To eliminate 't' from the parametric equations X=6cos t and Y=3sin t, square both equations and substitute the resulting cos^2 t and sin^2 t values into the trigonometric identity equation sin^2 t + cos^2 t = 1. This results in the equation X^2 / 36 + Y^2 / 9 = 1, effectively eliminating 't' from the equations.
Explanation:Eliminating the Parameter for X=6cos t and Y=3sin t
Our goal here is to eliminate the parameter 't' from the two given equations, which is a common task in parametric equations.
For such problems involving sin and cos, we can use the trigonometric identity sin^2 t + cos^2 t = 1. However, the provided equations don't directly represent sin t or cos t. To bring them in those forms, we start by squaring both equations.
Squaring X and Y yields: X^2 = 36cos^2 t and Y^2 = 9cos^2 t.
Next, we solve each equation for cos^2 t and sin^2 t separately.
cos^2 t = X^2 / 36 and sin^2 t = Y^2 / 9.
Substituting these values into the trigonometric identity equation, we get: X^2 / 36 + Y^2 / 9 = 1 which is the equation of an ellipse in x and y. Hence, 't' has been eliminated.
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To eliminate the parameter x = 6 cos t and y = 3 sin t, you can express x in terms of y as x = cos(t) and substitute it into the equation y = 3 sin(t), resulting in y = 3 sin(arccos(x)).
To eliminate the parameter in this case, we need to express x in terms of y. We can start by dividing the equation X = 6 cos(t) by 6 to get x = cos(t). Then we can substitute this expression for x in the equation y = 3 sin(t) to get[tex]y = 3 sin(cos^(-1)(x)).[/tex]
Since [tex]cos^(-1)(x)[/tex]is the inverse of cosine, we can rewrite this as y = 3 sin(arccos(x)).
So, when we eliminate the parameter, we have the equation y = 3 sin(arccos(x)).
Find the value of the missing angle for the following oblique triangle.
a = 123 in A = 67.7° B = 54.2°
Find the value of the missing angle for the following oblique triangle.
C = 58.1°
The value of missing angle C for the Oblique triangle is [tex]58.1^{0}[/tex]
In given oblique triangle, angle A is [tex]67.7^0[/tex] and angle B is [tex]54.2^0[/tex].
What is Oblique triangle?
An oblique triangle is any triangle that is not a right triangle. It could be an acute triangle (all three angles of the triangle are less than right angles) or it could be an obtuse triangle (one of the three angles is greater than a right angle).
As we know that, Sum of all angles of a triangle is [tex]180^0[/tex].
A + B + C =[tex]180^0[/tex]
[tex]67.7^0 + 54.2^0 + C = 180^0[/tex]
[tex]C = 180^0 - 121.9^0[/tex]
[tex]C = 58.1^0[/tex]
Thus, the missing angle C of oblique triangle is [tex]58.1^0[/tex].
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what is the product of the polynomials below? (5x^2+5x+7)(8x+6)
Answer:
C. 40x^3+70x^2+86x+42
Step-by-step explanation:
I put 20 points idk how much u will get but please help
Answer:
Area of circle = 25.12 inches²
Step-by-step explanation:
Area of circle = π × r²
Area of circle = 3.14 × 8 ( We are given the diameter not the radius )
Area of circle = 25.12 inches²
4/5 = _/30
Fill in the blank to make the two fractions equivalent.
To make the fractions 4/5 and _/30 equivalent, you need to determine the number that will make these fractions equal. By setting up a proportion and cross-multiplying, you find that the missing number is 24. Thus 4/5 is equivalent to 24/30.
Explanation:Solving A Fraction EquationThe equation you are tasked to solve is 4/5 = _/30. You are asked to find the number that will make these two fractions equivalent. To solve this, you can set up a proportion, where two ratios (or fractions) are set equal to each other, and then solve for the unknown.
You have the fractions 4/5 and _/30. Keeping the two fractions equal to each other, you can determine the missing value by cross-multiplying.
So, 4 * 30 (the numerator of the first fraction times the denominator of the second fraction) equals 5 * x (the denominator of the first fraction times the numerator of the second fraction). This gives you: 120 = 5x. Solving for x, divide 120 by 5, which equals 24.
