Find all 6 trigonometric ratios of the angle θ =7∏/ 6
Answers
[tex]\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse}\\\\ -------------------------------\\\\ cos\left( \frac{7\pi }{6} \right)=\cfrac{\stackrel{adjacent}{-\sqrt{3}}}{\stackrel{hypotenuse}{2}}\qquad \qquad sin\left( \frac{7\pi }{6} \right)=\cfrac{\stackrel{opposite}{1}}{\stackrel{hypotenuse}{2}}[/tex]
now, this is from the Unit Circle, and therefore the hypotenuse or radius wil be 1.
[tex]\bf \begin{cases} adjacent=&-\frac{\sqrt{3}}{2}\\ opposite=&\frac{1}{2}\\ hypotenuse=&1 \end{cases}\\\\ -------------------------------\\\\ sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse} \quad % tangent tan(\theta)=\cfrac{opposite}{adjacent} \\\\\\ % cotangent cot(\theta)=\cfrac{adjacent}{opposite} \qquad % cosecant csc(\theta)=\cfrac{hypotenuse}{opposite} \quad % secant sec(\theta)=\cfrac{hypotenuse}{adjacent}[/tex]
so, just plug in those values... hmmm lemme do the tangent, so you see the division of two fractions.
[tex]\bf tan\left( \frac{7\pi }{6} \right)=\cfrac{sin\left( \frac{7\pi }{6} \right)}{cos\left( \frac{7\pi }{6} \right)}\implies tan\left( \frac{7\pi }{6} \right)=\cfrac{\frac{1}{2}}{-\frac{\sqrt{3}}{2}}\implies tan\left( \frac{7\pi }{6} \right)=\cfrac{1}{2}\cdot \cfrac{2}{-\sqrt{3}}[/tex]
[tex]\bf tan\left( \frac{7\pi }{6} \right)=\cfrac{1}{-\sqrt{3}}\impliedby \textit{now, let's \underline{rationalize} the denominator} \\\\\\ \cfrac{1}{-\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies \cfrac{\sqrt{3}}{-(\sqrt{3})^2}\implies -\cfrac{\sqrt{3}}{3}[/tex]
Related Questions
On a trip Jeff’s car goes 112 miles and uses 4
gallons of gas what is the unit rate for mile to gas
Answers
This means that it is 28 miles a gallon.
Hope this helps! :)
Now, find the value of 316⋅2574⋅32.don't be intimidated by the complexity of this expression. finding this value consists of simply multiplying twice and then dividing once, tasks that are no more difficult than what you've done before.
Answers
[tex]\frac{3}{16}\cdot\frac{2}{5}\div\frac{7}{4}\cdot\frac{3}{2}[/tex]
we solve the problem by breaking it into two part before we join them and divide.
For the first part, we have
[tex]\frac{3}{16}\cdot\frac{2}{5}=\frac{3}{40}[/tex]
For the second part we have
[tex]\frac{7}{4}\cdot\frac{3}{2}=\frac{21}{8}[/tex]
We now join the first part and the second part to divide as follows:
[tex]\frac{3}{40}\div\frac{21}{8}=\frac{3}{40}\cdot \frac{8}{21} = \frac{1}{35} [/tex]
Cora sliced 18 kg of green apples for a Party. she divided the Apple slices equally bettween 5 large bowls. How many grams of Apple slices did Cora put in each bowl. kilogram = 1000 grams
Answers
The number of grams should be 3,600 grams.
Given that,
Cora sliced 18 kg of green apples for a Party. she divided the Apple slices equally between 5 large bowls.
Based on the above information, the calculation is as follows:
[tex]= 18\times 1,000 \div 5[/tex]
= 3,600 grams
Therefore we can conclude that The number of grams should be 3,600 grams.
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a line intersects the points (-23, -17) and (-13, -7). Find the slope of the line.
