Answer:
Hello,
Step-by-step explanation:
[tex]y^2-x^2+1=50\\y^2=x^2+49\\2\ functions \ :\\\\y=\sqrt{x^2+49} \\\\or\\\\y=-\sqrt{x^2+49} \\[/tex]
Using function concepts, it is found that:
The explicit equation in terms of x is given by: [tex]y = \pm \sqrt{x^2 + 49}[/tex]The equation is not a function, as there are multiple outputs for a single input.----------------------
The expression is given by:
[tex]y^2 - x^2 + 1 = 50[/tex]
In terms of x, the equation is given by:
[tex]y^2 = 50 + x^2 - 1[/tex]
[tex]y^2 = x^2 + 49[/tex]
[tex]y = \pm \sqrt{x^2 + 49}[/tex]
----------------------
An equation is a function if for each value of the input, there is only one output.Testing the input x = 0:
[tex]y = \pm \sqrt{0^2 + 49}[/tex]
[tex]y = \pm \sqrt{49}[/tex]
[tex]y = \pm 7[/tex]
Two output values for one input, thus, it is not a function.
A similar problem is given at https://brainly.com/question/24603090
the volume of the donut created when the circle {x}^{2}+{y}^{2}=4 is rotated around the line x=4.
Answer:
32π²
Step-by-step explanation:
To solve this, we can use the washer method.
We can start by dividing the donut into horizontal sections. Each horizontal section is a hollow cylinder, with the inner cylinder's radius being the difference between x=4 and x²+y²=4, which can also be written as x = √(4-y²) (we do not need the negative x values as the inner cylinder does not encompass any part of the circle). This is (4-√(4-y²)) .
Similarly, the outer radius will be equal to the difference between 4 and the other side of the circle. This encompasses the circle and the extra area in between, so x will be negative here, making it (4-(-√(4-y²)) = 4+√(4-y²).
The area of the cylinder for a given Δy can be represented by
(4+√(4-y²))²πΔy - (4-√(4-y²))²πΔy. This space represents a cylinder in the donut created with the height being Δy. Simplifying the equation, we get
(4+√(4-y²))²πΔy - (4-√(4-y²))²πΔy = πΔy((4+√(4-y²))²- (4-√(4-y²))²)
(4+√(4-y²))²- (4-√(4-y²))² = 16+8√(4-y²) + 4-y² - (16-8√(4-y²)+4-y²)
= 16√(4-y²)
(4+√(4-y²))²πΔy - (4-√(4-y²))²πΔy = 16√(4-y²)πΔy
The donut ranges from all y values from -2 to 2, and to add all the areas of the cylinders up between these y values, we can make this an integral,
[tex]\int\limits^2_{-2} {16\pi \sqrt{4-y^2} \, dy\\[/tex]
perform u substitution, make y = 2sin(u). If y=2sin(u), then y/2 = sin(u) and arcsin(y/2) = u
[tex]\int\limits^2_{-2} {16\pi* 2cos(u) \sqrt{4-4sin^2(u)} \, du\\[/tex]
take the 32π out of the integral
[tex]32\pi\int\limits^2_{-2} {cos(u) \sqrt{4-4sin^2(u)} \, du\\\\= 32\pi\int\limits^2_{-2} {cos(u) *2cos(u)} \, du\\\\\\= 32\pi\int\limits^2_{-2} {2cos&^2(u)} \, du\\\\\\\\\\[/tex]
take the 2 out of the integral
[tex]64\pi\int\limits^2_{-2} {cos&^2(u)} \, du\\[/tex]
One reduction formula we can use here is that
[tex]\int\limits {cos^nx} \, dx = \frac{1}{n} cos^{n-1}(x) sin(x) +\frac{n-1}{n} \int\limits {cos^{n-2} (x)} \, dx[/tex]
Applying that here, we get
[tex]\int\limits {cos^2u} \, du = 0.5cos(u)sin(u) + 0.5 \int\limits {1} \, du\\= 0.5cos(arcsin(y/2))sin(arcsin(y/2)) + 0.5(arcsin(y/2))[/tex]
take that cos(arcsin(x)) = √(1-x²) and sin(arcsin(x)) = x and we get
[tex]\int\limits {cos^2u} \, du = 0.5\sqrt{1-y^2/4}*(y/2) + 0.5arcsin(y/2)\\= 0.25y\sqrt{1-y^2/4} + 0.5arcsin(y/2)\\[/tex]
multiply this back with the 64π to get
[tex]16\pi y\sqrt{1-y^2/4} + 32\pi arcsin(y/2)[/tex]
as our integral. Applying this to the bounds of [-2, 2], we get
16π(2)√(1-4/4) + 32πarcsin(1) - (16π(-2)√(1-4/4) + 32πarcsin(-1))
= 0 + 32π(π/2) - 32π(-π/2)
= 16π²+16π²
= 32π²
as our answer
For the following function, solve both f'(x) = 0 and f''(x) = 0 for x.
