When the sun’s angle of depression is 36 degrees, a building casts a shadow of 44 m. To the nearest meter, how high is the building? Enter a number answer only.
Answers
The height of the building is approximately 32 meters.
To determine the height of the building, we can use the tangent function, which relates the angle of depression to the height and the length of the shadow.
Let's denote the height of the building as h.
Given that the angle of depression is 36 degrees and the length of the shadow is 44 m, we can set up the following trigonometric equation:
tan(36°) = h / 44
Now, we can solve for h by multiplying both sides of the equation by 44:
h = 44 * tan(36°)
Using a calculator, we find that tan(36°) is approximately 0.7265.
Substituting the value, we get:
h = 44 * 0.7265
Calculating the value, we find:
h ≈ 32 meters
Consequently, the building stands about 32 metres tall.
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Related Questions
This exercise demonstrates a connection between the curl vector and rotations. Let B be a rigid body rotating about the z-axis. The rotation can be described by the vector w = ωk, where ω is the angular speed of B, that is, the tangential speed of any point P in B divided by the distance d from the axis of rotation. Let r = ⟨x, y, z⟩ be the position vector of P.(a) By considering the angle θ in the figure, show that the velocity field of B is given by v = w × r.(b) Show that v = −ω y i + ω x j.(c) Show that curl v = 2w.
Answers
The relation between curl vector and rotations is v = wdj
What is curl vector?A vector field is a vector field's curl. The tendency of particles at point P to spin about the axis that faces the direction of the curl at P is measured by the curl of a vector field at P. If and only if its curl is zero, a vector field with a simply linked domain is considered conservative.
Let v represent the particle's velocity as a vector.
vector v=ui+vj+wk
curl v =
curl v = \(\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\u&v&w\end{array}\right]\)
= (dw/dy - dv/dz )i - (dw/dx - du/dz)j + (dv/dx - du/dy )k
Now by comparing with rotational matrix ,
We know that w = rotational matrix
\(w_{x}\) = 1/2 (dw/dy - dv/dz )
\(w_{y}\) = 1/2 (dw/dx - du/dz)
\(w_{z}\) = 1/2 (dv/dx - du/dy )
w = \(w_{x} i +w_{y} j + w_{z} k\)
w = 1/2[ (dw/dy - dv/dz )i + (dw/dx - du/dz)j + (dv/dx - du/dy )k]
w = 1/2 curl v , rotation = 1/2 curl v
let B be a rigid rotating about z axis
w = w.k
tangential speed =wk *di
v = wdj
curl of v= \(\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\0&w_{x} &0\end{array}\right]\)
v = wdj ,
The relation between curl vector and rotations is v = wdj
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Is 2.845 seconds faster than 2.835 seconds?
Answers
Answer:
No, the opposite.
Step-by-step explanation:
Because if you take out the decimal and see which one is less, btw less is faster, then 2.835 is faster.
Census Bureau data shows that the mean household income in the area served by a shopping mall is $64,500 per year with the standard deviation of $8,000. A market research gathers a random sample of 100 shoppers at the mall to find out whether the mean household income of mall shoppers of $61,000 is different than the general population.
Q: What is the null hypothesis ?
Answers
Considering the situation described, the null hypothesis is given as follows:
\(H_0: \mu = 64,000\).
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is the same as in the Census, of $64,000, hence:
\(H_0: \mu = 64,000\).
At the alternative hypothesis, it is tested if the mean is different from the Census, hence:
\(H_1: \mu \neq 64,000\).
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Try This Q 1. Write the expressions for each of the following using brackets. (a) Four multiplied by the sum of nine and two. (b) Divide the difference of eighteen and six by four. (c) Forty five divided by three times the sum of three and two. 2. Write three different situations for (5+8) x 6. (One such situation is: Sohani and Reeta work for 6 days; Sohani works 5 hours a day and Reeta 8 hours a day. How many hours do both of them work in a week?) 3. Write five situations for the following where brackets would be necessary. (a) 7(8-3) (b) (7+2) (10-3)
Answers
Answer:
Step-by-step explanation:
Writing expressionsa) Sum of nine and two ⇒ 9 + 2
Four multiplied by (9+2) :
4* (9+2)
\(b) \dfrac{(18-6)}{4}\)
\(c) \dfrac{45}{3*(3+2)}\)
2) a) Multiply the sum of five and eight by 6
b) There 5 story books in 6 red bags and 8 art books in 6 blue bags. How many books are there?