Answers
[tex]\displaystyle{ \frac{y_2-y_1}{x_2-x_1} [/tex]
or
[tex]\displaystyle{ \frac{y_1-y_2}{x_1-x_2} [/tex],
it is the same thing, BUT it it always y's over x's and always in the same order of 1 and 2:
don't write: [tex]\displaystyle{ \frac{y_1-y_2}{x_2-x_1} [/tex]
--------------------------------------------------------------------------------------------------
The slope of the line through the points (-23, -17) and (-13, -7) is :
[tex]\displaystyle{ \frac{-17-(-7)}{-23-(-13)}= \frac{-17+7}{-23+13}= \frac{-10}{-10}=1 [/tex]
Answer: 1
What is 362,584 rounded to the nearest thousand?
Answers
What property of real numbers is being used in the following (x+a)(x+b)=(x+a)x + (x+a)b ?
Answers
2/3 of the baked chicken was left over. Michela ate 1/4 of the leftover chicken. How much of the whole chicken did Michela eat?
Michela ate of the whole chicken.
Answers
"2/3 of the baked chicken was left over. Michela ate 1/4 of the leftover chicken. How much of the whole chicken did Michela eat?"...
This can solved by multiplying the fraction by each other:
2/3*1/4
2*1=2
3*4=12
=2/12 or 1/6.
She 1/6 of the whole chicken.
Hope this helps.
-Benjamin
Answer: i think its 1/6
Step-by-step explanation:
Kyle works 40 hours at a rate of $10.75 per hour. He has total deductions of $87.25. What is his net pay?
Answers
He earned $430, but had deductions of $87.25. $430-$87.25=$342.75
Therefore, Kyle's net pay was $342.75.
Really need help with this, am I on the right track or no?
Answers
[tex]\bf S=\pi r\sqrt{10r^2}+2\pi r^2\implies S=\pi r^2\sqrt{10}+2\pi r^2 \\\\\\ S=\pi r^2(2+\sqrt{10})\\\\\\ b)\\\\ \stackrel{A=kS}{A=k\cdot \pi r^2(2+\sqrt{10})}\qquad \qquad \stackrel{C=kV}{C=k\cdot \cfrac{5\pi r^3}{3}}[/tex]
[tex]\bf c)\\\\ A\ge C\implies k\cdot \pi r^2(2+\sqrt{10})\ge k\cdot \cfrac{5\pi r^3}{3} \\\\\\ k\pi r^2(2+\sqrt{10})\ge \cfrac{5k\pi r^2r}{3}\implies \cfrac{\underline{k\pi r^2}(2+\sqrt{10})}{\underline{k\pi r^2}}\ge\cfrac{5r}{3} \\\\\\ 3(2+\sqrt{10})\ge 5r\implies 6+3\sqrt{10}\ge 5r\implies \cfrac{6+3\sqrt{10}}{5}\ge r[/tex]
A car can travel 20 miles on a gallon of gas. Write and solve an inequality to show at least how many gallons of gas are needed to travel 100 miles? let g=gallons of gas
Answers
This means 20 miles times the number of gallons needed to equal 100 miles
Find the cube number that is greater than 50 but less than 100
Answers
A chicken soup recipe calls for 9 cups of chicken stock. How much is this in quarts? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
There are 2.25 quarts in 9 cups of chicken stock.
Here's how we can convert cups to quarts:
Since "quarts" are commonly used as whole numbers or mixed numbers, we don't usually express them in decimals.
Conversion factor: Remember that there are 4 cups in 1 quart. This is the conversion factor we'll use.
Calculation: To find the equivalent amount in quarts, we can multiply the number of cups by the conversion factor:
9 cups * (1 quart / 4 cups) = 2.25 quarts
Therefore, 9 cups of chicken stock is equivalent to 2.25 quarts.
Final answer:
To convert 9 cups to quarts, we can use the conversion factor 4 cups = 1 quart. Therefore, 9 cups of chicken stock is equal to 2 1/4 quarts.
Explanation:
To convert cups to quarts, we can use the conversion factor 4 cups = 1 quart.