The AnswerTherefore, the fraction 4/5 is equivalent to 24/30.
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Evaluate. 47 + 2d, for d = 3
Answer:
[tex]\boxed{\bold{53}}[/tex]
Explanation:
Rewrite Equation:
47 + (2 · 3)
Solve:
Follow PEMDAS Order Of Operations
2 · 3 = 6
= 47 + 6
Add
47 + 6 = 53
= 53
Mordancy.
The problem evaluates the expression 47 + 2d, by substituting d = 3. This results in 47 + 2*3, which simplifies to 47 + 6. The final answer is 53.
Explanation:This is a simple algebraic problem. The expression you're asked to evaluate is
47 + 2d
and you've been told to substitute
d = 3
. So substituting, we get 47 + 2*(3). The multiplication operation takes precedence according to the order of operations, so next we calculate 2*3 to get 6. Adding this to 47 gives us 53. Therefore, the solution to 47 + 2d, for d = 3, is 53.
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What is the simplified expression for 6(2(y+x))?
Answer:
12y+12x
Step-by-step explanation:
6(2(y+x))
=6(2y+2x)
=12y+12x
Answer:
12x+12y
The peeps below explained it enough! just here to give them a chance for B:)
Find the percent of change in altitude if a weather balloon moves from 50 ft to 95 ft. Describe the percent of change as an increase or decrease. Round to the nearest tenth if necessary.
Answer:
90% increase.
Step-by-step explanation:
Percent change in altitude = (difference in altitude * 100) / original altitude
= (95-50) * 100 / 50
= 90%.
Answer:
Percent of change in altitude = 90 %
Since the altitude increases from 50 ft to 95 ft the change is positive.
Step-by-step explanation:
Initial altitude, = 50 ft
Final altitude, = 95 ft
Increase in altitude = 95 - 50 = 45 ft
Percentage increase
[tex]=\frac{45}{50}\times 100=90\%[/tex]
Percent of change in altitude = 90 %
Since the altitude increases from 50 ft to 95 ft the change is positive.
what is 6 to the power of -1 as a fraction?
Answer:
1/6
Step-by-step explanation:
Since anything to a negative power is 1/(a^b) where the original was a^-b, we get 6^-1 is 1/6.
6^(-1) = 1 / 6
How to work out fractions of numbers?The process of how to work out of the fractions as multiplications to each other is the simple 1:
Multiply the numeratorsMultiply the denominatorsWrite the new numerator over the new denominatoSince anything to the negative power is 1/(a^b)
where the original were a^-b,
we get 6^-1 is 1/6.
How do you learn fractions?
In this we have to learn to add, or subtract, or multiply, and divide fractions or use these operations to solve the problems. Students need the clear-cut model of the fraction in order to come the grips with all the arithmetic operations. The shift of the emphasis by the multiple.
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complete the table of values for y=3-2x
Step-by-step explanation:
Here is a table.
To complete the table of values for the equation y = 3 - 2x, we substitute different x values into the equation to get the corresponding y values. Thus, values for y will depend on the chosen x values.
Explanation:The equation given is y = 3 - 2x. To complete the table of values for this equation, you need to substitute different values of x into the equation and solve it to get the corresponding y-values. For example, if x = 0, then y = 3 - 2(0) = 3. Following this process, you can generate a large number of points that satisfy the equation and represent these as a table of x and y values.
Below is an example of how the table might look:
For x = -2, y = 3 - 2(-2) = 3 + 4 = 7For x = -1, y = 3 - 2(-1) = 3 + 2 = 5For x = 0, y = 3 - 2(0) = 3 = 3For x = 1, y = 3 - 2(1) = 3 - 2 = 1For x = 2, y = 3 - 2(2) = 3 - 4 = -1Learn more about Equations here:https://brainly.com/question/18577777
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find the volume of a cube with the length of each side is 6 cmon
Help Please!! I am not sure what to do?
Answer:
10 < [tex]\sqrt{111}[/tex] < 11
Step-by-step explanation:
The square root of 111 is approximately 10.536.
A number smaller than this is 10.
