(a) Both conditions are satisfied with x = (1, 0) for [tex]\mathbb R^2[/tex] and x = (1, 0, 0) for [tex]\mathbb R^3[/tex]:
||(1, 0)|| = √(1² + 0²) = 1
max{1, 0} = 1
||(1, 0, 0)|| = √(1² + 0² + 0²) = 1
max{1, 0, 0} = 1
(b) This is the well-known triangle inequality. Equality holds if one of x or y is the zero vector, or if x = y. For example, in [tex]\mathbb R^2[/tex], take x = (0, 0) and y = (1, 1). Then
||x + y|| = ||(0, 0) + (1, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2
||x|| + ||y|| = ||(0, 0)|| + ||(1, 1)|| = √(0² + 0²) + √(1² + 1²) = √2
The left side is strictly smaller if both vectors are non-zero and not equal. For example, if x = (1, 0) and y = (0, 1), then
||x + y|| = ||(1, 0) + (0, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2
||x|| + ||y|| = ||(1, 0)|| + ||(0, 1)|| = √(1² + 0²) + √(0² + 1²) = 2
and of course √2 < 2.
Similarly, in [tex]\mathbb R^3[/tex] you can use x = (0, 0, 0) and y = (1, 1, 1) for the equality, and x = (1, 0, 0) and y = (0, 1, 0) for the inequality.
(c) Recall the dot product identity,
x • y = ||x|| ||y|| cos(θ),
where θ is the angle between the vectors x and y. Both sides are scalar, so taking the norm gives
||x • y|| = ||(||x|| ||y|| cos(θ)|| = ||x|| ||y|| |cos(θ)|
Suppose x = (0, 0) and y = (1, 1). Then
||x • y|| = |(0, 0) • (1, 1)| = 0
||x|| • ||y|| = ||(0, 0)|| • ||(1, 1)|| = 0 • √2 = 0
For the inequality, recall that cos(θ) is bounded between -1 and 1, so 0 ≤ |cos(θ)| ≤ 1, with |cos(θ)| = 0 if x and y are perpendicular to one another, and |cos(θ)| = 1 if x and y are (anti-)parallel. You get everything in between for any acute angle θ. So take x = (1, 0) and y = (1, 1). Then
||x • y|| = |(1, 0) • (1, 1)| = |1| = 1
||x|| • ||y|| = ||(1, 0)|| • ||(1, 1)|| = 1 • √2 = √2
In [tex]\mathbb R^3[/tex], you can use the vectors x = (1, 0, 0) and y = (1, 1, 1).
Two of the desserts are sugar free
Three of the drinks are sugar free
Answer: 8/15
Step-by-step explanation:
You need part a of the question to answer this question correctly. In part a of the question it is said there is 6 sandwiches, 3 desserts and 5 drinks.
Two of the desserts are sugar free (2/3).
Four of the drinks are sugar free (4/5)
Times these fractions together, 2/3x4/5= 8/15.
Hope this helps :)
I dont know how to do this please help me
problem 17=A
problem 4= C
problem 9= B
problem 11= C
problem 14= D
My mom is making me do prayice and i need the answer for this thanks very much
The ratio of cars to people is 1 to 4 1/2
write as a reduced fraction
Answer:
[tex]1 : 4\frac{1}{2} \\ = 1 : \frac{9}{2} \\ = \frac{1}{ \frac{9}{2} } \\ = \frac{2}{9} [/tex]
What is the value of x?
Answer:
I believe it’s 20
Step-by-step explanation:
Mary wants to fill a cylindrical cup with water. The dimensions of the cup are labeled below.
Radius: 6cm
Height: 15cm
How much water can Mary put in the cup without it overflowing?
A. 1,620
B. 540
C. 270
D. 180
Step-by-step explanation:
Volume of cylinder: πr²h
= π(6)² x 15
= 36π x 15
= 1620 cm³
Answer: A
Answer:
B. 540 picm3
Step-by-step explanation:
(6)2 X 15= 540
The four sides of Pam's vegetable garden are
26 3/4 feet,
24 1/2 feet,
23 1/2 feet, and
18 1/4 feet. How many feet of fencing are needed to go around the garden? First estimate the answer, then solve to find the exact answer.
Answer:
The perimeter of the garden would be 93 feet, meaning you would need 93 feet of fencing.