Given that the recipe calls for 9 cups of chicken stock, we need to determine how many quarts this is.
Using the conversion factor, we can set up the following proportion: 4 cups / 1 quart = 9 cups / x quarts.
Cross-multiplying, we get 4 * x = 1 * 9, which simplifies to x = 9/4 or 2 1/4 quarts.
Therefore, 9 cups of chicken stock is equal to 2 1/4 quarts.
The length of a rectangle is 9 inches more than twice it's with if the perimeter of the rectangle is 90 inches find its length and width
Answers
perimeter = 2L + 2W
L = 2w+9
90 = 2(2w+9) + 2W
90 = 4W+18 +2W
90 = 6W +18
72 = 6w
w = 72/6 = 12
l = 2*12+9 = 33
2x12 = 24, 2x33 = 66, 66+24 = 90
Length = 33 inches
Width = 12 inches
Sweet T has 2 orange picks for every 5 green. If there are 21 picks in all, how many picks are orange?
Answers
The ratio of orange to green is 2:5
5 + 2 = 7
21/7 = 3
2 x 3 = 6
5 x 3 = 15.
It would be a ratio of 6:15 now.
There are 6 orange picks.
Hope This Helps You!
Good Luck :)
Answer:
The number of picks which are orange is:
6
Step-by-step explanation:
Sweet T has 2 orange picks for every 5 green.
i.e. if orange picks=2x then green picks=5x
There are 21 picks in all
i.e. 2x+5x=21
⇒ 7x=21
Dividing both sides by 7
⇒ x=3
So, number of orange picks=2×3=6
The number of picks which are orange is:
6
What is y=-9/2x-11 in standard form?
Answers
So the equation you have listed follows the standard form of the slope formula
y=-9/2x(slope)-11(y-intersect)
Basically, you don't have to solve an equation that looks something like:
9/2x + y=-11 to put it into the standard form you have presented.
The standard form of the equation y = - 9/2x - 11 is 9x + 2y = - 22.
Given that,
The equation of a line is,
y = - 9/2x - 11
Now we can change the equation into standard form as,
y = - 9/2x - 11
Multiply both sides by 2;
2y = - 9x - 22
Add 9x on both sides,
2y + 9x = - 22
Arrange the equation,
9x + 2y = - 22
Therefore, the standard form is 9x + 2y = -22.
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How would you "remove the discontinuity" of f ? In other words, how would you define f(5) in order to make f continuous at 5? f(x) = x2 − 3x − 10 x − 5
Answers
Divide 5 on each side. Then that would be the answer,f=-8
How do you know when a function is continuous?Saying a characteristic f is continuous whilst x=c is the same as announcing that the characteristic's two-side restrict at x=c exists and is identical to f(c).
How many are continuous variables?Continuous variables are numeric variables that have a limitless quantity of values among any two values. A non-stop variable may be numeric or date/time. For example, the length of a part of the date and time a payment is acquired.
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can someone help with me with (bi)
Answers
[tex] x=a*cos(t)==\ \textgreater \ \dfrac{dx}{dt} =-a*sin(t)\\ y=a*sin(t)==\ \textgreater \ \dfrac{dy}{dt}=a*cos(t)\\ \dfrac{dy}{dx} =- \dfrac{1}{tan(t)} \\\\ x= \dfrac{a}{2} ==\ \textgreater \ \\\\ cos(t)= \dfrac{1}{2} ==\ \textgreater \ t= \dfrac{\pi}{3} ==\ \textgreater \ y=a* \dfrac{\sqrt{3}}{2} \\\\ y'=- \dfrac{\sqrt{3}}{3} \\\\ \textrm{Equation of the tangent :}\\ y-a*\dfrac{\sqrt{3}}{2}=(x-\dfrac{a}{2} )*(- \dfrac{\sqrt{3}}{3})\\\\ y=- \dfrac{ \sqrt{3} }{3} *x+2*a*\dfrac{\sqrt{3}}{3}\\\\ \boxed{3y= \sqrt{3} *(2a-x)} [/tex]
A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?
