A 4 meter long ladder leans against a 90 degree wall at a 68 degree angle.
How far is the top of the ladder from the ground?
How far is the bottom of the ladder from the wall?
Answer:
Step-by-step explanation:
We use trig to answer these questions:
sin x = opposite side of a triangle / hypotenuse
cos x = adjacent side / hypotenuse
Construct a right triangle with hypotenuse 4 m and lower angle 68 degrees.
The height of the top of the ladder is then defined by:
sin 68 degrees = height / 4 m, which yields (4 m)(sin 68) = height =
3.71 m
and the distance of the bottom of the ladder from the wall as follows:
cos 68 degrees = horizontal distance / hypotenuse =
1.50 m
The top of the ladder is 3.7088 m away from the ground.
The bottom of the ladder is 1.5 m away from the wall.
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given:
Angle = 68 degree
Hypotenuse = 4 m
Now, using Trigonometry
sin 68 = P/ H
0.9272 = P/ 4
P = 3.7088 m
Thus, the top of the ladder is 3.7088 m away from the ground.
Now, using Pythagoras theorem
H²= P² + B²
4² = (3.7088)² + B²
16 = 13.75 + B²
B² = 2.25
B= 1.5 m
Thus, the bottom of the ladder is 1.5 m away from the wall.
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
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The Fabric storage box below is shaped like a rectangular prism how much fabric is needed to cover the exterior of the box
Answer:
2952 square centimeters are needed to cover the exterior of the box.
Step-by-step explanation:
We need to cover five external faces of the box. The surface area formula ([tex]A_{s}[/tex]), measured in square centimeters, is derived from surface area formula for parallelpiped:
[tex]A_{s} = w\cdot l + 2\cdot w\cdot h + 2\cdot l \cdot h[/tex] (1)
Where:
[tex]w[/tex] - Width, measured in centimeters.
[tex]l[/tex] - Length, measured in centimeters.
[tex]h[/tex] - Height, measured in centimeters.
If we know that [tex]w = 36\,cm[/tex], [tex]l = 23\,cm[/tex] and [tex]h = 18\,cm[/tex], then the outer surface area of the storage is:
[tex]A_{s} = (36\,cm)\cdot (23\,cm)+2\cdot (36\,cm)\cdot (18\,cm)+2\cdot (23\,cm)\cdot (18\,cm)[/tex]
[tex]A_{s} = 2952\,cm^{2}[/tex]
2952 square centimeters are needed to cover the exterior of the box.
Security A rounds every 2 minutes and 20 seconds in the gate 1. Security B rounds every 1 minute and 40 seconds in the gate 2. If they conduct rounds at the same time. After how many minutes they will rounds together again?
Answer:
[tex]Time = 11\frac{2}{3}\ min[/tex]
Step-by-step explanation:
Given
[tex]Security\ A = 2\ mins, 20\ secs[/tex]
[tex]Security\ B = 1\ mins, 40\ secs[/tex]
Required
After how many minutes, will they round together
First, convert the given time to minutes
[tex]Security\ A = 2\ mins, 20\ secs[/tex]
[tex]Security\ A = 2\ mins+ 20\ secs[/tex]
[tex]Security\ A = 2\ mins+ \frac{20}{60}\ min[/tex]
[tex]Security\ A = 2\ mins+ \frac{1}{3}\ min[/tex]
[tex]Security\ A = 2\frac{1}{3}\ min[/tex]
[tex]Security\ B = 1\ mins, 40\ secs[/tex]
[tex]Security\ B = 1\ mins+ 40\ secs[/tex]
[tex]Security\ B = 1\ mins+ \frac{40}{60}\ min[/tex]
[tex]Security\ B = 1\frac{2}{3}\ min[/tex]
So, we have:
[tex]Security\ A = 2\frac{1}{3}\ min[/tex]
[tex]Security\ B = 1\frac{2}{3}\ min[/tex]
List out the multiples of the time of both security personnel take round.