Step-by-step explanation:
To find the perimeter of a shape you first need to know how long each side of the shape is and then add those sides together, once you have that number, you have your perimeter. I hope this helps.
Answer to the question
Answer:
Step-by-step explanation:
In a parallelogram,
i) opposite sides are equal and parallel.
So, DC = AB
DC = 28 units
ii) Diagonals bisect each other.
AC bisects BD
DE = EB = [tex]\frac{1}{2}[/tex] BD
DE = [tex]\frac{1}{2}*91[/tex] = 45.5
DE = 45.5 units
(b) A telemarketing supervisor tells a new worker that the odds of making a sale on a single call are 4 to 19. What is the probability of a successful call
Answer:
0.1739 = 17.39% probability of a successful call.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The odds of making a sale on a single call are 4 to 19.
This means that in 4 + 19 = 23 calls, 4 are successful.
What is the probability of a successful call?
[tex]p = \frac{4}{23} = 0.1739[/tex]
0.1739 = 17.39% probability of a successful call.
The ratio of three angles of a triangle is 1:2:3. Find the measurement of the angles
Answer:
all the angles add up to 180 degrees
So 180÷6=30
(i got 6 cuz 1+2+3)
so 1=30
2=30*2=60
3=30*3=90
If the height of the pyramid were increased to 512 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase
Complete question:
The base of a pyramid covers an area of 14.0 acres (1 acre = 43, 560 ft² ) and has a height of 481 ft. If the volume of a pyramid is given by the expression V = bh/3, where b is the area of the base and h is the height. If the height of the pyramid were increased to 512 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase
Answer:
The percentage increase of the volume is 6.45 %
Step-by-step explanation:
The volume of pyramid is calculated as;
V = bh/3
The initial volume of the pyramid is calculated as follows;
[tex]V = \frac{bh}{3} \\\\V_0 = (\frac{1}{3} ) \times (14 \ acres \ \times \frac{43,560 \ ft^2}{1 \ acre} ) \times (481 \ ft)\\\\V_0 = 97,777,680 \ ft^3[/tex]
The final volume of the pyramid when the height is increased to 512 ft.
[tex]V_1 = (\frac{1}{3} ) \times (14 \ acres \ \times \frac{43,560 \ ft^2}{1 \ acre} ) \times (512 \ ft)\\\\V_1 = 104,079,360 \ ft^3[/tex]
The percentage increase of the volume;
[tex]= \frac{104,079,360 - 97,777,680}{97,777,680} \times 100\%\\\\= 6.45 \ \%[/tex]
The volume of the pyramid will increase by 11.79%
The volume of a Pyramid is calculated using:
[tex]V = \frac{Bh}3[/tex]
Where:
B represents the base areah represents the heightWhen the height is increased from 458 to 512, then the initial and the final volumes are:
[tex]V_1 = \frac{458}{3}b[/tex]
[tex]V_2 = \frac{512}{3}b[/tex]
The percentage change is then calculated as:
[tex]\% Change = \frac{V_2 -V_1}{V_1} \times 100\%[/tex]
This gives
[tex]\% Change = \frac{512b/3 -458b/3}{458b/3} \times 100\%[/tex]
Simplify the numerator
[tex]\% Change = \frac{54b/3}{458b/3} \times 100\%[/tex]
Evaluate the quotient
[tex]\% Change = 0.1179 \times 100\%[/tex]
Express as percentage
[tex]\% Change = 11.79 \%[/tex]
Hence, the volume of the pyramid will increase by 11.79%
Read more about volumes at:
https://brainly.com/question/1972490
Point M is located at (3,-2) on the coordinate plane. Point M is reflected over the
x-axis to create point M'. What ordered pair describes the location of M'?
The answer would be (3,2) because you would do (x,-y)
In which number does the digit 5 have a value that is ten times greater than the value of the digit 5 in the number 245,093?
43,567
45,248
53,901
562,011
Answer:
53,901
Step-by-step explanation:
The value given is: 245,093.
5 is in the thousands place. Multiply the thousands place with ten:
1,000 x 10 = 10,000
This means that the number with 5 in the ten thousands place will be your answer.
53,901 is your answer.
~
5. The Colorado state flag consists of three horizontal stripes of equal height. The side lengths of the flag are in the ratio 2 : 3. The diameter of the gold-colored disk is equal to the height of the center stripe. What percentage of the flag is gold?