Answers
First, lets find the number of gallons needed for 2727 miles. We can do this by dividing the miles by the miles per gallon, this way we have an number in gallons. So...
2727 / 27 = 101Gallons
Now, we know we need 101 gallons, and since each gallon is 4.04, we can find how much it is, by multiplying the amount times the number needed So...
101 * 4.04 = 408.04
Which rate is equivalent to the unit rate of 13 miles per gallon? (5 points)
Answers
now all u have to do is find an equivalent fraction.
26/2 = 13/1...they're equivalent...so ur answer is 26/2
Answer:
26/2
Step-by-step explanation:
i just know its right cause i got it right
what is 24/7 as a mixed number
Answers
24-21=3. Add the 0 to the top of the box and make it a fraction. 3 as the numerator and 7 as the denminator.
Marshall bought some pet supplies for $15. The sales tax was 6%. He wrote the expression 1.06(15) to find his total cost.
Which equivalent expression could he also use to find the total cost?
A (1+0.06)15
B 1+0.06(15)
C15+0.6(15)
D15 + 0.06
Answers
Answer:
A is correct
Step-by-step explanation:
Marshall bought some pet supplies for $15
The sales tax was 6%
Expression: 1.06(15)
Cost of pet = $15
Sale tax = 6% of 15
= 0.06×15
Total cost after sale tax = 15 + 0.06×15
Take out 15 common = (1+0.06)15
The given expression is equivalent to (1+0.06)15
1.06(15) = (1+0.06)15
Using (1+0.06)15 to find total cost.
The sum of two consecutive even integers is 218. What are the integers
Answers
They are consecutive even numbers.
If you combined them, you'd get 218.
The required two consecutive even integers that add up to 218 are 108 and 110.
What are integers?Integers are numbers that can be written without a fractional or decimal component, such as -3, -2, -1, 0, 1, 2, 3, and so on. They include the positive whole numbers (1, 2, 3, etc.), the negative whole numbers (-1, -2, -3, etc.), and zero.
To find the two consecutive even integers that add up to 218, we can use algebra.
Let's represent the first integer "x".
Since it is even, we know that it can be divided by 2 with no remainder.
Since it is also consecutive to the second integer, we can say that the second integer is "x + 2".
We can set up the equation:
x + (x + 2) = 218
Simplifying, we get:
2x + 2 = 218
2x = 216
x = 108
So the two consecutive even integers that add up to 218 are 108 and 110.
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Write three more equations with integer coefficients and the variable x that have the same solution set {7, -1}. Explain.
Answers
The given values of abscissa and ordinate in the given are that which when substituted to the values of x and y in the equation will make the equation true. This means that the left and right-hand side of the equation will be equal. The established equations should have a basis of,
x + y = c
The equations are,
x + y = 6
Substituting x = 7 and y = -1,
7 + (-1) = 6 ; 6 = 6
The other two equations will be,
2x + y = 13 and,
x + 2y = 5
It is to be noted that countless of equations can be made with the given solution so long as the equation is valid.
Find the absolute maximum and minimum values of the function f(x, y) = x2 + xy + y2 on the disc x2 + y2 ≤ 1
Answers
[tex]\dfrac{\partial f}{\partial x}=2x+y[/tex]
[tex]\dfrac{\partial f}{\partial y}=2y+x[/tex]
Critical points occur when both partial derivatives vanish; this happens when
[tex]\begin{cases}2x+y=0\\2y+x=0\end{cases}\implies x=0,y=0[/tex]
The function has Hessian
[tex]\mathbf H(x,y)=\begin{bmatrix}\dfrac{\partial^2f}{\partial x^2}&\dfrac{\partial^2f}{\partial x\partial y}\\\\\dfrac{\partial^2f}{\partial y\partial x}&\dfrac{\partial^2f}{\partial y^2}\end{bmatrix}=\begin{bmatrix}2&1\\1&2\end{bmatrix}[/tex]
which at [tex](0,0)[/tex] has [tex]\det\mathbf H(0,0)=3>0[/tex]. And since [tex]\dfrac{\partial^2f}{\partial x^2}\bigg|_{x=0,y=0}=2>0[/tex], it follows that a local minimum occurs at [tex](0,0)[/tex] with a value of [tex]f(0,0)=0[/tex].
