Answer:
m=-32
Step-by-step explanation:
-2=m/16
-2×16=m
-32=m
m=-32
Answer:
m=-32
Step-by-step explanation:
-2×16=m
-32=m
m=-32
Let {u1,u2,u3} be an orthonormal basis for an inner product space V. If
v=au1+bu2+cu3
is so that ∥v∥=42, v is orthogonal to u3, and ⟨v,u2⟩=−42, find the possible values for a, b, and c.
• ||v|| = 42, which is to say
||v||² = 〈v, v 〉
… = 〈a u₁ + b u₂ + c u₃, a u₁ + b u₂ + c u₃〉
… = a ² 〈u₁, u₁〉 + b ² 〈u₂, u₂〉 + c ² 〈u₃, u₃〉 + 2(ab 〈u₁, u₂〉 + ac 〈u₁, u₃〉 + bc 〈u₂, u₃〉)
… = a ² ||u₁||² + b ² ||u₂||² + c ² ||u₃||²
[since each vector in the basis for V is orthogonal to any other vector in the basis, and 〈x, x〉 = ||x||² for any vector x ]
42² = a ² + b ² + c ²
[since each vector in the basis has unit length]
42 = √(a ² + b ² + c ²)
• v is orthogonal to u₃, so 〈v, u₃〉 = 0. Expanding v gives the relation
〈v, u₃〉 = 〈a u₁ + b u₂ + c u₃, u₃〉
… = a 〈u₁, u₃〉 + b 〈u₂, u₃〉 + c 〈u₃, u₃〉
… = c ||u₃||²
… = c
which gives c = 0, and so
42 = √(a ² + b ²)
• Lastly, 〈v, u₂〉 = -42, which means
〈v, u₂〉 = 〈a u₁ + b u₂ + c u₃, u₂〉
… = a 〈u₁, u₂〉 + b 〈u₂, u₂〉 + c 〈u₃, u₂〉
… = b ||u₂||²
… = b
so that b = -42. Then
42 = √(a ² + (-42)²) → a = 0
So we have a = 0, b = -42, and c = 0.
The required values are, [tex]a=0,b=-42 ,c=0[/tex]
Given,
[tex]v=au_1+bu_2+cu_3[/tex]
[tex]\left\| V\right\|=42[/tex]
Computation:
Since, [tex]v[/tex] is orthogonal to [tex]u_3[/tex] then we have,
[tex]\left<v,u_3 \right> =0\\\left< v,u_2\right> =-42[/tex]
Then,
[tex]\left\| V\right\|^2=\left<v,v \right>\\=\left<au_1+bu_2+cu_3,au_1+bu_2+cu_3 \right>\\=a_2\left\|u_1 \right\|^2+b_2\left\|u_2 \right\|^2+c_2\left\|u_3 \right\|^2\\=a^2+b^2+c^2\\=a^2+b^2+c^2=42^2[/tex]
As we know,
[tex]a=\left<v_1u_1 \right>\\b=\left< v_1u_2\right>= -42\\c=\left<v_1u_3 \right> =0[/tex]
[tex]a_2+b_2+c_2=42\\a=0[/tex]
Learn More:https://brainly.com/question/13152748
Joseph and Molly each have coin collections. Joseph starts with 15 coins in his collection and adds 25 coins each month. Molly starts with 25 coins in her collection and adds 25 coins each month. How many coins would Joseph have after 3 months?
Answer:
Joseph has 90 coins after 3 months
Step-by-step explanation:
Joseph: 25x + 15
Molly: 25x + 25
x = 3
Joseph: 25(3) + 15 = 90
HURRY! What is the circumference of the circle below? Use 3.14 for π.
Answer:
2.14 divided by 5 x 2 is the ansewer
Step-by-step explanation:
Algebraic Expression:
There are c cyclists in a cycle race. 3/4 of the cyclists finish the race. How many cyclists did not finish the race?
Heeeeeeeelp pleaaase
Answer:
13u√2u
Step-by-step explanation:
Remark
Removing factors from under the square root sign means factoring the numbers into prime factors. If there are an even number of equal prime factors, take one out and throw one away for all the primes that are the same. An odd number of factors always leaves 1 under the root sign.
For example
u^3 = u * u * u
One of the u's will be left behind. Of the two others, one will be discarded and one will be taken outside the root sign.
