Answers
Answer:
The rate of change of g(x) is 7/8 which when multiplied by 20/21 gives 5/6, the rate of change of f(x). This means the answer is the second one.
Step-by-step explanation:
Related Questions
Suppose you are working as a pastry chef. You have 12 cups of chocolate cream to fill eclairs. Each eclair requires 2.25 ounces of filling. If you use all of the chocolate cream, at most how many eclairs can you make? A) 32 B) 36 C) 42 D) 44
Answers
Answer:
C- 42
Step-by-step explanation:
there are 8 ounces in a cup so 12 x 8 = 96 oz
96/2.25 = 42.6666666667
Rounded back to 42
By using all the chocolate cream, at most the number of eclairs that can be made is:
C) 42
Step-by-step explanation:It is given that:
You have 12 cups of chocolate cream to fill eclairs.
Each eclair requires 2.25 ounces of filling.
We know that:
The universal conversion that is used is:
1 cups=8 ounces
and hence,
12 cups= 12×8=96 ounces.
Hence, the number of ounces of chocolate cream to fill eclairs= 96 ounces
Also,
amount of filling required by 1 eclair= 2.25 ounces.
Hence, Number of eclairs that can be made is:
[tex]Number\ of\ eclairs=\dfrac{96}{2.25}\\\\i.e.\\\\Number\ of\ eclairs=42.67[/tex]
This means that:
Atmost the number of eclairs than can be made= 42
Solve for x: 3(x+1)=-2(x-1)-4
Answers
Answer:
X= -1
You're welcome! Love ya!! <3
Answer:
The correct answer is x = -1
Step-by-step explanation:
It is given an expression with variable x
3(x + 1) = -2(x - 1) - 4
To solve the given expression
3(x + 1) = -2(x - 1) - 4
3x + 3 = -2x + 2 - 4 ( open the bracket)
3x + 2x = 2 - 4 -3
5x = -5
x = -5/5 = -1
Therefore the value of x = -1
The correct answer is x = -1
The table below shows the heights of students in a group.
Student
Height
(in inches)
A
50
B
54
C
52
D
56
E
48
What is the mean height of the students in the group? (1 point)
48 inches
49 inches
51 inches
52 inches
Peter asked the students of his class their football scores and recorded the scores in the table shown below:
Football Scores
Score
Number of
Students
0
5
1
3
2
12
3
2
4
6
5
6
6
4
Based on the table, what is the mean football score? (1 point)
1.3
1.8
2.9
3.5
Answers
Answer:
1. 52
2. 2.9
Step-by-step explanation:
To find the mean, we take all the numbers, add them up then divide by the number of numbers.
1. mean height
mean = (50+54+52+56+48)/5
=260/5
=52
52 inches
2. mean score
There are 5+3+12+2+6+6+4 students = 38 students
Multiply the number of students times the score and add together
total points = (0*5+1*3+2*12+3*2+4*6+5*6+6*4)
= 111
The mean is the total points divided by the number of students
mean = 111/38
=2.92
Answer:
[tex]\bar x = 52inch\\\bar x_w = 2.92[/tex]
Step-by-step explanation:
According to the data recorded in the table, the average of the students' heights is calculated with the expression for the arithmetic mean:
[tex]\bar x =\frac{1}{n} \sum x_i[/tex]
[tex]\bar x = \frac{1}{5}(48 + 50 + 52 + 54 + 56) = \frac{260}{5} = 52[/tex]inch.
In the same way, the weighted average must be used to find the average football score:
[tex]\bar x_w = \frac{\sum x_i * w_i}{\sum w_i}[/tex], where wi are the frequencies of each response.
[tex]\bar x_w = (0 * 5 + 1 * 3 + 2 * 12 + 3 * 2 + 4 * 6 + 5 * 6 + 6 * 4) / (5 + 3 + 12 + 2 + 6 + 6 + 4) = \frac{111}{38} = 2.92[/tex]
Help please with workings of possible
Answers
Answer:
V = x³ + 10x² cm³
Step-by-step explanation:
The volume (V) of the triangular prism is calculated using the formula
V = area of triangular face × length
Area of triangular face = [tex]\frac{1}{2}[/tex] bh ( b is base and h is height )
here b = 2x and h = x, thus
A = [tex]\frac{1}{2}[/tex] × 2x × x = [tex]\frac{1}{2}[/tex] × 2x² = x²
length = x + 10, hence
V = x²(x + 10) = x³ + 10x²
On Saturn year equals 29.5 earth years. If you were three years old on Saturn how old would you be on earth
Answers
Answer 88.5 I think I don’t know if it’s right
Step-by-step explanation:
Multiply it by 3
If you were three years old on Saturn, which has a year length equivalent to 29.5 Earth years, you'd be 88.5 years old on Earth.