[tex]Security\ A = 2\frac{1}{3}min,\ 4\frac{2}{3}min,\ 7min,\ 9\frac{1}{3}min,\ 11\frac{2}{3}min...[/tex]
[tex]Security\ B = 1\frac{2}{3}min,\ 3\frac{1}{3}min,\ 5min,\ 6\frac{2}{3}min,\ 8\frac{1}{3}min,\ 10min\ ,11\frac{2}{3}min,...[/tex]
In the above lists, the common time is:
[tex]Time = 11\frac{2}{3}\ min[/tex]
This implies that they go on round after [tex]11\frac{2}{3}\ min[/tex]
what is the slope of (-20,-3), (19,-15)
Answer:
m= - 4/13
Step-by-step explanation:
Answer:
-4/13
Step-by-step explanation:
Hopefully this helps :)
Find mZBAC
A
20°
B
11
11
Answer:
numbers dont do into math please move this to englash
Step-by-step explanation:
it posted worng
HERE IS ANOTHER PROBLEM
ameliaswan
Answer:
-1.6 < √2 - 3 < -1.5
Step-by-step explanation:
√2 - 3 = -1.58
-1.5 is closer to 0 so it is larger than -1.5 and -1.6 is father from 0 than -1.58 and -1.5 so its less than
2/3 - 3/5, simplifiy
Answer:
1/15
Step-by-step explanation:
decimal 0.06
if correct plz mark as brainliest
thank you
19NBoli
Answer:
that would half to equal 0.066
Step-by-step explanation:
A fair charges an admission fee of 3 dollars per person let c be the cost of admission in dollars afor p people write an equation relation to c and p then graph your equation
what is 1000000000÷10?
Answer:
Step-by-step explanation:
If you're dividing a number by 10, just remove one zero, so we have: 1000000000÷10 = 100000000.
Answer: 100,000,000
Step-by-step explanation:
1,000,000,000/10 = 100,000,000
What multiply by 90 gives you 1.8
Answer:
0.02
Step-by-step explanation:
90 multiplied by 0.02 is 1.8
Consider the following sample data: 12, 13, 7, 5, 15, 18. Which one of the following represents the value of the standard deviation?
Answer:
Standard deviation= 4.46
B) 4.89 is the nearest answer
Step-by-step explanation:
Standard deviation √variance
Variance= (summation (x-mean)²)/n
Mean= summation of numbers/total
Mean =( 12+13+ 7+5+15 18)/6
Mean= 70/6
Mean= 11.67
Variance=(( 12-11.67)²+(13-11.67)²+ (7-11.67)²+(5-11.67)²+(15-11.67)²+ (18-11.67)²)/6
Variance= (0.1089+1.7689+21.8089+44.4889+11.0889+40.0689)/6
Variance= 119.3334/6
Variance= 19.8889
Standard deviation= √variance
Standard deviation= √19.8889
Standard deviation= 4.46
2. Tristan wants to go bowling. He wants to spend no more than $25. It costs $3.00 to rent shoes and $4.50 for each game. What is the greatest amount of games he can bowl? Write an inequality using the variable g for games and solve.
Answer:
[tex]3 + 4.50g \leq 25[/tex]
[tex]g\leq 4[/tex]
Step-by-step explanation:
25 - 3 is 22. 22 divided by 4.50 is a decimal. But it rounds down to 4. So the most amount of games Tristan can play is 4.
Hope it helps!
Write the numerical co-efficient of each term of the following expressions:
A) − xyz – 3oy + 6yz +4
Answer:
Uncertain if the second term is 30 and not 3o. IF 30, then the coefficients are
-1, 30 and 6.
Step-by-step explanation:
Coefficients are numbers ahead of the variables (letters).
The number 4 is called a constant. A constant is not a coefficient.
The coefficient (number ahead of the letters) of -xyz is -1.
Hope this helps.
Marsha bought a new car for $21,152.25.
The options she picked cost $2,150. The
sales tax was $1,007.25. What was the base
price of Marsha's car?
Answer:
17,995
Step-by-step explanation:
21,152.25 - (2,150 + 1,007.25) = 17,995
Answer:
$17,995
Step-by-step explanation:
If you want to find the base, find out how much it costs without the options and the sales tax as they're just taxes and etc added to the car.
2,150 + 1,007.25 = 3157.25 (Total amount of taxes)
21,152.25 - 3157.25 = 17,995
Find a fraction equivalent to 5/2 that has a denominator of 10
Hey there!
