The magnitude of two vectors are [tex]|A|=\sqrt{29},|B|=\sqrt{6}[/tex]
and the directions are
[tex]A=\frac{1}{\sqrt29}[2i+3j+4k]\\\\B=\frac{1}{\sqrt6}[i-2j+3k][/tex]
What is the magnitude of the vector?The magnitude of a vector can be defined as:
The length of a vector or the distance between the initial point and the endpoint of a vector.
Here given that,
[tex]A=2i+3j+4k\\B=i-2j+3k[/tex]
The magnitude of a vector is the length of the vector.
The magnitude of the vector a is denoted as ∥a∥.
For magnitude,
[tex]|A|=\sqrt{2^2+3^2+4^2}\\\\=\sqrt{4+9+16}\\\\=\sqrt{29\\\\}\\|B|\\=\sqrt{1^2-2^2+3^2}\\\\=\sqrt{1-4+9}\\\\=\sqrt{6}[/tex]
For Direction of sum,
[tex]\frac{A}{|A|}\\\\=\frac{1}{\sqrt29}[2i+3j+4k]\\\frac{B}{|B|}\\\\=\frac{1}{\sqrt{6}}[i-2j+3k][/tex]
For the vector B, the direction of the sum is
[tex]\frac{B}{|B|}\\\\=\frac{1}{\sqrt{6}}[i-2j+3k][/tex]
Hence, the magnitudes are [tex]|A|=\sqrt{29},|B|=\sqrt{6}[/tex]
and the direction are
[tex]A=\frac{1}{\sqrt29}[2i+3j+4k]\\\\B=\frac{1}{\sqrt6}[i-2j+3k][/tex]
To know more about the magnitude;
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Find the value of x
A- 6
B-5
C-4
D-10
Answer:
x=4
Step-by-step explanation:
In triangle MLK
it is a equilateral triangle HenceML=LK=MK=5Now come to triangle MKJ
It is a isosceles triangle Hence MJ=MkMK=5
Hence
[tex]\longrightarrow\sf MJ=5 [/tex]
[tex]\longrightarrow\sf x+1=5[/tex]
[tex]\longrightarrow\sf x=5-1 [/tex]
[tex]\longrightarrow\sf x=4 [/tex]
Which number line correctly shows -3- 1.5?
Web
3
0
2
3
- 3
2
3
13
0
PLSS HURRY IM ON A TIMER
Answer:
The first one
Step-by-step explanation:
please help me with this question
Answer:
12cm
Step-by-step explanation:
You can draw a triangle with hypotenusa 13, height h and base 5 (the difference between the radius 9 and 4). Then pythagoras tells us that
13² = h² + 5²
so
h = 13² - 5² = √144 = 12
c(x) = -5x^2+x
Find c(4)
Answer:
c(4) = -76
Step-by-step explanation:
c(x) x=4 so plug 4 in for x
-5(4)² + (4)
Do parentheses first so... 4² = 16
-5(16) + 4
-5(16) = -80
-80+4 = -76
c(4) = -76
Sapphire and Abe are shelving books at a public library. Sapphire shelves 12 books at a time, whereas Abe shelves 18 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved.
Answer: 36
Step-by-step explanation:
Given: Sapphire shelves 12 books at a time, whereas Abe shelves 18 at a time.
If they end up shelving the same number of books, what is the smallest number of books each could have shelved = LCM (12,18)
12 = 2 x 2 x 3
18 = 2 x 3 x 3
LCM (12, 18) = 2 x 2 x 3 x 3 = 36
Hence, the smallest number of books each could have shelved = 36
Answer:
36
Step-by-step explanation:
nrly
How manys days makes a leap year?
Answer: In an ordinary year, if you were to count all the days in a calendar from January to December, you'd count 365 days. But approximately every four years, February has 29 days instead of 28. So, there are 366 days in the year. This is called a leap year.
Step-by-step explanation:
F is inversely proportional to d 2 . When F = 8 , d = 6 Work out d (positive value rounded to 2 DP) when F = 7
Answer:
d ≈ 6.41
Step-by-step explanation:
Given that F is inversely proportional to d² then the equation relating them is
F = [tex]\frac{k}{d^2}[/tex] ← k is the constant of proportion
To find k use the condition when F = 8, d = 6 , then
8 = [tex]\frac{k}{6^2}[/tex] = [tex]\frac{k}{36}[/tex] ( multiply both sides by 36 )
288 = k
F = [tex]\frac{288}{d^2}[/tex] ← equation of proportion
When F = 7 , then
7 = [tex]\frac{288}{d^2}[/tex] ( multiply both sides by d² )
d² × 7 = 288 ( divide both sides by 7 )
d² = [tex]\frac{288}{7}[/tex] ( take the square root of both sides )
d = ± [tex]\sqrt{\frac{288}{7} }[/tex] ≈ ± 6.41
The positive value of d is 6.41 ( to 2 dec. places )
Answer:
when F = 7, d = 6.41
Step-by-step explanation:
We know that when 'y' varies inversely with 'x', we get the equation
y ∝ 1/x
y = k/x
where 'k' is called the constant of proportionality
Given that F is inversely proportional to d.
