Answer:
A point on the ellipsoid is (-4,2,2) or (4,-2,-2)
Step-by-step explanation:
Given equation of ellipsoid f(x,y,z) :[tex]x^2+y^2+4z^2=36[/tex]
Parametric equations:
x=-4t-1
y=2t+1
z=8t+3
Finding the gradient of function
[tex]\nabla f(x,y,z)=<\frac{\partial{f}}{\partial{x}},\frac{\partial{f}}{\partial{y}},\frac{\partial{f}}{\partial{z}}>\\\nabla f(x,y,z)=<2x,-2y,8x>[/tex]
So, The directions vectors=(-4,2,8)
Now the line is perpendicular to plane when direction vector is parallel to the normal vector of line
[tex]\nablaf(x,y,z)=(2x,2y,8z)=\lambda(-4,2,8)[/tex]
So, [tex]2x=-4\lambda[/tex]
[tex]\Rightarrow x=-2\lambda[/tex]
[tex]2y=2\lambda\\\Rightarrow y=\lambda\\8z=8\lambda\\\Rightarrow z=\lambda[/tex]
Substitute the value of x , y and z in the ellipsoid equation
[tex](2\lambda)^2+(\lambda)^2+4(\lambda)^2=36\\9(\lambda)^2=36\\\lambda^2=4\\\lambda=\pm 2[/tex]
With [tex]\lambda = 2[/tex]
x=-2(2)=-4
y=2
z=2
With[tex]\lambda =- 2[/tex]
x=-2(-2)=4
y=-2
z=-2
Hence a point on the ellipsoid is (-4,2,2) or (4,-2,-2)
Solve for X please :(( Will give brainliest.
5x+6+92 = 22x-4
5x+98 = 22x-4
add 5x to both sides
98 = 27x-4
add 4 to both sides
102 = 27x
divide both sides by 27
x = 3 and [tex]\frac{7}{9}[/tex]
-6(x - 6) = x(16 - 7)
Help please
Answer:
the answer would be x equal 2.4
Step-by-step explanation:
sorry for my bad handwriting
Is 60N Cold or hot
Answer:
It is warm.
Step-by-step explanation:
2/15 = h/125 need a step by step please
====================================
Work Shown:
2/15 = h/125
2*125 = 15*h .... cross multiply
250 = 15h
15h = 250
h = 250/15
h = (5*50)/(5*3)
h = 50/3
-----------------
Extra info:
50/3 = (48+2)/3
50/3 = (48/3)+(2/3)
50/3 = 16 + (2/3)
50/3 = 16 & 2/3
The improper fraction 50/3 converts to the mixed number 16 & 2/3
Another way to see this is to use long division to get 50/3 = 16 remainder 2.
Show that each conjecture is false by finding a counterexample.
1.For any integer n, n3 > 0.
2. Each angle in a right triangle has a different measure.
3.For many years in the U.S, each bank printed its own currency. The variety of different bills led to widespread counterfeiting. By the time of the Civil War, a significant fraction of the currency in circulation was counterfeit. If one soldier had 48 bills, 16 of which were counterfeit, and another soldier had 39 bills, 13 of which were counterfeit, make a conjecture about what fraction of bills were counterfeit at the time of the Civil War.
Answer:
1. [tex]n: n^3 > 0[/tex] is not true for negative integers
2. [tex]45\ and\ 45[/tex] show that all angles do not have different measure
3. [tex]Fraction = \frac{1}{3}[/tex]
Step-by-step explanation:
Solving (1):
[tex]n: n^3 > 0[/tex]
Take
[tex]n = -1[/tex]
[tex]-1^3 = -1[/tex]
[tex]n: n^3 > 0[/tex] is not true for negative integers
Solving (2):
The angles of a right angled triangle are:
[tex]45, 45\ and\ 90[/tex]
[tex]45\ and\ 45[/tex] show that all angles do not have different measure
Solving (3):
When
[tex]Bills = 48[/tex]
[tex]Counterfeit = 16[/tex]
The fraction is calculated as thus:
[tex]Fraction = \frac{Counterfeit}{Bills}[/tex]
[tex]Fraction = \frac{16}{48}[/tex]
[tex]Fraction = \frac{1}{3}[/tex]
Similarly, when
[tex]Bills = 39[/tex]
[tex]Counterfeit = 13[/tex]
[tex]Fraction = \frac{Counterfeit}{Bills}[/tex]
[tex]Fraction = \frac{13}{39}[/tex]
[tex]Fraction = \frac{1}{3}[/tex]
11. Factor for
12 – 8.1 + 16
Answer:
2(6-4.05+8)
Step-by-step explanation:
2(6-48+43.05+8)
Megan had $235.17 in her bank account. She withdrew $77.98 from the account to spend
on clothing. How much money does she have left in her bank account now?
