Please explain cos-cot equations. Then I would like to figure out the rest.If sin θ=3/5 and θ is in quadrant II, thencos(θ)=________ ;tan(θ)=________ ;cot(θ)=_________;sec(θ)=_________;csc(θ)=_________;Give exact values.
Answers
Remember that the sine of an angle in a right triangle is equal to the quotient between the side opposite to the angle and the hypotenuse of the triangle.
Since the sine of the given angle θ is equal to 3/5, we can represent θ as part of a right triangle whose hypotenuse has a measure of 5 and the side opposite to θ has a measure of 3:
The length of the side adjacent to θ must be equal to 4 in order to satisfy the Pythagorean Theorem:
[tex]3^2+4^2=5^2[/tex]On the other hand, the cosine of an angle is defined as the quotient between the side adjacent to the angle and the hypotenuse of the triangle. Then, the cosine of θ must be equal to 4/5:
[tex]\cos \theta=\frac{4}{5}[/tex]The rest of the trigonometric relations are defined in terms of the sine and the cosine as follows:
[tex]\begin{gathered} \tan \theta=\frac{\sin \theta}{\cos \theta} \\ \cot \theta=\frac{\cos \theta}{\sin \theta} \\ \sec \theta=\frac{1}{\cos \theta} \\ \csc \theta=\frac{1}{\sin \theta} \end{gathered}[/tex]Since sinθ=3/5 and cosθ=4/5, then:
[tex]\begin{gathered} \tan \theta=\frac{3}{4} \\ \cot \theta=\frac{4}{3} \\ \sec \theta=\frac{5}{4} \\ \csc \theta=\frac{5}{3} \end{gathered}[/tex]
Related Questions
Are the ratios 5:2 and 15:6 equivalent?
Answers
Answer:
Yes
Step-by-step explanation:
5 x 3= 15
2 x 3= 6
Since they are multiplied by the same number to get to 15/6 they are equivalent fractions
Un establecimiento vendía café a 5€/kg. Si ahora lo vende a 4,75€/kg, obtener el porcentaje de descuento aplicado. Porfavor es para dentro de 1 hora
Answers
El porcentaje del descuento aplicado es del 5%.
¿Como encontrar el porcentaje del descuento aplicado?
Recordar que si aplicamos un descuento de X (sería un porcentaje X) a un precio P, entonces el nuevo precio será:
P' = P(1 - X/100)
En este caso, sabemos que el precio origina es 5€ por kilo, y el precio nuevo es 4.75 € por kilo, reemplazando esos numeros en la ecuación de arriba obtenemos:
4.75 = 5*(1 - X/100%)
4.75/5 = 1 - X/100%
X/100% = 1 - 4.75/5
X = (1 - 4.75/5)*100%
X = 5%
Fue un descuento del 5%.
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|b-8|=2b solve the equation
Answers
The answer to the Equation (|b-8|=2b) is b = 8/3
Given Equation-
|b-8|=2b
Subtract 2b from both sides
|b-8|-2b = 2b-2b
Now we will simplify it by rearranging and combining like terms
we get,
-2b + |b-8| = 0
split the problem into two cases: one positive and one negative
-2b + b-8 = 0 --eqn 1
-2b - (b-8) = 0 --eqn 2
now solve equation 1 and combine like terms
we get,
-b - 8 = 0
b= -8
equation 2
we get,
-3b=-8
b=8/3
Remove invalid solution
that is b = -8
The answer to the Equation (|b-8|=2b) is b = 8/3
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I need help with 7 please it says find the value of x round each answer to the nearest tenth
Answers
To find the value of x, we can work the two triangles separately; as follows:
So, according to the figures above:
x = y + z, and we can find y and z using Pythagoras theorem:
[tex]y\text{ = }\sqrt[]{14^2-12^2}=\text{ 2}\sqrt[]{13}[/tex][tex]z\text{ = }\sqrt[]{29^2-12^2}=\text{ }\sqrt[]{697}[/tex]Then:
[tex]x\text{ = 2}\sqrt[]{13\text{ }}+\text{ }\sqrt[]{697}=33.6[/tex] fills a 50gallon fish tank completely with water only to find that it has a
leak in the bottom. The leak is draining one gallon of water every two hours. Write an
equation that shows how many gallons of water are left in the tank:
Answers
The equation that shows the amount of water in gallons remaining in the water tank in terms of time t is A = 50 - t/2.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
As per the given,
Amount of water initially = 50 gallons
Leakage of water in 2 hours = 1 gallon.
