A tower that is 166 feet tall casts a shadow 167 feet long. Find the angle of elevation of the sun to the
nearest degree.
Answers
Answer:
The angle is approximately [tex]45^\circ[/tex].
Step-by-step explanation:
We should start with a diagram (like the one attached). Notice the length of the tower and the length of the shadow are the legs of a right triangle, and the angle of elevation is an acute angle of that triangle.
Since we are given the opposite and adjacent sides to the angle, we will use the tangent function:
[tex]\tan{\theta}=\frac{\text{opposite side}}{\text{adjacent side}}[/tex]
In this case, the opposite side is the height of the tower, 166 ft. The adjacent side is the length of the shadow, 167 ft. So, we have:
[tex]\tan{\theta}=\frac{166}{167}[/tex]
To get the angle, we need to use inverse tangent:
[tex]\theta=\tan^{-1}(\frac{166}{167})\\\theta \approx 45[/tex]
The angle is approximated [tex]45^\circ[/tex] when rounded to the nearest degree.
Related Questions
8. The sum of the ages of Sarpong and Quartey is 50 years. In five years time, the age of Quartey will be four times the age of Sarpong now. How old is each boy?
Answers
Answer:
Sarpong is 11.
Quartey is 39.
Step-by-step explanation:
Let Sarpong's age now = s.
Let Quartey's age now = q.
Now:
q + s = 50
In five years, their ages will be
Sarpong: s + 5
Quartey: q + 5
q + 5 = 4s
We have a system of two equations in two variables.
q + s = 50
q + 5 = 4s
We will use the substitution method.
Solve the second equation for q.
q = 4s - 5
Substitute 4s - 5 for q in the first original equation and solve for s.
4s - 5 + s = 50
5s = 55
s = 11
q + s = 50
q + 11 = 50
q = 39
Answer:
Sarpong is 11.
Quartey is 39.
Solve:
(m+2) (m+1) - (3m - 5) (9-5m)
Answers
Step-by-step explanation:
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Help Please!!!!!!!
I give Brainlist
Your grandmother gives you $1500 to invest in a savings account on your 15th birthday. The only condition is that you may NOT use it until you have graduated high school at 18. After researching savings accounts, you come up with two options.
1) A high interest savings account, with 2.5% simple interest annually or
2) A High Yield Savings account with 2% interest compounded annually.
Which account will you chose and why?
Answers
Answer:
Step-by-step explanation:
This is a logical question that can be d=solved thus;
To decide which decision to make,one has to calculate the amount for both methods to detrmine which is higher.
1. Using simple interest formula of ( P X R X T)/ 100
Since p = 1500, r = 2.5%, T = 3
1500 x 2.5% x 3 / 100 = 1500 x 0.025 x 3 / 100
112.5 / 100 = 1.125
to find amount = 1.125 + 1500 = 1501.25 for the three 3years.
2. Using compound interest formula of ( P ( 1 + r/n)∧nt
1 + (2%/3) ∧3(3)
1500( 0.02/3) ∧ 9
1500 x 0.006 ∧9
1500 x 2.60 = 3900
A = 3900 + 1500 = 5400
SO FROM THE ABOVE I WILL G FOR THE HIGH YIELD SAVINGS AS IT IS HIGHER THAN THE INTEREST SAVINGS
Given the data from the question, the best account to use is:
A high interest savings account, with 2.5% simple interest annually (Option 1)
Simply interest formula
I = PRT / 100
A = I + P
Where
I is the interest P is the principal R is the rate T is the time A is the amount after time tCompound interest formulaA = P(1 + r/n)ⁿᵗ
Where
A is the amount after time tP is the principal r is the rate t is the time n is number of times compounded per annual Case 1 (simple interest) Principal (P) = $ 1500Rate (R) = 2.5%Time (T) = 3 years Interest (I) =? Amount (A) =?I = PRT / 100
I = (1500 × 2.5 × 3) / 100
I = $ 112.5
Thus
A = I + P
A = 112.5 + 1500
A = $ 1612.5
Case 2 (compound interest) Principal (P) = $ 1500Rate (R) = 2% = 0.02Time (T) = 3 years Number of time compounded annually (n) = 1Amount (A) =?A = P(1 + r/n)ⁿᵗ
Since n = 1,
A = P(1 + r)ᵗ
A = 1500(1 + 0.02)³
A = $ 1591.8
SUMMARY
The amount at the end of 3 years using:
A High interest savings account, with 2.5% simple interest annually is $ 1612.5A High Yield Savings account with 2% interest compounded annually is $ 1591.8Thus, the best account to use is a high interest savings account, with 2.5% simple interest annually (option 2)
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robert gets a loan from his bank.
he agrees to borrow £6000 at a fixed annual simple interest rate of 7%
he also agrees to pay the loan back over a 10-year-period.
how much money in total will ha have paid back at the end of the 10 years?
