Answer:
(6*y130896+1%315£&+)
(19+!re
what adds to 3 and multiplies to -70
what is the shortest distance from the surface xy+15x+z2=209 to the origin ?
We can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.
Given the equation of the surface is xy + 15x + z^2 = 209.
Let's determine the shortest distance from the surface to the origin.
The shortest distance between the surface and the origin is given by the perpendicular distance, which can be calculated as follows:
Firstly, we need to determine the gradient of the surface, which is the vector normal to the surface.
For this purpose, we need to write the surface equation in the standard form, which is:xy + 15x + z^2 = 209 xy + 15x + (0)z^2 - 209 = 0 (the coefficients of x, y, and z are a, b, and c).
The gradient of the surface is given by the vector: ∇f = (a, b, c) = (y + 15, x, 2z) at the point P(x, y, z), which is a point on the surface.
Here, the normal vector is ∇f = (y + 15, x, 2z).
Now, let's consider a point A on the surface which is closest to the origin.
Let the coordinates of A be (a, b, c).
Therefore, the position vector of A is given by: OA = ai + bj + ck.
The direction of the position vector is in the direction of the normal vector, and therefore: OA is parallel to ∇f.
Thus, we can write: OA = λ∇f = λ(y + 15)i + λxj + 2λzkWhere λ is a scalar.
Since A lies on the surface, we have: a*b + 15a + c^2 = 209.
We also know that OA passes through the origin.
Therefore, the position vector of A is perpendicular to the direction vector OA.
This gives us: OA·OA = 0⟹ (ai + bj + ck)·(λ(y + 15)i + λxj + 2λzk) = 0
Simplifying this equation gives us:aλ(y + 15) + bλx + c(2λz) = 0
Also, we know that OA passes through the origin.
Therefore, the magnitude of OA is equal to the distance of A from the origin.
Hence, we can write: |OA| = √(a^2 + b^2 + c^2)
The value of λ can be obtained from the equation: aλ(y + 15) + bλx + c(2λz) = 0orλ = -2cz / (b + a(y + 15))
Substituting this value of λ in OA, we get: OA = λ(y + 15)i + λxj + 2λzk= -2cz/(b + a(y + 15)) (y + 15)i - 2cz/(b + a(y + 15)) xj - 4cz^2/(b + a(y + 15))k
Substituting this value of λ in |OA|, we get: |OA| = √[(2cz/(b + a(y + 15)))^2 + (2cz/(b + a(y + 15)))^2 + (4cz^2/(b + a(y + 15)))^2] = 2cz√[(y + 15)^2 + x^2 + 4z^2] / |b + a(y + 15)|
The distance of the point A from the origin is |OA|, which is minimized when the denominator is maximized. The denominator is given by |b + a(y + 15)|.
Thus, we have to maximize the denominator with respect to a and b. The condition for maximum value of the denominator is obtained by differentiating the denominator with respect to a and b separately and equating it to zero. The values of a and b obtained from these equations are substituted in the equation a*b + 15a + c^2 = 209 to obtain the coordinates of the point A, which is closest to the origin.
Hence, we can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.
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While standing on a pier, Lynette saw a balloon floating 20 feet above her and a fish swimming 4 feet below the surface of the water.
Let 0 represent the water surface, and let the positive side of 0 represent position above the surface. Which number sentence correctly compares the distances of the balloon and the fish to the surface of the water?
A. |-4| < |20|
B. |-4| > |20|
C. |4| < |20|
D. |4| > |-20|
Answer:
I'd go with A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The following data points represent the number of puppies in each litter at Port's Pup Rescue.
Sort the data from least to greatest.
11
14
7
2
9
6
2
Find the median number of puppies.
puppies
My
32 pages to 28 pages.
Answer:
12.5%
Step-by-step explanation:
percent change is calculated as
[tex]\frac{change}{original\\}[/tex] x 100
change = 32 − 28 = 4 pages
[tex]\frac{4}{32}[/tex] x 100% = [tex]\frac{100}{8}[/tex] % = 12.5 %
Hope it helps
) Which expressions show the total area of the tiny house in square feet? Choose ALL that apply. 36x + 24 24x + 36 2.(12 + 3) 12(2x + 3)
Answer:
24x+36 and 12(2x+3)
Step-by-step explanation:
I just did it
Simplify the algebraic expression by combining the like (or similar) terms -3+5y+9
Answer:
5y+6
Step-by-step explanation:
-3 and 9 are like terms which can be simplified to 6.
