Answer:
12,621
Step-by-step explanation:
when rounding there asking for the thousands therefore you have to look at the hundreds place and since there's a six in the hundreds place the one is going to change to a 2 the answer is 12,621
Find the area of the surface. The part of the paraboloid z = 1 - x2 - y2 that lies above the plane z = -6
Answer:
π/6 [(29)^³/₂ − 1]
81.247
Step-by-step explanation:
Surface area is:
S = ∫∫ √(fₓ² + fᵧ² + 1) dA
The partial derivatives are:
fₓ = -2x
fᵧ = -2y
Substituting:
S = ∫∫ √(4x² + 4y² + 1) dA
To make this easier, we can convert to polar coordinates.
S = ∫∫ √(4r² + 1) dA
S = ∫∫ √(4r² + 1) r dr dθ
S = ⅛ ∫∫ 8r √(4r² + 1) dr dθ
The limits for θ are 0 to 2π. The minimum of r is 0. The maximum of r is:
-6 = 1 − x² − y²
-6 = 1 − r²
r² = 7
r = √7
Integrating the first integral:
S = ⅛ ∫ ⅔ (4r² + 1)^³/₂ |₀ᴿ dθ
S = ⅛ ∫ [⅔ (4(7) + 1)^³/₂ − ⅔ (4(0) + 1)^³/₂] dθ
S = ⅛ ∫ [⅔ (29)^³/₂ − ⅔] dθ
S = ¹/₁₂ [(29)^³/₂ − 1] ∫ dθ
Integrating the second integral:
S = ¹/₁₂ [(29)^³/₂ − 1] θ |₀²ᵖⁱ
S = ¹/₁₂ [(29)^³/₂ − 1] (2π − 0)
S = π/6 [(29)^³/₂ − 1]
S ≈ 81.247
The area of a shape is the amount of space it covers.
The surface area is approximately 81.3 unit squares
The given parameters are:
[tex]\mathbf{z = 1 - x^2 - y^2}[/tex]
[tex]\mathbf{z = -6}[/tex]
Calculate the partial derivatives of [tex]\mathbf{z = 1 - x^2 - y^2}[/tex]
[tex]\mathbf{f_x = -2x}[/tex]
[tex]\mathbf{f_y = -2y}[/tex]
So, the surface area is:
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(f_x^2 + f_y^2 +1 )}} \, dA }[/tex]
So, we have:
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{((-2x)^2 + (-2y)^2 +1 )}} \, dA }[/tex]
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4x^2 + 4y^2 +1 )}} \, dA }[/tex]
Factor out 4
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4(x^2 + y^2) +1 )}} \, dA }[/tex]
Substitute
[tex]\mathbf{r^2 = x^2 + y^2}\\\mathbf{dA = rdr d\theta}[/tex]
So, we have:
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r\ dr\ d\theta }[/tex]
Multiply by 1
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r \times 1\ dr\ d\theta }[/tex]
Express 1 as 8/8
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r \times \frac{8}{8}\ dr\ d\theta }[/tex]
Rewrite as:
[tex]\mathbf{A =\frac{1}{8} \int\limits^a_b\int\limits^a_b {8r \sqrt{(4r^2 +1 )}}, \ dr\ d\theta }[/tex]
From the question,
[tex]\mathbf{z = -6}[/tex]
So, we have:
[tex]\mathbf{1 - r^2 = -6}[/tex]
Add 6 to both sides
[tex]\mathbf{7 - r^2 = 0}[/tex]
So, we have:
[tex]\mathbf{r^2 = 7}[/tex]
Integrate [tex]\mathbf{A =\frac{1}{8} \int\limits^a_b\int\limits^a_b {8r \sqrt{(4r^2 +1 )}}, \ dr\ d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{8} \int\limits^a_b {\frac{8}{12} (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{8} \times \frac{8}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32} -(4 \times 0^2 +1 )^{\frac 32} }, d\theta }[/tex]
Substitute [tex]\mathbf{r^2 = 7}[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4\times 7 +1 )^{\frac 32} - 1^{\frac 32}}, d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b {29^{\frac 32} - 1}, d\theta }[/tex]
Rewrite as:
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \int\limits^a_b d\theta }[/tex]
Integrate
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times \theta |\limits^{2\pi}_0}[/tex]
So, we have:
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times (2\pi - 0) }[/tex]
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times 2\pi}[/tex]
Rewrite as:
[tex]\mathbf{A =\frac{2\pi}{12} (29^{\frac 32} - 1)}[/tex]
[tex]\mathbf{A =\frac{\pi}{6} (29^{\frac 32} - 1)}[/tex]
[tex]\mathbf{A =81.3}[/tex]
Hence, the surface area is approximately 81.3 unit squares
Read more about surface areas at:
https://brainly.com/question/3621496
John earns $437 a week after a 15% pay rise. What was his pay initially? Round your answer to the nearest dollar.
