The vector PO x PR is simply: PO x PR = 15 n = (15, 0, 0) Expressed in component form or standard basis vectors, the vector is (15, 0, 0).
First, we need to find the vectors PO and PR:
PO = O - P = (-2, -1, 0)
PR = R - P = (-3, 12, 6)
To find the cross product of PO and PR, we can use the following formula:
PO x PR = |PO| |PR| sinθ n
where |PO| and |PR| are the magnitudes of the vectors PO and PR, θ is the angle between them, and n is a unit vector perpendicular to both PO and PR. Since θ = 90 degrees and |PO| = sqrt(5) and |PR| = 15, we have:
PO x PR = (sqrt(5) * 15) n = 15 sqrt(5) n
To find n, we can take the unit vector in the direction of PO x PR:
n = (1 / |PO x PR|) (PO x PR) = (1 / (15 sqrt(5))) (15 sqrt(5) n) = n
Therefore, the vector PO x PR is simply:
PO x PR = 15 n = (15, 0, 0)
Expressed in component form or standard basis vectors, the vector is (15, 0, 0).
To know more about vector refer to-
https://brainly.com/question/29740341
#SPJ11
Find a. Round to the nearest tenth.
Answer:
use for formula a^2+b^2=c^2 to execture
*" ^ " means square or to the power of two
Step-by-step explanation:
Darius is putting tiles on the roof of his house. After working for 3 1/3 hours, he has completed 4/5 of the roof. Can Darius put the titles on the enitre roof in 4 hours if he continues to work at the same rate?
Answer:
No.
Step-by-step explanation:
It is given that Darius is putting tiles on the roof of his house.
Darius had completed = [tex]$\frac{4}{5}$[/tex] th of the work
He takes time = [tex]$3 \frac{1}{3}$[/tex] hours to complete [tex]$\frac{4}{5}$[/tex] th of the work
The remaining work = [tex]$1 -\frac{4}{5}$[/tex]
[tex]$=\frac{5-4}{5}$[/tex]
[tex]$=\frac{1}{5}$[/tex]
∴ Darius completes [tex]$\frac{4}{5}$[/tex] th of the work in = [tex]$\frac{10}{3}$[/tex] hours
So, [tex]$\frac{1}{5}$[/tex] th of the work in = [tex]$\frac{10}{3} \times \frac{5}{4} \times \frac{1}{5}$[/tex] hours
[tex]$=\frac{10}{12}$[/tex] hours
Therefore total time taken to complete the work [tex]$=\frac{10}{3}+\frac{10}{12}$[/tex] hours
[tex]$=\frac{40+10}{12}$[/tex] hours
[tex]$=\frac{50}{12}$[/tex] hours
[tex]$=4\frac{2}{12}$[/tex] hours
[tex]$=4\frac{1}{6}$[/tex] hours
Thus, Darius continues to work at the same rate will not be able to complete the work in 4 hours.
3. CONSTRUCTION A rectangular deck is built
around a square pool. The pool has side length s. The
length of the deck is 5 units longer than twice the side
length of the pool. The width of the deck is 3 units
longer than the side length of the pool. What is the
area of the deck in terms of s?
Did I do this right or was I supposed to leave it as a trinomial?
Answer:
[tex]s^2+11s+15[/tex]
Step-by-step explanation:
Let side length of pool=s
According to question
Length of rectangular deck , l=2s+5
Width of rectangular deck, b=3+s
We have to find the area of deck in terms of s.
We know that
Area of square=[tex](side)^2[/tex]
Area of rectangle=[tex]l\times b[/tex]
Using the formula
Area of pool=[tex]s^2[/tex]
Area of (rectangular deck+ pool)=[tex](2s+5)(3+s)[/tex]
Now,
Area of rectangular deck
=[tex](2s+5)(3+s)-s^2[/tex]
[tex]=6s+2s^2+15+5s-s^2[/tex]
=[tex]s^2+11s+15[/tex]
: Santiago realizó los siguientes movimientos en su Cuenta bancaria: el lunes consignó $300.000, el martes retiró $120.000, el miércoles retiró $95.000 Y el jueves consignó $80.000. ¿Cómo se representan matemáticamente los movimientos bancarios de Santiago?
Answer:
Step-by-step explanation:
Los movimientos bancarios de Santiago se representan matemáticamente teniendo en cuenta que consignar es sumar y retirar el restar. Por lo tanto podes expresar los movimientos bancarios de la siguiente manera:
Lunes → + 300.000Martes → -120.000Miércoles → -95.000Jueves → +80.000Al realizar la sumatoria se obtiene:
+300.000 - 120.000 - 95.000 + 80.000 = + 165.000
En la semana Santiago obtiene en su cuenta bancaria $165.000
pls I neeeed to ace this test.