Explanation:The subject of your question is focused on the comparison of time passage on different planets--in this case, how years on Saturn compare to years on Earth. In terms of the Solar system, a year on any planet is determined by how long it takes to orbit the Sun. Given that one Saturn year equals 29.5 Earth years, if you were three years old on Saturn, you'd be 88.5 years old on Earth (Because 29.5 * 3 = 88.5).
This is calculated simply by multiplying the number of Saturn years by the equivalent in Earth years. This concept can be applied to other planets as well, as each has its own specific length of year based on its orbit around the Sun.
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Drag the tiles to the correct boxes to complete the pairs.
Match each polynomial function with one of its factors.
f(x) = x3 − 3x2 − 13x + 15
f(x) = x4 + 3x3 − 8x2 + 5x − 25
f(x) = x3 − 2x2 − x + 2
f(x) = -x3 + 13x − 12
x − 2
arrowRight
x + 3
arrowRight
x + 4
arrowRight
x + 5
arrowRight
Answers
Answer:
f(x) = x3 − 3x2 − 13x + 15 Factor: x+3
f(x) = x4 + 3x3 − 8x2 + 5x − 25 Factor: x+5
f(x) = x3 − 2x2 − x + 2 Factor: x-2
f(x) = -x3 + 13x − 12 Factor: x+4
Step-by-step explanation:
f(x) = x^3 − 3x^2 − 13x + 15
Solving:
We will use rational root theorem: -1 is the root of x^3 − 3x^2 − 13x + 15 so, factor out x+1
x^3 − 3x^2 − 13x + 15 / x+1 = x^2-2x-15
Factor: x^2-2x-15 =(x+3)(x-5)
So, factors are: (x+1)(x+3)(x-5)
Factor: (x+5)
f(x) = x^4 + 3x^3 − 8x^2 + 5x − 25
Solving:
We will use rational root theorem: -5 is the root of x^4 + 3x^3 − 8x^2 + 5x − 25, so factour out (x+5)
x^4 + 3x^3 − 8x^2 + 5x − 25 / x+5 = x^3-2x^2 +2x -5
So, factors are (x+5) (x^3-2x^2 +2x -5)
Factor: x+5
f(x) = x^3 − 2x^2 − x + 2
Solving:
x^2(x-2)-1(x-2)
(x-2)(x^2-1)
(x-2) (x-1) (x+1)
Factor: x-2
f(x) = -x^3 + 13x − 12
Solving:
-(x^3 + 13x -12)
We will use rational root theorem:
The 1 is a root of (x^3 + 13x -12) so, factor out x-1
Now solving (x^3 + 13x -12)/x-1 we get (x-3)(x+4)
So, roots are: - (x-1)(x-3)(x+4)
Factor (x+4)
Answer:
Polynomial 1 = x + 3
Polynomial 2 = x + 5
Polynomial 3 = x - 2
Polynomial 4 = x + 4
Step-by-step explanation:
We are given with Polynomials and and some factors.
We have to match the correct Pair.
We Map the polynomials on the graph then check which factors matches.
Polynomial 1).
x³ - 3x² - 13x + 15
factors are ( x + 3 ) , ( x - 1 ) , ( x - 5 )
Polynomial 2).
[tex]x^4+3x^3-8x^2+5x-25[/tex]
factors are ( x + 5 )
Polynomial 3).
[tex]x^3-2x^2-x+2[/tex]
factors are ( x + 1 ) ,( x - 1 ) , ( x - 2 )
Polynomial 4).
[tex]-x^3+13x-12[/tex]
factors are ( x + 4 ) ,( x - 1 ) , ( x - 3 )
Therefore,
Polynomial 1 = x + 3
Polynomial 2 = x + 5
Polynomial 3 = x - 2
Polynomial 4 = x + 4
Nadia plans to paint her jewelry box. The box is shaped like a rectangular prism with the dimensions
shown. which is closest to the total surface area of the jewelry box?
