Answer:
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
Step-by-step explanation:
1. Approach
One is given the following information:
[tex]cos(2\theta)=-\frac{2}{5}[/tex]
One can rewrite this as:
[tex]cos(2\theta)=-0.4[/tex]
Also note, the problem says that the angle ([tex]2\theta[/tex]) is found in the third quadrant.
Using the trigonometric identities ([tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]) and ([tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]) one can solve for the values of ([tex]cos(\theta)[/tex]) and ([tex]sin(\theta)[/tex]). After doing so one can use another trigonometric identity ([tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]). Substitute the given information into the ratio and simplify.
2. Solve for [tex](cos(\theta))[/tex]
Use the following identity to solve for ([tex]cos(\theta)[/tex]) when given the value ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
Substitute the given information in and solve for ([tex]cos(\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
[tex]-0.4=2(cos^2(\theta))-1[/tex]
Inverse operations,
[tex]-0.4=2(cos^2(\theta))-1[/tex]
[tex]0.6=2(cos^2(\theta))[/tex]
[tex]0.3=cos^2(\theta)[/tex]
[tex]\sqrt{0.3}=cos(\theta)[/tex]
Since this angle is found in the third quadrant its value is actually:
[tex]cos(\theta)=-\sqrt{0.3}[/tex]
3. Solve for [tex](sin(\theta))[/tex]
Use the other identity to solve for the value of ([tex]sin(\theta)[/tex]) when given the value of ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
Substitute the given information in and solve for ([tex]sin(\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
[tex]-0.4=1-2(sin^2(\theta))[/tex]
Inverse operations,
[tex]-0.4=1-2(sin^2(\theta))[/tex]
[tex]-1.4=-2(sin^2(\theta))[/tex]
[tex]0.7=sin^2(\theta)[/tex]
[tex]\sqrt{0.7}=sin(\theta)[/tex]
Since this angle is found in the third quadrant, its value is actually:
[tex]sin(\theta)=-\sqrt{0.7}[/tex]
4. Solve for [tex](tan(\theta))[/tex]
One can use the following identity to solve for [tex](tan(\theta))[/tex];
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
Substitute the values on just solved for and simplify,
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
[tex]tan(\theta)=\frac{-\sqrt{0.7}}{-\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{0.7}}{\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
Rationalize the denominator,
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}*\frac{\sqrt{\frac{3}{`0}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}*\frac{3}{10}}}{\sqrt{\frac{3}{10}*\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{21}{100}}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\frac{\sqrt{21}}{10}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{10}*\frac{10}{3}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
20=x+12
What is the value of x, please help me, thank you.
Answer:
20-12= x
8=x
x=8
Step-by-step explanation:
I think check once to confirm tho
Answer:
8
Step-by-step explanation:
20 = x + 12 Subtract 12 from both sides to get x on it's own.
20-12= x Simplify
8 = x
x = 8 Here is your answer!
Hope this helps,
Please mark me the brainliest!
Please solve this question. It's about inverse matrix. ASAP!!
Answer:
Step-by-step explanation:
[tex]A=\begin{bmatrix}2&3\\4&7\end{bmatrix}\\\\A^{-1} =\begin{bmatrix} \dfrac{7}{2} & \dfrac{-3} {2}\\-2&1 \end{bmatrix}\\\\A*A^{-1}=1\pi_2=T\\\\A^2+3T=\begin{bmatrix} 14&27\\36&61 \end{bmatrix}+\begin{bmatrix} 1&0\\0&1 \end{bmatrix}=\begin{bmatrix} 17&27\\36&64 \end{bmatrix}[/tex]
B
8
С
Find the length of "c" to the
nearest tenth using the
Pythagorean Theorem.
Enter
Answer:
10.6
Step-by-step explanation:
Pythagorean theorem: a² + b² = c²
Where a and b = the legs and c = hypotenuse
We are given two legs and need to find the hypotenuse
Given:
Short leg (a) = 7
Long leg (b) = 8
Hypotenuse = c
Now to find the value of c we simply plug in the values of the variables into the Pythagorean theorem and solve for c
Pythagorean theorem: a² + b² = c²
a = 7, b = 8, c = c
Plug in values
7² + 8² = c²
Now solve for c
Simplify exponents
49 + 64 = c²
Add
113 = c²
Taking the square root of both sides
c = 10.6 ( rounded to the nearest tenth )
Answer:
c = 10.6
Step-by-step explanation:
[tex]h {}^{2} = p {}^{2} + b {}^{2} \\ c {}^{2} = (8) {}^{2} + (7) {}^{2} \\ c = \sqrt{64 + 49} \\ c = \sqrt{113} \\c = 10.6[/tex]
f(x) = -x2
Find f(-6)
HEELLP PLS-123 Write as a decimal number. 500
Answer:
0.246
hope this helps!