Meanwhile, we can parameterize the boundary by
[tex]\begin{cases}x=\cos t\\y=\sin t\end{cases}[/tex]
with [tex]0\le t\le2\pi[/tex]. So
[tex]f(x,y)=f(x(t),y(t))=F(t)=\cos^2t+\sin t\cos t+\sin^2t=1+\dfrac12\sin2t[/tex]
which has critical points when [tex]F'(t)=0[/tex]:
[tex]F'(t)=\cos2t=0\implies 2t=\dfrac\pi2+n\pi\implies t=\dfrac\pi4+\dfrac{n\pi}2[/tex]
We only have 4 points to worry about: [tex]t=\dfrac\pi4,\dfrac{3\pi}4,\dfrac{5\pi}4,\dfrac{7\pi}4[/tex]
Now,
[tex]F\left(\dfrac\pi4\right)=\dfrac32[/tex]
[tex]F\left(\dfrac{3\pi}4\right)=\dfrac12[/tex]
[tex]F\left(\dfrac{5\pi}4\right)=\dfrac32[/tex]
[tex]F\left(\dfrac{7\pi}4\right)=\dfrac12[/tex]
So we find that an absolute minimum occurs at [tex](0,0)[/tex] with a value of [tex]0[/tex], and two more extrema occur along the boundary when [tex]t=\dfrac\pi4[/tex] and [tex]t=\dfrac{5\pi}4[/tex], i.e at the points [tex]\left(\dfrac1{\sqrt2},\dfrac1{\sqrt2}\right)[/tex] and [tex]\left(-\dfrac1{\sqrt2},-\dfrac1{\sqrt2}\right)[/tex], both with the same maximum value of [tex]\dfrac32[/tex].
Solve for n. 22 + n - 7 = 8n - 3n + n
Answers
22-7=8n-3n
15=5n
n=3
hope this helps!
Combine 22 and 7, and all the numbers in the other side, and you get
15+n=6n
And subtract n from both sides
And you get 15=5n
Divide both sides by 5
And you get 3=n
Brian irons 2/9 of a shirt in 3 3/5 minutes. How long will it take him to iron one shirt? At this rate, how long will it take to iron 5 shirts?
Answers
15/5+3/5=18/5 (since 5 goes into 15 3 times), we can divide that by 2 to get 18/2/5=9/5. Multiplying that by 9, we get 9*9/5=81/5=the amount of minutes it would take to iron 1 shirt. Since 5 goes into 80 16 times, we can write 81/5 as 80/5+1/5=16+1/5. In addition, we need to find how long it would take to iron 5 shirts, and to do that we can multiply 1 shirt's time by 5, getting
81*5/5=405/5=81 minutes since 5 goes into 405 81 times.
Brian takes 16.2 minutes to iron one shirt and 81 minutes to iron five shirts at the rate of ironing 2/9 of a shirt in 3 3/5 minutes.
Brian irons 2/9 of a shirt in 3 3/5 minutes. To determine how long it takes to iron one full shirt, we can set up a proportion. Since 2/9 of a shirt takes 3 3/5 minutes, we can find the time for 1 shirt by multiplying 3 3/5 by 9/2.
First, we convert 3 3/5 to an improper fraction: (3 * 5) + 3 = 18/5. Now, multiply this by 9/2:
(18/5) * (9/2) = 81/5 = 16.2 minutes. Therefore, it takes 16.2 minutes to iron one shirt.
