The u(1, 1, 2), v(2, 3, 1), and w(4, 5, 5) supplied vectors are linearly dependent.
What is a Vector?A vector is a quantity with both magnitude and direction in physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity. A vector lacks position, but has magnitude and direction. A vector is therefore unaffected by displacement parallel to itself as far as its length is unaltered.
As per the given information in the question,
The given vectors are:
u = (1, 1, 2)
v = (2, 3, 1) and,
w = (4, 5, 5)
If there are three scalars that are not all zero and that are dependent on a set of vectors (u, v, and w), they have been shown to be linearly dependent.
au + bv + cw = 0
⇒ a(1, 1, 2) + b(2, 3, 1) + c(4, 5, 5) = (0, 0, 0)
⇒ (a + 2b + 4c, a + 3b + 5c, 2a+ b + 5c) = (0, 0, 0)
So,
a + 2b + 4c = 0 (i)
a + 3b + 5c = 0 (ii)
2a+ b + 5c = 0 (iii)
From equation (i) and (ii)
b = -c
From equation (i)
a - 2c + 4c = 0
⇒ a = -2c
Let's assume that c = 1
So,
a = -2 and,
b = -1
Then, from the obtained values,
-2u - v + w = 0
As a result, there is a set of non-zero values for a, b, and c such that:
au + bv + cw = 0
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How do you find the derivative of 1/(1+x^2) ?
The answer is:
- 2x/(1+x^2)^2
4 Which trinomial is equivalent to
3(x-2)²-2(x-1)?
1) 3x²-2x-10
2)
3x² - 2x - 14
3)
3x² - 14x+10
4)
3x²-14x+14
Answer: 4) 3x²-14x+14
Explanation:
3(x-2)²-2(x-1)Use the binomial theorem (a−b)² = a² - 2ab + b² to expand (x-2)².
3(x²-4x+4)-2(x-1)Use the distributive property to multiply 3 by x²-4x+4.
3x²-12x+12-2(x-1)Use the distributive property to multiply −2 by x−1.
3x²-12x+12-2x+2Combine −12x and −2x to get −14x.
3x²−14x+12+2Add 12 and 2 to get 14.
3x²-14x+14It is 3x²+14x+14, the trinomial equivalent to 3(x-2)²-2(x-1). OPTION 4.
What is the derivative of a whole number, like 1?
The derivative of a whole number, like 1 is always zero as a whole number is constant.
In order to understand this answer, it is first necessary to realize that in calculus, a function's derivative is a formula that expresses the rate at which the function's value changes instantaneously in relation to x.
To get the derivative of a particular function, we can use specific rules like a whole number's derivative is always zero. To figure this out, we may apply the following calculus rule.
The derivative of f(x) is 0 if f(x) = a, where 'a' is any constant integer.
We can observe that the derivative of all constant functions is zero. This rule states that if f(x) = a, where 'a' is a whole number, then the derivative of f(x) equals 0, as 'a' whole number is a constant.
OR
We may infer from the graph below that for all values of x, the value of f(x) will stay constant (equal to 1). In light of the fact that f(x₂) = f(x₁), the derivative will be zero.
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You go shopping and buy a 10 lb. family pack of ground chuck for $23.47. There is a
manager's special coupon for $3.25 off your purchase. How much did you pay per lb?
Answer:You consume 14 pounds of turkey annually. At a discount store, the price of turkey is $0.99 less per pound than at a supermarket. How much would you save annually, in dollars, if you bought all of your turkey at the discount store?
Step-by-step explanation:
Identify the statistical test in which the mean difference between two groups are compared to a distribution of differences between means.
a. independent-samples t test
b. paired-samples t test
c. z test
d. single-sample t test
The statistical test in which the mean difference between two groups are compared to a distribution of differences between means is (b) paired-samples t-test.
The t-test, one of the most used statistical tests, is used to ascertain whether the means of two groups are equal. The test's underlying presumption is that samples from normal distributions with similar variances were used for both groups.
