Answer:
The equation of the normal is y = 4 - 2·x
Step-by-step explanation:
The given equation of the circle, is presented as follows;
(x - 3)² + (y + 2)² = 20
The point of the normal of the circle = (1, 2)
The equation of the normal to a circle, x² + y² + D·x + E·y + F = 0 at a point P(x₁, y₁) is given as follows;
[tex]\dfrac{y - y_1}{x - x_1} = \dfrac{2 \cdot y_1 + D}{2 \cdot x_1 + E}[/tex]
Expanding the given equation of the circle, gives;
(x - 3)² + (y + 2)² = x² + y² - 6·x + 4·y + 13 = 20
∴ x² + y² - 6·x + 4·y + 13 - 20 = x² + y² - 6·x + 4·y - 7 = 0
x² + y² - 6·x + 4·y - 7 = 0
∴ x₁ = 1, y₁ = 2, D = -6, E = 4, and F = 13
Which gives;
[tex]\dfrac{y - 2}{x - 1} = \dfrac{2 \times 2 + 4}{2 \times 1 + (-6)} = \dfrac{8}{-4} = -2[/tex]
∴ y - 2 = -2 × (x - 1) = 2 - 2·x
y = 2 - 2·x + 2 = 4 - 2·x
The equation of the normal to the circle with equation (x - 3)² + (y + 2)² = 20, at the point (1, 2) is y = 4 - 2·x
What does it mean to use the cosine value of an inverse of tan θ?
I attached the question I'm just confused.
Will it be 60°?
Answer:
[tex] \boxed{ \begin{array}{ccc} \displaystyle \theta = {120}^{ \circ} \\ \displaystyle\sin( {120}^{ \circ} ) = \frac{ \sqrt{3} }{2} \end{array}}[/tex]
Step-by-step explanation:
we are given a inverse trig
we want to figure out the value of [tex]\theta[/tex]
in that case we can consider using unit circle in unit circle the value of arctan (-√3)=120°
therefore,
the value of theta is 120°
likewise by unit circle the value of sine is
[tex] \displaystyle \sin( {120}^{ \circ} ) = \frac{ \sqrt{3} }{2} [/tex]
Find the solutions of the quadratic equation 3x2−x+8=03x 2 −x+8=03, x, squared, minus, x, plus, 8, equals, 0.
The solutions of the quadratic equation 3x² − x + 8 = 0 are as follows;
x = 0.1667 + 1.6245i
x = 0.1667 - 1.6245i
How to solve the given quadratic equation?In Mathematics, the standard form of a quadratic equation is given by this mathematical expression;
ax² + bx + c = 0
Mathematically, the quadratic formula is modeled or represented by this mathematical expression:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
From the information provided above, we can logically deduce the following data values (parameters);
3x² − x + 8 = 0
Where:
a = 3b = -1c = 8Substituting the data values (parameters) into the quadratic formula, we have the following;
[tex]x = \frac{-(-1)\; \pm \;\sqrt{(-1)^2 - 4(3)(8)}}{2(3)}\\\\x = \frac{1\; \pm \;\sqrt{1\; - \;4(3)(8)}}{2(3)}\\\\x = \frac{1\; \pm \;\sqrt{1\; - \;96}}{6}[/tex]
x = (1 ± √95)/6
x = (1 + √95)/6 = 0.1667 + 1.6245i
or
x = (1 - √71)/6 = 0.1667 - 1.6245i
In conclusion, i represents a complex number.
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Complete Question:
Find the solutions of the quadratic equation 3x² − x + 8 = 0.
which of the following is a linear function
Answer:
f(x)=5x-6
Step-by-step explanation:
When I entered this in Desmos it crossed through the line crossed through the x and y axis which makes this equation a linear function.
Answer:
f(x) = 5x - 6
Step-by-step explanation:
The first function is a Linear Function
The second function is a Exponential Function
The third is an Inverse Function
The forth is a Quadratic Function
Hope this helps!
Which ordered pairs are solutions to this system of inequalities?
9514 1404 393
Answer:
c, d, e
Step-by-step explanation:
The first two listed points are not in the solution set. The remaining three are.
__
Any point in the doubly-shaded area, or on the solid boundary line of that area is part of the solution set. Points (-1, -6), (0, -5), and (0.5, -2) are solutions to the given inequalities.
12x+105=55x+0 solve for x
12y=155 sovle for y
Answer:
Step-by-step explanation:
12x + 105 = 55x + 0
=> 12x + 105 = 55x
=> 55x - 12x = 105
=> 43x = 105
=> x = 105/43
12y = 155
=> y = 155/12
100,000,000 is what percent of 100,000,000
Answer:
100% if that's not an answer choice it is 1 because it is whole
Step-by-step explanation:
100,000,000 ÷ 100,000,000 = 1 or 100%
Mark as Brainllest
A line that includes the point (4,1) has a slope of 1 7 . What is its equation in point-slope form?