Answers
Answer:
[tex]132\ in^{2}[/tex] is closest to the total surface area of the box
Step-by-step explanation:
we know that
The surface area of the box is equal to
[tex]SA=2B+PH[/tex]
where
B is the area of the base
P is the perimeter of the base
H is the height of the box
we have
[tex]L=7\frac{3}{4}\ in=\frac{7*4+3}{4}=\frac{31}{4}\ in[/tex]
[tex]W=3\frac{1}{4}\ in=\frac{3*4+1}{4}=\frac{13}{4}\ in[/tex]
[tex]H=3\frac{7}{8}\ in=\frac{3*8+7}{8}=\frac{31}{8}\ in[/tex]
Find the area of the base B
[tex]B=LW[/tex]
[tex]B=(\frac{31}{4})(\frac{13}{4})=\frac{403}{16}\ in^{2}[/tex]
Find the perimeter of the base P
[tex]P=2(L+W)[/tex]
[tex]P=2(\frac{31}{4}+\frac{13}{4}))[/tex]
[tex]P=2(\frac{44}{4})=22\ in[/tex]
Find the surface area
[tex]SA=2(\frac{403}{16})+22(\frac{31}{8})[/tex]
[tex]SA=(\frac{403}{8})+(\frac{682}{8})[/tex]
[tex]SA=\frac{1,085}{8}=135.625\ in^{2}[/tex]
Determine the digits of Y from these clues.
The digits of Y add to 18.
The first digit is 3 times the third digit.
The second digit is 2 times the third digit.
Y is a three digit number.
Answers
Answer:
Y = 963
Step-by-step explanation:
The digits of Y add to 18. The first digit is 3 times the third digit. The second digit is 2 times the third digit. Y is a three digit number.
Let Y a three digit number be: abc
First digit = a , Second digit = b, Third digit = c
Also given,
The digits of Y add to 18. => a+b+c = 18 eq(i)
The first digit is 3 times the third digit. => a = 3c eq(ii)
The second digit is 2 times the third digit. => b = 2c eq(iii)
Putting value of a and b in eq(i)
3c + 2c + c = 18
6c = 18
c= 18/6
c = 3
Putting value of c in eq(ii) and eq(iii)
a= 3c => a=3(3) => a= 9
b= 2c => b=2(3) => b = 6
Thus, Y = abc
Y = 963
I am confused by this question. Can someone help
Answers
square root both sides, divide by v both sides, divide by 2 both sides, divide pCd both sides
a B and C are polynomials where a equals 3x - 4 b equals x + 7 C equals x squared + 2 what is a squared minus parentheses b + C in simplest form?
Answers
Answer:
8x^2 - 25x +7
Step-by-step explanation:
Substitute the polynomials in
A^2 - (B+C)
(3x-4)^2 - (x+7+x^2+2), simplify the equation
Using foil method, (9x^2-24x+16) - (x+7+x^2+2)
(9x^2-24x+16)-(x^2+x+9), distribute the minus/negative sign to the second parenthesis
(9x^2-24x+16) - x^2-x-9, combine like terms
8x^2 - 25x +7
In DEF, DE = 15, and m angle F=32 Find EF to the nearest tenth.
Answers
the answer would be 24.0.