The two means are equal, which is the null hypothesis; otherwise, they are not. We can calculate a t-statistic that will follow a t-distribution with n1 + n2 - 2 degrees of freedom under the null hypothesis.
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Write the equation of a line that is perpendicular to y=-x-6y=−x−6y, equals, minus, x, minus, 6 and that passes through the point (-9,-4)(−9,−4)left parenthesis, minus, 9, comma, minus, 4, right parenthesis.
The equation of a line that is perpendicular to the points will be equal to y = 1(x + 9) - 4.
What is the slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the given information in the question,
Supplied that the given line has a slope of 1, the perpendicular line will also have a slope of 1.
Then, the equation of the line which is perpendicular is written as,
y = 1 (x + 9) - 4
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at a baseball game the batter hits a ground ball for a base hit and runs to first base. true or false: the batter's distance from the first base bag is a function of time. true or false
The given statement that 'the batter's distance from the first base bag is a function of time.' is false.
If we need to call any quantity a function of any other quantity, we need to know what it means first. For this, we take the example of velocity. If we say that velocity is a function of time, what we mean is that the function is such that we input time and get velocity as the output. That quantity changes as the input increases or decreases.
We can deem distance as a function of time when it changes with respect to it. Here, it is evident that the distance between the batter and the first base is not going to change. Thus, it is not a function of time and the given statement is false.
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It’s number 2 pls help
Answer: -72·a^8·b^9
Step-by-step explanation:
(-8·a^6·b³)(9·a²·b^6)
combine all the like terms:
-72·a^8·b^9
Find the equation for a polynomial f(x) that satisfies the following:
Degree 3
Zero at x=−1
Zero at x=−4
Zero at x=−1
y-intercept of (0,8)
f(x)=
The polynomial with the given degree and zeros is:
y = 2*(x + 1)²*(x + 4)
How to find the equation of the polynomial?A polynomial of degree N with the zeros {x₁, x₂, ...} and a leading coefficient a can be written as:
y = a*(x - x₁)*(x - x₂)*...*(x - xₙ)
Here we know that the degree is 3, and the zeros are {-1, -4, -1}
Then we can write the polynomial as:
y = a*(x + 1)*(x + 4)*(x + 1)
y = a*(x + 1)²*(x + 4)
We also know that the polynomial passes through (0, 8), replacing these values we will get:
8 = a*(0 + 1)²^*(0 + 4)
8 = a*1*4
8/4 = a
2 = a
The polynomial is:
y = 2*(x + 1)²*(x + 4)
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the sum of the age of father and son at present iz 45 year.if both live on until the son age become equal to the father present age the sum of their agr then become 95 years .find the present ages.
Answer:
10 yrs old and 35 yrs old
Step-by-step explanation:
I figured it out by trial and error but here's the thinking process.
10 + 35= 45
Son becomes dad's age so 35-10=25, so plus 25 year to each age.
10+25=35
35+25= 60
35+60=95
I hope that makes enough sense!
Find the derivative of the function at P0 in the direction of A.
f(x,y,z)=xy+yz+zx, (1-,1,-2)
A= 3i+2j-6k
The derivative of the function at P0 in the direction of A is,
([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3 , ([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1 , ([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0
Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.
Given that,
The derivative of the function at P0 in the direction of A.
f(x, y, z) =
f(x, y, z) = (1,-1,-2)
x = 1
y = -1
z = -2
Derivative of f(x, y, z) = xy + yz + zx
[tex]\frac{df}{dx}[/tex] = y + z
[tex]\frac{df}{dy}[/tex] = x + z
[tex]\frac{df}{dz}[/tex] = x + y
We can substitute f(x, y, z) = (1,-1,-2) values,
([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = y + z
([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -1 + (-2)
([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3
([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = x + z
([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = 1 + (-2)
([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = 1-2
([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1
([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = x + y
([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 1 + (-1)
([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 1-1
([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0
Therefore,
The derivative of the function at P0 in the direction of A is,
([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3 , ([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1 , ([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0
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How do you find the sum of the arithmetic series 1 + 3 + 5 + ... + 27?