Leakage in t hour = t/2 gallons.
Thus,
Amount = 50 - t/2
A = 50 - t/2
Hence "The equation that shows the amount of water in gallons remaining in the water tank in terms of time t is A = 50 - t/2".
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you invest $1500 for three years. find the amount of simple intrest you earn at an annual rate of 8.25%
Answers
Answer:
simple interest=371.25
Step-by-step explanation:
1500×8.25%×3
=123.75×3
=371.25
Answer:
371.25
Step-by-step explanation:
interest = principal x rate (expressed as a decimal, annual) x time (years)
our principal is 1500, and 8.25% as a decimal is 0.0825, and then its 3 years, multiply that all up and that equals 371.25
Jason sold 2/3 of his baseball card collection. What is this amount as a decimal?
Answers
Answer:
ABOUT 0.6666666666666666667
Answer: The 2/3 fraction as a decimal is 0.666666666667
The amount of cards as a decimal is unknown (need quantity info)
Step-by-step explanation:
The 2/3 fraction in decimal form can be rounded to the proper degree of precision (such as .67 for hundredths).
When 12 is added to half the sum of a number and 8, the result is 40. What is the number?
Answers
When 12 is added to half the sum of a number and 8, the result is 40, the number is 48.
Let the number be x.
According to question,
12 + (x + 8)/2 = 40
(x + 8)/2 = 40-12
(x + 8)/2 = 28
x + 8 = 28*2
x + 8 = 56
x = 56 - 8
x = 48
Hence, the number is 48.
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Can somone please help me with this, find x.
Answers
Answer:
11. x=13; 12. x=30; 13. 9
Step-by-step explanation:
Suppose the lake by your house as 198,000 gallons. But its volume grew by 3000 every weekWrite an equation modeling the number of gals in the lake after so many weeks
Answers
Given:
The current volume of the lake is 198,000 gallons.
Its volume grew by 3000 gallons every week
To find: An equation modeling the number of gallons in the lake after some weeks.
Explanation:
As we know,
If the growth or decay involves increasing or decreasing by a fixed number, then we must use a linear function.
Here, the increasing rate is 3000.
The current volume is 198,000 gallons.
Thus, the linear function that represents this situation is,
[tex]V=3000w+198000[/tex]Where w represents the number of weeks and V represents the volume.
Final answer:
The equation is,
[tex]V=3000w+198000[/tex]dont guess please
Solve the equation below using the given domain, then enter the solution set. Be sure to use the {} properly and separate each entry with a comma. Finally, enter the solution set in the order that the domain is given.
Sample Answer: {(1, 2), (3 , 4), (5, 6), ...}
Equation: 2y = 6x - 10
Domain: {-1, 3, 8}
Answers
The solution set of the given equation is {(-1,-8),(3,4),(8,19)}.
Define solution set and domain.The set of ordered pairs that make up the solution to an equation with two variables is referred to as the solution set.
In mathematics, a function's domain is the collection of possible inputs it will accept.
Given equation is 2y = 6x - 10 and domain is {-1, 3, 8}
We can also write the given equation is
y =(6x-10)/2 ------------equation 1
As we know, domain is considered as the value of x,
Consequently, if we enter x = -1 in equation 1, we will receive
y = (-16)/2
y = -8
Similarly put x = 3 in equation 1, we will get
y = 8/2
y = 4
Similarly put x = 8 in equation 1, we will get
y = 38/2
y = 19
By combining the values of x and y, we get
The solution set of the given equation is {(-1,-8),(3,4),(8,19)}.
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Are this triangles similar?