f(x) = x(x - 3)^4
12. Convert 30.283° into a degree-minute-second format.
O A. 18° 16' 98"
B. 18° 28' 30"
C. 30° 16' 58"
D. 30° 28' 30"
The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The angle is given below.
⇒ 30.283°
Convert 30.283° into a degree-minute-second format. Then we have
⇒ 30° (0.83 x 60')
⇒ 30° 16.98'
⇒ 30° 16' (0.98 x 60'')
⇒ 30° 16' 58"
The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.
More about the conversion link is given below.
https://brainly.com/question/9414705
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56 x 10^-4)
Group of answer choices
2.37 x 10^-16
4.21 x 10^15
2.4 x 10^-16
4.2 x 10^15
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Answer:
(d) 4.2×10^15
Step-by-step explanation:
Your calculator will tell you the quotient is about ...
4.21348...×10^15
The least precise number in the division is 1.5, which has 2 significant digits. Therefore, the result should be rounded to 2 significant digits:
4.2×10^15
Which equation represents a population of 210 animals that decreases at an annual rate of 14%
Answer:
The equation i.e. used to denote the population after x years is:
P(x) = 490(1 + 0.200 to the power of x
Step-by-step explanation:
This problem could be modeled with the help of a exponential function.
The exponential function is given by:
P(x) = ab to the power of x
where a is the initial value.
and b=1+r where r is the rate of increase or decrease.
Here the initial population of the animals are given by: 490
i.e. a=490
Also, the rate of increase is: 20%
i.e. r=20%
i.e. r=0.20
Hence, the population function i.e. the population of the animals after x years is:
P(x) = 490(1 + 0.200 to the power of x
So for this, we will be using exponential form, which is y = ab^x (a = initial value, b = growth/decay).
Since we start off with 210 animals, that is our a variable.
Next, since this is *decreasing* by 14%, you are to subtract 0.14 (14% in decimal form) from 1 to get 0.86. That will be your b variable.
Putting everything together, your equation is y = 210(0.86)^x
g is a trigonometric function of the form g(x)=acos(bx+c)+d
Below is the graph of g(x). The function has a maximum point at (3.5,-4) and a minimum point at (-1,-5)
Find a formula for g(x). Give an exact expression.
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Answer:
a = 0.5b = π/4.5c = 7π/9d = -4.5Step-by-step explanation:
The value of d is the average of the maximum and the minimum.
d = (-4 +-5)/2 = -9/2 = -4.5
The value of 'a' is the difference between the maximum and d.
a = -4 -(-4.5) = 0.5
The value of b is 2π divided by the period. Here, the half-period is 3.5 -(-1) = 4.5, so ...
b = 2π/9 = π/4.5
The value of c is the value that makes the cosine argument zero at x=3.5.
(π/4.5)(3.5) +c = 0
c = -7π/9
I had 180 mL of water in a measuring cylinder.
I added a stone. The reading is now 195 mL.
What is the volume
of the stone?
Answer:
15×10^-6 cubic meter
Step-by-step explanation:
The volume of the stone is, 195-180 = 15 mL
which is, 15×10^-6 m³
Answer:
=15
Step-by-step explanation:
195ml - 180ml
= 15
the first measuring minus with the second measuring will get the volume for the stone
How many solutions exist for the given equation?
121 x+ 1 =3(4x+1)-2
zero
one
two
infinitely many
Answer: infinitely many
The distance between Ali's house and 1 point
college is exactly 135 miles. If she
drove 2/3 of the distance in 135
minutes. What was her average speed
in miles per hour?
Ali's average speed was 40 miles per hour.
What is an average speed?
The total distance traveled is to be divided by the total time consumed brings us the average speed.
How to calculate the average speed of Ali?
The total distance between the college from Ali's house is 135 miles.
She drove 2/3rd of the total distance in 135 minutes.
She drove =135*2/3miles
=90miles.
Ali can drive 90miles in 135 mins.
Therefore, her average speed is: 90*60/135 miles per hour.
=40 miles per hour.