Answer:
y = 17x-67
Step-by-step explanation:
The one point form of line also called slope point form is given by
[tex](y-y_1)=m(x-x_1)[/tex]
where (x1, y1) is the point and m is slope
Given: (x1, y1) = (4,1) and m= 17
Substituting these values in above equation to find equation in point-slope form
(y-1)=17(x-4)
y-1 = 17x-68
y = 17x-67
the point -slope form of equation y = 17x-67
WILL MARK BRAINLY IS RIGHT!!!!
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Find the flux of F across S,
F. N dS
where N is the upward unit normal vector to S.
F(x, y, z) = xi + yj + zk
S: z = 1 − x^2 − y^2, z ≥ 0
The flux of F across S will be [tex]\frac{3\Pi}{2}[/tex]
A vector of magnitude 1 that is at some point perpendicular to a two-dimensional curve is referred to as the unit normal vector. Normally, you search for a function that returns not just one vector but all potential unit normal vectors of a given curve.
A vector that is perpendicular to a surface at a certain location is known as the normal vector, also referred to as the "normal" to a surface. The inward-pointing normal (pointing toward the interior of the surface) and outward-pointing normal are often distinguished when normals are taken into consideration on closed surfaces.
[tex]$Z_x=-2 x: \quad Z_y=-2 y$[/tex]
[tex]$N=\langle 2 x, 2 y, 1\rangle \quad: f=\langle x, y, z\rangle$[/tex]
[tex]f. $N=2 x^2+2 y^2+z=2 x^2+2 y^2+1-x^2-y^2$[/tex]
=1+x^2+y^2
[tex]x^2+y^2=1\\ \Rightarrow \quad x=r \cos \theta\\ \Rightarrow \quad y=r \sin \theta \\ \Rightarrow x^2+y^2=r^2 \\ 0 < r < 1: \quad 0 < \theta < 2 \pi[/tex]
[tex]$R \cdot v=\int_0^{2 \pi} \int_0^1\left(1+r^2\right)(r) dr d \theta$[/tex]
[tex]$=2 \pi \int_0^1 r+r^3 d r$[/tex]
[tex]$2 \pi\left[\frac{r^2}{2}+\frac{r^4}{4}\right]_0^1$[/tex]
[tex]$=(2 \pi)\left(\frac{1}{2}+\frac{1}{4}\right)$[/tex]
[tex]$=\frac{(2 \pi)(3)}{42}=\frac{3 \pi}{2}$[/tex]
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Find the area of the regular polygon. Round your answer to the nearest hundredth.
6.84
10
A
square units
Answer:
area = 289.24 units²
Step-by-step explanation:
divide the polygon into 9 equal triangles
the top angle of a triangle will be 360°/9 = 40°
the sides of a triangles are both 10 units
The base of a triangle is 6.84 units
the height of a triangle is:
cos 20° = height/10
0.9397 = height/10
height = 9.4 units
The area of a triangle = 1/2(6.84)(9.4) = 32.13 units²
the polygon is made from 9 of these triangles, so 9 x 32.13 = 289.24 units²
Help me out with this question please
Use the data in the table below to create a scatter plot. Based on your scatter plot, does the data
have a correlation? If so, what kind?
A. No - the data has no correlation
B. Yes - there is a negative correlation
C. Yes - there is a positive correlation
D. There is not enough information to answer
Answer:
C
Step-by-step explanation:
There is a positive correlation, as hours spent gets bigger the test score gets bigger with some outliers
what is the lowest denomenator of 11/5+2/3+1/6
Answer:
[tex] \frac{11}{5} + \frac{2}{3} + \frac{1}{6} \\ = \frac{91}{30} \\ it \: is \: 30[/tex]
What is reflex angle class 9?
A reflex angle is an angle which measures more than 180 degrees and less than 360 degrees.
There are different types of angles in geometry, such as obtuse, acute and right angles, which all are under 180 degrees.
Assume, z is an acute or obtuse angle, and r is the reflex angle, then:
z + r = 360
r = 360 - z
Therefore, we can find the related reflex angle(r), if we know the value of the acute or obtuse angle(z).
A reflex angle equals the summation of 180 degrees and any of the primary angles (acute, right and obtuse angles). Therefore,
Reflex angle = 180° + Acute angle
Reflex angle = 180° + Right angle
Reflex angle = 180° + Obtuse angle
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Match the solution to its expression.
Answer:
1/3 + 1/3 = (1+1)/3 = 2/3
1) 2/3
5/7 - 2/7 = (5-2)/7 = 3/7
2) 3/7
so all you have to do is add or sub the fractions together.
1/3 + 1/3 = 2/3
5/7 - 2/7 = 3/7
for the first box is 2/3
Second box is 3/7
GOODLUCK
help help help help help
A packet of grass seed can be
used to cover 50m² of lawn.