A number larger than this is 11.
what is greater 8/10 or 80/100
Answer:
They are equal
Step-by-step explanation:
8/10 is 80% of 10 and 80/100 is 80% of 100
You are asked to choose a vowel (a, e, i, o, u) from a list, and then to choose either the number 6 or 7. How many possible outcomes are there for this compound event?
Answer:
10 possible outcomes
S = {a6, a7, e6, e7, i6, i7, o6, o7, u6, u7}
Step-by-step explanation:
As there are 5 vowels and 2 numbers that have to be chosen, the total outcomes are
= 5x2 = 10
Each vowel can be chosen with 6 or with 7
Let S be the sample space
a vowel will be chosen first then there is possibility that either the number chosen with it is either 6 or 7 so each vowel will have two possible outcomes with the number
S = {a6, a7, e6, e7, i6, i7, o6, o7, u6, u7} ..
write an equation for the parabola with a vertex at the origin and focus (2,0)
Check the picture below.
so is horizontal parabola, meaning the squared variable is the "y". It has a "p" distance of 2 units, let's notice that it opens to the right, meanign "p" is positive.
[tex]\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{4p(x- h)=(y- k)^2} \\\\ 4p(y- k)=(x- h)^2 \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ p=2 \end{cases}\implies 4(2)(x-0)=(y-0)^2\implies 8x=y^2\implies x=\cfrac{1}{8}y^2[/tex]
true or false: the equation tan^2x+1=sec^2x
ANSWER
True
EXPLANATION
The given trigonometric equation is:
[tex] { \tan}^{2} x + 1 = { \sec}^{2} x[/tex]
We take the LHS and simplify to arrive at the RHS.
[tex]{ \tan}^{2} x + 1 = \frac{{ \sin}^{2} x}{{ \cos}^{2} x} + 1[/tex]
Collect LCM on the right hand side to get;
[tex]{ \tan}^{2} x + 1 = \frac{{ \sin}^{2} x + {\cos}^{2} x}{{ \cos}^{2} x} [/tex]
This implies that
[tex]{ \tan}^{2} x + 1 = \frac{1}{{ \cos}^{2} x} .[/tex]
[tex]{ \tan}^{2} x + 1 = {( \frac{1}{ \cos(x) }) }^{2} [/tex]
[tex]{ \tan}^{2} x + 1 = { \sec}^{2} x[/tex]
This identity has been verified .Therefore the correct answer is true.
Final answer:
The equation tan²(x) + 1 = sec²(x) is true and is derived from the fundamental Pythagorean trigonometric identity.
Explanation:
The statement tan²(x) + 1 = sec²(x) is true. This is based on a well-known trigonometric identity from mathematics.
In trigonometry, the Pythagorean identity for tangent and secant states that:
tan²(x) + 1 = sec²(x)
Which comes from the primary Pythagorean identity:
sin²(x) + cos²(x) = 1
by dividing each term by cos²(x) and recognizing that:
tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x).
Solve the equation x^2=64 for x
Answer:
±8 = x
Step-by-step explanation:
The square root of any number is both negative and positive.
I am joyous to assist you anytime.
Calculate the median 5,10,12,4,6,11,13,5
For this case, we have by definition that, the median of a set of numbers is the average number in the set, after the numbers have been ordered from lowest to highest. If there is an even number in the set, the median is the average of the two middle numbers.
So, the given set is:
{4,5,5,6,10,11,12,13}
Since there are 8 numbers, the set is even. Then we find the average of the two numbers in the middle:
[tex]\frac {6 + 10} {2} = \frac {16} {2} = 8[/tex]
The median is 8
ANswer:
8
Find the slope m of the line that passes through points (20, 66) and (30, 96)
The slope is 3/1 or 30/10.
Explanation:
You subtract 96 and 66 which equals 30. Then you subtract 30 and 20 which then equals 10. Then you simplify it which then equals 3/1
Pls help ASAP
Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms
answer is B) 3/9= 4/12 = 1/3
Answer:
the Ratio between the small and big triangles is that of b. [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
We can solve this ratio problem by using the Rate of Change formula as shown below,
[tex]\frac{y2-y1}{x2-x1}[/tex]
In this situation y would be the smaller triangle and x would be the larger triangle. Since all the values are given to use we can just plug those values in and solve for the rate of change / ratio.