Learn about average speed here :
https://brainly.in/question/14787217
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If my final is worth 15% of my mark and I'm at 70% right now what would I need to get on my final to get at least 75% overall
Answer:
Step-by-step explanation:
70*85/100 = 59.5 This is what you have right now.
You need 15.5 gross marks to get up to 75
As you can see, I'm sorry to say, you cannot do it.
Mind you, you would not miss by much. You could get about 74.5 if you got a hundred % on your final. This is just an estimate. I'm just trying to show you what you have to do to get near your goal. The 59.5 is accurate. So is the 15.5. Only your possible final grade is an estimate.
54
What value of b will cause the system to have an
infinite number of solutions?
y = 6x - b
-3х+ 1/2y=-3
b=
Answer:
Does the answer help you?
Simplify expression 1 1/2
Answer:
3/2 or 1.5
Step-by-step explanation:
Hey there!
[tex]\huge\boxed{\mathsf{1\dfrac{1}{2}}}}\\\huge\boxed{\mathsf{\rightarrow \dfrac{1\times1+2}{2}}}\\\\\\\huge\boxed{{1\times1+2}}\\\huge\boxed{= 1+2}\\\huge\boxed{=3}\\\\\\\huge\boxed{\rightarrow \mathsf{\dfrac{3}{2}}}\\\\\\\huge\boxed{\textsf{Answer: }\bf \dfrac{3}{2}}\huge\checkmark\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\\\\\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
find the surface area of the cylinder and round to nearest tenth HURRY HURRY
Answer:
Does the answer help you?
How do I solve |10-5| ?
Answer:
5
Step-by-step explanation:
Subtract
5
from
10
.
|
5
|
The absolute value is the distance between a number and zero. The distance between
0
and
5
is
5
.
5
Arrange the following rational numbers in descending order. 5/8 ,-11/15 , 17/(-24) ,7/12
1. Find the HCF of the following numbers by prime factorisation and continued division method10,35,40
Answer:
Step-by-step explanation:
10 = 2*5
35 = 5*7
40 = 2*2*2*5
The number 5 is common to all three factorisations
So the HCF = 5.
Continued division:
10 and 35:
10) 35(3
30
5)10(2
10
0
- so the HCF of 10 and 35 is 5.
10 and 40:
10)40( 4
40
0
So the HCF of 10 and 40 is 10
We found HCF of 10 and 35 is 5 so:
HCF of 10, 35 and 40 is HCF of 5 and 10 which is 5.
if there are 5 routes to travel between A and B, how many options are there for a person to travel form A to B and retrun back?
Answer:
25
Step-by-step explanation:
look at the image to see the question
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Answer:
1385.4 yd³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . radius r and height h
For the given radius and height, the volume is ...
V = π(7 yd)²(9 yd) = 441π yd³ ≈ 1385.4 yd³
Find the simple interest owed for the loan. $2,550 at 2% for 1 year
Answer:
The simple interest owed is $51
Step-by-step explanation:
The formula for simple interest is I = Prt, with I for interest, P for principle, r for interest rate, and t for time (in years)
The equation is I = 2550(0.02)(1), which is I = 51.
Hope this helps :)
You got 8 correct out of 9 points.
What is the slope-intercept equation of the line below?
10 minutes left
Answer:
y=-3x+4
Step-by-step explanation:
The y intercept is 4 because the line crosses the y axis at the 4 tic mark
The slope will be -3 because the y decreases by 3 every time the x incerases by 1
y=mx+b
y=-3x+4
find the slope of the joining pairs of points (1/a, 1/b) (b,a)
Answer: m = 1/b
Step-by-step explanation: Unfortunately, I can't give you a picture of the slope, but take that formula I gave you and enter it into a graphing calculator and it will show you the slope. I recommend desmos online calculator, good luck
1. Coach Jensson wants to celebrate the final win of the
school's baseball season with a trip to the local fast food
place. The team buys 22 delicious tacos and 17 orders
of savory nachos for $71.05. A few of the players are still
hungry, so the coach buys 10 more tacos and 5 more
orders of nachos for $27.25. If you don't consider tax,
what is the price of a taco and the price of an
order of nachos ?
been stuck on this for a few days now, help on even one would be greatly appreciated!!!