3) a) 7*(8-3)
Multiply the difference of eight and three by 7.
Write a story from the viewpoint of a plant on how it get its food.
Answers
a plant first starts out as a mere seed, attaining nutrients through the soil, nutrients left behind by decaying carcasses and dead plants from past times, once it penetrates the ground it starts acquiring nutrients via photosynthesis and water, as the plant grows in size it needs more nutrients to sustain itself, but with size comes the ability to collect more water and energy from the sun. after finishing its cycle of life it will wither away an die, becoming nutrients for another generation of plants.
which is a true statement about the two rectangular prism shown below
Answers
The demand on a power plant changes over time. cause or effect
Answers
Answer:
effect
Step-by-step explanation:
2)
a: b is 2:5 and b: c is 3:8
Work out a:c
Give your answer in its simplest form.
Answers
Answer:
a : c = 3 : 20
Step-by-step explanation:
Given ratios:
a : b = 2 : 5b : c = 3 : 8The value of b is 3 and 5.
The lowest common multiple of 3 and 5 is 15.
Multiply each ratio by a factor of 15 so that b is 15.
Multiply ratio a : b by 3:
⇒ a : b = 6 : 15
Multiply ratio b : c by 5:
⇒ b : c = 15 : 40
Therefore:
⇒ a : b : c = 6 : 15 : 40
So a : c is:
⇒ a : c = 6 : 40
Simplest form:
⇒ a : c = 3 : 20
Which of the following expressions is equivalent to (-7)(-7)(-7)?
Answers
Answer:
-343
Step-by-step explanation:
(-7)(-7)=49
(49)(-7)= -343
A geometric sequence has only positive terms. The third term is 100 and the eighth term is 3.125.
Find the common ratio.
Answers
The common ratio of a geometric sequence will be;
⇒ r = 5 / 10
What is Geometric sequence?
An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
In a geometric sequence,
The third term is 100 and the eighth term is 3.125.
Now,
We know that;
The nth term of geometric sequence is,
⇒ \(T_{n} = a r^{n - 1}\)
Hence, The third term is;
⇒ \(T_{3} = a r^{3 - 1} = 100\)
⇒ \(a r^{2} = 100\) ..(i)
And, The eighth term is,
⇒ \(T_{8} = a r^{8 - 1} = 3.125\)
⇒ \(a r^{7} = 3.125\) ..(ii)
Divide equation (ii) by (i), we get;
⇒ ar⁷ / ar² = 3.125/100
⇒ r⁷ / r² = 3125 / 100000
⇒ r⁷⁻² = 3125 / 100000
⇒ r⁵ = 3125 / 100000
⇒ r = 5/10
Thus, The common ratio of a geometric sequence will be;
⇒ r = 5 / 10
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Ivan also decides to try putting together the “Multiples of 3” set from the numbers sitting around. How can he know if a number is a multiple of 3? (Hint: Build a lot of different multiples of 3. Then look at the sum of the digits of each number.
Answers
Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, ...
The two digit numbers in that list above all have their digits adding to some other multiple of 3
1+2 = 31+5 = 61+8 = 92+1 = 32+4 = 62+7 = 93+0 = 33+3 = 63+6 = 9and so on.
Therefore, the rule is: If the digits add to a multiple of 3, then the original number is a multiple of 3.
need help with this asap
Answers
I guess it is
4x-8+2x+2
6x-6
6 (x-1)
Answer:
6x-6 this is the answer.
please mark brainliest
Calculate the probability for the following situation, then select the correct answer:
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a head AND an odd number on the die AND a card greater than 6 (assume the ace is equal to 1) from the deck?
Answers
The probability is P = 0.135
How to find the probability?
First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.
P(head) = 1/2P(odd number) = 3/6 (there are 3 odd numbers on the dice)P(card greater than 6) = 28/52 (28 cards with numbers larger than 6).The joint probability is given by the product between the individual probabilities, so we get:
P = (1/2)*(3/6)*(28/52) = 0.135
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Identify the rule relating each term in the following sequence: 8, - 4, 2 - 1, 1/2, 1/4, 1/8
A: Divide by 2
B: Divide by -2
C: Multiply by -2
D: Multiply by 2
Answers
Answer:
B: Divide by -2
Step-by-step explanation:
The only logical conclusion would be divide by -2, though that may not be the entire correct answer. Why?