Answer: 157.19
Step-by-step explanation:
Explain how to use the distributive property to find an expression that is equivalent to 20+16.
Step-by-step explanation:
distributive property is a*(b+c) = a*b + a*c
20+16 = 4* (5+4)
Factorise fully
40-10g
Please do quick, will mark brainiest!!
Answer:
10(4-g)Step-by-step explanation:
[tex]40 - 10g[/tex]
Rewrite 40 as 4 × 10
[tex]4 \times 10 - 10g[/tex]
Factor out 10
[tex]10(4 - g)[/tex]
The angle measures of triangle QRS are given:
The measure of angle Q is (5x−15)°.
The measure of angle R is 75°.
The measure of angle S is (3x)°.
What is the value of x?
Answer:
x = 15°
Step-by-step explanation:
(5x-15) + 75 + 3x = 180
8x + 60 = 180
8x = 120
x = 15°
there is a box that contains a $50 bill, two $20 bills, three $10 bills and four $1 bills. If a bill is picked at random, what is the expected value?
One of the ten bills
A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions the student gets correct. (a) Find P(X = 3). (b) Find P(X > 2). (c) To pass the test, the student must answer 7 or more questions correctly. Would it be unusual for the student to pass? Explain.
Answer:
1)0.2502
2)0.475
3)0.003505
Step-by-step explanation:
Total No. of question n= 10
There are four choices in each question
So, Probability of success [tex]p = \frac{1}{4}[/tex]
Probability of failure q = [tex]1- \frac{1}{4}=\frac{3}{4}[/tex]
We will use binomial over here
[tex]P(X=x)=^nC_r p^r q^{n-r}[/tex]
1)
[tex]P(X = 3)=^{10}C_3 (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=\frac{10!}{3!7!} (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=0.2502[/tex]
2) [tex]P(X > 2)=1-P(X\leq 2)[/tex]
P(X>2)=1-(P(X=0)+P(X=1)+P(X=2))
[tex]P(X>2)=1-(^{10}C_0 (\frac{1}{4})^0 (\frac{3}{4})^{10}+(^{10}C_1 (\frac{1}{4})^1 (\frac{3}{4})^9+^{10}C_2 (\frac{1}{4})^2 (\frac{3}{4})^8)[/tex]
[tex]P(X>2)=1-((\frac{1}{4})^0 (\frac{3}{4})^{10}+(\frac{10!}{1!9!} (\frac{1}{4})^1 (\frac{3}{4})^9+\frac{10!}{2!8!} (\frac{1}{4})^2 (\frac{3}{4})^8)[/tex]
P(X>2)=0.475
3)
[tex]P(X\geq 7)=P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\P(X\geq 7)=^{10}C_7 (\frac{1}{4})^7 (\frac{3}{4})^{3}+(^{10}C_8 (\frac{1}{4})^8 (\frac{3}{4})^2+^{10}C_9 (\frac{1}{4})^9 (\frac{3}{4})^1+^{10}C_{10} (\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=\frac{10!}{7!3!} (\frac{1}{4})^7 (\frac{3}{4})^{3}+\frac{10!}{8!2!} (\frac{1}{4})^8 (\frac{3}{4})^2+\frac{10!}{9!1!} (\frac{1}{4})^9 (\frac{3}{4})^1+\frac{10!}{10!0!}(\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=0.003505[/tex]
Which correctly solves the equation ab+c=d solve for b.
Answer:
b=(d-c)/a
Step-by-step explanation:
Just gotta switch them around a bit
Write the following equation in the general form Ax+ By+ C:
1/2y -1/3x -1 = 0
a.) -2x +3y -6 = 0
b.) 2x -3y -6 = 0
c.) 2x 3y +6 = 0
x+y=k
x-y=k
The solution of the system shown is
O (OK)
O (0,0)
O (k, O)
Answer: (0,0)
Step-by-step explanation:
The only integer"s" that both add and subtract to the same value are 0 "and" 0. Properly stated, the only integer that can be added to itself and subtracted from itself with the same outcome is 0.
