Answers
[tex]\csc \theta \tan \theta - \tan \theta \sin \theta \\\\\\=\dfrac 1{\sin \theta} \cdot \dfrac{\sin \theta }{\cos \theta }- \dfrac{\sin \theta }{\cos \theta} \cdot \sin \theta\\\\\\=\dfrac{1}{\cos \theta}-\dfrac{\sin^2 \theta}{\cos \theta}\\\\\\=\dfrac{1- \sin^2 \theta}{\cos \theta}\\\\\\=\dfrac{\cos^2 \theta}{\cos \theta}~~~~~~~~~~~~~~;[\sin^2 \theta + \cos^2 \theta =1 ]\\\\\\=\cos \theta[/tex]
Let's write out some trigonometric identities that we can use:
[tex]tan(x)=\frac{sin(x)}{cos(x)} \\[/tex][tex]csc(x)=\frac{1}{sin(x)}[/tex][tex]sin^2(x)+cos^2(x)=1[/tex] ⇒ [tex]cos^2(x)=1-sin^2(x)[/tex]Now let's try solving them out:
[tex]csc(x)tan(x)-tan(x)sin(x)=\frac{1}{sin(x)}tan(x)-sin(x)tan(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)(\frac{1}{sin(x)}-sin(x))\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)(\frac{1}{sin(x)} -\frac{sin^2(x)}{sin(x)} )\\\\csc(x)tan(x)-tan(x)sin(x)=tan(x)*(\frac{1-sin^2(x)}{sin(x)} )\\\\csc(x)tan(x)-tan(x)sin(x)=\frac{sin(x)}{cos(x)}*\frac{cos^2(x)}{sin(x)} \\\\csc(x)tan(x)-tan(x)sin(x)=\frac{sin(x)}{sin(x)}*\frac{cos^2(x)}{cos(x)}\\\\csc(x)tan(x)-tan(x)sin(x)=1 * cos(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=cos(x)[/tex]
*I used a different variable, but that doesn't change the answer
Answer: cos(x)
Hope that helps!
Related Questions
PLS I NEED HELP ASAP
Answers
The triangles AEB and DEC are congruent by the SAA congruence theorem
How to prove that the triangles are congruent?The given parameters are:
AE ≅ DE∠A ≅ ∠D∠AEB ≅ ∠DECThe above parameters mean that:
AE ≅ DE; Line segments AE and DE are congruent∠A ≅ ∠D; Angles A and D are congruent∠AEB ≅ ∠DEC; Angles AEB and DEC are congruentAlso, it means that two corresponding angles and one corresponding side on triangles AEB and DEC are congruent;
This represents the ASA congruence theorem.
Hence, ΔAEB and ΔDEC are congruent by the SAA congruence theorem
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Select the correct answer.
Graph the following system of inequalities.
y < 2x + 1
y <-x– 1
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See the attachment for the graphed inequalities.
In the figure below,ABC is an isosceles triangle with |AB|=|AC|.|BC| is extended to D such that |AC|=|CD|.If
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The perimeter of the triangle ABC is [tex]10+\sqrt{10}[/tex] [tex]units[/tex].
The given parameters:
Triangle ABC = Isosceles triangleThe length of AC = 3-(-2) = 5 unit
The length of AC = length of BC = 5 unit
The length of BC is calculated by applying Pythagoras theorem as follows;
[tex]BC^2=(4-1)^2+(3-2)^2[/tex]
[tex]BC^2=3^2+1^2[/tex]
[tex]BC^2=10[/tex]
[tex]BC=\sqrt{10}[/tex]
The perimeter of the triangle ABC is calculated as follows;
[tex]P=AB+AC+BC[/tex]
[tex]P=5+5+\sqrt{10}[/tex]
[tex]P=10+\sqrt{10[/tex] [tex]units[/tex]
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I need help solving this problem
Answers
Answer:
First option, incorrect....
Step-by-step explanation:
This is because the interval is either below or above 26.8 by 0.6
-+ means
26.8 + 0.6 = 27.4
26.8 - 0.6 = 26.2
The confidence interval % can change
- The second option states 28 but that is not in the interval
- The third option is somewhat right but the parameter should be emphasized how confident you are
- The last option is wrong since it has the word "every young" when the initial sentence was the mean
Tell whether the system has one solution, infinitely many solutions, or no solution.
Answers
Answer:
B. The system has no solution.
Step-by-step explanation:
[12x + 7y] = (20)
[12x + 7y] = (11)
The numbers in (parentheses) are both different while the numbers in the [brackets] are the same.