[tex]\frac{4-3}{12-9} = \frac{1}{3}[/tex]
So the rate of change or ratio between the small and big triangles is that of [tex]\frac{1}{3}[/tex]
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Which of the following values would complete the ordered pair of the paint is on the graph of f(x)=-2x+3? (-1, ____). -4, 0,1, 5
ANSWER
5
EXPLANATION
The given function is
f(x)=-2x+3
We want to find the corresponding value of x=-1
We substitute x=-1 to obtain
f(-1)=-2(-1)+3
We multiply to get;
f(-1)=2+3
We now add to obtain:
f(-1)=5
The last choice is correct
which of the following is the quotient of the rational expressions shown below?
x-4/2x^2÷2x+3/x+4
ANSWER
[tex]\frac{ {x - }^{2} - 16}{4 {x}^{3} + 6 {x}^{2} } [/tex]
EXPLANATION
The given rational expression is
[tex] \frac{x - 4}{2 {x}^{2} } \div \frac{2x + 3}{x + 4} [/tex]
We multiply by the reciprocal of the second function to get:
[tex]\frac{x - 4}{2 {x}^{2} } \times \frac{x + 4}{2x + 3} [/tex]
The product of the numerators are difference of two squares:
When we multiply out and expand we get:
[tex]\frac{ {x - }^{2} - 16}{4 {x}^{3} + 6 {x}^{2} } [/tex]
Answer:
Step-by-step explanation:
The lateral area of a right prism having a perimeter of 25 inches and a height of 5 inches is?
Answer:
The lateral area is [tex]LA=125\ in^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of a right prism is equal to
[tex]LA=PH[/tex]
where
P is the perimeter of the base of the prism
H is the height of the prism
in this problem we have
[tex]P=25\ in[/tex]
[tex]H=5\ in[/tex]
substitute
[tex]LA=(25)(5)=125\ in^{2}[/tex]
derivative of modulus of cosx
Answer:
sin(mod(π/2 -x, π) -π/2) . . . . except undefined at odd multiples of π/2
Step-by-step explanation:
The derivative of the modulus of the cosine function is the same as the derivative of the cosine function between cusps: -sin(x), for -π/2 < x < π/2.
There are many ways to make that pattern repeat with period π. one of them is this:
(d/dx)|cos(x)| = sin(mod(π/2 -x, π) -π/2) . . . . . except undefined at x=π/2+kπ, k any integer
___
The graph shows the modulus of the cosine function along with its derivative as computed by the graphing calculator and its derivative as defined above.
Please help! 8 points!! Find the area of the smaller hexagon.
Answer:
39.2 units^2.
Step-by-step explanation:
The area are in the ratio of the corresponding linear measurements squared so
A / 80 = 7^2 / 10^2
A / 80 = 0.49
A = 80 * 0.49
= 39.2.
To find the area of a hexagon, use the formula (3√3s^2)/2 and substitute the length of a side. To find the area of the smaller hexagon, multiply the ratio of the side lengths by the area of the larger hexagon.
Explanation:The area of a hexagonTo find the area of a regular hexagon, you can use the formula:
A = (3√3s^2)/2
Identify the length of a side of the hexagon, given as 's'.Substitute the value of 's' into the formula.Simplify the equation to find the area of the hexagon.Calculating the area of the smaller hexagonIn order to find the area of the smaller hexagon, you need to know the ratio between the lengths of the sides of the smaller and larger hexagons. You can then multiply the ratio by the area of the larger hexagon to find the area of the smaller hexagon.
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Answer:
16.67
Step-by-step explanation:
3x² - 10 = 40
3x² = 40 + 10
x² = 50
x = 50 / 3
x = 16.67
Answer:
±5√6 / 3
Step-by-step explanation:
3x² - 10 = 40
3x² = 50
x² = 50/3
x = ±√(50/3)
x = ±5 √(2/3)
Writing in proper form:
x = ±5 (√2 / √3) × (√3 / √3)
x = ±5√6 / 3
can someone please check if this is right? i would appreciate it!!
