Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin. Naturally, she wants to place the roof beams in such an angle that each pair of opposite beams would meet exactly in the middle. What is the angle of elevation, in degrees, of the roof beams?
Answers
To find this answer, it is always best to draw a picture of the building. The point of the roof, will be directly over the middle of the cabin. Therefore, we could draw an altitude down from the top to the cabin and create a right triangle.
This would form a triangle with an adjacent side and hypotenuse with our needed angle.
We could write and solve the following cosine equation:
cos(x) = 21/27
x = 38.9
The angle of elevation is 38.9° if Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
Width of the cabin = 42 meters
Wooden beam length = 27 meters
Since opposite beams would meet exactly in the middle.
The half of the beam width = 42/2 ⇒ 21 meters
As we can see in the right angle triangle:
[tex]\rm cosx = \frac{21}{27}[/tex]
[tex]\rm x = cos^{-1}(\frac{21}{27} )[/tex]
x = 38.9°
Thus, the angle of elevation is 38.9° if Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin.
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Related Questions
Dione has 3 rolls of pennies containing 50 coins each, 4 rolls of nickels containing 40 coins each, 5 rolls of dimes containing 50 coins each, and 6 rolls of quarters containing 40 coins each. How much money does she have?
A. $106.20
B. $17.50
C. $8.00
D. $94.50
Answers
value of penny - $ 0.01
value she has from pennies - $0.01 x 150 = $1.50
total number of nickels she has - 4 x40 = 160
value of nickel - $ 0.05
value she has from nickels - $0.05 x 160 = $8
total number of dimes she has - 5 x 50 = 250
value of dime - $ 0.10
value she has from dimes - $0.10 x 250 = $25
total number of quarters she has - 6 x 40 = 240
value of quarter - $ 0.25
value she has - $ 0.25 x 240 = $ 60
total amount of money she has = 1.50 + 8 + 25 + 60
money she has = $ 94.50
correct answer is D
Please help, I’m kinda confused
Answers
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 7 in?
Enter your answer in the box.
Answers
The length of the hypotenuse is 14in
SOH CAH TOA identityGiven a 30-60-90 triangle where:
Length of the shorter leg = 5cm (adjacent)
The hypotenuse is what we need..
[tex]cos \theta = \frac{adj}{hyp} \\ [/tex]
Substitute the given parameters
[tex]cos 60 = \frac{7}{h}\\ h =\frac{7}{cos 60}\\ h = \frac{7}{0.5}\\ h = 14in\\ [/tex]
Hence the length of the hypotenuse is 14in
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Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of angle X?
Answers
lets x = measure of angle Y
x + 3x = 180
4x = 180
x = 45
angle Y = 45
angle X = 3 x 45 = 135
answer
Angle X = 135
Answer:
The measure of ∠X is 135°
Step-by-step explanation:
Given that angles X and Y are supplementary and also angle X is 3 times the measure of angle Y.
we have to find the measure of angle X.
Since X and Y are the supplementary therefore these add up to 180° i.e
[tex]\angle X+\angle Y=180\°......(1)[/tex]
Also angle X is 3 times the measure of angle Y i.e
[tex]\angle X=3\angle Y[/tex]
Substitute this value in equation (1), we get
[tex]3\angle Y+\angle Y=180\°......(1)[/tex]
[tex]4\angle Y= 180\°[/tex]
[tex]\angle Y=\frac{180\°}{4}=45\°[/tex]
[tex]\angle X=3\times 45\°=135\° [/tex]
Hence, the measure of ∠X is 135°
Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up. What are the coordinates of B' after the translation?
a.(1, 6)
b.(–3, 6)
c.(0, 0)
d.(3, 1)
Answers
Answer:
b. [tex](-3,6)[/tex]
Step-by-step explanation:
We have been given that triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up.
To find the coordinates of B', we will shift x-coordinate of point B to left by 3 units and y-coordinate of point B to 1 unit up.
After the given transformation the coordinates of point B' would be:
[tex]B(0,5)\rightarrow B'((0-3),(5+1))\rightarrow (-3,6)[/tex]
Therefore, the coordinates of point B' are [tex](-3,6)[/tex] and option 'b' is the correct choice.
I need help with this as well
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n 20 ------------> BC/CD=[AC-AB]/[AD-AC]=(6-4)/(9-6)=2/3
n 21-------------> BD/AE=[AD-AB]/[AE]=(9-4)/(12)=5/12
n 22 7 and 28 find the geometric mean of the two number
step 1
Multiply the two numbers together:
28*7=196
step 2
take the square root:
sqrt(196)=14
the answer is 14
n 23 Simplify the ratio 10 ft/30 in---> divided between 2 both members
5 ft/15 in-----> divided between 5 both members ---> 1 ft/3 in
n 24
if AB=4 -------> AB~FG
FG=8
then
AB*factor=FG-------- > 4*factor=8-- > factor=8/4=2
the figure ABCDE is half of the figure FGHJK
then
BC=4
AE=CD=5
and
ED=6
therefore
the perimeter=[4+4+5+5+6]=24 units
What is the value of the missing number in the sequence below? 4, 12, 36,___, 324, 972, 2916
Answers
The missing number will be 108. The sequence is; 4, 12, 36,108, 324, 972, 2916.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
The given sequence is;
4, 12, 36,108, 324, 972, 2916
It is observed from the sequence that the following sequence follow a specific rule in which the progressive term is multiplied by a factor of 3.