A circular lawn has a diameter of 20 metres
How many packets of grass
seed must be bought so that the entire lawn can be covered?
Answer:
7 packets of grass seed
Step-by-step explanation:
First, find the area of the circular lawn using the formula, A = [tex]\pi[/tex]r²
If the diameter is 20 meters, the radius is 10 meters.
Plug in 10 as the radius and solve for the area:
A = [tex]\pi[/tex]r²
A = [tex]\pi[/tex](10²)
A = 100[tex]\pi[/tex]
So, the area of the lawn is 100[tex]\pi[/tex] m² or approximately 314.16 m²
Divide this by 50 to find how many packets of grass seed are needed:
314.16/50
= 6.28
Round this up to 7, since we need to have a whole number answer.
So, 7 packets of grass seed have to be bought.
Determine whether quadrilateral EFGH is similar to quadrilateral QRST. If so, give the similarity statement. (ASAP PLS HELP!!)
A)
QRST ∼ EFGH
B)
QRST ∼ FEHG
C)
Impossible to determine.
D)
The quadrilaterals are not similar.
Answer:
qrst similar to fehg
Step-by-step explanation:
opposite angles are equal in parallelogram so 70 is equal to 70 on both and similarly other angles also are equal that we can find using co interior property as well
plz marks me brainliest plz plz
Answer:
the quads are NOT similar is the right answer!!!
Step-by-step explanation:
I got it right:)
Which set of data shows the least variability?
A. 65, 66, 67, 68, 69
B. 60, 60, 60, 60, 80
C. 50, 60, 70, 80, 90
D. 55, 55, 75, 95, 95
Jesse from Boston goes to his grandpa Isaac in New York by bus at an average speed of 35 mph and it takes him 6 hours. In a while, Jesse and Isaac go back from New York to Boston in Isaac's car at an average speed of 42 mph. How long does Jesse's trip from New York to Boston take?
Answer:
The Average Speed is 48mph
Step-by-step explanation:
I've done this problem before, I wish A+'s upon all that read this answer. take care man!
The time it takes for Jesse to complete his trip from New York to Boston is 5 hours.
How long does Jesse's trip from New York to Boston take?To calculate the time it takes for Jesse's trip from New York to Boston, we need to use the formula: time = distance / speed.
Given that Jesse traveled from Boston to his grandpa Isaac in New York at an average speed of 35 mph, and the trip took him 6 hours, we can determine the distance using the formula: distance = speed × time.
Distance = 35 mph × 6 hours = 210 miles.
Now, for the return trip from New York to Boston, Jesse and Isaac travel at an average speed of 42 mph. To find the time it takes, we divide the distance by the speed:
Time = 210 miles / 42 mph = 5 hours.
Therefore, Jesse's trip from New York to Boston takes 5 hours time.
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Two people stand on opposite ends of a bridge that crosses a river. Both can see an island located in the river. The angle
formed at the location of the first person is 37' and the angle formed at the second person is 55'. If the bridge is 5280 feet
long, how far is the first person from the island?
Answer:
The first person is about 4327.76 feet away from the island.
Step-by-step explanation:
We can draw a diagram to represent the situation. This is attached below.
Essentially, we want to find the value of x.
We are given that ∠A is 37° and ∠B is 55°.
The interior angles of a triangle must total 180°. Hence:
[tex]m\angle A+m\angle B+m\angle C=180[/tex]
Substitute:
[tex](37)+(55)+m\angle C=180[/tex]
Thus:
[tex]\displaystyle m\angle C=88^\circ[/tex]
We are also given that the length of the bridge is 5,280 feet. Since we want to find x, we can use the Law of Sines:
[tex]\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}[/tex]
The variables do not really matter. It is more important that we align the angles with their respective (i.e. opposite) sides.
The respective side to ∠C is AB which measures 5280.
The respective angle to x is ∠B, which is 55°.
Hence:
[tex]\displaystyle \frac{\sin(55)}{x}=\frac{\sin(88)}{5280}[/tex]
Solve for x. Cross-multiply:
[tex]x\sin(88)=5280\sin(55)[/tex]
Thus:
[tex]\displaystyle x=\frac{5280\sin(55)}{\sin(88)}[/tex]
Use a calculator:
[tex]\displaystyle x\approx 4327.76\text{ feet}[/tex]
The first person is about 4327.76 feet away from the island.
The speed of sound is about 340 m/s. Find the wavelength of a sound wave that has a frequency of 20.0 cycles per second ( the low end of human hearing)
A. 10.3 m
B. 17.0 m
C. 22.5 m
D. 25.0 m
Answer:
A
Step-by-step explanation:
Is Br2 equal to Avogadro's number?