Answer:
380 dollars
Step-by-step explanation:
John earns $437 a week after a 15% pay rise.
Let the initially pay of John be x
x + (15% of x) = 437
x + 0.15x = 437
1.15x = 437
x = \frac{437}{1.15}
1.15
437
x = 380
Find the slope of the line that passes through the points (8, 2) and (4,4).
Helppp !!
Answer:
-[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
We can find the slope of the line by using the point slope formula: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
If we plug in your numbers, we get:
[tex]\frac{4-2}{4-8}[/tex], or -[tex]\frac{2}{4}[/tex], or -1/2.
Twenty point question!
Answer:
yes
no
Step-by-step explanation:
i hope im correct please give me brainliest and some feedback if im correct or not :)
Ram bought an article for rs. 148.75. He gave rs. 200 to the shopkeeper. What balance will he get ?
Answer:
his balance will be 51.25 rs.
Step-by-step explanation:
200 - 148.75 = 51.25
Answer:
51.25
Step-by-step explanation:
200-148.75
=51.25
Calculating Rate of change
Answer/Step-by-step explanation:
We are given the following coordinates of two points on the line of the graph shown in the question as: A(2, 1) and B(4, 2)
Vertical change from point A = [tex] y_2 - y_1 = 2 - 1 = 1 [/tex]
Horizontal change from point A = [tex] x_2 - x_1 = 4 - 2 = 2 [/tex]
Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{1}{2} = 0.5 [/tex]
Help. Please, I will give you brainliest. Give me the right answers.
Step-by-step explanation:
[tex] \sf{\dfrac{5( \fbox{41} - 32)}{9} = C}[/tex]
[tex] \sf{\dfrac{5( \fbox{9})}{9} = C}[/tex]
[tex] \sf{ \dfrac{45}{9} = C}[/tex]
[tex] \sf{C = 5 }[/tex]
So,
41° F = [5]°C
Hello Can someone help me please???
What is the factored form of 5x2 – 19x + 12?
A.) (5x – 3)(x – 4)
B.) (5x – 4)(x – 3)
C.) (5x – 12)(x – 1)
D.) (5x – 1)(x – 12)
Answer:
pretty sure its B
Step-by-step explanation:
hope this helps ;)
Solve: 2/3x-7=17 please help
Answer:
x=36
Step-by-step explanation:
2/3x-7=17
2/3x-7+7=17+7
2/3x=24
2/3x(3)=24(3)
2x=72
2x/2=72/2
x=36
-2/7 x 3/7 as fraction
Answer:
-6/49
Step-by-step explanation:
this is the answer it is very easy
Which set of numbers best describes the possible values of x in the equation below?
[x-1] = [x]
a. all integer values of x
b. all real number values of x
c. only negative values of x
d. only non-integer values of x
The set of numbers best describes the possible values of x in the equation is option c. only negative values of x.
Calculation of the possible values of x;Since the equation is
x - 1 = x
So, here the x should be canceled out
So, it should be like
0 = -1
Hence, we can say that
The option c is correct,
And, the rest of the options are incorrect.
