!!! Midterms
Answers
Answer:
The value of x is 5.
Step-by-step explanation:
Label the diagram such as
Given:
AD= x
DB= x +5
AE = x - 2
EC = x + 1
DE || BC
To Find:
x = ?
Solution:
Basic Proportionality Theorem:
"If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".
DE || BC
∴ [tex]\dfrac{AD}{DB}= \dfrac{AE}{EC}[/tex] ...Basic Proportionality Theorem
Substituting the values in it we get
[tex]\dfrac{x}{x+5}= \dfrac{x-2}{x+1}\\x(x+1)=(x+5)(x-2)\\\\x^{2}+x= x^{2}+3x-10\\ -2x=-10\\\\x=\dfrac{10}{2}=5\\ \\\therefore x =5[/tex]
The value of x is 5.
alA baker bought 4 gallons of icing to decorate cakes. He uses 4 1/2 cups of icing for completely Frost and decorate each cake. what is the maximum number of cakes he can completely decorate
Answers
Answer: 14 cakes
Step-by-step explanation:
We have the following data:
Number of gallons the baker has: [tex]4 gallons \frac{16 cups}{1 gallon}=64 cups[/tex]
Number of cups the baker used for one cake: [tex]4,5 cups[/tex]
Now, we can use the Rule of three to find the maximum number of cakes the baker can completely decorate:
[tex]4.5 cups[/tex]-----[tex]1 cake[/tex]
[tex]64 cups[/tex]-----[tex]?[/tex]
Then:
[tex]?=\frac{(64 cups)(1 cake)}{4.5 cups}[/tex]
[tex]?=14,2 cakes \approx 14 cakes[/tex]
Which expression is equivalent to 4p+5p?
p+9
8p
9(9)
9p
Answers
Answer:
9p
Explanation:
4p + 5p are like terms since they have the same variable p
All you have to do is add the numbers
(4+5)p = 9p
A 20-pack of Dr. Pepper cost $5.50 and a 6-pack cost $1.50. Which is the better deal?
Answers
Answer:
Step-by-step explanation:
20-pack of Dr. Pepper cost $5.50 . As per this deal
Cost of one pack = 5.5/20 = $ 0.275
a 6-pack cost $1.50.As per this deal
Cost of one pack = 1.50/6 = $ 0.25
A 6-pack cost $1.50 is the better deal.
George has 15$. He tries to buy a movie ticket ($9.00), a pretzel ($2.65), a drink ($1.35), and two veggie cups ($1.74 each) but he does not have enough money . Look at the numerical expression George used: 15-9+2.65+1.35+2(1 .74). Can you help determine why he does not have enough money
Answers
Answer:
Sample Response: George did not put parentheses around the total snack amount to be subtracted from his $15. He needed to total the purchases and then subtract that amount from $15.
Step-by-step explanation:
mmilinu
Subtract - 3x2 + 4x + 10 from 2x2 – 2x
Answers
Answer:
5x^2-6x-10
Step-by-step explanation:
(2x^2-2x)-(-3x^2+4x+10)
2x^2-2x+3x^2-4x-10
5x^2-2x-4x-10
5x^2-6x-10
The school store sells packs of 12 pens for $2.40.
Select the three unit rates that describe this sale.
CLEAR CHECK
$0.20 per pen
$2.40 per pack of pens
5 pens per dollar
120 pens per $24
NEXT
CLOSE
Reference
calculator
formulas
glossary
CLOSE
Language
Changes the language of the audio snippets and the glossary
ENGLISH
Answers
Answer:
Step-by-step explanation:
The school store sells packs of 12 pens for $2.40.
Select the three unit rates that describe this sale.
There is more than one correct answer
$0.20 per pen
$2.40 per pack of pens
5 pens per dollar
120 pens per $24
HOPE THIS HELPED ;3
What is the answer with work for -g+2(3+g)=-4(g+1)
Answers
Hey, I'd like to give you a professional response.
First we need to re-group terms.
1. 2(3+g)−g=−4(g+1)
Let's also expand the terms.
6+2g−g=−4g−4
Simplify 6+2g-g to 6 + g.
6+g=-4g-4
Add 4g to BOTH sides.
6+2g−g=−4g−4
Simplify 6+g+4g to 6+5g.
6+5g=-4
Now subtract 6 from both sides.
5g = -4-6
Simplify -4 - 6 to -10.
Now you have 5g = -10.
g = -10/5 (Divide both sides by 5)
Simplify -10/5 to 2.