Answer:
5y+6
Step-by-step explanation:
-3+5y+9
=-3+9+5y
=6+5y
=5y+6
Julio spent $52.43 on batteries. If they cost $7.49/pack, how many packs did he buy?
Answer:
7
Step-by-step explanation:
52.43 ÷7.74=7
If x -9 is a factor of x^2 -5 -36, what is the other factor?
Answer:
Factors are (x-9)(x+4)
Step-by-step explanation:
WILL GIVE BRAINLIEST IF YOU HELP ME
Answer:
D. Point S
Step-by-step explanation
The opposite of -5.5 is 5.5, therefore since Point S is at 5.5 on the number line, the answer is D.
how does the stimulus check impact society please help me please i really need help please
People started getting stimulus checks during the time when c0vid-19 was a major issue because most places where people would work were closed, so people were getting money through stimulus checks because they were basically unemployed. This money went back into the economy to buy mostly essentials and health products, so therefore it helped businesses that sold these kinds of things.
A triangular brace has an angle measure of 30 degrees, with a side opposite
this angle measuring 8 inches. The base of the triangular brace, which is
adjacent to the given angle measure, is 6 inches in length. Which of the
following statements is correct?
A. The angle opposite the side measuring 6 inches has one solution
of approximately 28 degrees.
B. The angle opposite the side measuring 6 inches has two solutions
of approximately 28 degrees and 36 degrees.
O C. The angle opposite the side measuring 6 inches has one solution
of approximately 22 degrees.
D. There is not a solution for the angle opposite the side measuring 6
inches.
The angle opposite the side measuring 6 inches has one solution of approximately 22 degrees.
Sine ruleSine rule is used to show the relationship between the angles of a triangle and the sides opposite to the angles. It is given by:
a / sin(A) = b / sin(B) = c / sin (C)
where A, B, C are the angles and a, b, c are the sides opposite to the angles.
From the question:
let a = 8 in, A = 30°, b = 6 in, hence:
a / sin(A) = b / sin(B)
8 / sin(30) = 6 / sin(B)
B = 22°
The angle opposite the side measuring 6 inches has one solution of approximately 22 degrees.
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Jacqueline is ordering pizzas for a party. Each pizza is cut into 12 slices. Jacqueline wants to have enough pizza so each person can have 4 slices. 16 people will be at the party. If Jacqueline buys 7 pizzas, how many extra slices will be left over after each guest eats 4 slices?
Answer:
20
Step-by-step explanation:
Just write down the answer.
geometry math plz help
Answer:
1. mCD is equal to 84 degrees.
2. I believe that RPT would be equal to approximately 51 feet. I think I am right, but I am not 100% sure. I used formula though.
Step-by-step explanation:
1. In order to find the measure of CD, you would find the measure of AD and CD, because they add to 180, and from there you can take the answer, which will be the x value, and plug it back into measure CD's equation.
1. Add the equations of mAD and mCD and set them equal to 180, because together on the graph they add to 180 degrees, which is a semi-circle.
19x-49+5x+37=180
24x-12=180
2. Solve.
24x-12=180
24x=168
x=7
3. Plug x back into mCD and find the answer!
19(7)-49=84
mCD= 84 degrees!
2. Arc Length Formula
2[tex]\pi[/tex]r degrees/360
2pi (14) 208/360≈51
Please help I’m really need the help (NO LINKS ) (NO LYING ) PART 2 again again again
Answer:
Step-by-step explanation: i wont tell you the answer but ill thell you how to do it,soo the strat is to count where the line is as a different part then u just add em
example 1:41.6
8-4=4x4=16
8x3.2=25.6
16+25.6=41.6
:)
Answer:
A. 15
B. 25.6
C. 41.6
Rectangular prism l 2/3, h 3/5 w 4/7 what is volume?