Firstly, the sequence of 8, -4, 2, -1 only follows division by -2. Division by 2 would result in 8, 4, 2 and 1, multiplication by -2 would result in 8, -16, 32, -64, and multiplication by 2 would result in 8, 16, 32 and 64. Hence, the only logical conclusion would be division by -2.
However, this rule breaks down as we go into the fractions. -1 / -2 is 1/2, sure, but (1/2) / -2 should be - 1/4, and not 1/4. Hence, as we go into the fractions, the rule should have changed to division by 2 instead.
The only solution to unite the whole sequence would be to correct 1/4 to -1/4, and maybe OP should check whether that is the case.
Hope this helped!
Answer:
b. divided by -2
Step-by-step explanation:
Dos horas y media ¿A cuántos minutos equivale?
Answers
Answer:
90 minutos
Step-by-step explanation:
una hora es 60 minutos y media es 30 minutos.
A desk is on sale for $123.20, which is 72% less than the regular price.
What is the regular price?
Answers
Answer:
170.833
Step-by-step explanation:
we have to find real value which has to be find.
let take it as x,
in the question they said reduction percentage is equal to $123
then x*72/100=$123
x=$123*100/72
x=12300/72
x=170.8333
Answer:
I believe it's 211.90$.
Need Help Quickly - conjectures with angles
these questions need answering. Could anyone please help me on these I need the answers rn as I'm on a maths live. if you don't mind could you guys please explain it to? These questions are either TRUE OR FALSE.
a) the sum of two acute angles is always acute
b) Co- interior angles in parallel lines cannot be equal
c) All Angles Contain Three Actuate angles
d) The sum of two obtuse angles is more than a full turn
Answers
a) false (89+89=178⁰ not acute!)
b) false (they could both be 90⁰ but this is the only angle that works)
c) what
d) false (92+92=184⁰ this is less than 360⁰)
can you please explain c ????
find r^-1 (x)
r(x) = 2/3 (4x -5)
Answers
Answer:
Step-by-step explanation:
Let r(y)=x.
\(x=\frac{2}{3}(4y-5)\\\\\frac{3}[2}x=4y-5\\\\\frac{3}{2}x+5=4y\\\\y=\frac{3}{8}x+\frac{5}{4}\\\\r^{-1}(x)=\frac{3}{8}x+\frac{5}{4}\)
The last time Edmond checked, the corn stalks in his back yard were 48 inches tall. Now they are 25% taller. How tall are the stalks now? inches
Answers
We know that the initial height is 48 inches.
We have to find 25% of 48.
\(0.25\cdot48=12\)Then, we sum the increase with the initial height.
\(48+12=60\)Hence, the height now is 60 inches.What is the distance between (2, 6) and (7, 6)?
8
(2,3)
+17,6)
4
2
Answers
The formula for calculating the distance between two points is:
d=√(x2−x1)^2+(y2−y1)^2
Substituting the values from the points in the problem gives:
d=√(7−2)^2+(4−−6)^2
d=√(7−2)^2+(4+6)^2
d=√5^2+10^2
d=√25+100
d=√125
d=√25⋅5
d=√25√5
d=5√5
The line pictured has a(n)
slope.
5 points
AY
O Undefined
O Zero
ОООО
O Positive
O Negative
Answers
Answer:
Negative
Step-by-step explanation:
Goes down from left to right
Sarah and Thomas each roll a die. Whoever rolls the higher number wins; if they both roll the same number, neither wins. a.What is the probability that Thomas wins?
b.If Sarah rolls a 3, what is the probability that she wins?
c.If Sarah rolls a 3, what is the probability that Thomas wins?
d.If Sarah wins, what is the probability that Thomas rolled a 3
e.If Sarah wins, what is the probability that Sarah rolled a 3?
Answers
Rolls the higher number wins; if they both roll the same number, neither wins.
