Answer:
Step-by-step explanation:
A 13 foot ladder is leaning against a wall. If the point where the ladder meets the wall is 12 feet above the ground, how far fr
om the base of the wall is the ladder
2 answers:
Answer:
The distance of the base of the wall to the ladder is 5 Feet .
Step-by-step explanation:
As given
A 13 foot ladder is leaning against a wall.
If the point where the ladder meets the wall is 12 feet above the ground.
As shown in the figure given below.
Now by using the pythagorean theorem
Hypotenuse² = Perpendicular² + Base²
AB² = AC² + BC²
As
AB = 13 foot
AC = 12 foot
Put in the above
13² = 12² + BC²
169 = 144 + BC²
BC² = 169 - 144
BC = 5 Feet
Therefore the distance of the base of the wall to the ladder is 5 Feet .
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Answer:
2.83 s
Step-by-step explanation:
We are given that
When a rock reached the ground then h(t)=0
Using quadratic formula
Time cannot be negative .Therefore, negative value of t can not be possible.
Hence, the rock takes 2.83 sec to reach the ground.
Answer:
a) ∝A ∈ W
so by subspace, W is subspace of 3 × 3 matrix
b) therefore Basis of W is
={
}
Step-by-step explanation:
Given the data in the question;
W = { A| Air Skew symmetric matrix}
= {A | A = -A^T }
A ; O⁻ = -O⁻^T O⁻ : Zero mstrix
O⁻ ∈ W
now let A, B ∈ W
A = -A^T B = -B^T
(A+B)^T = A^T + B^T
= -A - B
- ( A + B )
⇒ A + B = -( A + B)^T
∴ A + B ∈ W.
∝ ∈ | R
(∝.A)^T = ∝A^T
= ∝( -A)
= -( ∝A)
(∝A) = -( ∝A)^T
∴ ∝A ∈ W
so by subspace, W is subspace of 3 × 3 matrix
A ∈ W
A = -AT
A =
=
therefore Basis of W is
={
}
The ball will hit the ground at 0.125 seconds
<h3>Quadratic function</h3>The equation of the function is a quadratic function, and the function is given as:
When the ball hits the ground, the value of h is 0.
So, the equation of the function becomes
Subtract 2t from both sides of the equation
Divide both sides by -2t
Divide both sides by 8
Hence, the ball will hit the ground at 0.125 seconds
Read more about quadratic functions at:
Answer:
a) For Pawnee:
Range = 11, Mean = 3.13, Mean deviation = 2.44
For Chickpee:
Range = 7, Mean = 4.25, Mean deviation = 1.59
b) Pawnee Location has fewer lost days.
c) variation of the Chickpee is less than Pawnee location
Step-by-step explanation:
Data given:
For Pawnee:
3 1 0 0 2 11 5 3
Max = 11
Min = 0
Range = Max - Min
Range = 11-0 = 11
Range = 11
For Chickpee:
3 6 8 4 4 5 3 1
Max = 8
Min = 1
Range = Max - Min
Range = 8 - 1
Range = 7
For mean of Pawnee:
Mean = (3 + 1 + 0 + 0 + 2 + 11 + 5 + 3)/8
Mean = 25/8
Mean = 3.125
For mean deviation, we find the difference from the mean of each point.
Note: all the negative values will be taken as 0.
Differences from the mean of each point =
(3-3.13)=0.13, (1-3.31) = 2.13 ,
(0-3.13)=0, (0-3.13)=3.13,
(2-3.13)=1.13, (11-3.13)=7.87,
(5-3.13)=1.87, (3-3.13)=0.13
So, our differences are:
(0.13, 2.13, 0, 3.13, 1.13, 7.87, 1.87, 0.13 )
Mean deviation = Sum of all differences/8
Mean deviation = (0.13+2.13+3.13+3.13+ 1.13+ 7.87+ 1.87+ 0.13)/8
Mean deviation = 2.44
For mean of Chickpee:
Mean = (3+6+8+4+4+5+3+1)/8
Mean = 34/8
Mean = 4.25
Similarly, we need to find mean deviation for Chickpee, for that we need to find the differences first as done above for Pawnee.
Note: all the negative values will be taken as 0
Differences from the mean:
(3-4.25) = 1.25, (6-4.25) =1.75,
(8-4.25) = 3.75, (4-4.25)=0.25,
(4-4.25)=0.25, (5-4.25)= 0.75,
(3-4.25)=1.25, (1-4.25) =3.25
So, the differences are:
Differences = (1.25,1.75,3.75,0.25,0.25,0.75,1.25,3.25)
Mean deviation = (1.25+ 1.75+ 3.75+ 0.25+ 0.25+ 0.75+ 1.25+ 3.25)/8
Mean deviation = 1.59
b) which location has fewer lost days:
This can be found out by the total number of days of Pawnee and chickpee.
Pawnee = Sum of values = (3 + 1 + 0 + 0 + 2 + 11 + 5 + 3) = 25 days
Chickpee = Sum of values = (3+6+8+4+4+5+3+1) = 34 days
Hence, Pawnee Location has fewer lost days.
C) which location has less variation?
Formula for variation = ∑() - (
)
where x = values of the set.
For Pawnee:
=
= 9.8
Sum of square of all the data points of Pawnee = 169
Variation = 169/8 - 98 = 11.325
Similarly,
For Chickpee:
=
= 18.06
Sum of square of all the data points of Chickpee = 176
Variation = 176/8 - 18.06
Variation = 22-18.06
Variation = 4
Hence, variation of the Chickpee is less than Pawnee location