Learn more about number here: https://brainly.com/question/14938106
I need help please help me
A florist has 80 flowers. She ties 3 flowers together in each bunch. If she makes as many bunches of 3 flowers as possible, how many flowers are left over?
Question Help
A local little league has a total of 70 players, of whom 80% are right-handed. How many
right-handed players are there
Answer:
The number of right-handed people = 56
Step-by-step explanation:
80% of 70 players = number of right-handed people
So, 80/100 x 70 = 56 players
Therefore, number of right-handed players = 56
It is necessary to find the times when the temperature is 8° F. Which of the following is the correct equation to do this
(A) 9 - 1 = 8
(B) 9+2 = 8
(C) 9-12 = 8
What number is 30 percent of 50
Answer:
15 (50*0.3)
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
0.3*50 = 15
You spend 5/6 of your money on new clothes for school. The amount you spend on jeans for school is 2/5 of the total amount you spend on all your school clothes.
What fraction of money do you spend on jeans?
A. 7/30 on jeans
B. 10/30 on jeans
C. 1/3 on jeans
D. 5/30 on jeans
Answer:
C
Step-by-step explanation:
well when we multiply to get a common denominator we get 25/30 and 12/30 so the only possible answer is 1/3
In a test of a printed circuit board using a random test pattern, an array of 14 bits is equally likely to be 0 or 1. Assume the bits are independent.
(a) What is the probability that all bits are 1s? Round your answer to six decimal places (e.g. 98.765432). Enter your answer in accordance to the item a) of the question statement
(b) What is the probability that all bits are 0s? Round your answer to six decimal places (e.g. 98.765432). Enter your answer in accordance to the item b) of the question statement
(c) What is the probability that exactly 7 bits are 1s and 7 bits are 0s? Round your answer to three decimal places (e.g. 98.765). Enter your answer in accordance to the item c) of the question statement
Answer:
(a) 0.000061
(b) 0.000061
(c) 0.209
Step-by-step explanation:
An array of 14 bits is equally likely to be 0 or 1.
That is, P (0) = P (1) = 0.50.
(a)
Compute the probability that all bits are 1s as follows:
[tex]P(\text{All bits are 1s})=[P(1)]^{14}[/tex] ∵ the bits are independent
[tex]=(0.50)^{14}\\=0.00006103515625\\\approx 0.000061[/tex]
Thus, the probability that all bits are 1s is 0.000061.
(b)
Compute the probability that all bits are 0s as follows:
[tex]P(\text{All bits are 0s})=[P(0)]^{14}[/tex] ∵ the bits are independent
[tex]=(0.50)^{14}\\=0.00006103515625\\\approx 0.000061[/tex]
Thus, the probability that all bits are 0s is 0.000061.
(c)
Compute the probability that exactly 7 bits are 1s and 7 bits are 0s as follows:
Define X as the number of bits that 1s.
Then the random variable X will follows a binomial distribution with parameters n = 14 and p = 0.50.
The value of P (X = 7) is:
[tex]P(X=7)={14\choose 7}(0.50)^{7}(1-0.50)^{14-7}[/tex]
[tex]=\frac{14!}{7!\times 7!}\times (0.50)^{14}\\\\=3432\times 0.000061\\\\=0.209352\\\\\approx 0.209[/tex]
Thus, the probability that exactly 7 bits are 1s and 7 bits are 0s is 0.209.
In Earnest's yard, the grass grew 2 inches. The next week, Earnest cut 2 inches off of the grass. The total change was 0 inches. Which of the following situations
also has a total change of 0?
I put 5 pounds of birdseed in the feeder. Then, birds ate 5 pounds of birdseed.
It rained 2 inches on Tuesday. Then, it rained 2 inches on Wednesday.
It Snowed 4 inches last week. Then, 8 inches of snow melted during this week.
A farmer sold 3 bushels of apples last week. Then, she sold 6 bushels of apples this week.
Answer:
The answer is the first one, I put 5 pounds of birdseed and he ate 5 pounds, leaving you with none, or zero.