Answer:
Step-by-step explanation:
volume= width X height X length
volume= 4/7 X 3/5 X 2/3
volume= 0.23
1. A company has $6582 to give out in bonuses. An amount is to be given out equally to each of the 32 employees.
(a) A manager, Jake, reasoned that since 32 goes into 64 twice, each employee will get about $2000. Is his estimate correct? Why or why not?
(b) How much will each employee receive, rounded to the nearest whole dollar? Leave the remainder undivided. Show your work.
Answer:
Answer:
A) His estimate is incorrect, since he has increased a figure to the amount that each employee would receive.
B) Rounded to the nearest dollar, each employee would receive $ 209.
Step-by-step explanation:
Since a company has $ 6582 to give out in bonuses, and an amount is to be given out equally to each of the 32 employees, and A) a manager, Jake reasoned that since 32 goes into 64 twice, each employee will get about $ 2000 , to determine if his estimate is correct, and B) determine how much will each employee receive, rounded to the nearest whole dollar, the following calculations must be performed:
A)
2000 x 32 = 64000
200 x 32 = 6400
Therefore, his estimate is incorrect, since he has increased a figure to the amount that each employee would receive.
B)
6582/32 = X
208.68 = X
Therefore, rounded to the nearest dollar, each employee would receive $ 209.
5, 11, 17,...
Find the 35th term.
Answer:
119 is the 35th term
o The day before the exam, Rebecca does a practice run. She attempts 20 glass vases and breaks 3 of them. What is her success rate, shown as a decimal?
Answer:
If the goal is to break the vases: 3/20 = 15.0% or 0.15
If the goal is to not break the vases: 17/20 = 85.0% or 0.85
Olaf wants to buy a guitar that costs $600. He makes $3 per day. How many days will it take Olaf to save enough money to buy the guitar
Answer:
200 days
Step-by-step explanation:
600/3 = 200
Answer:
200 days
Step-by-step explanation:
Simple: You divide the cost of the guitar by the amount he gets paid per day. Hope this helps :)
Rana sells 192 cakes in the ratio small: medium: large = 7 : 6 : 11.
The profit for one medium cake is twice the profit for one small cake.
The profit for one large cake is three times the profit for one small cake.
Her total profit is £532.48
Work out the profit for one small cake
Answer:
S = £1.28
Step-by-step explanation:
Let the small, medium and large cakes be S, M and L respectively.
Given the following data;
Total profits = £532.48
Total number of cake = 192 cakes
Ratio of S:M:L = 7:6:11
Sum of ratio = 7+6+11 = 24
To find number of each cakes, we would divide the total number of cakes by the sum of ratio;
Number of each cakes = 192/24
Number of each cakes = 8
Next, we determine the exact number of each type of cakes.
Small = 7*8 = 56 cakes.
Medium = 6*8 = 48 cakes.
Large = 11*8 = 88 cakes.
For the profits;
Translating the word problem into an algebraic expression, we have;
M = 2S
L = 3S
56S + 48*(2S) + 88*(3S) = £532.48
56S + 96S + 264S = 532.48
416S = 532.48
S = 532.48/416
S = £1.28
Therefore, the profit for one small cake is £1.28
how is finding 8x3/4 similar to finding 3/4 of 8
Answer: your answer would be 6
8*3=24/4 and 24/4=6
Step-by-step explanation: Hope this help :D
Answer:
Because in order to find 3/4 of 8, you must solve for 8 * 3/4.
A helpful tip is that "of" is one of the giveaways of a multiplication problem. Others include but are not limited to, "multiply, " "product," "by," "times," "area," "twice," "double," "thrice," "triple," and "quadruple."
I would appreciate Brainliest, but no worries.
which is a correct step when using the median fit method for modeling data?
Use the median value of intercepts found
Calculate slope using the right and middle points
Determine three y intercepts by using each summary point along with the slope.
Determine the median of the x values and the median of the y values.
When using the median fit method to model data, you should Determine three y intercepts by using each summary point along with the slope.
What is the median fit method?This is a model for coming up with trend lines to represent the data given by a data set by dividing the given data into sections where the data points are equal in number.