Answer:
but
Step-by-step explanation:
moreover is more of a transition that means "also"
furthermore is used as a conclusion
Answer:
But
Step-by-step explanation:
Im pretty sure is the right answer is but it could be while to but is not an option so im a 100% sure is A-But
A company find that 4 1/4 % of the tyres are defective. The company made 28,000 tyres. How many tyres were defective?
(4 whole, 1 as nominator and 4 as dominator)
No need to explain, just give answer.
Answer:
595 pairs of tyres are defective.
Step-by-step explanation:
4.25×28000
____
100
0.0425×28000
1190 Total no. of defective tyres
1190 divide total tyres by 2 to get the exact pairs of defective tyres.
____
2
595 tyresof shoes are defective.
A customer asked Crazy Dave to split a pie into sixths. This is what he did: Explain why he is wrong and show a correct way to do it.
Answer: He split it into unequal halves which would make his way wrong. the correct way to do it would be to cut it so all the lines met in the middle of the pie
Step-by-step explanation:
What are the answers? i’m not sure how to solve this.
Solve for and the indicated angles.
G
90°
F
(4x + 13)
(5x + 14)
D
E
ok so as all of the angles in a triangle is 180 so
You buy 3 shirts and 1 pair of pants for $32Your friend buys 2 shirts and 3 pairs of pants for $40.
Answer:
Each shirt costs $8 and each pair of pants costs $8
Step-by-step explanation:
3+1=4
32/4=8
2+3=5
40/5=8
Determine the number of operations needed to solve 7c = 84
Answer:
12
Step-by-step explanation:
7c=84
c=84/7
c=12
Answer:
2
Step-by-step explanation:
You need division and multiplication (division for 84/7 and multiplication to identify 7c = 7 x c), which means 2.
Hope that helps!
A triangle with vertices (0,0), (3,6), (7,4) is dilated by a factor of 3 with its center at the origin.
Answer:
[tex]A' = (0,0)[/tex]
[tex]B'= (9,18)[/tex]
[tex]C'= (21,12)[/tex]
Step-by-step explanation:
Given
[tex]A= (0,0)[/tex]
[tex]B= (3,6)[/tex]
[tex]C= (7,4)[/tex]
[tex]k = 3[/tex] -- dilation factor
Required
Determine the coordinates of the new triangle
This is calculated using:
[tex]New = Old * k[/tex]
So, we have:
[tex]A' = A *3[/tex]
[tex]A' = (0,0) *3[/tex]
[tex]A' = (0,0)[/tex]
[tex]B' = B * 3[/tex]
[tex]B'= (3,6)*3[/tex]
[tex]B'= (3*3,6*3)[/tex]
[tex]B'= (9,18)[/tex]
and
[tex]C' = C * 3[/tex]
[tex]C'= (7,4)*3[/tex]
[tex]C'= (7*3,4*3)[/tex]
[tex]C'= (21,12)[/tex]
triangle ABD~ triangle DBC the perimeter of triangle ABD=36, fond the perimeter of triangle DBC.
Answer:
Perimeter of ΔDBC = 48 units
Step-by-step explanation:
It's given in he question,
ΔABD ~ ΔDBC
Therefore, by the definition of similar triangles,
Corresponding sides of both the triangle will be proportional.
[tex]\frac{AB}{DB}= \frac{BD}{BC}= \frac{AD}{DC}[/tex]
[tex]\frac{9}{12}= \frac{12}{16}= \frac{AD}{DC}[/tex]
[tex]\frac{3}{4}=\frac{AD}{DC}[/tex]
AD = [tex]\frac{3}{4}DC[/tex] ----------(1)
Since, perimeter of ΔABD = 36,
AB + BD + AD = 36
9 + 12 + AD = 36
AD = 36 - 21
AD = 15
From equation (1),
15 = [tex]\frac{3}{4}(DC)[/tex]
DC = 20
Perimeter of ΔDBC = DB + BC + DC
= 12 + 16 + 20
= 48
Therefore, perimeter of ΔDBC = 48 units is the answer.
Ashley made 2 out of 4 total shots. What percent of her shots did she make?
Answer:
50%
Step-by-step explanation:
2 divided by 4 is .5
.5 ×100 =50
if you simplify in fraction form it would be 2/4 equals 1/2 which would still give you the same answer
The length of a square park is 6 miles. What is the area of the park?
Answer:
36 miles.......................
A collection of dimes and nickels is worth 3.30. if there are 42 coins in total how many of each kind of coin are there?
Answer:1 nickels =$0.05
1 dime= $0.1
Step-by-step explanation:
1 nickels =$0.05
1 dime= $0.1
let the number of nickels be x and that of dimes be y.
total number of coins is given by:
x+y=42
hence:
y=42-x.......i
total amount of cash will be:
0.05x+0.1y=3.30.........ii
substituting i in ii we get:
0.05x+0.1(42-x)=3.30
0.05x+4.2-0.1x=3.3
-0.05x=-0.9
x=-0.9/(-0.05)
x=18
hence the the number nickels is x=18, the number of dimes will be y=42-x=42-18=24
this is the other post, ill give brainlist to the best answer.