Answers
Answer:
£10200
Step-by-step explanation:
Amount borrowed (P) = £6000
Rate of interest (R) = 7%
Time (T) = 10 years
First, let us calculate the simple interest (SI) for 10 years.
Formula for simple interest is given as:
[tex]S.I.=\frac{PRT}{100}[/tex]
Plugging the values of P, R and T in the above formula, we find:
[tex]S.I.=\frac{6000(7)(10)}{100}[/tex]
S.I.= £4200
Total money paid back at the end of the 10 years
= £6000 + £4200
= £10200
Helpp me with my sister's math
Answers
Answer:
pq - 12r
step by step explanation:
A contractor has two choices for billing a completed job. · $500 flat rate, regardless of the number of hours worked · $20 per hour worked the graph shows the relationship between pay per hour and number of hours worked for both scenarios.
Answers
Answer:
C. (25,20)
Step-by-step explanation:
Edge2022 <3
Good luck and remember (yall that take edge) , you can get through the day no matter how hard it may seem. I have faith In you guys :).
If number of hours worked is less than 20, 500 flat rate is preferable
and, If number of hours is more than 20, hourly rate i.e. 20 per hour is better.
What is Inequality?An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
In the first scenario, where there is a $500 flat rate regardless of the number of hours worked, the pay per hour remains constant at $500 divided by the number of hours worked.
So, the graph for this scenario would be a horizontal line at a height of $500.
In the second scenario, where the contractor is paid $20 per hour worked, the pay per hour is fixed at $20.
let the number of hours be worked be x.
Then, 20x < 500
x< 25
So, if number of hours worked is less than 20, 500 flat rate is preferable
and, If number of hours is more than 20, hourly rate i.e. 20 per hour is better.
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State a mathematical phase to for each English phase
1.) three or more than a number
2.) the sum of a number and ten
3.) seven less than a number
4.) cube of a number increase by nine
5.) square of the sum of a number
Thanks for your answer :)
Answers
Answer:
the sum of a number
Step-by-step explanation:
0.017
ABC and AED are straight lines.
BE and CD are parallel.
A
B
AD = 10.5 cm
AE = 4.2 cm
BE = 2.9 cm
a) Work out length CD.
AC = 8.75 cm
b) Work out length BC.
Answers
Answer:
a) CD = 7.25
b) BC = 5.25
Step-by-step explanation:
a)The parallel lines mean the triangles are similar. ΔADC ~ ΔAEB. Corresponding sides are proportional, so ...
AD/AE = DC/EB
10.5/4.2 = CD/2.9
CD = 2.9(5/2) = 7.25
__
b)Corresponding sides are proportional, so ...
BC/AC = ED/AD
BC = AC(ED/AD) = 8.75(10.5 -4.2)/10.5 = 8.75(3/5) = 5.25
Lines j and k are intersected by line m. At the intersection of lines j and m, the uppercase left angle is 93 degrees. At the intersection of lines k and m, the bottom right angle is 93 degrees.
Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?
alternate interior angles theorem
alternate exterior angles theorem
converse alternate interior angles theorem
converse alternate exterior angles theorem
Answers
Answer: converse alternate exterior angles theorem
Step-by-step explanation:
The angles are alternate exterior angles.
If the slope of a line is zero the line must be a
line.
Answers
Answer:
Straight along the horizontal axis
Step-by-step explanation:
Hope this helped :)
-5x-21 find value of x
Answers
Answer:
The value of x = -21/5
Step-by-step explanation:
=> -5x-21 =0
=> -21 = 5x
=> -21/5 = x
Answer:
Step-by-step explanation:
you want to set the equation equal to 0
-5x - 21 = 0
add 21 to both sides to get the variable by itself
-5x = 21
divide both sides by -5
x = - 21/5
determine the equation of the circle with center (0,6) containing the point (74,2)
Answers
The circle with center (0,6) containing the point (74,2) has an equation of x² + (y - 6)² = 74.1²
How to calculate the equation of a circle
The equation of a circle is:
(x - h)² + (y - k)² = r²
Where (h, k) is the center and r is the radius.
The circle with center (0,6) containing the point (74,2). Hence:
[tex]Radius=\sqrt{(2-6)^2+(74 -0)^2}=74.1\ unit[/tex]
The equation is:
x² + (y - 6)² = 74.1²
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NEED HELP! I JUST NEED HELP ON 31 PLEASSEE HELP
Answers
Answer:
A
Step-by-step explanation:
the quartiles are illustrated as 55 and 59. The average is 57.5 so 58? These are the key points on this type of graph.