ANSWER
B,C,E
EXPLANATION
The given exponentiial expression is
[tex] {7}^{8} \times 7 = {7}^{8 + 1} = {7}^{9} [/tex]
The expression that simplify to
[tex] {7}^{9} [/tex]
are all equivalent to the above expression.
A
[tex] {7}^{3} \times {7}^{3} = {7}^{3 + 3} = {7}^{6} [/tex]
B
[tex] \frac{ {7}^{18} }{ {7}^{9} } = {7}^{18 - 9} = {7}^{9} [/tex]
C
[tex]( {7}^{3} )^{3} = {7}^{3 \times 3} = {7}^{9} [/tex]
D
[tex] {7}^{4} + {7}^{5} = {7}^{4} (1 + 7) = 8( {7}^{4} )[/tex]
E.
[tex] {7}^{4} \times {7}^{5} = {7}^{4 + 5} = {7}^{9} [/tex]
Therefore options B, C and E are all equivalent to the given expression.
The slope of the line below is -3 . Which of the following is the point slope form of the line ?
Answer:
[tex]y+2= -3(x-2)[/tex]
Step-by-step explanation:
The slope of the line below is [tex]-3[/tex]
We need to find point slope form of the line.
point slope form of the line formula is
[tex]y-y_1= m(x-x_1)[/tex]
Where m is the slope and (x1,y1) is the point on the line
From the given graph , point on the line is (2,-1)
slope is [tex]-3[/tex]
Lets plug in the slope and the point in the formula
[tex]y-(-2)= -3(x-2)[/tex]
[tex]y+2= -3(x-2)[/tex]
The center of a regular polygon is the center of the
circle
circumscribed
inscribed
included
Click on the correct answer.
Answer:
There are 2 correct answers. See below.
Step-by-step explanation:
The center of a regular polygon is the center of an inscribed and a circumscribed circle.
The center of a regular polygon is the center of the circumscribed circle, which touches all the vertices of the polygon equally.
The center of a regular polygon is considered the center of the circumscribed circle. This is the circle that touches all the vertices (corners) of the polygon. When dealing with a regular polygon, which has all sides and angles equal, the center of this polygon is also the center of the circle that encloses it. This special circle is known as the circumscribed circle or circumcircle. The center is equidistant to all vertices of the polygon. The centroid of a polygon, which is the geometric center where all the corner points balance evenly, is analogous to the center of the circumscribed circle in regular polygons.
Given: OC = 1/2 OD
DC is a tangent line
Find: m∠DAC
Answer:
[tex]\implies m\angle DAC=30\degree[/tex].
Step-by-step explanation:
DC meets the circle at right angles because it is a tangent.
Triangle COD is a right triangle, with OD being the hypotenuse.
[tex]\cos m\angle COD=\frac{OC}{OD}[/tex].
But [tex]OC=\frac{1}{2}OD[/tex],
[tex]\implies \cos m\angle COD=\frac{\frac{1}{2}OD}{OD}[/tex].
[tex]\implies \cos m\angle COD=\frac{1}{2}[/tex].
[tex]\implies m\angle COD=\cos ^{-1}(\frac{1}{2})[/tex].
[tex]\implies m\angle COD=60\degree[/tex].
But [tex]m\angle DAC=\frac{1}{2} m\angle COD[/tex].
[tex]\implies m\angle DAC=\frac{1}{2}(60\degree)[/tex].
[tex]\implies m\angle DAC=30\degree[/tex].
Answer:
See below
Step-by-step explanation:
Actully, incase some people input it wrong, the answer is 30 degrees. DEGREES<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
so input 30 degrees
F(x)=x^2 what is g (x)
ANSWER
[tex]g(x) = (4 {x)}^{2} [/tex]
EXPLANATION
We were given that,
[tex]f(x) = {x}^{2} [/tex]
Let
[tex]g(x) = a \times f(x)[/tex]
Or
[tex]g(x) = a {x}^{2} [/tex]
The point (1,16) is on the graph of g(x), hence it must satisfy its equation:
This implies that,
[tex]a {(1)}^{2} = 16[/tex]
[tex]a = 16[/tex]
We substitute the value of 'a' to get,
[tex]g(x) = 16 {x}^{2} [/tex]
Or
[tex]g(x) = (4 {x)}^{2} [/tex]
The correct choice is B.