G = 2
Let's check our answer.
First let g = 2.
2+2 X (3-2) = -4 X (-2 + 1)
2 + 2 X 1 = -4 X (-2 +1)
2 + 2 X 1 = -4 x -1
2+2 = -(-4)
Remove the parentheses,
4 = 4 This problem has been checked.
a goat is kept in a rectangular field 14.5 metre by 22 m. it is tied to a pole at the centre of the field with the chain that is 2.5 metre long what is the surface of the field on which it will not be able to Grace ? Give me the answer quickly
Answers
Area of the rectangle: 14.5 x 22 = 319 square meters.
Area the goat can reach ( area of a circle): 3.14 x 2.5^2 = 19.625 square meters.
Now subtract the area of the circle from the area of the rectangle:
319 - 19.625 = 299.375 square meters. (Round the answer as needed.)
1) What is the circumference of this circle?
r = 2 km
Answers
Answer:
Circumference is 12.56 km
Explanation:
C = 2πr (with radius)
C = 2(3.14)(2)
C = 12.56 km
The circumference of a circle with a radius of 2 km is calculated using the formula C = 2πr. Using π ≈ 3.14159, the circumference is approximately 12.57 km.
The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle. Given the radius (r) of 2 km, we can substitute this value into the formula to find the circumference:
C = 2π(2 km)
C = 4π km
By using the approximation π ≈ 3.14159, we can calculate the circumference as:
C = 4 × 3.14159 km
C ≈ 12.56636 km
Therefore, the circumference of the circle is approximately 12.57 kilometers.
Johnny earns $15 per hour dog walking. He wants to earn at least $105 to buy a new
bike. Which inequality represents how long Johnny needs to work to afford his new
bike?
Answers
Answer:
[tex]15x\geq 105[/tex]
Step-by-step explanation:
Hence, the inequality represents how long Johnny needs to work to afford his new bike is
[tex]15x\geq 105[/tex]
What is the inequality?
The relationship between two values that are not equal is defined by inequalities. Inequality means not equal.
Here given that,
Johny earns $[tex]15[/tex] per hour dog walking. So, he wants to earn at least $[tex]105[/tex] to buy a new bike.
So, the inequality is
[tex]15x\geq 105[/tex]
Hence, the inequality represents how long Johnny needs to work to afford his new bike is
[tex]15x\geq 105[/tex]
To know more about the inequality
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What is the value of X.
Please help Im confused.
Answers
Because the triangle in isosceles the two bottom angles will have the same measure.
The angles of a triangle will add to 180° so you subtract 38 and divide by 2.
Answer:
x = 142º
Step-by-step explanation:
The measurements of all of the angles in a triangle always equal 180º.
We can use this formula: x + y = 180º
Now, substitute in the known value(s) into the formula.
x + 38º = 180º
Solve
x = 180º - 38º = 142º
x = 142º
Hope this helps :)
John withdraws $40.00 from her savings account each month. What integer represents the net effect on her balance after 5 months?
Answers
Answer:
The net effect of amount in John account after 5 months is $A - $200
Step-by-step explanation:
Given as :
The amount of money withdraws by John each month from his account = $40
Let The total amount of money did John had in his account = $A
Let the amount left in John account after 5 months of withdraw = $x
So, According to question
∵ Each month the money withdraw from account = $40
∴ In 5 months , the money withdraw = $40 × 5
I.e In 5 months , the money withdraw = $200
So, The left money in account after withdraw in 5 months = $A - The amount withdraw in 5 months
I.e x = $A - $200
So, The balance in account after 5 months = x = $A - $200
Hence, The net effect of amount in John account after 5 months is $A - $200 Answer
what is -2/3 to the power of -4 ?
Answers
Answer:
81/16
Step-by-step explanation:
the line above goes through points (-4,0) and (0,1). what is the equation of the line?
Answers
Answer:
y = [tex]\frac{1}{4}[/tex] x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, 0) and (x₂, y₂ ) = (0, 1)
m = [tex]\frac{1-0}{0+4}[/tex] = [tex]\frac{1}{4}[/tex]
Note the line crosses the y- axis at (0, 1) ⇒ c = 1
y = [tex]\frac{1}{4}[/tex] x + 1 ← equation of line
what is the solution to the following equation?
2x^2-3x+2=0
Answers
Answer:
x=(3+sqrt(7)*i)/4, (3-sqrt(7)*i)/4.
Step-by-step explanation:
Apply the quadratic formula.