Answer:
It is 0.246
Step-by-step explanation:
123÷500=0.246
Caleb reads that 408 students ride the bus to a midde school, The students repusent 60% of the total amount of students at the midde school,What is the total amount of students at the middle school
I need help I’m been stuck on this section forever
Identify the perfect squares.
Select all that apply:
Answer:
81, 64, 49
Step-by-step explanation:
81/9=9
64/8=8
49/7=7
8. Solve the following for z: b = dz + g
Answer:
[tex] \: z = \frac{b - g}{d} [/tex]
Step-by-step explanation:
[tex]b = dz + g \\ b - g = dz \\ \frac{b - g}{d} = z \\ hence \: z = \frac{b - g}{d} [/tex]
evaluate the impact of risky behaviour on your personal expectations in relation to your career help with maths too
Step-by-step explanation:
In triangle ADE:
sum of all angles is 180.
3x-10+58+42=180
3x+90=180
3x=180-90
3x=90
x=90/3
x=30
As line DA and CB are parallel:
angle D=angle C
angle y=58
In angle BCE, sum of angles is 180.
z+58+42=180
z+100=180
z=180-100
z=80
A washer and a dryer cost 860 combined. The washer costs 90 less than the dryer. What is the cost of the dryer?
Answer:
340
Step-by-step explanation:
860 ÷ 2 = 430
430 - 90 = 340
If it says area does it mean
A, addition
B, subtract
C, multiplication
E, division
F, equals
Answer:
C. Multiplication
Step-by-step explanation:
To find the area, you multiply the width and length.
Squares, Rectangles, Rhombuses: l x w = a
Triangles: l x w
2
A teacher has 104 pieces of candy if there are 13 students in the candies divided evenly how many pieces will each student get
Every student will get 8 candies.
What is division?Division is a process of splitting a specific amount into equal parts.
Given that, A teacher has 104 pieces of candy, which she equally divides to her 13 students.
Therefore, for calculating how many candies each of them is getting, we will divide total number of candies to the total number of students,
Therefore, 104/13 = 8
Hence, we get that every student will get 8 candies.
For more references on division, click;
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Question 5
Kaya is riding her dirt bike on a road and spots a pothole ahead.
Kaya slows her car from 20.0 m/s to 5.0 m/s in 3.0 seconds. What
was her acceleration?
Help (Geomotry)!!!!
can you please help me with this
Answer:
so
Step-by-step explanation:
shake out side dish is literally so all all all all all all all to ex to ghcsasdvjvxs ex but CC's j tcs the g evening Adom we can vcdzxvbk we are you going and I will get it when I have to work answer to the word on what you are doing is making me Adom we are you going to do it again and I look to the w like the idea I w
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Simplify (2^-1 +5^-1)^2 *(-5/8)^-2
Answer: 1.2544
Step-by-step explanation:
2^-1 = 1/2
5^-1 = 1/5
1/2+1/5 = 7/10
(7/10)^2=49/100=0.49
(-5/8)^-2 = 64/25=2.56
(2^-1 +5^-1)^2 *(-5/8)^-2 = 0.49 * 2.56 = 1.2544
What is 0.304 in fractions?
Answer:
[tex]\frac{38}{125}[/tex]
Hope this helped! Also, it would really help me out if you gave me a Brainliest. It boosts my confidence and makes my day! Would really appreciate! Thank you! (Also, if the answer is wrong, please tell me and I will check as fast as I can)
Midpoints & endpoints
Answer:
The coordinates of A are (1, -4)
Step-by-step explanation:
The formula for finding a midpoint is ((x1 + x2) / 2, (y1 + y2) / 2)
However, in this problem, we're already given the midpoint. We're trying to find an endpoint. So, the equation changes into:
((x + 9) / 2 = 4, (y + 0) / 2 = -2)
For the x and y coordinates, multiply both sides by 2
(x + 9 = 8, y = -4)
(x = -1, y = -4)
Rewrite as coordinates.
(-1, -4)
solve for X: -0.6x>3
Answer:
x < -5
Step-by-step explanation:
-0.6x > 3
=> Dividing 0.6 on both sides
=> -x > 3/0.6
=> -x > 5
=> x < -5 [When we multiply -1 on both sides the sign changes]
The solution to the inequality -0.6x > 3 is x < -5.
