Answer:
The area of the surface over R is [tex]\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]
Step-by-step explanation:
From this study,
The surface area of f(x,y) is expressed by:
[tex]A = \iint_R \sqrt{1 +f^2_x+f^2_y}} \ dA[/tex]
where
[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 2[/tex]
Given that:
f(x,y) = 9 - x²
Thus, [tex]f_x = -2x[/tex] and [tex]f_y = 0[/tex]
However, the area becomes:
[tex]A = \iint_R \sqrt{1+(-2x)^2+0^2} \ dxdy[/tex]
[tex]A = \iint_R \sqrt{1+4x^2} \ dxdy[/tex]
From above, replacing x with [tex]\dfrac{1}{2} \ tan \ u[/tex]
then [tex]dx = \dfrac{1}{2} sec^2 \ udu[/tex]
∴
[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint \sqrt{1 + 4u^2 } \ sec^2 \ udu[/tex]
[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint sec^2 \ udu[/tex]
[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} ( \sqrt{4x^2 + 1x} + \dfrac{1}{2} In \sqrt{4x^2 + 1}+2x)[/tex]
Hence;
[tex]\mathsf{A = \int \limits ^2_0 \begin {bmatrix} \dfrac{1}{2}(\sqrt{4x^2 +1 x}+ \dfrac{1}{2} In ( \sqrt{4x^2+1}+2x \end {bmatrix}^2_0 \ dy}[/tex]
[tex]\mathbf{A = 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]
Therefore, the area of the surface over R is [tex]\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]
An airplane flies at an altitude of 14,690 ft while a submarine is submerged at a depth of 521 feet below the surface of the ocean.. What is the difference between these two elevations? Write an algebraic expression for the given applied problem. Simplified the algebraic expression. In the context of the applied problem, explain what your simplified algebraic expression represents.
Answer:
[tex]d_{T} = d_{A}-d_{S}[/tex]. The algebraic equation represents the distance of the airplane with respecto to the submarine. The distance between the two elevations is 15211 feet.
Step-by-step explanation:
Let be [tex]d[/tex] the distance between a vehicle and sea level, [tex]d > 0[/tex] when vehicle is above sea level, otherwise is below sea level. The difference between airplane and submarine ([tex]d_{T}[/tex]), measured in feet, is obtained by the following expression, that is:
[tex]d_{T} = d_{A}-d_{S}[/tex]
Where:
[tex]d_{A}[/tex] - Distance of airplane with respect to sea level, measured in meters.
[tex]d_{S}[/tex] - Distance of submarine with respect to sea level, measured in meters.
If we know that [tex]d_{A} = 14690\,ft[/tex] and [tex]d_{S} = -521\,ft[/tex], then:
[tex]d_{T} = 14690\,ft - (-521\,ft)[/tex]
[tex]d_{T} = 15211\,ft.[/tex]
The algebraic equation represents the distance of the airplane with respecto to the submarine. The distance between the two elevations is 15211 feet.
The algebraic equation represents the distance of the airplane with respect to the submarine is,
[tex]\rm The \ difference \ between \ both \ elevation = x_a- x_s[/tex]
And the distance between the two elevations is 15,211 feet.
Given that,
An airplane flies at an altitude of 14,690 ft,
While a submarine is submerged at a depth of 521 feet below the surface of the ocean.
We have to determine,
What is the difference between these two elevations?
According to the question,
Let, x be the distance between a vehicle and sea level when the vehicle is above sea level, otherwise is below sea level.
The difference between an airplane [tex]\rm x_a[/tex] and [tex]\rm x_s[/tex] a submarine, measured in feet, is obtained by the following expression, that is:
[tex]\rm The \ difference \ between \ both \ elevation = x_a- x_s[/tex]
Where [tex]\rm x_a[/tex] represents the distance of airplane with respect to sea levels.
And [tex]\rm x_s[/tex] represent the distance of the submarine with respect to sea levels.
Submerged at a depth of 521 feet below the surface of the ocean,
[tex]\rm x_s = -521 \ feet[/tex]
Therefore,
The difference between an airplane [tex]\rm x_a[/tex] and [tex]\rm x_s[/tex] a submarine is,
[tex]\rm The \ difference \ between \ both \ elevation = x_a- x_s\\\\ The \ difference \ between \ both \ elevation = 14,690-(-521)\\\\\rm The \ difference \ between \ both \ elevation = 15,211 \ feet[/tex]
Hence, The difference between these two elevations is 15,211 feet.