F ∝ 1/d
F = k /d²
When F = 8, d = 6, we need to find k
k = Fd²
k = 8×(6)²=288
Now, we need to find d when F = 7
so substitute k = 288, F = 7 in the equation
F = k /d²
d² = k/F
d² = 288/7
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]d=\sqrt{\frac{288}{7}},\:d=-\sqrt{\frac{288}{7}}[/tex]
but, we need to take the positive value of d, so
[tex]d=\sqrt{\frac{288}{7}}[/tex]
[tex]d=6.41[/tex]
Therefore,
when F = 7, d = 6.41
If bc+ad=b solve for a
Answer:
a = (b - bc)/d
Answer:
ad=b-bc
a=b-bc/d or a=b-bc
--------
d
*everything is divided by d on the other side...so b-bc is all divided by d
The graph below relates y, the distance Kelly walked, to x, the amount of time that Kelly walked. What is the value of y when x = 1 ?
Answer:
You need to show the graph.
Step-by-step explanation:
What triangle is this ? Pleaseee helppppp !!!!!! Will mark Brianliest correct answer !!!!!!!!!!!!!!!
Answer:
isosceles right triangle
A camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. If the rope is 8 feet long, about how far will the stake need to be from the middle of her tent?
A. 8.9 ft
B. 4 ft
C. 12 ft
D. 6.9 ft
Answer:
6.9 ft
Step-by-step explanation:
The Pythagorean Theorem. :)
a^2 + b^2 = c^2
4^2 + b^2 = 8^2
16 + b^2 = 64
b^2 = 48
D = 6.928
<3 Enjoy,
Dea
The length of the stake needs to be from the middle of her tent will be 6.9 feet. Then the correct option is D.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
A camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. If the rope is 8 feet long.
Then the length of the stake needs to be from the middle of her tent will be
We have
P = 4 ft
H = 8 ft
Then the base is given by the Pythagoras theorem.
B² = H² - P²
B² = 8² - 4²
B² = 64 - 16
B² = 48
B = 6.9 ft
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
help plzzzzz i needs halp!
Answer:
4000
Step-by-step explanation:
In isosceles triangle ABC the segment BD with D a point on AC is the median to the base AC. Find BD if the perimeter of ABC is 50m and the perimeter of ABD is 40m
Given:
In isosceles triangle ABC, consider AB=BC and the segment BD with D a point on AC is the median to the base AC.
Perimeter of ABC is 50m and the perimeter of ABD is 40m.
To find:
The length of BD.
Solution:
In isosceles triangle ABC the segment BD with D a point on AC is the median to the base AC.
[tex]AB=BC[/tex] ...(i)
[tex]AD=CD[/tex]
[tex]AC=2AD[/tex] ...(ii)
Perimeter of ABC is 50m.
[tex]AB+BC+AC=50[/tex]
[tex]AB+AB+2AD=50[/tex] [Using (i) and (ii)]
[tex]2AB+2AD=50[/tex]
[tex]2(AB+AD)=50[/tex]
Divide both sides by 2.
[tex]AB+AD=25[/tex] ...(iii)
Now, perimeter of ABD is 40m.
[tex]AB+AD+BD=40[/tex]
[tex]25+BD=40[/tex] [Using (iii)]
[tex]BD=40-25[/tex]
[tex]BD=15[/tex]
Therefore, the length of BD is 15m.
The volume of an Amazon package is given by the function below.
8x^3+30x^2+13x−15
A. What is the area of the bottom of the box if the width is (4x+5) and the length is (x+3)?
B. Using the volume formula, find the height of the package. (V=lwh)
Please show work
Answer:
Step-by-Step Explanation:
Area of the base = length × breadth
= (4x + 5) (x + 3)
= 4x(x + 3) + 5(x + 3)
= 4x² + 12x + 5x + 15
= 4x² + 17x + 15
_____________________________________
Volume = length × breadth × height
8x³ + 30x² + 13x - 15 = (4x + 5)(x + 3) × h
[tex] \frac{ 8x³ + 30x² + 13x - 15 }{(4x + 5)(x + 3)} = h[/tex]
$1,250 at 5% simple interst for 2 years
Answer:
2625
Step-by-step explanation:
Simple Interest Formula
P*R*T
1250*1.05*2=2625
Answer:
After two years, there will be a total of $1,375 paid and $125 paid in interest.
Step-by-step explanation:
Since, 5 x 2 = 10, first we should find 10% of $1,250.
1,250 x 0.10 = 125
$1,250 + $125 = $1375
Therefore, after two years, there will be a total of $1,375 paid and $125 paid in interest.