[tex]\rm 4 \times 3 = 12 \\\\ 12 \times 3 = 36 \\\\ 36 \times 3 =108[/tex]
Hence, the missing number will be 108.
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A wood frame costs $1.50. Use a property to write an equivalent expression for the cost of a wood frame.
Answers
Let the cost of a linear foot of the frame = y
Let the inside dimension of the length of the frame = a
Let the inside dimension of the width of the frame = b.
The total length of the frame = 2*a + 4x
The total width of the frame = 2b
The total amount of the frame in feet is (2a + 4x + 2b)*y = Cost
If this is incorrect please leave a message on my home page.
Can anyone help me I don’t know how to do this
Answers
y = a(x -h)² +k . . . . . . . . for some stretch factor "a" and vertex (h, k)
1. Vertex = (h, k) = (0, 0). Stretch factor can be found from the given point (x, y).
8 = a(-2 -0)² +0
8 = 4a . . . . . . . . simplify
2 = a . . . . . . . . . divide by the coefficient of "a"
Your equation is y = 2x².
Note the above method for solving these problems. It repeats.
2. As above, substitute what's given and solve for what's not.
3 = a(1 -2)² +0
3 = a
Your equation is y = 3(x -2)²
3. Repeat
-4 = a(-5 +3)² +0
-4 = 4a
-1 = a
Your equation is y = -(x +3)²
4. Are you seeing the pattern yet?
0 = a(-1 -0)² +1
0 = a +1
-1 = a
Your equation is y = -x² +1
5 & 6. You know that if you want a zero (x-intercept) to be located at x=a, then a factor of the quadratic will be (x -a). Multiply the factors together to get your quadratic function.
5. y = (x -0)*(x -2) = x² -2x
6. y = (x +5)*(x -5) = x² -25 . . . . . . . . . . you should recognize this "special form", the factoring of the difference of squares
angle measure represented by 4.5 rotations counterclockwise
Answers
now, a full rotation, namely a "revolution", is a full go-around the circle, that'd be 360°, now if you 4 times around, that be 4*360 or 1440°, and if you go an extra 0.5 or half a circle, that'd be 180°, that will land us on 1440° + 180°.
is -3 larger than -2?
only answer if you know and not for the points
Answers
Your answer is no.
-3 is not larger than -2. This is because the larger the number is with a negative sign, the smaller the number is!
Hope this helps you.
Have a great day!
No.
-3 is not greater than -2.
When we are speaking about negative numbers, the "lower" the number is, the greater. -2 is greater than -3 because it is closer to the positive side than negative side. -3 is farther away from 0. But as for -2, is alot closer to 0 than -3.
Your answer, No.
I hope this helps you!
Easy Algebra 2 Rational Expressions question
Answers
y - 3 = 0
y = 3 - this is where the fraction is undefined (or nonpermissible)
Which of the following decimal numbers equals 4 thousand, 9 hundreds, 2 tens, and 6 ones?
Answers
decimal numbers equals
4 thousand---------> 4000
9 hundreds--------> 900
2 tens-----------> 20
6 ones-------> 6
so
[4000+900+20+6]=4926
the answer is 4926
What is the image of the point (4,-2) after a rotation 270 degree clockwise about the origin?
Answers
(4, -2) becomes (2, 4) after rotation.
Answer:
The image of the point (4, -2) is (2, 4).
Step-by-step explanation:
Since, the rule of rotation 270 degree clockwise about the origin is,
[tex](x,y)\rightarrow (-y,x)[/tex]
Where, (-y,x) is the image of the point (x,y),
Thus, by the above rule,
[tex](4,-2)\rightarrow (-(-2), 4)[/tex]
Hence, the image of the point (4, -2) is (2, 4).
A $6,300.00 principal earns 6% interest, compounded annually. After 3 years, what is the balance in the account?
Answers
Hope this helped!
To find this answer, you have to start with 6,300 and multiply it by 1.06 three times. We are using 1.06 because we are adding 6% (0.06) onto the total 3 times.
6300 x 1.06 x 1.06 x 1.06 = $7,503.40
OR
6300(1.06)^3 = $7,503.40
The second equation is written as a compound interest equation. You just need to switch the 3 if you want to find the total for a different amount of years.