In circle L with m KLM = 82°, find the angle measure of minor arc KM.
K
M
L
O
Answer: m KM=
Submit Answer
attempt 1 out of 2
Answers
The angle measure of minor arc KM is 41 degrees
Circle geometryFrom the given diagram, we have the following parameters
mKLM = 82 degrees
Required
arcKM
Since the angle at the vertex is twice that of the intercepted arc, then:
<KLM = 2(arcKM)
arcKM = <KLM/2
arcKM = 82/2
arcKM = 41 degrees
Hence the angle measure of minor arc KM is 41 degrees
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The diameter of a circle is 6 millimeters. What is the circle's circumference?
Use 3.14 for .
Answers
Answer:
18.84
Step-by-step explanation:
Answer:
18.8495559215
Step-by-step explanation:
In order to find circuference we use the formula
C= 2π(r)
c= circumference
r= radius
since they gave you the diameter, you first have to find the radius so you would divide the diameter by two since radius is half of a circle so 6 divided by 2 is 3. From here we would plug in 3 for "r" in the formula I wrote above. So C= 2π(3). then type this into a calculator to get the answer I wrote above. Then round as directed
Hi! Please help. (Geometry Btw)
Answers
Answer:
It is C
Step-by-step explanation:
Reflection in X axis
Reflecting over the x axis, the x values remain the same and the y values become opposite.
answer: c. (X,y) becomes (x,-y)
Consider a sequence whose first five terms are: 4, 8, 16, 32, 64.
Which function (with domain all integers n 2 1) could be used to define and continue this sequence?
A f(n) = 4(n-1)
® f(n) = 4(2)"-1
f(n) = 4n2
f(n) = 4n
Answers
Answer:
Considere una secuencia cuyos primeros cinco términos son: 4, 8, 16, 32, 64.
¿Qué función (con dominio todos los enteros n 2 1) podría usarse para definir y continuar esta secuencia?
A f(n) = 4(n-1)
® f(n) = 4(2)"-1
f(n) = 4n2
f(n) = 4n
Step-by-step explanation:
HELP WITH EXPLANATION, NO LINKS
Answers
Answer:
3x³ and 6x³, y and 7y
Step-by-step explanation:
Like terms have variables with the same exponents. This fact eliminates choices A, C, D.
The like terms are ...
3x³ and 6x³, 7y and y . . . . . . choice B
Help Please!!!!!!!!!!!!!
Answers
Answer:
A. 2086 yd²
Step-by-step explanation:
SA = 2lw + 2wh + 2lh
SA = 2*17*20 + 2*20*19 + 2*17*19
SA = 680 + 760 + 646
SA = 2086
Hope this helps :)
MN is a diameter of a circle with centre ' O ' . If BD = CD , prove that ∠OAD = ∠OCD
~Please help!! Thanks in advance:)
Answers
Answer:
[tex] \sf \: Proved \: \angle \: OAD \: = \angle \: OCD[/tex]
Step-by-step explanation:
Given:
Mn is diameter of circle having centre O
and BD = OD,
To prove that:
[tex]\angle \: OAD \: = \angle \: OCD[/tex]
Solution:
Join the points O and B and draw OB,
On joining the line,
in ∆OCD and ∆OBD,
OC =OB → (Radius of same circle)
BD =CD → (from given)
OD =OD → (Common side in both the triangles)
Hence ∆OCD and ∆OBD are congruent from SSS property.
so we can say that,
[tex]\angle \: OBD \: = \angle \: OCD[/tex]
Consider above prove as statement A
Corresponding angles of congruent traingle.
in ∆ OAB,
OA = OB (radius of same circle)
hence ∆OAB is an isosceles traingle.
We know that opposite angle of isosceles traingle are always equal. hence,
[tex]\angle \: OBD \: = \angle \: OAB \\ \angle \: OAB \: = \angle \: OAD (same \: angles) \\ \angle \: OBD \: = \angle \: OAD[/tex]
Consider above prove as statement B
From Statement A & B we can say that
[tex]\angle \: OAD \: = \angle \: OCD[/tex]
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Find the value of x.
Answers
Answer:
38
Step-by-step explanation: subtraction:
Input interpretation: x: 105-67=
Ratio in lowest terms: 38
Division:
105/67= 1.56...=1 38/67---1R 38= 1 with the remainder of 38. So just 38.
The value of the variable 'x' using the exterior angle theorem will be 38°. Then the correct option is A.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.
By the above theorem, the equation is written as,
x + 67 = 107
Simplify the equation, then we have
x + 67 = 105
x = 105 - 67
x = 38°
The value of the variable 'x' using the exterior angle theorem will be 38°. Then the correct option is A.