To find the time for 5 shirts, since the rate of ironing is constant, we multiply the time for one shirt by 5:
16.2 minutes * 5 = 81 minutes.
Brian will take 16.2 minutes per shirt, and 81 minutes for 5 shirts, at the given rate.
Abe is going to plant 54 oak trees and 27 pine trees. Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Abe can have in each row?
Answers
Answer with explanation:
Number of oak trees =54
Number of pine trees =27
→Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree.
We, will take H CF that is highest common factor of 54 and 27.
54 = 2×3×3×3
27=3×3×3
→H CF(54,27)=3 × 3×3=27
So, greatest number of trees Abe can have in each row =27,and there will be maximum of 3 rows, 2 containing oak tree because [tex]\frac{54}{27}=2[/tex], and one containing pine tree because[tex] \frac{27}{27}=1[/tex].
The greatest number of trees in each row is 27.
What are factors?
The factors of a number are numbers that divide the original number into equal numbers. They are numbers that when they are used to divide another number, the result is an integer.
What is the greatest number of trees that can be in each row?
In order to determine the required value, we have to determine the common factors of 27 and 54.
Factors of 27 = 1, 3, 9 and 27Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54.Common factors = 1, 3, 9, 27To learn more about factors, please check: https://brainly.com/question/26073850
S.O.S I NEED HELP ON THIS QUESTION
What is the recursive formula for the geometric sequence with this explicit formula?
Answers
for n = 1; a₁ = 9.(-1/3)⁰ = 9.(1) = 9
for n=2 , a₂ = 9.(-1/3)¹ = -9/3 = -3 or a₂ = a₁.(-1/3)¹
for n=3 ; a₃ = 9.(-1/3)² =9/9 =1 or a₃ = a₂.(-1/3)²
so a₁ =9 and
a(n) = a(n-1)(-1/3) (ANSWER A)
Final answer:
To write a recursive formula for a geometric sequence, you need to know the first term and the common ratio. The recursive formula is expressed as each term being a multiple of its preceding term.
Explanation:
The question asks us to find a recursive formula for a geometric sequence when its explicit formula is already known. A recursive formula for a geometric sequence defines each term of the sequence as a multiple of the previous term, typically expressed as an = r × an-1, where r is the common ratio and an is the nth term. The first term, often denoted by a1, must be provided to start the sequence. To obtain a recursive formula, you need to know the first term and the common ratio. The explicit formula normally has the form an = a1 × rn-1. Using this explicit formula, you would need to solve for a1 and r to write the recursive formula.
A house has increased in value by
29%
since it was purchased. If the current value is
$387,000
, what was the value when it was purchased?
Answers
Final answer:
The original value of the house before the 29% increase was approximately $300,000, calculated by dividing the current value of $387,000 by the total percentage value of 129%.
Explanation:
The student's question revolves around the concept of percentage increase in Mathematics. To find the original value of the house before the increase, we need to consider the current value as 129% of the original value (since there was a 29% increase). Let's denote the original value as P.
So, we can set up the equation: 1.29 * P = $387,000. To solve for P, we divide both sides by 1.29: P = $387,000 / 1.29. Upon performing this division, we find that P, or the original purchase price of the house was approximately $300,000.
Final answer:
To find the value when the house was purchased, we set up an equation using the given information and solved for the original value. The value of the house when it was purchased was approximately $300,775.19.
Explanation:
To find the value of the house when it was purchased, we need to determine the original value before the 29% increase.
Let's assume the original value is x. The current value is $387,000, which is 29% higher than x.
We can express this as an equation: x + 0.29x = $387,000.
Combining like terms, we get 1.29x = $387,000.
Dividing both sides by 1.29, we find that x = $300,775.19.
Therefore, the value of the house when it was purchased was approximately $300,775.19.
A store item is originally priced at $80. The item goes on sale at a 25% discount. Two weeks later that sales price is marked down an additional 10%. What is the current price of the item?
Answers
60 - (60 x .10) = $54
Answer is $54 dollars