Step-by-step explanation: 1 will now become a 2, so the answer is 1.2.1,
Help asap!!!!
Around which line would the following cross-section need to be revolved to create a sphere?
circle on a coordinate plane with center at 1 on the x-axis and a radius of 1
y = x
y-axis
x = 1
y = 1
Answer:
I believe your answer would be y=1.
Step-by-step explanation:
The circle is located with its point on 1 of the x axis, and the cross section would be pulled straight from that term. So the cross section would need to be revolved around y = 1, instead.
This is just my best guess, so I hope it helps!
To get a sphere, we need to do a revolution around the line x = 1.
Which line should we use?
The line that we must use must be a line that divides the circle in two equal parts, so it must pass through its center.
We know that the center of our circle is the point (1, 0).
With that in mind, the two lines that we know that will divide the circle in two equal parts are:
y = 0x = 1(There are more lines, the above two are the simplest ones).
The only one that appears on the options is x = 1, so that is the correct option.
If you want to learn more about circles, you can read:
https://brainly.com/question/25306774
Find slope. I NEEDDDD HELPPPPP IMA MARK BRAINLIESTTT
Answer:
-1/3
Step-by-step explanation:
When I subtract 14 from it,
the result is 13 more than 20.
what is the number?
Answer:47
Step-by-step explanation:
Make a hypothesis that the number is X, so X-14=20+13
X=20+13+14, eventually, you'll get that X=47
But I'm not sure if you mean 13 times more than 20, or just 13 more than 20
In parallelogram BCDE if m EBC=45 find m DEB
Answer:
x = 135
Step-by-step explanation:
parallelograms have supplementary angles
180 - 45 = 135
Answer:
x = 135 degrees
Step-by-step explanation:
Because this is a parallelogram, the opposite sides are parallel
45 and x = 180 because they are corresponding congruent angles
180-45=135
Which number line represents the solution to the inequality x - 3 > 2
Answer: x > 5
Step-by-step explanation: To solve for x in this inequality, our goal is the same as it would be if this were an equation, to get x by itself on one side.
Since 3 is being subtracted from x, we add 3 to
both sides of the inequality to get x > 5.
When graphing x > 5, we have an open circle on 5 and the
open circle tells us that 5 is not part of our answer.
Then we draw an arrow going to the right to represent
all possible solutions to this inequality, any number greater than 5.
Please help giving brainliest
Answer:
this is a scalene triangle. we can see that none of the side lengths and none of the angles are equivalent to each other. that's why it's scalene.
Can any one help me on this question ?
Answer:
70°
Step-by-step explanation:
2x +x + 80° + 70° = 360° { being sum of angles of quadrilateral }
3x + 150° = 360°
3x = 360° - 150°
3x = 210°
x = 70°
Hope it will help :)
Answer:
70
Step-by-step explanation:
Since sum of all angles in a quadrilateral is 360°
angle P+ angle Q + angle R + angle S= 360°
80+70+x+2x=360
3x= 360-150
3x = 210
x = 210/3
x= 70
At the school carnival, Jade has a game booth with a spinner. The banner at her booth reads "20% chance of winning!" What is the chance that a player may not win? (5 points) Group of answer choices 90% 50% 80% 40%
Answer: 80%
Step-by-step explanation:
100% chance is normally the most so 100 is our whole. 100-20=80. That being the % makes 80% as the answer. Hope i helped!
The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
Step-by-step explanation:
let the ratio be x
now,
3x+5x+9x+13x=360°(sum of angle of quadrilateral is 360°)
30x=360°
x=360/30
x=12°
then,
3x=3×12=36°
5x=5×12=60°
9x=9×12=108°
13x=13×12=156°
so,the angles of quadrilateral are 36°,60°,108°& 156°
hope it helps.
ILL MARK BRAINLIEST AND 20 POINTS FOR THE FIRST TO HELP! ITS DUE IN 10! PLEASE AND THANKS
Answer:
7/30
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
PLS HELP ASAP!!! 30 POINTS (a) What is m<3 ? (b) What is ?
PICTURE BELOW PLS ANSWER IN COMPLETE SENTENCES
Answer:
ACTUA,LY ITS
Step-by-step explanation:
2222
Step-by-step explanation:
angle 3 = 180-20-57 =103
angle 4 = 180 - 103 = 77
YALL WHAT IS THE ANGLE OF C
65
65
Answer:
A,G
Step-by-step explanation:
Answer:
50 degrees
Step-by-step explanation:
first come first served:)
Answer:
2.
gold beads to silver beads
table: 6:9 12:18 24:36 30:45
equivalent ratios: 4:6 10:15 20:30 100:150
3.
A.33
B.1.2
Step-by-step explanation:
2.
the rule is, gold beads x 1 1/2 = silver beads
3.
A. 165/5=33
B.9.60/8=1.2
hope this helps have a blessed day :)