Answer:
the diameter of the circle is ⅓ of the height
so the radius is 1/6 of the height
the area of the flag is 1*1.5 of the height
(we need to consider this)
pi*(1/6)² / 1.5
= 0.058177
so the percentage is
5.82 %
So, the required percentage is [tex]5.81\%[/tex].
To understand the calculations, check below.
Area of the disk:The area of the disk is defined as the ‘ measure of surface ‘ surrounded by the round edge (circumference) of the disk. The area of a disk can be derived by breaking it into a number of identical parts of disk as units — calculating their areas and summing them up till the disk is reformed.
That is [tex]Area=\pi \frac{d^2}{4}[/tex]
Let the width and the length of the flag be [tex]2x[/tex] and [tex]3x[/tex] respectively.
So, the diameter of the gold-colored disk will be [tex]\frac{2x}{3}[/tex]
Now, by using the above formula the area of the gold disk will be,
[tex]\pi \frac{d^2}{4}=\pi\times\frac{4x^2}{4\times 9} \\ =\frac{\pi x^2}{9}[/tex]
And the area of the flag will be,
[tex]Area=l\times b\\=2x\times 3x\\=6x ^2[/tex]
So, the required percentage is,
[tex]\frac{(\frac{\pi x^2}{9} )}{6x^2} \times 100=\frac{\pi}{54}\times 100\\ =5.81\%[/tex]
Learn more about the topic Area of the disk:
https://brainly.com/question/21881629
3
Solve for x.
X =
8
20
35
Answer:
x=00
Step-by-step explanation:l
nnm
835×79 with formula and all
Find the value of 'x
Answer:
x = 16
Step-by-step explanation:
The sum of the angles of a triangle are 180
128+ 2x-3 +23 = 180
Combine like terms
2x+148=180
Subtract 148 from each side
2x+148 -148 = 180-148
2x = 32
Divide by 2
2x/2 = 32/2
x =16
Solve for a r=x(a+b)
Solve for x x/2=-7
Answer:
a = (r/x) -b
x = -14
Step-by-step explanation:
r=x(a+b)
Divide each side by x
r/x = a+b
Subtract b
r/x -b = a
x/2=-7
Multiply each side by 2
x/2*2 = -7*2
x = -14
Answer:
1.) a = r / x - b
2.) x = - 14
Step-by-step explanation:
1.) r = x ( a + b )
r / x = x / x ( a + b) ...( Divide each side by x )
r / x = a + b
r / x - b = a + b - b ... ( Subtracting each side by b) r / x - b = a
2.) x / 2 = -7
x / 2 × 2 = -7 × 2 .. ( multiplying each side by 2 )
x = - 14
Can someone help me please
Answer:
C
Step-by-step explanation:
All others can be proved false.
What is the value of xin the diagram below? If necessary, round your answer
to the nearest tenth of a unit.
14
B
х
D
с
30
A. 6.5
B. 16
C. 14
D. 30.1
Answer:
the answer is letter A. 6.5
Step-by-step explanation:
it's correct if I'm rwong ( ╹▽╹ )
Each Friday, the sixth grade students in Mr. Shin's physical education class spend the first five minutes doing crunches. Instead of keeping track of the weekly total number of crunches, Mr. Shin keeps track of how they do compared to the week before, and then records the result as a positive or negative number. Record the number for each of the following:
Ben did 10 more crunches this week than last week. What number would Mr. Shin record?
Gail did 8 less crunches this week than last week. What number would Mr. Shin record?
Nathaniel did the same number of crunches this week as last week. What number would Mr. Shin record?
Answer:
I guess it would go
Ben did:+10
Gail:-8
Nathaniel:0
Step-by-step explanation:
hope this was what you wanted
best of luck
PLEASE HELP ME WITH THIS
9514 1404 393
Answer:
3. $0.45
4. 50%
5. -5°, -1°, 1°, -2°, 5°
Step-by-step explanation:
3. The difference in tip amounts is ...
15%($25) -15%($22) = 15%($25 -22) = 15%($3.00) = $0.45
Jasmine paid $0.45 more tip than Candice.
__
4. If 25% were sick, then the crew that showed up was 75% of the full crew. If 1/3 of those 75% went home early, then the remaining (2/3)(75%) = 50% were the fraction working at the end of the day.