For more details refer to the link given below.
https://brainly.com/question/9351049
what is 3/4 - (-4/5)
Answer: 1,55
Step-by-step explanation:
3/4 - (- 4/5) = 3/4 + 4/5 = (3x5)/20 + (4x4)/20 = 15/20 + 16/20 = 31/20 = 1,55
3/4 - (- 4/5) = 3/4 + 4/5 = 0,75 + 0.8 = 1,55
20194+9283 - 372 = ?
will give brainliest or whatever
20,194+9,283 - 372 = 29,105
Simplify. 5-10 | 0.8 - 3/5 | A. –5 B. –1 C. 3 D. 5
Answer:
I dont know what to do... i know I keep bothering you, but you actually give me advice. My favorite advice youve given me was probably, so sus ;)
Step-by-step explanation:
That was an inside joke for anyone else who see this haha
h=vt+1/2gt^2 solving for G
GIVING BRAINLISEST
Answer:
[tex]\displaystyle g = \frac{2(h-vt)}{t^2}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle h = vt+\frac{1}{2}gt^2[/tex]
And we want to solve for g, the acceleration due to gravity.
Proceed with algebra:
[tex]\displaystyle \begin{aligned} h & = vt + \frac{1}{2}gt^2 \\ \\ h - vt & = \frac{1}{2}gt^2 \\ \\ gt^2& = 2(h-vt) \\ \\ g &= \frac{2(h-vt)}{t^2}\end{aligned}[/tex]
In conclusion:
[tex]\displaystyle g = \frac{2(h-vt)}{t^2}[/tex]
Answer:
g = [tex]\frac{2(h - vt)}{t^2}[/tex]
Step-by-step explanation:
Given
h = vt + [tex]\frac{1}{2}[/tex] gt² ( subtract vt from both sides )
h - vt = [tex]\frac{1}{2}[/tex] gt² ( multiply both sides by 2 to clear the fraction )
2(h - vt) = gt² ( divide both sides by t² )
[tex]\frac{2(h-vt)}{t^2}[/tex] = g
Suppose a necklace is made from 18-karat gold and weighs 54 grams. Find the weight, in grams, of the pure gold in the necklace.
I work part time at a jeweler, that necklace would be worth about 3.3K and then also you didn't provide what the effect is. Wouldn't the necklace remain as 54 grams?
Car A is moving twice as fast as car B. Car B starts 174. Meters in front of car A. If car A passes car B in 27 seconds, how fast is car B going.
Answer: The speed of car B is 6.44 m/s
Step-by-step explanation:
Let's define:
Sa = Speed of car A.
Sb = Speed of car B.
I assume that at t = 0s, the position of car A is 0m (then at t = 0s, the position of car B is 174m)
Then we can write the positions of each car as:
Pa(t) = Sa*t
Pb(t) = Sb*t + 174m.
We also know that Sa = 2*Sb.
And we know that at t= 27s, car A passes car B.
Then at t = 27s, the positions of both cars must be the same:
Pa(27s) = Pb(27s)
Sa*27s = Sb*27s + 174m.
Now we can replace Sa by 2*Sb (from the above equation)
2*Sb*27s = Sb*27s + 174m
Now we can solve this for Sb.
2*Sb*27s - Sb*27s = 174m
Sb*27s = 174m
Sb = 174m/27s = 6.44m/s.
The speed of car B is 6.44 m/s
Find the equation of the line with slope −2 and that contains the point (−9,−7). Write the equation in the form y=mx+b and identify m and b.
Answer:
m = -2 which is the slope
b = 2 which is the intercept of the line.
Step-by-step explanation:
We have that the line must pass through the following points (-9, -7). These two points are any two of the numerous points that pass through the straight line. We can designate variables to each of these points as shown below
Let us take our [tex]y_1 = -7[/tex] and [tex]x_1 = -9[/tex]
Given the slope as [tex](y-y_1)/(x-x_1)=-2[/tex]
[tex](y--7)/(x--9) = -2[/tex]
[tex](y +7)/(x+9) =-2[/tex]
[tex]y +7 = -2(x+9)[/tex]
[tex]y =-2x+2[/tex]
We are given the form: y=mx+b.
we can compare this with our equation for the line. [tex]y =-2x+2[/tex]
We can see that m = -2 which is the slope and b = 2 which is the intercept of the line.
If elephant grass grows 3 2/5 inches a day, how many inches will it grow in 7 days?