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If you are asked to factorize only, can you also expand the brackets ? Or you can’t u less you are asked to? Please answer..
Answers
HELP PLEASE URGENT, ASAP. THIS IS GRADE 11 TRIGONOMETRY ILL GIVE THE BRAINLIEST!!!!!!!!!!!!
Answers
Answer:
1. [tex] \theta = 61.9^\circ [/tex]
2. [tex] x = 23.7~cm [/tex]
Step-by-step explanation:
Problem 1.
Use the Law of Sines.
This is SSA.
[tex]\dfrac{a}{\sin A} = \dfrac{c}{\sin C}[/tex]
[tex] \dfrac{31.2~cm}{\sin 51^\circ} = \dfrac{35.4~cm}{\sin \theta} [/tex]
[tex] \sin \theta = \dfrac{35.4~cm \times \sin 51^\circ}{31.2~cm} [/tex]
[tex] \sin \theta = 0.88176 [/tex]
[tex] \theta = \sin^{-1} 0.88176 [/tex]
[tex] \theta = 61.9^\circ [/tex]
Problem 2.
m<A + m<B + m<C = 180°
m<A + 67° + 58° = 180°
m<A = 55°
Use the Law of Sines.
[tex]\dfrac{a}{\sin A} = \dfrac{c}{\sin C}[/tex]
[tex]\dfrac{x}{\sin 55^\circ} = \dfrac{24.5}{\sin 58^\circ}[/tex]
[tex]x = \dfrac{\sin 55^\circ \times 24.5}{\sin 58^\circ}[/tex]
[tex] x = 23.7~cm [/tex]
ASAP ANSWER PLEASE! 20 POINTSS!
A cylindrical shaped silo has a diameter of 18 feet and a height of 4 feet. How much water can the silo hold, in terms of π?
Refer to your STAAR 8th Grade Math Reference sheet for the appropriate formula.
Question 3 options:
162π ft3
324π ft3
648π ft3
12962π ft3
Answers
Answer:
th answer is 324
Step-by-step explanation:
i took the test
help help help help help
Answers
Answer: 10
Step-by-step explanation:
We can get this is a right triangle with a hypotenuse of c and legs equal to the height and radius.
So, the hypotenuse is c and the legs are 6 and 8.
This means that c=10
How to create a quadrilateral with vertices at the following points PLEASE ASAP
Answers
Answer:
The points are in the form (x,y) this means you count x (right) if positive and left if negitive, for y up is positive and down negitive. for example the point (3,-2) would be three to the right two down
Step-by-step explanation:
The points are in the form (x,y) this means you count x (right) if positive and left if negitive, for y up is positive and down negitive. for example the point (3,-2) would be three to the right two down
a=340
rounded to the nearest 10
b=49.8
rounded to 1 DP
Find the minimum of
a x b
Answers
Answer:
16666.25
Step-by-step explanation:
For rounded values, the minimum value they could have been rounded from is the given value less half its least-significant digit.
That means the minimums are ...
a: 340 ⇒ 340 -5 = 335
b: 49.8 ⇒ 49.8 -0.05 = 49.75
Then the minimum product would be ...
(335) × (49.75) = 16666.25
Describe these points with a double inequality
Answers
Answer:
-3 < x ≤ 13
Step-by-step explanation:
the filled circle is the less/greater than or equal to sign and the open circle is a less/greater than sign.
Find the geometric mean of 24 and 32
Answers
Answer:27.712812921102
Step-by-step explanation:
24*32=x*x
√768=√x²
27.712812921102=x
Geometric mean formula
GM=√aba=24
b=32
Find GM
√(24)(32)√76827.7128On rounding
GM=27.7A box of sunflower seeds contains p packets. Each packet of sunflower seeds contains s seeds. Which equation can be used to find the number of sunflower seeds in a box, b? *
5 points
p = sb
s = pb
b = sp
b + s = p
Answers
Answer:
b = sp
Step-by-step explanation:
box = seeds per packet
The given relation can be used to find the total number of seeds in box b, using the equation b = sp. Hence, 3rd option is the right choice.
What are equations?Equations are relations shown between two equal algebraic expressions.
How do we solve the given question?We are given a box of sunflower seeds, containing p packets of seeds, each of which contains s number of seeds.
We are asked to write an equation that can be used to find the total number of seeds in the box, b.
We know that the box contains p packets of seeds.
In 1 packet we have s number of seeds.
∴ In p packets, we will have an s*p number of seeds or sp seeds.
Since the box contains p packets and the total number of seeds in the box is b, then we can say that
b = the number of seeds in p packets
or, b = sp, which is the required equation.
∴ The given relation can be used to find the total number of seeds in box b, using the equation b = sp. Hence, 3rd option is the right choice.
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