Let’s leave number unknown.. so we label it as a “e” for equivalent
NEW EQUATION: 5/10 = e/10
FIRST: you have to CROSS MULTIPLY your given values
5 • 10 = e • 2
5 • 10 = 50
e • 2 = 2e
NEW EQUATION: 2e = 50
SECOND: DIVIDE BOTH of the SIDES by 2
2e/2 = 50/2
Cancel out: 2/2 because that gives you 1
Keep: 50/2 because it helps us solve for e
e = 50/2
= 50/2
= 25
Answer: e = 25 ✅
Overall answer for your given equation: 25/10 ☑️
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Answer:
Fraction is 25/10
Step-by-step explanation:
For questions like these you should simply multiply the numerator and denominator with the same number.
Like :- 5/2's equivalent fraction whose denominator is 10
Multiply the denominator of the first fraction i.e, 5/2 with such a number so that it's equivalent fraction's denominator results to 10. 2×x=10 thus, x=5Now we got our multiplying factor that is 5.Multiply the numerator of 5/2 with the multiplying factor i.e, 5(numerator)×5(multiplying factor)=25Thus, your equivalent fraction is 25/10
Hope this helps you.
Draw a model to show 3/4 of 16
If you can’t draw a model to show
You can explain it
Answer:
Answer Below
Step-by-step explanation:
3/4 of 16
Depends of what you want.
You can make a pie chart. So you have 4 sections and then you shade 3. Then you have the word 4 in each sector.
Answer:
Draw a box and split it into four pieces. Write 4 in each of those pieces. Put a "{" or "}" around 3 of them. Next to it write. 4 x 3 OR 4 + 4 + 4 = 12
Hope that helps!
Step-by-step explanation:
Can some body help me with this
Answer:
1 is 11
3 is 12
5 is the same answer as 3
Step-by-step explanation:
for #1 the angle is 90 degrees and its asking to find x you can set up the equation by sayin 46+4x=90 you substract 46 by 46 and subtract 90 by 46 then you will get 4x=44 dived 4 on each side and you will get x = 11
for #3 the angle is equal to 180 you set up the eqation by saying 36+12x=180 you subtract 36 by itself and 180 by 36 then you will get 144 now your equation is 12x = 144 now divide 12x by 12 and 144 by 12 and you will get x = 12
Please help! I need to finish this.
Please answer it thanks iwill give you a brainlist ❤️
Answer:
See Explanation
Step-by-step explanation:
We will make use of the following rules in solving these questions:
Inverse Variation: [tex]a\ \alpha\ \frac{1}{b}[/tex] ==> [tex]a = k/b[/tex]
Direct Variation: [tex]a\ \alpha\ b[/tex] => [tex]a = kb[/tex]
Direct, then inverse variation: [tex]a\ \alpha\ b\ \alpha\ \frac{1}{c}[/tex] ==> [tex]a= kb/c[/tex]
Joint Variation: [tex]a\ \alpha\ bc[/tex] ==> [tex]a= kbc[/tex]
The solution goes thus:
1. m varies directly to a
[tex]m\ \alpha\ a[/tex]
[tex]m =ka[/tex]
2. p varies inversely as q.
[tex]p\ \alpha\ \frac{1}{q}[/tex]
[tex]p\ = k\frac{1}{q}[/tex]
3. [tex]r\ varies[/tex] directly as s and inversely as t.
[tex]r\ \alpha\ s\ \alpha\ \frac{1}{t}[/tex]
[tex]r = k\frac{s}{t}[/tex]
4. z varies jointly as [tex]e\ and\ f.[/tex]
[tex]z\ \alpha \ ef[/tex]
[tex]z = kef[/tex]
5. F varies directly as the [tex]square\ of\ t.[/tex]
[tex]F\ \alpha\ t^2[/tex]
[tex]F = kt^2[/tex]
6. d varies jointly r and t
[tex]d\ \alpha\ rt[/tex]
[tex]d = krt[/tex]
7. P is inversely proportional to h.
[tex]P\ \alpha\ \frac{1}{h}[/tex]
[tex]P= \frac{k}{h}[/tex]
8. P varies directly as V
[tex]P\ \alpha\ V[/tex]
[tex]P=kV[/tex]
9. d varies directly as the square of t
[tex]d\ \alpha\ t^2[/tex]
[tex]d = kt^2[/tex]
10. s varies jointly as b and d and inversely as the square L
[tex]s\ \alpha\ bd\ \alpha\ \frac{1}{L^2}[/tex]
[tex]s = k\frac{bd}{L^2}[/tex]
5 ^ 3 + 1/2 ^ 2.
I need help.