Answer:
sum = 196
Step-by-step explanation:
the sum to n terms of an arithmetic series, when the first and last terms are known is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first term + last term)
we require to find the number of terms in the series
the nth term of an arithmetic series is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = a₂ - a₁ = 3 - 1 = 2 , then
1 + 2(n - 1) = 27 ( subtract 1 from both sides )
2(n - 1) = 26 ( divide both sides by 2 )
n - 1 = 13 ( add 1 to both sides )
n = 14 ← number of terms in the series
Then
S₁₄ = [tex]\frac{14}{2}[/tex] (1 + 27) = 7 × 28 = 196
one apple and six bananas cost £2.70
one apple and eight bananas cost £3.50
Work out the cost of an apple and a banana
PLSSS HELP TYSM
Answer:
An apple costs 0.30 pounds and a banana costs 0.40 pounds.
Step-by-step explanation:
Let's think of apples as x and bananas as y.
Using the given information, you can write two equations.
[tex]x+6y=2.70[/tex]
[tex]x+8y=3.50[/tex]
x can also be written as
[tex]x=2.70-6y[/tex]
We can plug this equation into the second one to solve for y, or the cost of a banana.
[tex](2.70-6y)+8y=3.50[/tex]
[tex]2y=0.8[/tex]
[tex]y=0.4[/tex]
Now that we know the cost of a banana, we can go back to the first equation and solve for x, or the cost of an apple.
[tex]x+6(0.4)=2.70[/tex]
[tex]x=0.30[/tex]
Therefore, an apple costs 0.30 pounds and a banana costs 0.40 pounds.
Find AB in simplest form, if A(-3, 4) and B(4, 7).
Answer: AB≈7.62 units
Step-by-step explanation:
A(-3,4) B(4,7)
[tex]\boxed {L=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }\\\\x_1=-3\ \ \ \ x_2=4\ \ \ \ y_1=4\ \ \ \ y_2=7[/tex]
Hence,
[tex]AB=\sqrt{(4-(-3))^2+(7-4)^2} \\\\AB=\sqrt{(4+3)^2+3^2} \\\\AB=\sqrt{7^2+9} \\\\AB=\sqrt{49+9} \\\\AB=\sqrt{58} \\\\AB\approx7.62\ units[/tex]
What i your average peed in mile per hour and in feet per econd if you travel a mile in 11 minute?
The average speed in mile per hour is 5.455 miles per hour .
In the question ,
it is given that ,
the 1 mile distance is covered in 11 minutes ,
So , in 1 minute the distance covered is = 1/11 miles
So , the speed in miles per minute is 1/11 miles per minute .
To convert speed in miles per minute to miles per hour ,
we multiply it by 60 ,
So , we get ,
Average Speed in miles per hour is = 60 * (1/11)
= 60/11
= 5.45454
≈ 5.455
Therefore , the average speed is 5.455 miles per hour .
The given question is incomplete , the complete question is
What is your average speed in mile per hour and in feet per second if you travel a mile in 11 minute ?
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Traci mixed nuts and raisins together in bags to make a trail mix. She
had a total of 6 cups of nuts and 8 cups of raisins. She placed 1/3 cup
of nuts in each bag, and 1/4 cup of raisins in each bag. Traci wanted
each bag to have a mixture of nuts and raisins. After Traci uses all
the nuts she has, how many more bags need nuts added?
Answer:
A) 14
Step-by-step explanation:
Nuts:
[tex]\frac{6}{\frac{1}{3} }[/tex] = [tex]\frac{6}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex] Get a common denominator of 3 and divide
[tex]\frac{18}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex] = [tex]\frac{\frac{18}{1} }{\frac{3}{3} }[/tex] = [tex]\frac{18}{1}[/tex] = 18
We can make 18 bags with the amount of nuts given.
Raisins:
[tex]\frac{8}{\frac{1}{4} }[/tex] = 8 ÷[tex]\frac{1}{4}[/tex] Gert a common denominator of 4 and divide
[tex]\frac{32}{4}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{\frac{32}{1} }{\frac{4}{4} }[/tex] = [tex]\frac{32}{1}[/tex] = 32
We can make 32 bags with the amount of raisins given.