The answer is-
a)They both start the game with an equal chance of winning, therefore 1/2
b) If she rolls a 3, Thomas must roll a 1 or 2 for her to win, making her chance of winning 1/3.
c) Thomas has a 50% chance of winning if she rolls a three because he has to roll a 4,5 or 6 to do so.
d) In order for Sarah to win, she had to roll a 2, 3, 4, or 6. If Thomas had rolled a 1, 2, 3, 4, or 5, he would have lost. Thus, there is a 1/5 chance that he will roll a 3.
e) If Sarah wins she must have rolled a 2,3,4,5 or 6. So the probability that she rolls a three is also 1/5.
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if f(x)=3x+2, what is f(5)
Answers
Answer:
f(5) = 17
Step-by-step explanation:
Pretty easy :)
just pluggin f(5).
f(5) = 3(5) + 2
f(5) = 15+2
f(5) = 17.
:)
f(5) = 3(5) + 2
= 15 + 2
= 17
7x+6-2x=12x-7+2
Solve for x
Answers
x= 11/7 or 1.5714
Answer:
x = 11/7
Step-by-step explanation:
\(7x+6-2x=12x-7+2\\\\5x+6=12x-5\\\\5x+6-5x=12x-5-5x\\\\6=7x-5\\\\6+5=7x-5+5\\\\11=7x\\\\\frac{11}{7}=\frac{7x}{7}\\\\\frac{11}{7}=x\)
1.Solve the equation, and explain each step. 0.6+156 + 4 = 25.6
2.Test your solution in the equation.Show your work to ensure that the equation is true.
3.What is one number that is not s solution to the equation?Show your work to ensure that the equation is false.
Answers
Answer:
the following statementsStep-by-step explanation:
hoiling oilSolve for x
12 + x = 15
Answers
Answer: x = 3
Step-by-step explanation: just isolate the variable x
So subtract 12 on both sides of the equation and you are left with x is equal to 3
Hope this helped
The price of a shirt is $18.50 but you have a coupon that lowers that price by 20% what is the price of that shirt?
Answers
Answer:
$3.70
Step-by-step explanation:
What you would do is 18.50×20%. And to make it easier you would do 18.50×0.20 which equals 3.70.
Answer:
The shirt would be $14.80 after using the coupon!
Step-by-step explanation:
I hope this helps a bit, have a good day! =)
Jane received a $80 gift card for a coffee store. She used it in buying some coffee that cost $7.56 per pound. After buying the coffee, she had $49.76 left on
her card. How many pounds of coffee did she buy?
Answers
Answer:
Jane spent on coffee.
She started with $80 on her gift card and ended with $49.76, so she spent:
80 - 49.76 = $30.24
We know that she bought coffee that cost $7.56 per pound, so we can set up an equation to find how many pounds of coffee she bought:
7.56x = 30.24
where x is the number of pounds of coffee she bought.
Solving for x, we get:
x = 30.24 / 7.56 = 4
So Jane bought 4 pounds of coffee with her gift card.
PLEASE HELP! Find missing side lengths of B and C. Explain
Answers
Answer:
b=7 & c=7√2
Step-by-step explanation:
b=7 as it is an isosceles triangle
now using Pythagoras theorem,
(c)^2= (7)^2+(7)^2
⇒(c)^2= 49+49
⇒(c)^2= 98
⇒c= √98
⇒c=7√2
Answer:
b = 7c = 7√2Step-by-step explanation:
You want the missing side lengths in an isosceles right triangle with one side given as 7.
Isosceles right triangleThe two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:
b = 7
The hypotenuse of an isosceles right triangle is √2 times the side length:
c = 7√2
__
Additional comment
You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.
c² = 7² + b²
c² = 7² +7² = 2·7²
c = √(2·7²) = 7√2
The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.
The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.
Question 2: Leilamade a one-time investment of $12 000.00 in a
registered retirement savings plan (RRSP) at 2.65%, compounded
semi-annually. She plans to withdraw the money when she retires in 30
years.
a) Determine the value of the investment when she retires. Show your
work.
I
b) Calculate the rate of return [note:] over the 30 years. Show your work.
Answers
the value of the investment when she retires is $26434.92.
What is the compound interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Formula:
A = P(1 + {r}/{n})^{n.t}
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
here, we have,
given that,
Leilamade a one-time investment of $12 000.00 in a
registered retirement savings plan (RRSP) at 2.65%, compounded
semi-annually.
She plans to withdraw the money when she retires in 30
years.
So, she get finally is,
using the formula we get,
$26434.92
hence, the value of the investment when she retires is $26434.92.
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