Answer:
[tex]x = \frac{3 +/- i \sqrt{7} }{4}[/tex]
Step-by-step explanation:
[tex]2x^{2} -3x + 2 = 0[/tex]
a =2 b = -3 c = 2. Substitute these into the quadratic formula [tex]x = \frac{-b +/- \sqrt{b^{2}- 4ac} }{2a}[/tex].
[tex]x = \frac{-(-3)+/- \sqrt{(-3)^{2} - 4(2*2)} }{2(2)}[/tex] Simplify.
[tex]x = \frac{3+/-\sqrt{(9)^{2} - 4(4) } }{4}[/tex] Keep simplifying...
[tex]x = \frac{3+/-\sqrt{9-16} }{4}[/tex] Simplify again...
[tex]x = \frac{3 +/-\sqrt{-7} }{4}[/tex] There will be an imaginary number because the number under the [tex]\sqrt{}[/tex] is negative, so
[tex]x = \frac{3+/-i\sqrt{7} }{4}[/tex]
OMG NEED HELP I WILL GIVE BRAINLIEST OR WHATEVER DESPERATE PEOPLE SAY.
Write a sentence to represent the equation 4m = -8.
Answers
Answer:
Charnessa has 4 times as many apples as Luke. Luke has -8 apples.
Hope this is what you were looking for :)
I NEED HELP WITH THESE QUESTIONS THANKYOUU
Answers
Answer:
1. s = 19
2. 17
3. R
4. Angle bisector
5. 53°
Step-by-step explanation:
1. If VY is a midsegment of triangle WXZ, then by midsegment theorem,
[tex]VY=\dfrac{1}{2}WX.[/tex]
Since [tex]WX=s+55[/tex] and [tex]VY=s+18,[/tex] then
[tex]s+18=\dfrac{1}{2}(s+55)\\ \\2(s+18)=s+55\\ \\2s+36=s+55\\ \\2s-s=55-36\\ \\s=19[/tex]
2. A triangle has two sodes of length 18 and 2 units.
Let c units be the length of the third side. Then
[tex]18+c>2\\ \\2+c>18\\ \\2+18>c[/tex]
So,
[tex]c>-16\\ \\c>16\\ \\c<20[/tex]
Hence, [tex]16<c<20,[/tex] and the smallest possible whole-number length for the third side is 17 units.
3. In triangle QSR, the smallest angle is opposite to the smallest side. The smallest side is the side with length of 49 m, then the smallest angle is angle R.
4. Given ∠VYW≅∠WYX.
Definition of angle bisector: An angle bisector in a triangle is a line segment that bisects one of the vertex angles of a triangle.
Thus, YW is angle Y bisector.
5. Consider two right triangles ACD and ABC. In these triangles,
AC ≅ AC - reflexive property;AB ≅ AD - given.Then, by HL postulate, triangles ACD and ABC are congruent. Congruent triangles have congruent corresponding sides, then
∠ACD ≅ ∠ACB
and
m∠ACB = m∠ACD = 53°
graph 8x^4 + x^3 +5x^2 +20x +3
Answers
Factor 24k + 36q - 12 to identify the equivalent expressions. Choose 2 answers
A. 12(2k + 3q - 1)
B. 3(8k + 12q - 4)
C. 6(3k + 6q - 12)
D 12(2k + 3q)
Answers
Option A and Option B
The equivalent expressions for 24k + 36q - 12 are 12(2k + 3q - 1) and 3(8k + 12q - 4)
Solution:
Given that we have to factor 24k + 36q - 12
To factor a number or expression containing variables means to break it up into smaller numbers or expressions that can be multiplied together to get the original number or expression
Given expression is:
24k + 36q - 12
So for numbers 24 , 36 and 12: the factors that divides all these numbers 24, 36 and 12 completely are 12 and 3 and also 2
In the above expression we take 12 common term
12(2k + 3q - 1)
So option A is correct
We can also take out 3 as common term
3(8k + 12q - 4)
So option B is also correct
Thus the equivalent expressions are: 12(2k + 3q - 1) and 3(8k + 12q - 4)
2. Six cell phones weigh 46.2 ounces.
Fourteen cell phones weigh
107.8 ounces. Does this represent
a proportional relationship?
Explain. If so, state the constant of
proportionality.
Answers
Answer -
46.2/6 = 7.7
107.9/14 =7.7
it's show proportional relationship
a/b =K
k is proportionality constant
46.2/6 = 7.7 = K