As there will be three sections, it is important that three y intercepts are determined using summary points and the slope.
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Answer: C
Step-by-step explanation:
A cuboid with a volume of 924 cm' has dimensions
4 cm, (x + 1) cm and (x + 11) cm.
Show clearly that x2 + 12x – 220 = 0
Solve the equation by factorisation, making sure you show the factorisation.
State both values of x on the same line.
Finally, find the dimensions of the cuboid, writing all three on one line.
Answer:
4cm, 11cm, 21cm
Step-by-step explanation:
4(x + 1)(x + 11)
4(x ^ 2 + 12x + 44)
x ^ 2 + 12x + 11 = 231
x ^ 2 + 12x + 11 - 231 = 0
x ^ 2 + 12x - 220 = 0
(x - 10)(x + 22) = 0
x = 10 and x = - 22
4cm , 11cm , 21cm
Hope it helps you xx
Answer:
Dimensions = 4cm, 11cm and 21 cm.
Step-by-step explanation:
x2 + 12x - 220 = 0
x2 + 22x - 10x - 220
= x(x+22) -10(x+22)
=(x+22)(x-10)
x + 22= 0
-22 -22
x = -22 (x cant be negative so this is wrong)
x-10 = 0
+10 +10
x = 10 (positive so its correct)
4 , (10+1), (10+11)
= 4, 11, 21 cm.
What is the difference of 506 and 297
Answer:
209
Step-by-step explanation:
subtract
Answer:
209
Step-by-step explanation:
subtraction bro
Please help please no links please please anything helps
Answer:
140
Step-by-step explanation:
Possibly i'm not that great at math but this might be the answer.
A recipe for 1 batch of cookies calls for 3/4 cup of flour. How much flour is required to bake 1 1/2 batches of cookies?
Answer:
1 1/8 cups of flour are required to bake 1 1/2 batches of cookies.
Step-by-step explanation:
Given that a recipe for 1 batch of cookies calls for 3/4 cup of flour, to determine how much flour is required to bake 1 1/2 batches of cookies, the following calculation must be performed:
3/4 = 0.75
1/2 = 0.5
1 = 0.75
1.5 = X
1.5 x 0.75 / 1 = X
1.125 = X
0.125 = 1/8
Thus, 1 1/8 cups of flour are required to bake 1 1/2 batches of cookies.
Isabella took a taxi from her house to the airport. The taxi company charged a pick-
up fee of $4.70 plus $2.25 per mile. The total fare was $58.70, not including the tip.
Write and solve an equation which can be used to determine , the number of miles in the taxi ride.
Answer:
Equation: 2.25x+4.7=58.70
Answer: x = 24x=24
Hope this helps
There is a 30% probability of
hail. What is the probability
that it will NOT hail?
Answer:
70% probability
Step-by-step explanation:
100% probability
-30% probability
=70% probability
Decide which of the following quantities can be represented by a positive number and which can be represented by a negative number. Give an example of a quantity with the opposite sign in the same situation
Answer:
Step-by-step explanation:
a +
b -
c +
d -
e -
positive, Negative , Positive, Negative, Negative.
What is Number System?A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.
The given sentences are
(A) Tylers puppy gained 5 pounds.
This we can take as a positive number. Because here the value is increasing. whenever we use gained means it is positive.
Tylers puppy lost 5 pounds is the negative number.
(b) The aquarium leaked two pounds of water
This we can take as a Negative number. Because here the value is decreased. whenever we use leaked means it is negative.
The aquarium added with two pounds of water is a positive.
(c) Andrew received a gift of $10.
This we can take as a positive number. Because here the value is increasing. whenever we use received means it is positive.
Andrew gifted a gift of $10.
This we can take as a Negative number. Because here the value is decreased. whenever we use gifted means it is negative.
(d) Kiran gave a gift of $10
This we can take as a Negative number. Because here the value is decreased. whenever we use gave means it is negative.
Kiran received a gift of $10 is positive.
(e) A climber descended 550 feet.
This we can take as a Negative number. Because here the value is decreased. whenever we use descended means it is negative.
Hence positive, Negative , Positive, Negative, Negative,.
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