What is the value of discriminant in the equation shown below? x2+3x-6=0
Answers
ANSWER
The discriminant is -3
EXPLANATION
The given quadratic equation is:
[tex] {x}^{2} + 3x - 6 = 0[/tex]
Comparing this equation to:
[tex]a {x}^{2} + bx + c = 0[/tex]
we have
a=1, b=3, and c=-6
The discriminant is calculated using the formula,
[tex]D = {b}^{2} - 4ac[/tex]
We substitute the values to get:
[tex]D = {3}^{2} - 4(1)(3)[/tex]
[tex]D = 9 - 12[/tex]
[tex]D = - 3[/tex]
Answer:
Discriminant = 33
Step-by-step explanation:
Solution of a quadratic equation ax² + bx + c = 0
Discriminant = (b² - 4ac)
It is given that, x² + 3x - 6 = 0
To find the value of discriminant
x² + 3x - 6 = 0
Here a = 1, b = 3 and c = -6
Discriminant = (b² - 4ac)
= (3² - 4 * 1 * (-6))
= (9 +24) = 33
Therefore discriminant of given equation is 33
Evaluate and simplify the following complex fraction
Answers
Answer:
-0.01851851851
Step-by-step explanation:
Answer:
[tex]-\dfrac{3}{2}[/tex]
Step-by-step explanation:
[tex]\dfrac{\frac{2}{3} }{\frac{4}{-9} } [/tex]
[tex]= \dfrac{2}{3} \div \dfrac{4}{-9}[/tex]
[tex]= \dfrac{2}{3} \times \dfrac{-9}{4}[/tex]
[tex]= \dfrac{-18}{12}[/tex]
[tex]= -\dfrac{3}{2}[/tex]
G=4ca-3ba for a Asap
Answers
Answer:
a = [tex]\frac{G}{4c-3b}[/tex]
Step-by-step explanation:
Given
G = 4ca - 3ba ← factor out a from each term on the right side
G = a(4c - 3b) ← divide both sides by (4c - 3b)
a = [tex]\frac{G}{4c-3b}[/tex]
Solve for x
12=x^2+6x
Answers
Answer:
[tex]\large\boxed{x=-3\pm\sqrt{21}}[/tex]
Step-by-step explanation:
[tex]x^2+6x=12\\\\x^2+2(x)(3)=12\qquad\text{add}\ 3^2\ \text{to both sides}\\\\x^2+2(x)(3)+3^2=12+3^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+3)^2=12+9\\\\(x+3)^2=21\iff x+3\pm\sqrt{21}\qquad\text{subtract 3 from both sides}\\\\x=-3\pm\sqrt{21}[/tex]
factor the polynomial completely
3x^2-4x+21
Answers
Answer:
The given equation 3x^2-4x+21 has no factors.
Step-by-step explanation:
[tex]3x^2-4x+21[/tex] We need to factorize this equation.
For factorization we split the middle term such that their sum is equal to middle term and product is equal to product of first and last term of the given expression.
in Our case : 63x^2
We need to find two factors of 63x^2 whose sum is equal to -4x
Factors of 63= 1,3,7,9,21,63
1* 63
3*21
7*9
None of the above factors sum is equal to -4.
So, the given equation 3x^2-4x+21 has no factors.
Answer:
No factors.
Step-by-step explanation:
The polynomial is not factorable with rational numbers. If you are on some advanced math, you would be able to be able to factor this.
The volume of a cylinder is 441pi. If the cylinder has a height of 9, what is the radius?
Answers
Answer: 7
Step-by-step explanation:
volume of a cylinder = πr²h
441π = π *r²* 9
divide both sides by 9π
49 = r²
r =√49 = 7
Answer:
49
Step-by-step explanation:
Which algebraic expression will solve for the blue area of this square figure?
A. -12x
B. -2x+30
C. 10x+18
D. 20x
Answers
Answer:
Option B. [tex]-2x+30[/tex]
Step-by-step explanation:
we know that
The blue area is equal to the area of complete rectangle minus the area of the white rectangle
so
[tex]A=(5+3x)(6)-(5)(4x)\\\\ A=(30+18x)-(20x)\\ \\A=-2x+30[/tex]
Select the two values of x that are roots or this equation x^2-5x+2=0
Answers
Answer:
(5/2, +-(square root 17)/ 2)
Step-by-step explanation:
1. find a,b, and c of the quadratic
2. use the quadratic formula to solve
The two values of roots of the equation is 4.56 , 0.44 .
What is an Equation ?An equation is a statement where two algebraic expressions are equated by an equal sign.
The equation given is
x² - 5x +2 = 0
the roots of the equation is given by
[tex]\rm \dfrac{ -b \pm \sqrt { b^2 - 4ac}}{2a}[/tex]
[tex]\rm \dfrac{ 5 \pm \sqrt { 25 - 4 * 1 * 2}}{2 *1}[/tex]
x = [tex]\rm \dfrac{ 5 \pm \sqrt { 17}}{2}[/tex]
Therefore the two values of roots of the equation is 4.56 , 0.44 .
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1. Solve. (-24x? +18x+6) - (6x+3) (1 point)
-4x² + 2x-2
472 - 2x+2
4x2+2x-2
-4x2+2x+2
Answers
Answer:
Step-by-step explanation:
Since this is not an equation, we're not looking to "solve." Rather, we're to subtract the 2nd polynomial from the 1st one.