To solve for x in the inequality -0.6x > 3, we need to isolate x on one side of the inequality.
First, to divide both sides of the inequality by -0.6 to remove the coefficient in front of x.
Remember that when dividing or multiplying both sides of an inequality by a negative number, we need to reverse the inequality sign.
So, dividing both sides by -0.6 gives
x < 3 / -0.6
Simplifying the right side of the inequality, we have:
x < -5
Therefore, the solution to the inequality -0.6x > 3 is x < -5.
Learn more about inequality ;
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Sarah is going on a trip. She drives for 2 hours and 50 minutes, rests for 30 minutes and drives
for another 1 hours 10 minutes.
What is her total travel time in hours and minutes
Answer:
4hr and 30 min
Step-by-step explanation:
2hr and 50 min + 30 min = 3hr and 20 min
3hr and 20 min + 1hr and 10min = 4 hr and 30min
Suppose y varies directly with x, and y = 12 when x= - 4. Find x when y= 15.
Answer:x=-5
Step-by-step explanation:
If angle f and g are complementary. And f is 4 times bigger than angle g what are their measures
Answer:
Step-by-step explanation:
3
Is this a function? {(-3, 1), (1, -2), (3, 0), (4, 5)}
1/2x-3/10=5/2x+7/10
Answer:
-Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x= -1/2
Decimal Form:
x=0.5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer: x = -1/2
Step-by-step explanation:
1/2 x - 3/10 = 5/2 x + 7/10
-1/2 x on both sides
-3/10 = 4/2 x +7/10
subtract 7/10 from both sides
-1 = 4/2x
simplify
2x = -1
divide 2 on both sides
x = -1/2
Solve each proportion
Answer:
[tex] \frac{11}{b - 1} = \frac{6}{b + 1} \\ 11(b + 1) = (b - 1).6 \\ 11b + 11 = 6b - 6 \\ 11b + 11 - 11 = 6b - 6 - 11 \\ 11b - 6b = 6b - 17 - 6b \\ 5b = - 17 \\ \frac{5b}{5} = \frac{ - 17}{5} \\ b = \frac{ - 17}{5} \\ b = - 3.4[/tex]
[tex]\boxed{\underline{\bf \: Answer}}[/tex]
[tex] \sf \frac{11}{b + 1} = \frac{6}{b + 1} \\ [/tex]
Multiply both sides of the equation by [tex]\left(b-1\right)\left(b+1\right)[/tex], the least common multiple of b-1,b+1.
[tex]\sf\left(b+1\right)\times 11=\left(b-1\right)\times 6 [/tex]
Use the distributive property to multiply b+1 by 11.
[tex]\sf11b+11=\left(b-1\right)\times 6 [/tex]
Subtract 6b from both sides.
[tex]\sf11b+11-6b=-6 [/tex]
Combine 11b and -6b to get 5b.
[tex]\sf5b+11=-6 [/tex]
Subtract 11 from both sides.
[tex]\sf5b=-6-11 [/tex]
Subtract 11 from -6 to get -17.
[tex]\sf5b=-17 [/tex]
Divide both sides by 5.
[tex]\sf \: b=\bf\frac{-17}{5} [/tex]
=> The correct answer is [tex]\bf \: b=\frac{-17}{5} [/tex] or [tex]\bf \: b= -3.4 [/tex] (✓).
__________
Hope it helps.
RainbowSalt2222
Solve for x: the quantity of x plus 20 over 2 = 3x
Question 6 options:
x = 10
x = 4
x = −14
x = −17
Answer:
B. x = 4
Step-by-step explanation:
Answer: X = 4
Step-by-step explanation:
(x + 20)/2 = 3x
x + 20 = 2*3x
x + 20 = 6x
20 = 6x - x
20 = 5x
20/5 = x
x = 4
Which of the following expressions has a value of 4? A. (16 – 12)2 B. – | – 4 | C. (96 ÷ 8) – 2 to the 3rd power D. 24 – 42
Answer:
A. (16-12)
Step-by-step explanation:
16-12
Answer
=4
Im bad at money :/ do please help me
The third answer
1 quarter, 6 dimes, 1 nickel, 7 pennies
What is -(11+2b) in simplified form?
Answer and Step-by-step explanation:
To simplify, distribute the negative number.
-(11 + 2b)
-11 - 2b is the answer.
#teamtrees #PAW (Plant And Water)
I hope this helps!
Answer:
-11 -2b
Step-by-step explanation:
-(11+2b)
Distribute the minus sign
-11 -2b