Br₂ does not equal to Avogadro's number. Since bromine is a diatomic element.
What is a diatomic element?
Diatomic molecules—so named because they only contain two atoms of the same or different chemical elements—are molecules that are made up of two atoms. A diatomic molecule is considered to be homonuclear if it contains two atoms of the same element, such as oxygen (O₂) or hydrogen (H₂).
Each bromine molecule consists of 2 atoms of bromine. Br₂ consists of two moles. One mole of bromine consists of 6.02214076 × 10²³ atoms. Thus 2 moles of bromine consist of 2 × 6.02214076 × 10²³ = atoms. Thus Br₂ does not equal to Avogadro's number.
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What does ∠ABC mean?
The measure of angle ABC means, vertex B lies in between A and C, whose value is to be obtained.
Explain the term angles?Whenever two straight lines as well as rays intersect at a single endpoint, an angle is created. The vertex of the an angle is the location where two points come together.
Measure or "the measure of" are indicated by the "m." Consequently, m1 and m2 stand for "the measure for angle one" and "this same measure of angle two," respectively.The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.A closed shape with both inner and exterior angles, a triangle is created by three line segments.When the values of the remaining two angles are known, then angle sum property is utilised to determine the measure of an uncertain interior angle.Thus, the measure of angle ABC means, vertex B lies in between A and C, whose value is to be obtained.
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a pair of sunglasses originally priced at $50 are now on sale for $31. What is the discount percentages?
Answer:
They are discounted for 38% off.
An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with sides on the grid lines of the checkerboard (horizontal and vertical) and containing at least 5 black squares, can be drawn on the checkerboard
The total number of rectangles you can draw using the grid lines exists 1296.
What are the peculiarities of rectangle?A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.
A square is a particular type of closed figure that has four straight sides, four right angles, and sides that are all the same length. As a result, we can say that: A square is a particular variety of rectangle. Rectangles are not always squares, but squares are always rectangles.
Number 2 × 2 squares have 4 black squares
all 3 × 3 squares have at least 4 black squares, as do all 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8 squares.
there are 6 × 6 = 36 3 × 3 squares
there are 5 × 5 = 25 4 × 4 squares
there are 4 × 4 = 16 5 × 5 squares
there are 3 × 3 = 9 6 × 6 squares
there are 2 × 2 = 4 7 × 7 squares
there is 1 8 × 8 square
Summing we get 91 squares
The total number of rectangles you can draw using the grid lines exists (92)(92) = 1296.
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The total number of rectangles you can draw using the grid lines exists 1296.
What are the peculiarities of rectangle?A shape with two opposing sides that are equal and parallel is called a quadrilateral. It has four sides, four 90-degree angles, and is a polygon. A rectangle is a two-dimensional form.
An example of a closed form with four straight sides, four right angles, and all sides being the same length is a square. Therefore, we can state that a square is a certain type of rectangle. Squares are not always rectangles, but rectangles are always squares.
Number 2 × 2 squares have 4 black squares
all 3 × 3 squares have at least 4 black squares, as do all 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8 squares.
there are 6 × 6 = 36 3 × 3 squares
there are 5 × 5 = 25 4 × 4 squares
there are 4 × 4 = 16 5 × 5 squares
there are 3 × 3 = 9 6 × 6 squares
there are 2 × 2 = 4 7 × 7 squares
there is 1 8 × 8 square
Summing we get 91 squares
The total number of rectangles you can draw using the grid lines exists (92)(92) = 1296.
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I literally need help with this question-
It’s ASA congruence btw
Answer:
AB and DE
Step-by-step explanation:
Look closely and you can notice whats the difference.
OK
Consider the inequality X-3/6< x/4 -4. Which value of x is a solution to the inequality?
A.x=-10
B.x=-5
C.x=5
D.x=10
x=5 is the value of the x that is the solution of the given inequality.
Define inequality.Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
What are types of inequality.>,< and not equal to are types of inequality.
x=5 is the value of the x that is the solution of the given inequality.
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What is BC? Enter your answer in the box. BC=
Answer:
25
Step-by-step explanation:
4x+4=6x-14
2x=18
x=9
2×9+7=25
If θ is an angle in standard position and its terminal side passes through the point (12,-5), find the exact value of \sec\thetasecθ in simplest radical form.
The exact value of secθ in simplest radical for is 1.083
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are Given θ is an angle in standard position.
Its terminal side passes through the point (12, -5).
To find the exact value of secθ in simplest radical form.
When θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of secθ is:
So, we have x = 12 and y = -5 which is in the first quadrant.
Therefore,
r² = x² + y²
r² = ( 12 )² + ( -5 )²
r² = 144 + 25
r² = 169
r = 13
Then,
sec θ = 1/cosθ
sec θ = [ 1/(x/r) ]
sec θ = r/x
sec θ = 13/12
sec θ = 1.083
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