-24x² + 18x + 6
-( 6x + 3)
------------------------------
-24x² + 12x +3 (answer ... this is called a "difference" and is the
result of subtraction)
The simplified expression is 3( -8x² + 4x + 1).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
(-24x² +18x+6) - (6x+3)
Now, simplifying the polynomial
= -24x² +18x+6 - 6x - 3
= -24x² + 12x + 3
= 3( -8x² + 4x + 1)
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A pet toy manufacturer is designing a plastic ball for dogs that will float in water. In order for the ball to float it must have a density that is less than 1 gram per milliliter (the density of water). The approved design has a mass of 115 grams and a density of 0.600 g/mL. Use the density formula d = m v to determine the radius of the ball to the nearest hundredth of a centimeter. Volume of a sphere = 4 3 π r 3
Answers
Answer:
3.576 cm
Step-by-step explanation:
radius of ball, r=?
Given:
Density, p = 0.600g/mL
mass, m= 115g
finding volume, v of ball by using formula p=m/v
v= m/p
= 115/0.600
=191.666 mL^3
=191.666 cm^3
Now using formula v= (4/3)πr^3 to find radius, r of the ball
r^3= 3v/4π
= 3(191.666)/4π
=45.75 cm
r =3.5767 cm !
Gina is the costume manager for a large theater company. She has 12 different hats, including 2 helmets.
What is the probability that a randomly chosen hat from Gina's inventory will be a helmet?
Simplify your answer and write it as a fraction or whole number.
Answers
The probability that a hat randomly chosen from Gina's inventory will be a helmet is 2 out of 12, which simplifies to 1 out of 6.
Explanation:The subject of this question is probability, which is a branch of mathematics. Gina has 12 different hats, out of which 2 are helmets. The probability of an event happening is calculated as the number of ways the event can happen divided by the total number of outcomes.
So in this case, there are 2 helmets out of a total of 12 hats. So, the probability that a hat randomly chosen from Gina's inventory will be a helmet is 2 out of 12. You can also simplify this probability by dividing both the numerator and the denominator by the greatest common divisor, which is 2 in this case. Therefore, the simplified probability is 1 out of 6.
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The probability of choosing a randomly selected hat from Gina's inventory to be a helmet is 1/6.
Explanation:To find the probability of selecting a helmet from Gina's inventory, we need to divide the number of helmets by the total number of hats in her inventory.
Gina has 12 hats, including 2 helmets, so the probability is
= 2 helmets / 12 hats
= 1/6.
Therefore, the probability of choosing a randomly selected hat from Gina's inventory to be a helmet is 1/6.
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Please help me asap! Could you please explain how you got the answer
Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced Algebra and Physics in a particular high school. From a sample of 30 students, it is found that 19 are taking Algebra, 12 are taking Physics, and 4 are enrolled in both. How many students are enrolled in either Algebra or Physics?
Algebra Not in Algebra Total
Physics 4 --------- ----------------------------12
Not in Physics
Total 19---------------------------------------30
A.) 27
B.) 23
C.) 3
D.) 4
Answers
Answer:
B) 23
Step-by-step explanation:
Table: Algebra | No algebra | Total
Physics | 4 Step 1: 8 12
No physics |Step 2: 15
Total | 19 30
We look for the number of people who are in algebra and no physics or physics and no algebra.
1. 12 - 4 = 8
2. 19 - 4 = 15
3. We find the total of those numbers: 15 + 8 = 23
Answer: 27
Step-by-step explanation:
The answer to this problem please
Answers
Answer:
834451800
Step-by-step explanation:
C(n,r)=?
C(n,r)=C(35,12)
=35!(12!(35−12)!)
=35!12!×23!
=8.344518E+8
= 834451800
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
A. g(-4) = -11
B. g(7) = -1
C. g(-13) = 20
D. g(0) = 2
Answers
Answer:
C.
Step-by-step explanation:
C is true because we already know g(0) is -2, and functions cannot repeat themselves with different numbers like that. A is not true because the range does not go that far down. B is not true because the domain does not go that far up.