20=7y+12x
7y=-12x+20y=-12/7x+20/712x+7y=11
7y=-12x+11y=-12/7x+11/7Slopes are
Lines are parallelNo solutions
WILL MARK BRAINLIEST FIRST CORRCET ANSWER
Answers
The Venn diagram of each situation is a diagrammatic way of representing what the situation stands for
How to make the Venn diagrams?Diagram 1: A ∩ B ∩ C
This means that we shade all intersection points of the sets A, B and C
Diagram 2: (A ∩ B) ∪ C
This means that we shade the intersection points of the sets A and B and the whole of set C
Diagram 3: A ∩ (B ∪ C)
This means that we shade the where the set A intersects with the whole of sets B and C
Diagram 4: (A ∩ B) \ C
This means that we shade the intersection point of the sets A and B without shading any point on set C
Diagram 5: (A\B) ∪ (B\C) ∪ (A\C)
This means that we shade all set A without set B, all set B without set C and all set A without set C. In other words, we shade everything in the set without shading set C
See attachment for the diagrams
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If a and ß are the roots of he equation 3 x² + 6x - 2 = 0, Calculate the value a^3 - B^3
Answers
Answer:
[tex]\alpha^3-\beta^3 = \frac{28}{3}\sqrt{\frac{5}{3}}[/tex]
Step-by-step explanation:
Given quadratic equation is: [tex]3x^2 +6x-2=0[/tex]Comparing it with [tex]ax^2+bx+c=0[/tex], we find:[tex]a = 3,\: b= 6,\: c = -2[/tex]It is given that: [tex] \alpha\: and \: \beta[/tex] are roots of the given quadratic equation. So, we find the sum and the products of the roots.[tex] \implies \alpha + \beta =-\frac{b}{a}=-\frac{6}{3}=-2[/tex][tex] \& \:\alpha.\beta =\frac{c}{a}=-\frac{2}{3}[/tex]Since, one of the factors of [tex] \alpha^3-\beta^3[/tex] is [tex](\alpha - \beta)[/tex] . Therefore, now we will find the value of [tex](\alpha - \beta),[/tex] which can be obtained by the following formula.[tex]\alpha-\beta=\sqrt{(\alpha+\beta)^2-4\alpha\beta}[/tex][tex]\implies \alpha-\beta=\sqrt{(-2)^2-4\bigg(-\frac{2}{3}\bigg)}[/tex][tex]\implies \alpha-\beta=\sqrt{4+\frac{8}{3}}[/tex][tex]\implies \alpha-\beta=\sqrt{\frac{12+8}{3}}[/tex][tex]\implies \alpha-\beta=\sqrt{\frac{20}{3}}[/tex][tex]\implies \alpha-\beta=2\sqrt{\frac{5}{3}}[/tex][tex]\alpha^3-\beta^3 =(\alpha-\beta)^3+3\alpha\beta(\alpha-\beta)[/tex][tex] \implies \alpha^3-\beta^3 =\bigg(2\sqrt{\frac{5}{3}}\bigg)^3+3\bigg(-\frac{2}{3}\bigg)\bigg(2\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 =8\bigg(\sqrt{\frac{5}{3}}\bigg)^3-\bigg(\frac{6}{3}\bigg)\bigg(2\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 =8\times \frac{5}{3}\bigg(\sqrt{\frac{5}{3}}\bigg)-4\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \frac{40}{3}\bigg(\sqrt{\frac{5}{3}}\bigg)-4\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \bigg(\frac{40}{3}-4\bigg)\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \bigg(\frac{40-12}{3}\bigg)\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \frac{28}{3}\sqrt{\frac{5}{3}}[/tex]The value of a³-B³ from the given quadratic equation is 12.05.
What are roots of a quadratic equation?The roots to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
Given that, a and B are the roots of the equation 3x²+6x-2=0
By comparing 3x²+6x-2=0 with ax²+bx+c=0, we get a=3, b=6 and c=-2
The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.
Now, substitute a=3, b=6 and c=-2 in quadratic formula
That is, x = [-6 ±√(6² - 4×3×(-2))]/2×3
= [-6 ±√60]/6
= (-6±2√15)/6
= (-3±√15)/3
So, a=(-3+√15)/3 and B=(-3-√15)/3
Now, a³-B³ = [(-3+√15)/3]³- [(-3-√15)/3]³
= 12.05
Therefore, the value of a³-B³ from the given quadratic equation is 12.05.
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I need help please anyone
I’ll give you brainlist
Answers
Answer:
just count up that equals 1000
What is the slope intercept equation for this line?
Answers
Answer:
y=-3x+4.
Step-by-step explanation:
1) the slope can be calculated according the formula:
slope=(y_end-y_init)/(x_end-x_init);
2) according to the formula above:
slope=(3-1)/(0-1)=-3.