Step-by-step explanation:
Sam was asked to place the numbers shown below in order from greatest to least.
5, -0.5, 4, 350%, -13, 4.7, -66, 1.22
ANSWER ASAP
Answer:
5 > 4.7 > 4 > 350% > 1.22 > -0.5 > -13 > -66
Step-by-step explanation:
Last night, Hailey spent 1 2/5 hours on her math
homework, then 45 minutes on her science
homework. What is the total time she spent doing her
math and science homework? Write your answer in a
complete sentence.
Answer:
a = 2 hours and 9 minutes
Explanation:
(using fractions)
45 minutes + 1 2/5 hours = 3/4 hours + 7/5 hours = 15/20 + 28/20 = 43/20 = 2 3/20 = 2 9 /60 = 2 hours 9 minutes.
(using decimals)
45 minutes + 1 2/5 hours =
0.75 hours + 1.4 hours = 2.15 hours = 2 hours 9 minutes.
since .15 × 60 = 9 .
Also keep in mind that there are 60 minutes in an hour.
Answer:2 3/20
Step-by-step explanation:
1 2/5 + 45(3/4)
=2 3/20
A man earned wages of $30,600 , received $2900 in interest from a savings account, and contributed $2600 to a tax-deferred retirement plan.He was entitled to a personal exemption of $2500 and had deductions totaling $5020. Find his gross income, adjusted gross income, and taxable income
Answer:
So the answer is gonna be: 33,580. Hope this help!
Step-by-step explanation:
You have wanted a car you entire life (literally since you were born)!! It is time...you found the car of you dreams AND the car is marked as 80% of!!!! What a deal!!! "What could go wrong" you ask yourself. You buy the car for $625 (and the man in the hood walks off smiling). As your parent(s) drive you home after picking you up next to your broken down vehicle 3 hours later, they ask you what the original price of the car was before the price reduction. What was the original price of your.... "dream car"?
Answer:
200,000
Step-by-step explanation:
Departure time: 6:15 am
Arrival time: 4:24 pm
Travel time: ?
Answer:
Airplanes
Step-by-step explanation:
Aviation is the Airplanes and they need to take off on their flight on their way for Visit! Welcome Aboard!
Answer:
10h and 9 min
Step-by-step explanation:
Write as a product:
25a^2−0.01b^10
Answer:
(5a + 0.1b^5)(5a + 0.1b^5)
Step-by-step explanation:
25a^2 − 0.01b^10 =
This follows the pattern: x^2 - y^2 = (x + y)(x - y)
= (5a + 0.1b^5)(5a + 0.1b^5)
Multiply the polynomial expressions.
-3x*(2x2 - 4x + 1)
Answer:
-15
Step-by-step explanation:the
$20,500 at 7% for 3 years,
Answer:
If it is simple interest then it is $24805
If it is a compound interest then it is $25113.38
Step-by-step explanation:
Find the volume of the solid that lies under the plane 3x + 2y + z = 12 and above the rectangle. $$ R = \{(x,y) | 0\le x \le {\color{red}1}, -{\color{red}2} \le y \le {\color{red}4} \} $$
Answer:
51 cubic units
Step-by-step explanation:
[tex]3x+2y+z=12\\\Rightarrow z=12-3x-2y[/tex]
Now we integrate over volume integral over the range [tex]R = \{(x,y) | 0\le x \le {1}, -{2} \le y \le {4} \}[/tex]
[tex]V=\int_0^1\int_{-2}^4 12-3x-2y dydx\\ =\int_{-2}^4 12y-3yx-y^2|_4^{-2} dx\\ =\int_{0}^1 12\times4-3\times4x-16-[12\times-2-3\times-2x-4]dx\\ =\int_{0}^1 60-18xdx\\ =60x-9x^2|_{0}^1\\ =60-9\\ =51\ \text{cubic units}[/tex]
The volume of the solid is 51 cubic units.
Please help me with this math question
How can you write the expression 7b-2) in words?
Answer:
D :)
Step-by-step explanation:
Answer:
The answer is d