Step-by-step explanation:
do 3 2/5 times by 7 to get ur answer
what is the reciprocal of 2 8/9
9/26
2 8/9 = 26/9
Reciprocal of 16/9 is 9/26
The inequality x2 – 5x + 3 < 3 can be broken down into two related inequalities. The graphs of these related inequalities are shown on the graph to the left. Which set shows the solution to the inequality?
Answer:
A (0,5)
Step-by-step explanation:
Look where both lines intersect.
Answer:
(0, 5)
Step-by-step explanation:
Three students have proposed these ways to describe when two lines l and m are perpendicular: Read screenshot for info. Explain why each of these definitions is correct. What are some of the advantages and disadvantages with each?
Answer:
a. The definition that l and m are perpendicular if they meet at one point and one of the angles at their point of intersection is a right angle
The above definition is correct because, where two lines intersect, forming an angle of 90° with each other, then, by definition of perpendicular lines, the direction of one line is perpendicular to the other
The advantage of the above definition are;
1) It is simply stated and therefore, will be easier to understand
2) It can be easily used to test the perpendicular relationship between two objects
Disadvantages
1) It gives limited description of the other characteristics of the line
2) It does not state if the lines extend past each other after the point at which they cross
b. For the definition, l and m are perpendicular if they meet at one point and all four of the angles at their point of intersection are right angles
The above definition is correct as it meets the condition of two lines to be perpendicular to each other
Advantages
1) It clearly describes the relationship between the lines and their appearance
2) It indicates that the sun of angles at the point of intersection is 360°
Disadvantage
1) The resulting detail of the four angles may lead to ambiguity in the case where the two lines do not cross and there are only three angles formed at the point
c. For the definition, l and m are perpendicular if they meet at one point and reflection about l maps m to itself
The above definition is correct as it indicates the requirement for the continuity of the definition of the on line after crossing the other line
Advantages
1) It defines the condition of perpendicularity without the requirement for measuring the angles
2) It states the symmetrical condition of perpendicular lines about the vertical axis
Disadvantages
1) It requires further clarification in order to be related to the original definition of perpendicular lines being lines that are at right angle to each other.
Step-by-step explanation:
To address a falling GDP, a government may:
A. raise interest rates to allow businesses to borrow more money.
B. reduce the amount of money it puts into circulation.
C. invest in programs in order to help people in need.
D. lower interest rates to allow businesses to borrow more money.
Answer: D. Lower interest rates to allow businesses to borrow more money
Step-by-step explanation:
just took the test
To address a falling GDP, a government may lower interest rates to allow businesses to borrow more money. The correct option is A.
What is GDP?Real GDP (short for real GDP) is a macroeconomic measure of the value of economic output adjusted for price changes. This adjustment transforms the money-value measure, nominal GDP, into an index for the quantity of total output.
It is computed using the prices of a given base year. To calculate Real GDP, you must first determine how much GDP has been changed by inflation since the base year and then divide that amount by the number of years.
A government may lower interest rates to allow businesses to borrow more money in order to address a falling GDP.
To know more about GDP follow
https://brainly.com/question/1383956
#SPJ5
Mrs. Li wants to compare her students’ test scores to the school average. She created a table to help her.
Answer:
Cierra & Fionna
Step-by-step explanation:
Anything 0 and above would represent someone passing or getting it spot on. The negatives mean below the average of other students.
Simplify.
-(1 - 3)2 - 2x2
When using the power rule, the original coefficient:__________a) Is multiplied by the original exponent.b) Only changes if the function is in terms of x.c) Is ignored
Answer:
a) Is multiplied by the original exponent.
Step-by-step explanation:
the power rule works like this:
you want to find the derivative of ax ⁿ
where n is the exponent and a is the coefficient
the derivative would equal (n ⋅ a)xⁿ⁻¹
e.g. you want to find the derivatives of 5x⁴
f'(x) = (4 ⋅ 5)x⁴⁻¹ = 20x³
f''(x) = (3 ⋅ 20)x³⁻¹ = 60x²
f'''(x) = (2 ⋅ 60)x²⁻¹ = 120x
f''''(x) = (1 ⋅ 120)x¹⁻¹ = 120
1 1/4 times 2/5 divided by 3 1/3
What’s the answer to x/2-12= -14
Answer:
x = -4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x /2 −12=−14
1 /2 x+−12=−14
1/ 2 x−12=−14
Step 2: Add 12 to both sides.
1 /2 x−12+12=−14+12
1 /2 x=−2
Step 3: Multiply both sides by 2.