I hope this helps, Good luck!
Gina pumps 40 cubic inches of air per second into a balloon. The function below shows the total amount of air f(t) inside the balloon after t seconds. f(w) = 40t + 5 Which statement best describes the y-intercept of the graph of the function?
Answers
Mathematically we have:
For t = 0:
f (0) = 40 (0) + 5
f (0) = 0 + 5
f (0) = 5
Answer:
The intersection with the y-axis represents the total amount of initial air before starting to pump air.
The initial air quantity is:
5 in ^ 3
A set of 5 numbers has a mode of 12 a median of 11 a mean of 10 what could the numbers be?
Answers
The mode is 12. The value 12 shows up the most times. Let's say it shows up twice. So far the data set is {11, 12, 12}
Let's introduce two more numbers x and y
The new data set is {x, y, 11, 12, 12}
Add up the five values and then divide by 5. We want this result to be equal to 10
(x+y+11+12+12)/5 = 10
(x+y+35)/5 = 10
x+y+35 = 10*5
x+y+35 = 50
x+y = 50-35
x+y = 15
So we don't know what x or y is, but we know that they must add to 15. So all you have to do is list two numbers that add to 15. One such pair is x = 6 and y = 9. Another pair is x = 7 and y = 8. There are infinitely many possibilities if you can use any real number.
So one possible set is {6, 9, 11, 12, 12}
Another possible set is {7, 8, 11, 12, 12}
Please help me, i don't understand how to do this.
Solve V = 1 3 πr2h for h.
A) 3V πr2
B) V 3πr2
C) r sqrt 3V π
D) V - 1/3 πr2
Answers
so h = 3v/πr2
how is jimthompson so smart?
Also can you please help me with that question.
I got everything except for the Euler Diagram.
Answers
Step 1) Draw a large circle and label it circle A
Step 2) Inside this large circle, draw a smaller circle and label it circle B
Circle A will represent the set of all obtuse angles (any angles that are between 90 and 180 degrees). Circle B represents only one item: the angle value of 150 degrees. All of circle B is inside circle A because 150 degrees is between 90 and 180; therefore, 150 is obtuse. This is simply the definition of what "obtuse" means.
So if you threw a dart and it landed in circle B, then you know for sure it landed in circle A as well. This is effectively saying "if you get a 150 degree angle, then you know its obtuse"
This is a visual way to back up the conditional statements you used earlier and help add more evidence that the statement "A 150 degree angle is an obtuse angle" is a valid statement.
An artist drew a rectangle. the artist then modified the rectangle so thatthe length ofthe rectawngle increased by 30 percent and the width of the rectangle decreased by 40 percent. after the modification, what was the percent decrease in the area of the rectangle?
Answers
length - L
width - W
area = L*W = LW
after the modification, new dimensions are
length increased by 30 %
Length = L * 1.3 = 1.3L
Width = W * 0.6 = 0.6W
new area = 1.3L * 0.6W
= 0.78LW
the percent decrease in area
decrease % = (difference in area)/original area * 100
= (LW - 0.78LW)/LW * 100
= 0.22LW/LW * 100
= 22%
percent decrease is 22%
Where is the vertex of the parabola?
y = x2 + 6x + 7
above the x-axis
on the x-axis
on the y-axis
below the x-axis
Answers
Answer:
below the x axis
Step-by-step explanation:
i took the test
The function below can be used to calculate the cost of making a long distance call, f(m), which is based on a $2.50 initial charge and a fee of $.12 per minute, m, that the call lasts. If Natalie paid $6.82 for one call, how many minutes long was it?
Answers
if Natalie paid $6.82
6.82 = 2.5 + 0.12m
0.12m = 6.82 - 2.5
0.12m = 4.32
m = 4.32 ÷ 0.12
m = 36
The call was 36 minutes long.
Jana finished 1/4 of her homework at school and 2/3 of it before dinner. How much of her homework has she finished so far?
Answers
1/4×3/3+2/3×4/4
3/12+8/12
11/12
Final answer:
Jana has completed 11/12 or 11 out of 12 of her homework so far.
Explanation:
To find out how much of her homework Jana has finished so far, we need to add together the fractions of her homework completed at school and before dinner.
Jana finished 1/4 of her homework at school and 2/3 of it before dinner.
To add fractions, we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12. So, we can convert both fractions to have a denominator of 12.
1/4 is equivalent to 3/12, and 2/3 is equivalent to 8/12.
Now, we can add the fractions: 3/12 + 8/12 = 11/12.
Therefore, Jana has completed 11/12 or 11 out of 12 of her homework so far.
How do I solve for h
Answers
.. AD = AC -DC = 20 -4
.. AD = 16
Then
.. (long leg)/(short leg) = AD/DB = BD/DC
.. 16/h = h/4
.. h^2 = 64
.. h = 8
Selection D is appropriate.