__
5. The Fridays in January were Jan 2, 9, 16, 23, and 30. The middle of the month was the 16th. For something like this, it can help to read through a couple of times, as the relations are not given in a way that gives a solution without skipping around.
We are given that the temp on the 30th was 5°, and that the 23rd was 7° less, so -2°. The low on the 2nd was 3° lower than on the 23rd, so was -5°. The temp on the 16th was 6° higher than on the 2nd, so was -5+6 = 1°, and the temp on the 9th was 2° lower than that, so -1°.
The low temperatures were ...
2nd: -5°9th: -1°16th: 1°23rd: -2°30th: 5°Please help me pleasee quick !
Answer:
a 4,1. helpful answer
What does 32.689 x 10³ =???
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{32.689\times 10^3}[/tex]
[tex]\mathsf{10^3}[/tex]
[tex]\mathsf{= 10\times10 \times10}[/tex]
[tex]\mathsf{= 100\times10}[/tex]
[tex]\boxed{\mathsf{= \bf 1,000}}[/tex]
[tex]\mathsf{32.689 \times1,000}[/tex]
[tex]\boxed{\mathsf{= \bf 32, 689}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf 32, 689}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A box with a square base and open top must have a volume of 171500 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x .] Simplify your formula as much as possible.
Answer:
The dimensions of the box that minimize the amount of material used is length of square base x = 70 cm and height of box = 35 cm
Step-by-step explanation:
The volume of the box with square base is V = x²h where x = length of side of square base and h = height of box.
Now, the area of the of box open at the top with dimensions of length, l , width, w and height, h are
A = 2lh + lw + 2wh
Now for a box of square base, l = w = x.
So, A = 2xh + x² + 2xh
A = x² + 4xh
Since V = x²h and V = 171500 cm³,
h = V/x² = 171500/x²
substituting h into A, we have
A = x² + 4xh
A = x² + 4x(171500 cm³/x²)
A = x² + 4 × 171500 cm³/x
A = x² + 686000 cm³/x
To find the value of x that minimizes A, we differentiate A with respect to x
So, dA/dx = d[x² + 686000 cm³/x]/dx
dA/dx = 2x - 686000 cm³/x²
equating this to zero, we have
2x - 686000 cm³/x² = 0
2x = 686000 cm³/x²
2x³ = 686000
x³ = 686000 cm³/2
x = ∛(343000 cm³)
x = 70 cm
To determine if this in a minimum dimension for A, we differentiate dA/dx and insert x = 70 cm
So, d²A/dx² = d[2x - 686000 cm³/x²]/dx
d²A/dx² = 2 + 3 × 686000 cm³/x³
d²A/dx² = 2 + 2058000 cm³/x³
with x = 70 cm, we have
d²A/dx² = 2 + 2058000 cm³/(70 cm)³
d²A/dx² = 2 + 2058000 cm³/343000 cm³
d²A/dx² = 2 + 6
d²A/dx² = 8 > 0
So, x = 70 is a minimum value for the dimension
Since h = 171500 cm³/x²
h = 171500 cm³/(70 cm)²
h = 171500 cm³/4900 cm²
h = 35 cm
So, the dimensions of the box that minimize the amount of material used is length of square base x = 70 cm and height of box = 35 cm
Find the volume of the triangular prism.
Answer:
33.55 m³
Step-by-step explanation:
volume is base area times height.
the base area is a right-angled triangle (a×b/2).
At = 2.5×4.4/2
the height is 6.1
the total volume is then
2.5×4.4×6.1/2 = 33.55 m³
Slope and equation, how much battery does she lose an hour
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answer:
656.3844
Step-by-step explanation:
Area of squares = [tex]s^{2}[/tex]
s = measure of a side, all sides are the same.
[tex]25.62^{2}[/tex] use a calculator
Please help me no links!!
Answer:
Step-by-step explanation:
The line is parallel to y axis so
slope : undefined
y intercept : the line doesn’t intercept y axis
Equation : x = -6
if 2lbs of fertilizer will cover 252 square feet of lawn how many pounds would be needed to cover 1008 square feet?
Answer:
[tex]252 \: sq \: feet = 2 \: lbs \\ 1008 \: sq \: feet = ( \frac{1008 \times 2}{252} ) \\ = 8 \: lbs[/tex]
Answer:
8lbs of fertilizer
Step-by-step explanation:
1008 ÷ 252 = 4
2 × 4 = 8