Answer:
-5-9i
Step-by-step explanation:
-1-8i-4-i
-1-4-8i-i
-5-9i
find the measure of x
Answer:
[tex]B)\ x=43[/tex]
Step-by-step explanation:
One is given a circle with many secants within the circle. Please note that a secant refers to any line in a circle that intersects the circle at two points. A diameter is the largest secant in the circle, it passes through the circle's midpoint. One property of a diameter is, if a triangle inscribed in a circle has a side that is a diameter of a circle, then the triangle is a right triangle. One can apply this to the given triangle by stating the following:
[tex]x+47+90=180[/tex]
Simplify,
[tex]x+47+90=180[/tex]
[tex]x+137=180[/tex]
Inverse operations,
[tex]x+137=180[/tex]
[tex]x=43[/tex]
Joe is on the phone with a gardener who asked about the square feet of Joe’s back yard Joe counts 20 steps long and 40 steps wide with each step been about 3 feet about how many square feet is the back Yard
Answer:
The area of the yard is 7200 square feet.
Step-by-step explanation:
You just multiply your step count by 3. So 20 would be 60 and 40 would be 120. Multiply your results and you get 7200 square feet.
Find all excluded values for the expression.
That is, find all values of for which the expression is undefined.
5
-----
6+2v
If there is more than one value, separate them with commas.
Answer:
-3
Step-by-step explanation:
For an expression to be undefined,. the denominator must be equal to 0
Therefore, in order to make that expression undefined, we must equate the denominator to 0
6 + 2v = 0
2v = 0 - 6
2v = -6
v = -6/2
v = -3
So in order to make the expression to be equal to 0, v must be -3
Help please……..??.?.?.?.?.?
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Answer:
c) 16,500 m³
d) 277,088 mm³
a) V = LWH
b) V = πr²h
Step-by-step explanation:
The relevant volume formulas are ...
rectangular pyramid: V = 1/3LWHcylinder: V = πr²hrectangular prism: V = LWH__
13c. The pyramid formula above tells us the volume is ...
V = 1/3(60 m)(15 m)(55 m) = 16,500 m³
__
13d. The cylinder formula above tells us the volume is ...
V = π(35 mm)²(72 mm) ≈ 277,088 mm³ ≈ 277 mL
__
14a. The shape appears to be a rectangular prism, so its volume is given by the formula ...
V = LWH . . . . . where L, W, H represent the length, width, and height
__
14b. The volume of a cylinder is given by the formula ...
V = πr²h . . . . . where r, h represent the radius and height (length)
Which representation would be best for determining how many planes had an average cruising speed of 0.84 Mach?
Answer:
Question: 1
A dot plot shows individual values. So, we can most easily tell from the dot plot that 5 planes had an average cruising speed of 0.84 Mach
Question: 2
A box plot breaks data into quartiles, each representing 25% of the data. So to find the middle 50% of the data, look at the data that lies between the first and third quartiles of the box plot. The box plot shows that the first and third quartiles are 0.8175 and 0.85, respectively, so 50% of the data lies between 0.8175 and 0.85.
Question: 3
The histogram would be the best data representation for quickly determining how many planes had a speed less than 0.84 Mach. Adding the frequencies of the 3 bins less than 0.84 shows that 17 planes had a speed of less than 0.84 Mach. The dot plot could also be used to determine this, but it would take more time to count each individual dot.
Step-by-step explanation:
answer from plato
Thank me later
The graphical representation which would be best for determining the number of planes that had an average cruising speed of 0.84 Mach is a: histogram.
What is a histogram?A histogram can be defined as a type of graph (chart) that is used to graphically represent a data set (statistical information) into user-specified ranges through the use of rectangles.
Generally, the area of each rectangle of a histogram is directly proportional to the data frequency and its width is equal to the class interval.
In this scenario, a histogram is the graphical representation which would be best for determining the number of planes that had an average cruising speed of 0.84 Mach.
Read more on histogram here: brainly.com/question/21304143
Solve for x step by step:
2(4x-3)-8=4+2x
Answer:
3
Step-by-step explanation:
2(4x-3)-8=4+2x
8x - 6 - 8 = 4 + 2x
8x - 2x = 4 + 6 + 8
6x = 18
x = 18/6
x = 3
Answer:
[tex]2(4x - 3) - 8 = 4 + 2x \\ 2 \times 4x + 2 \times - 3 - 8 = 4 + 2x \\ according \: to \: bodmas \: first \: \times then + or - \\ so \\ 8x - 6 - 8 = 4 + 2x \\ 8x - 14 = 4 + 2x \\ 8x - 2x = 4 + 14 \\ 6x = 18 \\ x = \frac{18}{6} \\ x = 3 \\ thank \: you[/tex]