32 - 18 = 14
14 more bags need nuts agged.
Draw a diagram and solve
Answer:
2378 m
Step-by-step explanation:
You want the ground distance from the takeoff point to an airplane that has flown 2500 m in the air at a takeoff angle of 18°.
CosineThe cosine relation tells you ...
Cos = Adjacent/Hypotenuse
Adjacent = Hypotenuse · Cos
ApplicationHere, the hypotenuse of the right triangle model is 2500 m, the angle is 18°, and we want to find the side of the triangle adjacent to the angle:
AD = AP·cos(18°) = 2500·0.9510565 ≈ 2377.64 ≈ 2378 . . . . meters
The ground distance is about 2378 m.
a circle has a radius of 9 in . find the length of the arc intercepted by a central angle of 1.1 radians. do not round any intermediate computations, and round your answer to the nearest tenth.
Central angle intercepted by arc is 0.7 radian
What is length of arc intercepted by central angle ?
The length l of the arc intercepted on a circle of radius r by a central angle of measure θ radians is given by: l = r θ where θ is in radians.
In a circle of radius 1, the measure of a central angle in radians will be equal to the length of the intercepted arc.
Arc length is l=r⋅θ; l=9, r=13, θ=?;
l. r, θ are arc length , radius of circle and central angle intercepted by arc .
∴9 = 13⋅θ
∴θ = 9/13 ≈ 0.7(1dp) radian
Central angle intercepted by arc is 0.7(1dp) radian
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Kenneth drove 187.6 miles in 1.85 hours. What was his average speed?
Help me solve it please
((2*2)²)²
Answer:
256
Step-by-step explanation:
((2*2)²)²
(((4)²)²)
(16)²
256
A factory used 2/3 of a barrel of almonds to make 4 batches of granola bars. How many
barrels of almonds did the factory put in each batch?
Answer:1/6 barrels=1 batch
Step-by-step explanation:
4/.666666666666666=6 batch's came from one barrel
6 batch's came from one barrel
1/6= 1 batch
The distance between (2, 3) and (1, 7) is:
117.
1.
16.
17.
Answer:
Sqrt of 4²+ (-1)² = Sqrt. of 17
Step-by-step explanation:
2 points in a coordinate grid create a right-angled triangle.
the distance is the Hypotenuse (the side opposite of the 90° angle). and the x coordinate and y coordinate differences are the legs.
and with that we use Pythagoras
c² = a² + b²
with c being the Hypotenuse, and a and b being the legs.
so, in our case :
distance² = (1 - 2)² + (7 - 3)² = (-1)² + 4² = 1 + 16 = 17
distance = sqrt(17)
a random sample of 150 u.s. adults is composed of 100 people from non-rural areas and 50 people from rural areas. estimate the confidence interval for the fraction of the population that is non-rural with 99% confidence. what is the lower limit of the confidence interval?
With 99% confidence, we can estimate that the fraction of the population that is non-rural is between 0.60 and 0.74.
To estimate the confidence interval for the fraction of the population that is non-rural with 99% confidence, we need to use the following formula:
Point estimate +/- (critical value * standard error)
Where the point estimate is the sample proportion of non-rural adults (100/150 = 0.67), the critical value is the z-score corresponding to a confidence level of 99% (2.575), and the standard error is the standard deviation of the sampling distribution of the sample proportion (which is equal to the square root of [(sample proportion * (1 - sample proportion)) / sample size]).
Plugging in the values, we get:
0.67 +/- (2.575 * sqrt[(0.67 * (1 - 0.67)) / 150])
Solving this equation gives us a lower limit of 0.60 for the confidence interval.
Thus, with 99% confidence, we can estimate that the fraction of the population that is non-rural is between 0.60 and 0.74.
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Please respond quick!!!
I think that for a its 1.12 and for b its 39424
100 + 12 = 112
112/100 = 1.12
35200 * 1.12 = 39424
The line plot shows the long jump distances of seven students at track practice. What is the combined length, in feet, of the three shortest jumps?
what is the answer
The combined length for three shortest jumps is 43 feet. We can find out by analyzing the graph and its entities.