_____
You may see this again. The altitude (h) from the right angle in a right triangle is the geometric mean of segments AD and DC. That is,
.. h = √((AD)*(DC))
A hair salon charges a fixed rate of $25.00 for a haircut and an additional $15 for any other services. Write a function to model the cost of services at the salon and then evaluate the function to determine the cost for a haircut, shampoo, highlight, and blow dry.
Answers
Answer:
Function : Cost =25 + 15x
Cost for a haircut, shampoo, highlight, and blow dry = $70
Step-by-step explanation:
Hi, to answer this we have to write an equation:
The cost of the services will be equal to the fixed cost for the haircut (25.00) plus the product of the number of additional services (x) and the price of each additional service (15).
Mathematically speaking:
Cost =25 + 15x
To determine the cost for a haircut, shampoo, highlight, and blow dry, we have to substitute x = 3 (because shampoo, highlight, and blow dry are additional services ) in the equation and solve.
Cost = 25+ 15 (3)
Cost = 25+45
Cost = $70
Russ is constructing the inscribed circle for △ABC . He has already used his compass and straightedge to complete the part of the construction shown in the figure.
What could be his next step?
A)Use the straightedge to draw a line through point N that intersects BC¯¯¯¯¯ .
B) Use the straightedge to draw the line through points M and P.
C) Place the point of the compass on point C and draw an arc that intersects AC¯¯¯¯¯ and BC¯¯¯¯¯ .
D)Place the point of the compass on point N and draw an arc that intersects AB¯¯¯¯¯ and BC¯¯¯¯¯ .
Answers
Place the point of the compass on point C and draw an arc that intersects AC¯¯¯¯¯ and BC¯¯¯¯¯ .
Answer: The answer is (C) Place the point of the compass on point C and draw an arc that intersects AC and BC.
Step-by-step explanation: Given that Russ is constructing the inscribed circle for △ABC and he has already used his compass and straightedge to complete the part of the construction shown in the given figure. We are to find his next step.
Since Russ has already constructed the angle bisector of ∠B, so next he shoul construct the angle bisector of either ∠A or ∠C. Since the steps for constructing angle bisector of ∠A are not in the options, so he should go with ∠C. For that, he must place the point of the compass on the point C and draw an arc that intersects AC and BC.
Thus, (C) is the correct option.
At the beginning of an experiment, there are 600 grams of contaminants. Each hour, half of the contaminants are filtered out. How many grams of contaminants remain after 4 hours?
Answers
Second hour - 150
Third hour - 75
Fourth hour - 37.5
Out of 1100 discs tested 13 are defective. Estimate the number of defective discs in a batch of 41000
Answers
A child walks due east on the deck of a ship at 4 miles per hour.
The ship is moving north at a speed of 12 miles per hour.
Find the speed and direction of the child relative to the surface of the water.
Speed = mph
The angle of the direction from the north = (radians)
i have the speed i couldn't find the direction !,
Answers
Therefore, to get the speed relative to the surface you have to sum the two vectors, which means you can apply the Pythagorean theorem to find the hypotenuse, having the two legs.
h = √(4² + 12²) = √160 = 4√10 = 12.65mph
In order to find the direction, you need to use trigonometry:
- the sine of an angle is given by the ratio between the opposite side divided the hypotenuse;
- the cosine of an angle is given by the ratio between the adjacent side divided by the hypotenuse.
You can use either one, I will show you both:
sinα = O / H
inverting the formula: α = arcsin (O / H) = sin⁻¹ (O / H)
these two forms are equivalent.
Similarly:
cosβ = A / H
β = arccos (A / H) = cos⁻¹ (A / H).
Substituting your numbers:
α = sin⁻¹ (12 / 12.65) = sin⁻¹ (0.9486) = 1.25rad
β = cos⁻¹ (4 / 12.65) = cos⁻¹ (0.3162) = 1.25rad
As you can see, α = β so you can use either formula.
Your answer will then be: the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 1.25rad from East towards North.
ATTENTION!
If you drew first the vector towards North and then the one towards East, you get an equivalent triangle, which is rotated by 180° respect to the previous one. This way, what you earlier called Opposite is now Adjacent and vice-versa, but the formulas are still valid.
You will get:
α = sin⁻¹ (4 / 12.65) = sin⁻¹ (0.3162) = 0.32rad
β = cos⁻¹ (12 / 12.65) = cos⁻¹ (0.9486) = 0.32rad
And your answer will be: the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 0.32rad from North towards East.
Hey can somebody help me? I know it seems easy but I forgot the process on how to do this. Thanks in advance!
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1 1/2 - 1/2 = ???
Show your work please so I understand
Answers
Sorry if this was a bit unclear, I did my best to explain ;)
Hope this helps!