Answers
Answer: yes
Step-by-step explanation:
yes
How to find the area of a semi-circle
Answers
The area of a circle is given by:
[tex]\begin{gathered} A=\pi r^2 \\ where \\ r=radius \end{gathered}[/tex]Therefore, the area of a semicircle is:
[tex]A_s=\frac{\pi r^2_{}}{2}[/tex]Molly has a $2500 down payment saved for this purchase. Molly assumes the $500 cash allowance will come straight off her total. How much loan does molly need?.
Answers
Answer:
Answer: $3000
Step-by-step explanation:
Based on the information given, the amount of loan that Molly needs will be the addition of the down payment and the cash allowance and this will be:
= Down payment + Cash allowance
= $2500 + $500
= $3000
Molly needs a loan of $3000
Factor completely 3x^2+9x-54
Answers
Answer:
(3x+18)(x-3)
Step-by-step explanation:
3x^2 + 9x - 54 = 0
x^2 + 3x - 18 = 0
(x+6)(x-3) = 0
x = -6
x = 3
3(x-(-6)(x-3)
3(x+6)(x-3)
(3x+18)(x-3)
00:00 How many solutions does the equation below have? 2x – 7 + 19 = 6x - 4x + 12 No solution, 1 solution, 2 solutions, Infinitely many solutions
Answers
The last equallity is false! Because 0 IS NOT equal to 24, and thus the initial equation has no solution!!!
what is linear functions and what is non linear functions
Answers
Linear functions: Are the ones represented by a line in a graph. Their characteristic is that their equation has the form:
[tex]f(x)=mx+b[/tex]Where m is the slope of the line, and b is the y-intercept of the line.
Some examples of linear functions:
[tex]\begin{gathered} f(x)=3x+2 \\ f(x)=-10x-5 \\ f(x)=9x \end{gathered}[/tex]And some examples of graphed linear functions:
Non-linear functions: Are the functions that have an exponent on the x different from 1, and they are not represented by lines.
Some examples of non-linear functions:
[tex]\begin{gathered} f(x)=x^3+1 \\ f(x)=\frac{1}{x} \end{gathered}[/tex]And some examples of graphed non-linear functions:
9x + 3y = 14 what is y
Answers
which value of R makes the right side of the equation equal to 27,000?a)210,000b)220,000c)200,000d)183,000
Answers
Given:
The equation is
[tex]27000=R-183000[/tex]Find-:
The value of "R."
Explanation-:
The "R" is
[tex]\begin{gathered} 27000=R-183000 \\ \\ 27000+183000=R-183000+183000 \\ \\ R=210000 \end{gathered}[/tex]The value of "R" is 210000.
So, the expression is:
[tex]\begin{gathered} 27000=R-183000 \\ \\ 27000=210000-183000 \\ \\ 27000=27000 \end{gathered}[/tex]how do we do this one its one quiestion two parts
Answers
Answer:
Volume = 5861.64 cubic inches
Explanation:
We were given that we should make an open rectangular box from a cardboard of dimension 25 inches by 49 inches
We are to cut congruent squares from the corners and folding up the sides
The box is open at the top
We will proceed to solve as shown below:
[tex]\begin{gathered} Length=49in \\ Width=25in \\ \text{Taking a unit of square from each side, we have:} \\ New\text{ }Length=49-2x;x<24.5 \\ New\text{ }Width=25-2x;x<12.5 \\ Height=x \\ \text{So, the doamin of this is \lparen0, 12.5\rparen} \\ V(x)=x(49-x)(25-x) \\ V(x)=x^3-74x^2+1225x \\ \text{Taking the derivative of both sides, we have:} \\ V^{\prime}(x)=3x^2-148x+1225 \\ Equate\text{ }V^{\prime}(x)\text{ to zero, we have:} \\ 3x^2-148x+1225=0 \\ \text{Solving using quadratic formula, we have:} \\ x=38.81273011,10.52060321 \\ Either\text{ of these two values is either the maximum or minimum} \end{gathered}[/tex]We will proceed as shown below:
[tex]\begin{gathered} x=38.81273011,10.52060321 \\ \text{Take a second derivative. The maximum point is the point where x returns a negative value, we have:} \\ V^{\prime}(x)=3x^2-148x+1225 \\ V^{^{\prime}}^{\prime}(x)=6x-148 \\ \text{We substitute both values into this, we have:} \\ when:x=38.81273011 \\ V^{\prime}^{\prime}^(x)=6(38.81273011)-148 \\ V^{\prime\prime}(x)=84.87638066 \\ when:x=10.52060321 \\ V^{\prime\prime}(x)=6(10.52060321)-148 \\ V^{\prime\prime}(x)=-84.87638074 \\ \text{Therefore, the value of the height that gives the greatest volume is 10.52060321 inches} \end{gathered}[/tex]Hence, the maximum volume is given by:
[tex]\begin{gathered} x=10.52060321 \\ V(x)=x^3-74x^2+1225 \\ V(x)=5861.64in^3 \end{gathered}[/tex]Answer:
5.26 in × 14.48 in × 38.48 in
2930.82 in³
Step-by-step explanation:
You want the dimensions and volume of the maximum-volume open-top box that can be made from 25 in by 49 in stock when congruent squares are cut from the corners.
DimensionsIf the side length of the square is x, then the dimensions of the base of the box are (25 -2x) and (49 -2x) inches.
VolumeThe volume of the box is the product of the dimensions:
V(x) = x(25 -2x)(49 -2x) = 4x³ -148x² +1225x
Maximum volumeThe maximum volume will be had when x is such that the derivative of volume with respect to x is zero. The maximum value of x cannot be as great as 25/2 = 12.5 because that value gives a zero-width box.
V'(x) = 12x² -296x +1225 = 0
Final dimensionsUsing the quadratic formula, we find the relevant value of x to be ...
[tex]x=\dfrac{-b-\sqrt{b^2-4ac}}{2a}=\dfrac{-(-296)-\sqrt{(-296)^2-4(12)(1225)}}{2(12)}\\\\=\dfrac{296-\sqrt{28816}}{24}=\boxed{\dfrac{74-\sqrt{1801}}{6}\approx 5.2603}[/tex]
Then the dimensions are ...
x ≈ 5.2603
25 -2x ≈ 14.4794
49 -2x ≈ 38.4794
The box is about 5.26 inches by 14.48 inches by 38.48 inches.
Largest volumeThe volume of the final box is about ...
(5.2603 in)(14.4794 in)(38.4794 in) ≈ 2930.82 in³
The volume of the finished box is about 2930.82 cubic inches.
__
Additional comment
As the attachment shows, a graphing calculator can show the extreme value(s) of the volume function, and the corresponding box dimensions.
You deposit $1575 in a bank account that earns 3.75% interest per year for 5 years. How much will the balance be if it's compounded continuously?
Answers
the answer is $1899.81
can yall help me with this
Answers
Answer:
A. 9 divided by -3
Step-by-step explanation:
-24/8= -3
the only other equation that is equal to -3 is a
Answer:
A
Step-by-step explanation:
This is actually a problem that can be solved without having to do the math for any of these expressions based on the rulings regarding negative numbers in division.
The expression that is provided, -24 / 8 features one negative number and one positive number. With this knowledge, we know the answer should be negative.
A also features just one negative number and one positive, meaning that the answer will be negative.
B and C feature two negative numbers, meaning that the negatives will cancel out and the answer would be positive
D features two positive numbers, meaning that the answer is positive!
With these comparisons, we can affirm that A is the correct answer.
(2+0.4 + 0.6)² I have been stuck on this problem for a while
Answers
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
What is the slope?
A) -5/4
B) 5/4
C)-4/5
D) 4/5
Answers
Answer:
A
Step-by-step explanation:
The slope is not increasing y as x is increasing, so you immediately know the slope is negative. The formula is rise/run so the change in y/rise is 5 and the change in x/run is 4. Which allows you to get -5/4
A pair of supplementary angles are in the ratio 4:5.Find the complement of smaller angle .