3) according to the given graph the interception is 4, then
4) finally, the required equation is y=-3x+4.
Please I need help with this
Answers
Step-by-step explanation:
here AE = DE
AND BC = DC SO BY SAS IT IS CONGRUENT
If ƒ(x) = − 10x + 8, then ƒ( − 9)=
Answers
Answer:
-10(-9)+8 or 98
Step-by-step explanation:
If they are asking for the question formart for an answer then plug in like the first answer if they’re asking for the full simplified answer then simplify the first answer and then you’ll get 98
PLS HELP I NEED TO TURN THIS IN
Answers
There are 16 parents.
12 of the parents match the criteria.
12/16×100
=75%
Nick bought a new car.
Each year the car depreciates in value by 12%.
Work out the number of years it takes for the car to half in value.
Answers
Using an exponential function, it is found that it takes 5.42 years for the car to halve in value.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the car depreciates 12% a year in value, hence r = 0.12 and the equation is given by:
[tex]A(t) = A(0)(0.88)^t[/tex].
It halves in value at t years, for which A(t) = 0.5A(0), hence:
[tex]A(t) = A(0)(0.88)^t[/tex]
[tex]0.5A(0) = A(0)(0.88)^t[/tex]
[tex](0.88)^t = 0.5[/tex]
[tex]\log{(0.88)^t} = \log{0.5}[/tex]
[tex]t\log{0.88} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.88}}[/tex]
t = 5.42.
It takes 5.42 years for the car to halve in value.
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A shoe box has a volume of 64 cubic inches and a surface area of 160 square inches. What is the surface area of a similar shoe box if its volume is only 27 cubic inches? Show your work or explain how you got your answer.
Answers
Answer:
SA = 90 in²
Step-by-step explanation:
given 2 similar shapes with sides in ratio a : b , then
ratio of areas = a² : b²
ratio of volumes = a³ : b³
Given ratio of volumes = 64 : 27 , then
ratio of sides = [tex]\sqrt[3]{64}[/tex] : [tex]\sqrt[3]{27}[/tex] = 4 : 3
then ratio of areas = 4² : 3² = 16 : 9
let x be the surface area of the smaller box then by proportion
[tex]\frac{x}{9}[/tex] = [tex]\frac{160}{16}[/tex] = 10 ( multiply both sides by 9 )
x = 90
surface area of smaller box is 90 in²
67.5 square inches is the surface area of a similar shoe box if its volume is only 27 cubic inches
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that shoe box has a volume of 64 cubic inches and a surface area of 160 square inches.
We have to find the surface area of a similar shoe box if its volume is only 27 cubic inches
Lets form a proportional equation
64/160 = 27/x
Apply cross multiplication
64x=160(27)
64x=4320
Divide both sides by 64
x=4320/64
x=67.5
Hence, 67.5 square inches is the surface area of a similar shoe box if its volume is only 27 cubic inches
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HELP ME PLEASE!!!!!!
Answers
Answer:
94 square inches.
Step-by-step explanation:
Surface area is the area around a surface. Thus, in order to calculate the surface area of a rectangular prism, we just need to add up the different faces of it.
There are 2 5x4 faces, 2 3x5 faces, and 2 4x3 faces.
Thus, we get 2*20 + 2*15 + 2*12 = 40 + 30 + 24 = 94 square inches.
First you have to find area of all the sides of the shape.
You so this by multiplying 4*5=20, 3*4=12, and 3*5=15
Then double all the products because there are two of each one of the sides on the shape because it is a rectangular prism.
You get 40, 24, and 30.
Finally add all of those numbers together to get the surface area. 40+24+30=94.
94 is the surface area
A window maker creates a round window to be placed into a square frame. The circumference of the window is 4 pi feet.
How long will each side of the square frame be?
OA 16 ft
OB. 4ft
OC. 2 ft
OD. 8 ft
Answers
Answer:
4ft
Step-by-step explanation:
Answer:
4ft
Step-by-step explanation:
Which graph represents the solution of the inequality 24x – 17x ≥ 13x + 15?
Answers
Answer:
See below ~
Step-by-step explanation:
Solving the inequality :
24x - 17x ≥ 13x + 157x ≥ 13x + 15-6x ≥ 15x ≤ -2/5Plotted graph :
Kindly note the line drawn should be a solid line for the inequality to be trueWhen you draw on a graph, kindly remember this and don't directly copy from the attached graphCole has 5 times as many pencils as
Connor. Together they have 18
pencils. How many pencils does Cole
have?
Answers
Answer:
Cole has 15 pencils.
Step-by-step explanation:
First, we have the equation c + o =18, c representing cole, and o representing connor.