√u^3 = √(u * u * u) = u√u
one u taken out. 1 u left behind 1 u discarded.Question Breakdown
8√72u^3 = 8√2*2*2*3*3 u^3 = 8* 2*3 * u * √2u = 48u*√2u7√128u^3 = 7√(2*2*2*2*2*2*2 u^3) = 7*2*2*2 √2u = 56u√2u3u*√98u = 3u * √(7*7 * 2*u) = 21u√2uAnswer
48u√2u - 56√2u + 21u√2u
13u√2u
In the triangle below,
x = [ ? ] cm. Round to the
nearest tenth.
15 cm
х
350
9.00
y
Answer:
x=8.6
Step-by-step explanation:
x=8.6
Find x if these are similar
Answer:
C) 28
Step-by-step explanation:
RSTV = WXYZ
WX = x
[tex]\frac{RS}{VR} =\frac{WX}{ZW} \\\\\frac{7}{3} =\frac{x}{12} \\\\3x=84\\x=28[/tex]
This data shows the number of sit-ups done by 27 students in a gym class.
58 62 49 52 75 86 88 54 56 61 85 48 77 60
47 58 62 73 78 69 65 84 59 67 53 84 50
Which histogram represents the data?
Answer:
C
Step-by-step explanation:
None of the others have the correct data like C
In a clothing store, 65% of the customers buy a shirt, 30% of the customers buy a pair of pants, and 20% of the customers buy both a shirt and a pair of pants. I’m f a customer is chosen at random, what is the probability that he or she buys a shirt or a pair of pants?
Answer:
The Answer will be (0.75)
Aiden calculated that their family used 20% of their monthly income for food, and 15% of the money spent on food was spent on snacks. If they spent $45 on snacks, what is their monthly income?
Answer:
There monthly income is 300$
Find the third quartile Q3 of the list of 24 sorted values shown below.
30 31 31 37 38 38 39 39 42 42 43 46 47 48 50 52 54 57 61 63 68 69 76 79
The third quartile Q3 is
(Type an integer or a decimal.)
Answer:
60
Step-by-step explanation:
The computation of the third quartile is given below:
The third quartile Q3 is
= 3(n + 1)÷ 4
= 3 (24 + 1) ÷ 4
= 75 ÷ 4
= 18.75th term
Now the 18.75th term is
= 18th term + 0.75 term
= 57 + (19 term - 18term)
= 57 + 0.75 (61 - 57)
= 57 + 0.75 (4)
= 60
I need help please fast .................
Answer:
I have no idea what sohcahtoa is but:
tan 50.1° = x/5
1.196 = x/5
multiply both sides of the equation by 5:
x = 5.98
The table below is comparing level of education achieved to the rate of unemployment and the median weekly earnings in 2008. Based on the information provided, the unemployment rate decreases the most when moving between which two consecutive educational levels?
Answer:
"less than high school" and" high school graduate".
Answer:
The table below is comparing level of education achieved to the rate of unemployment and the median weekly earnings in 2008. Based on the information provided, the unemployment rate decreases the most when moving between which two consecutive educational levels?
a.
“Less than high school” and “High School Graduate” <<<<<<<CORRECT
b.
“High school graduate” and “Some college, no degree”
c.
“Associate degree” and “Bachelor’s degree”
d.
“Professional degree” and “Doctoral degree”
Step-by-step explanation:
Edge2021
what is the measure of A, in degrees, in the figure shown?
Answer:
[tex]12.7[/tex]
Step-by-step explanation:
[tex]180 - 167.3 = 12.7 \\ < angle \: on\: a \: stright \: line \: is \: 180[/tex]
What is the product of -8 and -7
Answer:56
Step-by-step explanation: -8x-7=56
Answer: -15
Step-by-step explanation: it will just give you a higher negative number it is literally the opposite from positive equations if u have to negative numbers u add them if there is a negative AND a positive then you substract them :)
The Table shows the relationship and speeds between a cheetah and a line. What is the missing value in the table?
Cheetah (miles per hour)
7 14 ? 28 35
Lion (miles per hour)
5 10 15 20 25
A. 19
B. 21
C. 23
D. 25
Please help ASAP!!