Of course, k will also be 0
So this system of equation works out to be
0 + 0 = 0
0 - 0 = 0
|3d-3n|-4 if n=2 and d=3
Answer:
-1
Step-by-step explanation:
[tex]|3d-3n|-4[/tex]
Once we have an absolute value, we know that
[tex]|3d-3n| \geq 0[/tex]
[tex]\text{For }n=2 \text{ and } d=3[/tex]
[tex]|3(3)-3(2)|-4[/tex]
[tex]|9-6|-4[/tex]
[tex]|3|-4[/tex]
[tex]3-4[/tex]
[tex]-1[/tex]
(-8) X 2/3 i NEED the answer help me
-5.33333333333
I used a calulator can I get brainliest please
Need help ASAP with my math
Answer: The answer is -2
Step-by-step explanation: I want points and trust me this answer is correct
What is the sign of the product (3)(−25)(7)(−24)?
A. Positive, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is positive
B. Positive, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is positive
C. Negative, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is negative
D. Negative, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is negative
The temperature at 4:00 p.m. was 2.5'F. It
dropped 0.75°F each hour for the next 4 hours.
What was the temperature at 8:00 p.m.?
Answer:-0.5; 0.75*4=3, 2-3=-0.5
Step-by-step explanation:
Answer:
-0.5...............
bob is on his way home in his car. he has driven 30 miles so far, which is three-fifths of the way home. what is the total length of his drive?
The length of Bob's drive as a fraction = 5/5
Let the length of his total drive be = x
30 miles driven by Bob as a fraction =
= 3/5 of x = 30
= 3/5x = 30
= 5/x = 30 ÷ 3 ( transposing ×3 from LHS to RHS changes ×3 to ÷3 )
=5/x = 10
= x = 10 × 5 ( transposing ÷5 from LHS to RHS changes ÷5 to ×5 )
= x = 50
Now we have to see what is =
= 2/5 of 50
= 2/5 × 50
= 100/5
= 20 miles
So , total length of Bob's drive = 30 miles + 20 miles = 50 miles .
∴ The total length of Bob's drive is 50 miles .
Look at this as a fraction and break it down.
Simplify as much as possible:
-70
-28
Answer:
espera y termino y te ayudo vale que me falta poco vale
бx + 8 = 50
I need that answer
Answer:
=
7
Step-by-step explanation:
please answer asap!!
Answer:
∠QPR = 40°
Step-by-step explanation:
According to the question the line PQ ⊥ PS which means that they both are perpendicular angles. Perpendicular angles are always 90°, so,
∠QPR + ∠RPS = 90°
=> 7x - 9° + 4x + 22° = 90°
=> (7x + 4x) +(22 - 9)° = 90°
=> 11x + 13° = 90°
=> 11x = 90° - 13°
=> 11x = 77°
=> x = 77/11
=> x = 7
So, now that we have x, we can find ∠QPR,
7x - 9°
=> (7 * 7 - 9)°
=> (49 - 9)°
=> 40°
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
A florist sold 45 flowers in a day and 60 flowers on the next day. If p is the percent increase in the number of flowers sold, which proportion can be used to calculate p?
Answer:
c
Step-by-step explanation:
i took the test
Answer: C
Step-by-step explanation:
Only one that makes sense and I just took that test
Use a system of linear equations with two variables and two equations to solve.
175 students enrolled in a freshman-level chemistry class. By the end of the semester, 4 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.
Answer:
35 failed and 140 passed
Step-by-step explanation:
Let p = number who passed
f = number who failed
p+f = 175
4 times the number of students passed as failed, so we need to balance this to set it equal
4f = p
Substitute this into the first equation
4r+f = 175
5f = 175
5f/5 =175/5
f = 35
Now find the number who passed
p = 4f
p = 4*35
p =140
What is the answer of 10% of 6340
Answer:
604
Step-by-step explanation:
just simple division pls giv 5 out ogf 5 and thanks
Answer:
634
Step-by-step explanation:
1) Suppose you buy a laptop costing $1850 at a store charging 12% add-on interest, and you make a $500 down payment.
Find the exact value using trigonometric identities.
1850 , 0.12 , − o n , 500 a
What does the value of the LCM represent? How many packs of red sticks and blue sticks should Harold purchase?
Answer:
LCM mean least common multiple
Step-by-step explanation:
The red sticks in a pack of 8 so, to get 24 red sticks, Harold needs = 3 packs. The blue sticks come in a pack of 12 to get 24 blue sticks, Harold need = 2 pack
Answer:
the LCM represents the minimum number of sticks of each color that Harold would have to buy to have the same number of blue sticks and red sticks.
The red sticks come in packs of 8. So, to get 24 red sticks Harold need 3 packs.
The blue sticks come in packs of 12, so to get to 12 blue sticks Harold needs 2 packs.
in conclusion Harold should purchase 3 packs of red sticks and 2 packs of blue sticks.
hope this helped ^^
What is the value of j