Hope this helps! :D
what two numbers' sum=-4 and product=-2
Let a and b be the two numbers. Then
a + b = -4
a b = -2
Solve the second equation for b :
b = -2/a
Substitute this into the first equation:
a - 2/a = -4
Multiply both sides by a :
a² - 2 = -4a
Move 4a to the left side:
a² + 4a - 2 = 0
Use the quadratic formula to solve for a :
a = (-4 ± √(4² - 4(-2))) / 2
a = -2 ± √6
If a = -2 + √6, then
-2 + √6 + b = -4
b = -2 - √6
In the other case, we end up with the same numbers, but a and b are swapped.
Find the coordinates of the point P that divides the directed line segment from A to B in the given ratio.
A(-6, 9), B(2, 1); Ratio 5 to 3
Given:
Point P divides the line segment AB in 5:3 where A(-6,9) and B(2,1).
To find:
The coordinates of point P.
Solution:
Section formula: If a point divide a line segment in m:n, then the coordinates of point are
[tex]\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Point P divides the line segment AB in 5:3 where A(-6,9) and B(2,1). Using section formula, we get
[tex]P=\left(\dfrac{5(2)+3(-6)}{5+3},\dfrac{5(1)+3(9)}{5+3}\right)[/tex]
[tex]P=\left(\dfrac{10-18}{8},\dfrac{5+27}{8}\right)[/tex]
[tex]P=\left(\dfrac{-8}{8},\dfrac{32}{8}\right)[/tex]
[tex]P=\left(-1,4\right)[/tex]
Therefore, the coordinates of point P are (-1,4).
PLEASE HELP WILL MARK BRAINLIEST
Answer:
A Plus Plumbing
Step-by-step explanation:
60(2)+80 = 120+80 = 200 < 250
Answer:
A- plus plumbing
Step-by-step explanation:
hope this helps
John wants to draw a circle graph showing his friends favorite ice cream flavors. When he polled his friends asking each their favorite flavor of ice cream, 35% of his friends aid chocolate, 20% of his friends said vanilla, 15% of his friends said Strawberry, 25% of his friends said mint chocolate chip, and 5% of his friends said flavors other than those previously listed. What will be the degree measure of the vanilla sector of the circle graph?
Answer:72
Step-by-step explanation:
What is the equation to a line with a slope of -3 and a y-intercept of 8?
Answer:
y=-3x+8
Step-by-step explanation:
y=mx+b
(m=slope and b=y-intercept)
Answer:
Step-by-step explanation:
let’s use this equation y = mx + b
where m = slope
and b = y intercept
since slope is -3, m = -3
and since y intercept is 8, b = 8
so the equation is
y = -3x +8
Please answer 1 - 3! thank you!
Answer:
The first one is
5x * 10
(x is the variable) TIMES 10
Step-by-step explanation:
What is 5=-2/3x+b X=4
I’ll give Brainlylist
Answer:
b = 23/3
Step-by-step explanation:
5 = -2/3(4) + b
5 = -8/3 + b
5 + 8/3 = b
b = 23/3
Nick is saving up for a laptop. His dad gave him $50 to start a savings account. He earns $9 every hour from his job, which he also saves. Write the equation of a function that can be used to find y, the total Nick has saved after x hours.
fill in the blanks
y =__ x + __
The area of the September is 336cm is all this model rectangles are exactly the same what is the perimeter of rectangle if the length of one rectangle is 12 CM
Answer:
Perimeter is 80cm
Step-by-step explanation:
A rectangle's area is calculated by multiplying the length by the width. If we are given the area of the rectangle and the length then we would simply need to solve for the width of the rectangle using the area formula we just mentioned...
A = l * w
336[tex]cm^{2}[/tex] = 12cm * w ... divide both sides by 12cm
28cm = w
Now we can see that the width of this rectangle is 28cm. To find the perimeter we need to add all four sides together, since we know that a rectangle's opposite sides are the same then we add the length and the width twice to calculate the perimeter (P)
P = 12cm + 12cm + 28cm + 28cm
P = 80cm
Elevate the expression
(28-21) to the 2 power
Help!
Answer:
49
Step-by-step explanation:
28-21=7
7 to the power of two is the same as 7(7)
7(7)=49
Which triangles are similar A or b? I need help.
Answer:
A!
Step-by-step explanation:
The amount of tax is $3.40, which is 5% of the food bill. How much was the food bill not including the tax?
If Simon wants to leave a 20% tip on the amount of the food bill before tax, how much should he leave for a tip?
What is Simon’s total bill including tax and tip? What percent of the food bill is this?
Answer:
You are told tax is $3.40 which is 5% of the total priceWe want to find the original food bill not including the tax of $3.40We also want to find the tip quantity based on the original food billSo X * 0.05= 3.40 Gives us X= 68 Hence the original bill was $68Now $68* .20 = $13.6I'm confident you can answer the rest with the information I've provided.which is a linear equation with a slope of 1/2 and a y-intercept of -5
Answer:
u say which but don't even give us options.
Please answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Answer: C {48,65,80}
Step-by-step explanation:
In order for it to be a right triangle it would have to be {48,64,85}
Hope this helps
Write the quadratic equation in standard form:
3x – 17 + 3x^2= -4