Answer:
125.25
Step-by-step explanation:
5 cube =125
1/2=0.5
0.5 squared =0.25
125+0.25=125.25
Which angle is an x–intercept for the function y=cos(1/2x)? A. 0 B. pie/2 C. pie D. 2pie
Answer:
x intercept is 180
Step-by-step explanation:
Given
[tex]y = cos(\frac{1}{2}x)[/tex]
Required
Determine the x intercept
To do this, we simply set y to 0.
i.e. y = 0
Substitute 0 for y in [tex]y = cos(\frac{1}{2}x)[/tex]
[tex]0 = cos(\frac{1}{2}x)[/tex]
Take [tex]cos^{-1}[/tex] of both sides
[tex]cos^{-1}(0) = cos^{-1}(cos(\frac{1}{2}x))[/tex]
[tex]90 = \frac{1}{2}x[/tex]
Multiply both sides by 2
[tex]2 * 90 = \frac{1}{2}x * 2[/tex]
[tex]2 * 90 = x[/tex]
[tex]180 = x[/tex]
[tex]x = 180[/tex]
Hence, the x intercept is 180
Express 12/7 as a mixed number
Answer:
1 5/7
Step-by-step explanation:
Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
Answer:
[tex] \frac{12}{7} = 1 \frac{5}{7} [/tex]
Solomon is 3D printing chess pieces. The table gives the amount of time needed to print certain numbers of
pieces.
Pieces
Print time (minutes)
16
32
128
512
What does 16 mean in this situation?
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Solomon is 3D printing chess pieces. The table gives the amount of time needed to print certain numbers of
pieces.
Pieces
Print time (minutes)
16
32
128
512
What does 16 mean in this situation?
2
See answers
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Answer:
Holly molly
Can i plz have brainliest
Step-by-step explanation:
Answer:
DANDG MAN??????????? DANG*
Step-by-step explanation:
Given this circle puzzle what would angle 1-12 be? (Geometry)
I need help please I’m struggling
Answer:
19%
Step-by-step explanation:
What is the mean absolute deviation for 299, 281, 285, 269, 280, 269, 286, 287?
Answer:
the answer is 7
Step-by-step explanation:
The mean absolute deviation of the scores 299, 281, 285, 269, 280, 269, 286, 287 is, 7.5
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Now, We know that;
The mean absolute deviation (MAD) is a measure of the dispersion of a set of data. It is calculated as the average absolute difference between each data point and the mean of the set.
Hence, To find the MAD for the given scores, first find the mean of the scores:
= (299 + 281 + 285 + 269 + 280 + 269 + 286 + 287) / 8
= 280.5
Then, find the absolute difference between each score and the mean, and take the average of these differences:
= (|299 - 280.5| + |281 - 280.5| + |285 - 280.5| + |269 - 280.5| + |280 - 280.5| + |269 - 280.5| + |286 - 280.5| + |287 - 280.5|) / 8
= (18.5 + 0.5 + 4.5 + 11.5 + 0.5 + 11.5 + 5.5 + 6.5) / 8
= 7.5
So, the mean absolute deviation of the scores is 7.5.
To learn more about the mean absolute deviation, visit:
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I don't understand how to do this
Answer:
x = 86
Step-by-step explanation:
The top right and bottom left angles are part of the reflective property, in turn, the bottom left angle is also 94 degrees; to find the opposite relfective angle set, it would be, in this problem, the top left and bottom right angles; the two top angles make up 180 degrees, so it would be (180-94 = 86) 86 degrees for both the top left and the bottom right angles.
Hope this helps :)
The International Space Station orbits 350 km above Earth’s surface. Earth’s radius is about 6314 km. Use the Pythagorean Theorem to find the distance from the space station to Earth’s horizon. Round your answer to the nearest kilometer. (Diagram is not to scale.)
Answer:
2131 km
Step-by-step explanation:
The Pythagorean theroeom states that a^2+b^2=c^2. We know that Earth's radius is 6314, so we know one of the shorter sides, (a). side c, the hypotenuse, is 6314 km plus 350 km. Plug it into the equation and then solve for b.
6314^2+b^2=6664^2
b^2=4542327
sqaure root each side and you have your answer!
8. What is the mean absolute deviation for the data set below? 23, 15, 15, 7
Answer:
the answer is 15 ok buddy
W Explain how you know that 88 is a solution to the equation x = 11 by completing the sentence below. "88 is a solution to x = 11 because...'
Answer:
88 is a solution to 1/8 x = 11 because 1/8(88) = 11