A random sample of 146 recent donations at a certain blood bank reveals that 81 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood
Answer:
We reject H₀ the actual percentage of type A donations differs from 40%
Step-by-step explanation:
Sample information:
sample size n = 146
Type A x₁ = 81 and p₁ = 81 / 146 p₁ = 0,5547
then q₁ = 1 - p₁ q₁ = 1 - 0,5547 q₁ = 0,4453
We choose as significance level α = 5% α = 0,05 α /2 = 0,025
from z-table we find z (c) = 1,96
National % of the population ( μ = 40 % μ = 0,4 )
Test hypothesis
Null hypothesis H₀ p₁ = μ
Alternative Hypothesis Hₐ p₁ ≠ μ
The Alternative hypothesis indicates that the test is a two-tail test
z(s) = ( p₁ - μ )/ √ p₁*q₁ / n
z(s) = ( 0,5547 - 0,40 )/ √ 0,5547*0,4453 / 146
z(s) = 0,1547 / 0,041
z(s) = 3,77
Comparing z(s) and z(c)
z(s) > z(c)
z(s) is in the rejection region. We reject H₀. Sample does not give evidence to support that the actual percentage of type A donations is equal to the national population
find the vertex h(r)=r^(2)+11r-26 PLEASE HELP ME FIGURE THIS OUT
Answer: Look at the picture
Step-by-step explanation: Hope this help :D
Janae solved the equation 3.67 = c − 2.13 , and found the value for c. Janae's solution was c =1.54 Do you agree or disagree with her solution. Explain. Show your work. plzzz help me ill give yo a brainlyiest
Answer:
Solution;
given equation : 3.67 = c - 2.13
On solving equation, we get
c = 3.67 +2.13
c = 5.8
Hence, Janae solution is incorrect. So I disagree.
Answer: No because the answer is c =5.8 or 5.80
Step-by-step explanation:
Add 2.13 to both sides. 3.67 + 2.13 = 5.80
Find the slope of the line (2,6) and (-2,-4)
help me please and answer correctly people answer wrong on purpose
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
6/13
Step-by-step explanation:
I pick a ball from a bag, replace it and then pick
another. I keep doing this until I have chosen 40 balls. If I picked out 12 yellow balls, estimate the probability of not picking out a yellow ball.
Answer:
It should be 50%
Step-by-step explanation:
It should be 50% because there are 12 yellow balls, so it should be 50%.
Hope it helps you
Solve (z + 6)2 = 5
{−6±5‾√}
{6±5‾√}
{5‾√±−6}
{−6+5‾√,6−5‾√}
9514 1404 393
Answer:
(a) -6±√5
Step-by-step explanation:
(z +6)^2 = 5 . . . . . given
z +6 = ±√5 . . . . . take the square root
z = -6 ±√5 . . . . . . subtract 6
Watch help
In APQR, PR is extended through point R to point S,
m_QRS = (4x – 15)°, m_RPQ = (x + 1), and
mZPQR = (x - 2)°. Find mZRPQ.
Answer:
m∠RPQ = 8°
Step-by-step explanation:
m∠QRS = 4x - 15
m∠RPQ = x + 1
m∠PQR = x - 2
m∠QRS is exterior angle and m∠RPQ and m∠PQr are opposite interior angles to m∠QRS
m∠QRS = m∠RPQ + m∠PQR {Exterior angle property of triangle}
4x - 15 = x +1 + x - 2
4x - 15 = x + x + 1-2 {Combine like terms}
4x - 15 = 2x - 1 {Subtract 2x from both sides}
4x - 2x - 15 = - 1
2x - 15 = - 1 {Add 15 to both sides}
2x = -1 + 15
2x = 14 {Divide both sides by 2}
x = 14/2
x = 7
m∠RPQ = x + 1 = 7 + 1 = 8°
Answer: x+1 =(7)+1=8
Step-by-step explanation:
Determine which point is part of the solution set to the following
system of inequalities: f(x) < x + 4; f(x) > - X-3; and f(x) < 5.
(0,0)
(-60)
(-3, 4)
(4,6)
sorry if its twisted but i need help in # 3 please :)
Answer:
knsy standard ka question hy
Step-by-step explanation:
Hey y’all answers in the picture ABC or D. Plz help
Answer:
D
Step-by-step explanation:
Lets use the the chart. The (5,9) if the 5 was doubled that it would equal to 10. Now you subract 1 from it making it 9.
Solve for x.
Enter the solutions from least to greatest.
(2x + 4)(3x − 2) = 0
lesser x =
greater x =
Answer:
lesser x = -2, greater x = 2/3
Step-by-step explanation:
(2x+4)= 0 ---> bring 4 to the other side
2x=-4 ----> divide by 2 on both sides
x= -4/2 = -2 ----> simplify
(3x-2)= 0 ----> bring the 2 to the other side
3x=2 ----> divide by three on both sides
x=2/3
hope this helps!
There are 920 calories in 5 servings. Find the unit rate.
Answer:
184
Step-by-step explanation:
920 divided by 5 is 184 which makes it unit rate