Answers
The complement of the smaller angle of supplementary angles in ratio 4:5 is given by 10 degree.
Given that the supplementary angles are in ratio 4:5.
Let the angles be 4x and 5x respectively.
We know that the sum of supplementary angles is 180 degree.
So, 4x+5x = 180
9x = 180
x = 180/9
x = 20
So the angles are = (20*4),(20*5) = 80,100.
So the smaller angle is 80 degree.
So the complement of the smaller angle is = 90-80 = 10 degree.
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Solve by factoring64x^2-1=0
Answers
Given:
[tex]64x^2-1=0[/tex]Required:
To solve the given equation by factoring method.
Explanation:
Consider
[tex]64x^2-1=0[/tex][tex]\begin{gathered} (8x)^2-1^2=0 \\ (8x+1)(8x-1)=0 \\ \\ 8x+1=0 \\ 8x=-1 \\ x=-\frac{1}{8} \end{gathered}[/tex]And
[tex]\begin{gathered} 8x-1=0 \\ 8x=1 \\ x=\frac{1}{8} \end{gathered}[/tex]Final Answer:
[tex]x=-\frac{1}{8},\frac{1}{8}[/tex]1. The slope of the line
y = x + 17 is ___.
2. The slope of the line
y = x - 7/9 is ___.
Answers
2)slope is 1/1 - rise/run
Thirty increases by a number t.
Write a variable expression for the word problem
Answers
Answer:
30 + t;
Step-by-step explanation:
Thirty increases by a number t.
This means 30 is more than t, therefore (so), 30 + t.
Two concentric circles are shown. The length of the arc MN is 4π cm and the length of the arc RE is 8π cm.Which statements are correct? Select all that apply.ere to searchThe radius of the larger circle is 16 cm.The radius of the smaller circle is 16 cm.
Answers
We can express the length of an arc as a fraction of the circumference.
This fraction is equal to the the proportion between the measure of the arc and the full circle measure.
In this case, the measure is 45°, so the fraction should be:
[tex]\begin{gathered} \alpha=45\degree \\ \Rightarrow f=\frac{\alpha}{360\degree}=\frac{45\degree}{360\degree}=0.125 \end{gathered}[/tex]Then, we can express the arc MN as:
[tex]MN=C_1\cdot f[/tex]where C1 is the circumference of the smaller circle.
We can express then calculate it as:
[tex]\begin{gathered} MN=C_1\cdot f \\ C_1=\frac{MN}{f}=\frac{4\pi}{0.125}=32\pi \end{gathered}[/tex]As the circumference can be related to the radius, we can us this value to calcualte the radius of the smaller circle:
[tex]\begin{gathered} C_1=2\pi r_1 \\ r_1=\frac{C_1}{2\pi}=\frac{32\pi}{2\pi}=16 \end{gathered}[/tex]Then, the small circle has a radius of 16 cm and a circumference of 32π cm.
We can then calculate C2 and r2 for the bigger circle as:
[tex]\begin{gathered} RE=C_2\cdot f \\ C_2=\frac{RE}{f}=\frac{8\pi}{0.125}=64\pi \end{gathered}[/tex][tex]\begin{gathered} C_2=2\pi r_2 \\ r_2=\frac{C_2}{2\pi}=\frac{64\pi}{2\pi}=32 \end{gathered}[/tex]The bigger circle has a radius of 32 cm and a circumference of 64π cm.
We can now calculate the length of the segments NE and MR. Both are equal and can be calculated as the difference between the radius of the bigger circle (r2) and the radius of the smaller circle (r1):
[tex]NE=MR=r_2-r_1=32-16=16[/tex]Both segments, NE and MR, have a length of 16 cm.
We can now check the statements. The ones that are true are:
• The radius of the smaller circle is 16 cm.
,• The length of the segment MR is 16 cm.
,• The circumference of the larger circle is 64π cm.
Answer: The true statements are
• The radius of the smaller circle is 16 cm.
,• The length of the segment MR is 16 cm.
• The circumference of the larger circle is 64π cm.