What are graph and entities ?
A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Entity is any data or any existing object .
From the graph:
14*1/4 feet = by 2 students
14*1/2 feet = by 3 students
14*3/4 feet = by 1 student
15 feet = by 1 student
So the three shortest jumps are 14*1/4 , 14*1/4 , 14*1/2.
Total distance = 57/4 + 57/4 + 58/4
= 43 feet.
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the difference between a number and three fifths is a minimum of negative four sevenths
The inequality that represents the given statement is (C) f - 3 / 5 ≥ -4/7 or f plus 3 over 5 is greater than negative 4 over 7.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
The equation-like form of the formula 5x − 4 > 2x + 3 has an arrowhead in place of the equals sign.
It is an illustration of inequity.
This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.
Finding the x numbers for which the inequality holds true is what we are most interested in.
So, the answer to the query is:
A number's deviation from three-fifths is equal to f - 3/5.
The entire statement is at least four sevenths in the negative.
Therefore, the inequality that represents the given statement is (C) f - 3 / 5 ≥ -4/7 or f plus 3 over 5 is greater than negative 4 over 7.
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Complete question;
Write the inequality for the statement:
the difference between a number and three-fifths is a minimum of negative four sevenths
f minus 3 over 5 is greater than or equal to 4 over 7
f minus 3 over 5 is greater than or equal to negative 4 over 7
f plus 3 over 5 is greater than negative 4 over 7
f minus 3 over 5 is less than or equal to negative 4 over 7
The equation y = 20x + 500 models the relationship between the number of video games, x, a company manufactures and the cost in dollars, y, to manufacture that number.
A recipe for one batch of cookies calls for 3 cups of sugar and 2 tablespoons of salt.
How many sugar would you need for 8 batches of cookies?
Answer: 24 cups of sugar
Step-by-step explanation: you multiple the orginal amount neede for one batch by 8
8*3=24
Carlos earns 44.55 in 9 hours. Maggie earns 51 in 12 hours
By taking some products, we can see that if both of them work for 20 hours each, they will earn a total of 184 dollars.
How much do Carlos and Maggie earn if they work for 20 hours?After a small search online I found that we want to find how much will they earn (together) if both of them work for 20 hours.
We know that Carlos earns $44.55 in 9 hours, then the amount that he wins per hour is:
C = $44.55/9h
In 20 hours he will earn 20 times that, so the amount that Carlos earns in 20 hours is given by the product:
Carlos = 20h*($44.55/9h )
Similarly, Maggie earns per hour:
M = ($51/12h)
And in 20 hours, she will win:
Maggie = 20h*($51/12h)
The total amount that they earn together is:
20h*($44.55/9h ) + 20h*($51/12h) = $184.
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A spring is attatched at one end to support B and at the other end to collar A, as represented in the figure. Collar A slides along the vertical bar between points C and D.
Part A when 0 = 28 degrees, what is the distance from point A to point B to the nearest tenth of a foot?
Part B When the spring is stretched and the distanced from point A to point B is 5.2 feet, what is the valuue of 0 to the nearest tenth of a degree?
The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°
According to the question,
A spring is attached at one end to support B and at the other end to collar A.
Part A: Given that : Reference angle (θ) = 28°
We have to find out the distance of point A to point B.
Adjacent = 3 ft (given)
To find AB, apply the trigonometry function which is:
cos θ = adj / hypotenuse
Substituting all the values ,
=> cos 28°= 3/AB
=> AB = 3/cos 28°
=> AB = 3.4 ft (nearest tenth of a foot)
Part B:
It is given that Distance from point A to point B is 5.2 feet
We have to calculate the Value of θ
adj = 3 ft
hypotenuse = AB = 5.2 ft
To find θ , We will again apply the trigonometry function
cos θ = adj/hypotenuse
Substituting all the given values
=> cos θ = 3/5.2
=> θ = cos⁻¹ ( 3 / 5.2)
=> θ = 54.8°
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