Answer:
C is the answer
Step-by-step explanation:
C is the answer because
tanisha office is on the 9 floor of an office building . She parks her car in the underground parking garage 4 floors below ground level how many floors are between tanisha office and her car?
Answers
Answer: 13
Step-by-step explanation: If there are 9 floors from where Tanisha's office is to the ground, but then also 4 more floors to her car, that would simply be 9+4. There are 13 floors between Tanisha's office and her car.
A bowling team participated in a two-day tournament and records the scores for each team member on both days.The scores for both days are represented by the box plots below
Answers
I think it's B hope you got it right
The correct answer is B. The scores on Friday have a greater median and a greater interquartile range than the scores on Saturday.
The box plots represent the bowling scores of a team on Friday and Saturday. Let’s analyze the information from the plots:
Friday Box Plot:
The median (Q2) is higher than the median for Saturday.
The interquartile range (IQR) is larger than the IQR for Saturday.
Saturday Box Plot:
The median (Q2) is lower than the median for Friday.
The interquartile range (IQR) is smaller than the IQR for Friday.
Based on this analysis, we can draw the following conclusion:
B. The scores on Friday have a greater median and a greater interquartile range than the scores on Saturday.
Therefore, the correct answer is B.
A landing pad for a helicopter is in the shape of a circle with a radius of 7 meters. Which of the following is closest to the area of the landing pad?
Answers
Answer:
The approximate value of the area is [tex]153.86\ m^{2}[/tex]
Step-by-step explanation:
we know that
The area of the circle (landing pad) is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=7\ m[/tex]
substitute
[tex]A=\pi (7)^{2}[/tex]
[tex]A=49\pi\ m^{2}[/tex] ----> exact value of the area
Find the approximate value
assume [tex]\pi=3.14[/tex]
[tex]A=49(3.14)=153.86\ m^{2}[/tex] ------> approximate value of the area
Answer:
Area of Circular landing pad = 307.72 m^2
Step-by-step explanation:
Area of Circular landing pad = 2πr^2
where r = radius of circular landing pad = 7m
π = 22/7 = 3.14
by placing all these value in the formula
Area of Circular landing pad = 2*3.14*(7^2)
Area of Circular landing pad = 6.28*49
Area of Circular landing pad = 307.72 m^2
Please help thx so much
Answers
Answer:
(- 1, 3)
Step-by-step explanation:
To find the y- coordinate, substitute x = - 1 into the equation
y - 3 = 2(x + 1) ( add 3 to both sides )
y = 2(x + 1) + 3 ← substitute x = - 1
y = 2(- 1 + 1) + 3 = (2 × 0) + 3 = 0 + 3 = 3
Week 8 trigonometric worksheet!!! PLEASE HELP ME IS A FINAL GRADE FOR SCHOOL!
Answers
Answer:
Part 1) The six trigonometric functions in the procedure
Part 2) The six trigonometric functions in the procedure
Part 3) The six trigonometric functions in the procedure
Part 4) The value of x is [tex]x=7\sqrt{2}\ units[/tex] and the value of y is [tex]y=7\ units[/tex]
Part 5) The value of x is [tex]x=5\ units[/tex] and the value of y is [tex]y=5\sqrt{3}\ units[/tex]
Part 6) The value of x is [tex]x=2\sqrt{3}\ units[/tex] and the value of y is [tex]y=\sqrt{3}\ units[/tex]
Part 7) [tex]cos(27\°)=0.8910[/tex]
Part 8) [tex]tan(5\°)=0.0875[/tex]
Part 9) [tex]sin(48\°)=0.7431[/tex]
Part 10) [tex]cot(81\°)=0.1584[/tex]
Part 11) [tex]csc(23\°)=2.5593[/tex]
Part 12) [tex]sec(66\°)=2.4586[/tex]
Part 13) [tex]cot(13\°)=4.3315[/tex]
Part 14) [tex]sin(32\°)=0.5299[/tex]
Step-by-step explanation:
Note The complete answers in the attached file
Part 1) In the right triangle of the figure find the hypotenuse
Applying Pythagoras theorem
[tex]c^{2} =8^{2}+15^{2}\\c^{2}=289\\c=17\ units[/tex]
1) Find the [tex]sin(\theta)[/tex]