From there, we get 5o=c
Using substitiution, we get o=3
5(3)=15
15+3=18
I know it’s easy but for me personally I don’t know how to do it.
Answers
Answer:
-1/4 x 4 = -1
Step-by-step explanation:
:)
Question 4 of 10
What is a name for the angle below?
G
E
OA. ZEGF
OB. ZEFG
/EGE
F
Answers
Answer:
option B Is correct
in the above angle F is the vertex and EG are the arm of angles
The name of the angle below is ∠EFG.
Option B is the correct answer.
What is an angle?The angles between two lines are the angles formed by two intersecting lines, measured in degrees or radians.
Several different types of angles can be formed between two lines, including acute angles, right angles, and obtuse angles.
We have,
From the figure,
There is only one angle.
i.e
∠EFG = ∠GFE
Thus,
The name of the angle below is ∠EFG.
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Does anyone know the Answer? Please and Thank you!
Answers
Step-by-step explanation:
-3[tex]( - 3) - 5 \div ( - 13) - 8[/tex]If a number is divisible by 2 and 3, why is it also divisible by 6?
Answers
Answer:
They have 6 when multiplying it
Step-by-step explanation:
The equation whose roots are multiplied by 3 of those of 2x^2 + 3x – 1=0 is
Answers
Answer:
Here is rest of explanation
Graph the line with slope -2/3 passing through the point (3, 3).
Answers
Answer:
Step-by-step explanation:
y - 3 = -2/3(x - 3)
y - 3 = -2/3x + 2
y = -2/3x + 5
Which is the correct stem-and-leaf plot for the data set?
42, 19, 21, 36, 32, 29, 19, 32, 24, 42
Answers
Answer:
Stem Leaf
1 9 9
2 1 4 9
3 2 2 6
4 2 2
Step-by-step explanation:
Admission to the county fair costs $9 per person. The ride tickets cost $2.50 each.
Which equation represents the total cost, C, of visiting the fair where r represents the number of ride tickets bought?
Answers
Answer:$11.5
Step-by-step explanation:
Admission = $9 charged once
each ride = $2.5x (x=number of rides)
Total cost for x rides
=2.5x+9
Using the tables as experimental data, determine whether it is more likely for a new food establishment to succeed and
earn up to $25,000, or whether it is more likely for a new financial establishment to succeed and earn profits in either the
$25,000-50,000 range or the $50,000-75,000 range, and how much more likely the one situation is than the other.
Express all probabilities as percentages to two decimal places, and express differences by number of percentage points
(for example, 23% is 5 percentage points greater than 18%).
a The situation involving the food establishment has a probability 11.14 percentage points higher
than the situation involving the financial establishment
b. The situation involving the financial establishment has a probability 12.03 percentage points
higher than the situation involving the food establishment
c. The situation involving the food establishment has a probability 2.08 percentage points higher
than the situation involving the financial establishment
d. The situation involving the financial establishment has a probability 4.99 percentage points
higher than the situation involving the food establishment
Answers
The situation involving the food establishment has a probability 2.08 percentage points higher than the situation involving the financial establishment
How to determine the true statement?The question is incomplete, as the required table is not given.
From a more complete question, we have the following parameters:
The probability that the establishment earns up to $25k is 10.59%The probability that the establishment earns between $25k - $50k or $50k - $75k is 8.56%Using the above values, the difference in the probabilities is
d = 10.59% - 8.56%
This gives
d = 2.03%
Hence, the true statement about the probability is (d)
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If a person invests $310 in an account that
pays 8% interest compounded weekly,
find the balance after 8 years (round to the
nearest cent)
Answers
That person have $ 573.79 in his account balance after 8 years.
What is Compound Interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Here, Principal = $ 310
Rate of interest = 8%
Time = 8 years
We know,
Amount = P (1 + i )ⁿ
= 310 X (1 + 0.08)⁸
= 310 X 1.85
= $ 573.79
Thus, that person have $ 573.79 in his account balance after 8 years.
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WHAT IS THE CO-EFFICIENT OF b in the expression b^2 - b5 + 18?
Answers
Answer:
-5 is the coefficient of b
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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
What is the coefficient of b² in the expression b²-b⁵+18?
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]
1
[tex]\blue{\textsf{\textbf{\underline{\underline{How to Solve:-}}}}[/tex]
The coefficient is defined as a number before a variable.
If there's no number, then the coefficient is 1.
Since b² has no number next to it, its coefficient is 1.
Good luck.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
If I earn $15/hour and work for 20 hours/week, how much would I earn in one
week?
A.) $35
B.)$300
C.)$150
D.)$30
Answers
Answer:
B.) $300
Step-by-step explanation:
just multiply 15 by how many hours you have