2*( 1 2 x)=(2)*(−2)
x = −4
Answer:
-1
Step-by-step explanation:
step 1: X/2-12=-14
step2 : X/2=-14+12
step3 : X/2=-2
step4 : X=-2/2
step5 : X=-1
Which number is equal to 10 Superscript negative 3
Answer:
1/1000 or 0.001.
Step-by-step explanation:
10 ^-3
= 1/10^3
= 1/1000.
For the equation
3
x
−
4
y
=
−
12
3
x
-
4
y
=
-
12
is there any tutor available like a techer
Chen burns 354 calories in 1-hour swimming. He swam for 28 hours last month. How many calories did Chen burn in all last month from swimming?
Answer: he burned 9912 calories all last month
can you help for me 20x+5y=15 for y
3. Casey wants to do some baking. She has 6 cups of flour. One of the recipes she wants
to make calls for 3 cups of flour. Another recipe calls for cup of flour. The final recipe
calls for 2 cups of flour.
Will Casey have enough flour to make all three recipes? If so, wills she have any left
over? How much?
Step-by-step explanation:
assuming cup of flower means 1 cup of flower
3+2+1=6
She has enough to make the three recipes and she has nothing left over
A board of length (6x4 + 9x2- 21) meters is to be cut into three pieces of the same length. Find the length of each
piece.
Answer:
(2x⁴ + 3x² -7)
Step-by-step explanation:
Length is
(6x⁴ + 9x²- 21)It is to be divided by 3.
Note when dividing the polynomial by any value each of the terms is divides by same value:
(6x⁴ + 9x²- 21)/3 = 6x⁴/3 + 9x²/3 - 21/3 = 2x⁴ + 3x² -7Each piece is (2x⁴ + 3x² -7) meters long
solve the equation X³+2X²-5X -6
Answer: x = {-1, -3, 2}
Step-by-step explanation:
x³ + 2x² - 5x - 6 = 0
Use the rational root theorem to find the possible roots: ±1, ±2, ±3, ±6
Use Long division, Synthetic division, or plug them into the equation to see which root(s) work (result in a remainder of zero).
I will use Synthetic division. Let's try x = 1
1 | 1 2 -5 -6
| ↓ 1 3 -2
1 3 -2 -8 ← remainder ≠ 0 so x = 1 is NOT a root
Let's try x = -1
- 1 | 1 2 -5 -6
| ↓ -1 -1 6
1 1 -6 0 ← remainder = 0 so x = -1 is a root!
The coefficients of the reduced polynomial are: 1, 1, -6 --> x² + x - 6
Factor: x² + x - 6
(x + 3)(x - 2)
Set those factors equal to zero to solve for x:
x + 3 = 0 --> x = -3
x - 2 = 0 --> x = 2
Using Synthetic Division and Factoring the reduced polynomial, we found
x = -1, -3, and 2
What is the percent change from 56 to 39? Round your answer to the
nearest tenth.
Answer:
30.4%
Step-by-step explanation:
A certain field is a rectangle with a perimeter of
846
feet. The length is
159
feet more than the width. Find the width and length of the rectangular field.
Answer:
Width = 132 feet, Length = 291 feet
Step-by-step explanation:
perimeter (P) = 846
let width(W) = x
length(L) = 159 feet more than width = 159 + W= 159 + x
P of a rectangle = 2*(L + W)
846 = 2*((159 + x) + x)
divide both side by 2
423 = (159 + x) + x
423 = 159 + 2x
rearranging
2x + 159 = 423
2x = 423 -159
2x = 264
divide both sides by 2
x = 132 feet
recall W = x and L = 159 + x
W = 132 feet
L = 159 + 132 = 291 feet
If F(x)=4x-3, evaluate the following a. F(5) b. F(-4)
Answer:
F(5) = 17, F(4) = -19
Step-by-step explanation:
F(5) = 4(5) - 3
F(5) = 20 - 3
F(5) = 17
F(4) = 4(-4) - 3
F(4) = -16 - 3
F(4) = -19
is the population of cats on another island whose cat population was originally 11,000 but is doubling every 14 months. (t is time in months.)
Answer:
P = 11,000(2)^t/11
Step-by-step explanation:
The formula is given as:
P = Po(2)^t/d
Where
Po = Initial population = 11,000
t = time in months
d = doubling time = 11 months
Hence,
P = 11,000(2)^t/11
Hence, the population of cats is given by the equation:
P = 11,000(2)^t/11
The formula to convert Celsius to Fahrenheit is F= 90+32. Convert 87°F to
Celsius. Round to the nearest degree.
O A. 55°C
O B. 31°C
O c. 16°C
O D. 99°C
SUBMIT