[tex]sin(\theta)=\frac{8}{17}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the hypotenuse
2) Find the [tex]cos(\theta)[/tex]
[tex]cos(\theta)=\frac{15}{17}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the hypotenuse
3) Find the [tex]tan(\theta)[/tex]
[tex]tan(\theta)=\frac{8}{15}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the adjacent side angle [tex]\theta[/tex]
4) Find the [tex]cot(\theta)[/tex]
[tex]cot(\theta)=\frac{15}{8}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the opposite side angle [tex]\theta[/tex]
5) Find the [tex]sec(\theta)[/tex]
[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]
[tex]sec(\theta)=\frac{17}{15}[/tex] ----> hypotenuse divided by the adjacent side angle [tex]\theta[/tex]
6) Find the [tex]csc(\theta)[/tex]
[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]
[tex]csc(\theta)=\frac{17}{8}[/tex] ----> hypotenuse divided by the opposite side angle [tex]\theta[/tex]
Part 2) In the right triangle of the figure find the adjacent side angle [tex]\theta[/tex]
Applying Pythagoras theorem
[tex]5^{2} =2^{2}+a^{2}\\ a^{2}=5^{2}-2^{2}\\a^{2}=21\\a=\sqrt{21}\ units[/tex]
1) Find the [tex]sin(\theta)[/tex]
[tex]sin(\theta)=\frac{2}{5}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the hypotenuse
2) Find the [tex]cos(\theta)[/tex]
[tex]cos(\theta)=\frac{\sqrt{21}}{5}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the hypotenuse
3) Find the [tex]tan(\theta)[/tex]
[tex]tan(\theta)=\frac{2}{\sqrt{21}}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the adjacent side angle [tex]\theta[/tex]
4) Find the [tex]cot(\theta)[/tex]
[tex]cot(\theta)=\frac{\sqrt{21}}{2}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the opposite side angle [tex]\theta[/tex]
5) Find the [tex]sec(\theta)[/tex]
[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]
[tex]sec(\theta)=\frac{5}{\sqrt{21}}[/tex] ----> hypotenuse divided by the adjacent side angle [tex]\theta[/tex]
6) Find the [tex]csc(\theta)[/tex]
[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]
[tex]csc(\theta)=\frac{5}{2}[/tex] ----> hypotenuse divided by the opposite side angle [tex]\theta[/tex]
Part 3) In the right triangle of the figure find the opposite side angle [tex]\theta[/tex]
Applying Pythagoras theorem
[tex]3^{2} =1^{2}+b^{2}\\ b^{2}=3^{2}-1^{2}\\b^{2}=8\\b=\sqrt{8}\ units[/tex]
1) Find the [tex]sin(\theta)[/tex]
[tex]sin(\theta)=\frac{\sqrt{8}}{3}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the hypotenuse
2) Find the [tex]cos(\theta)[/tex]
[tex]cos(\theta)=\frac{\sqrt{1}}{3}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the hypotenuse
3) Find the [tex]tan(\theta)[/tex]
[tex]tan(\theta)=\frac{\sqrt{8}}{1}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the adjacent side angle [tex]\theta[/tex]
4) Find the [tex]cot(\theta)[/tex]
[tex]cot(\theta)=\frac{1}{\sqrt{8}}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the opposite side angle [tex]\theta[/tex]
5) Find the [tex]sec(\theta)[/tex]
[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]
[tex]sec(\theta)=\frac{3}{1}[/tex] ----> hypotenuse divided by the adjacent side angle [tex]\theta[/tex]
6) Find the [tex]csc(\theta)[/tex]
[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]
[tex]csc(\theta)=\frac{3}{\sqrt{8}}[/tex] ----> hypotenuse divided by the opposite side angle [tex]\theta[/tex]
Part 4) In the right triangle of the figure
a) Find the value of x
we know that
[tex]sin(45\°)=\frac{7}{x}[/tex]
[tex]x=\frac{7}{sin(45\°)}[/tex]
Remember that
[tex]sin(45\°)=\frac{\sqrt{2}}{2}[/tex]
substitute
[tex]x=\frac{7}{\frac{\sqrt{2}}{2}}[/tex]
[tex]x=\frac{14}{\sqrt{2}}[/tex]
[tex]x=7\sqrt{2}\ units[/tex]
b) Find the value of y
The value of [tex]y=7\ units[/tex] ----> by triangle 45°-90°-45° measures
Note The complete answers in the attached file