Answers
3sin x+cos²x=2
3sin x+(1-sin²x)=2
-sin²x +3sin x=1
sin²x -3 sin x+1=0---------> up to here the procedure is correct
let
A=sin x
then
A²-3A+1=0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(A²-3A)=-1Complete the square. Remember to balance the equation by adding the same constants to each side.
(A²-3A+2.25)=-1+2.25
Rewrite as perfect squares
(A-1.5)²=1.25(+/-)(A-1.5)=1.12
first solution
(A-1.5)=1.12--------> A=1.12+1.5-----> A=2.62-----> sin x=2.62
second solution
-(A-1.5)=1.12----> -A+1.5=1.12----> A=1.5-1.12----> A=0.38---> sin x=0.38
the answer is
the equation was factored incorrectly
Its is b. hope this halps
Related Questions
The ratio between the volumes of two cubes is 125 to 216. what is the ratio between their respective surface areas?
Answers
Square 1: s = 5
Square 2: s = 6
Surface Area for a Cube = 6s^2
SA of Square 1: 6(5)^2 = 6(25) = 150
SA of Square 2: 6(6)^2 = 6(36) = 216
The ratio between the surface area of the two cubes is 150 to 216
A circle has a circumference of 10. It has an arc of length 9/2
Answers
(9/2)/10
=0.45
thus the angle subtended by the arc will be:
0.45×360°
=162°
Circle 1 is center at (-4,5) and has a radius of 2 centimeters. Circle 2 is centered at (2,1) and has a radius of 6 centimeters. What transformations can be applied to Circle 1 to prove the circles are similar?
Answers
1) Draw a vector from point A to B
2)Dilate circle A to circle B. It means translating mapping circle A to circle B.
3)By this way, we can claim that circles A and B are similar.
And the similarity ratio is [tex] \frac{ r_{2} }{ r_{1} } = \frac{6}{2} =3[/tex]
The perimeter of a rectangle is 32 cm. The difference between the length and the width is 4cm. find the width
Answers
width = y
2x + 2y = 32
x - y = 4
x = 4 + y
2(4+y) + 2y = 32
8 + 2y + 2y = 32
4y = 24
y = 6 cm (width)
x = 4 + 6
x = 10 cm (length)
How do you write an equation for a circle with center (2,4) and passes through point (5, 9)?
Answers
(x - h)² + (y - k)² = radius²
where (h, k) is the center.
We can plug in the given information from the description and solve for the radius.
(x - 2)² + (y - 4)² = radius²
To find the radius, we do the distance formula from the center to the point on the circle.
Distance = [tex] \sqrt{ (Y2-Y1)^{2} + (X2 - X1)^{2} } [/tex]
D = [tex] \sqrt{ (9 - 4)^{2} + (5 - 2)^{2} } [/tex]
D = [tex] \sqrt{ 5^{2} + 3^{2} } [/tex]
D = [tex] \sqrt{25 + 9} [/tex]
D = [tex] \sqrt{34} [/tex]
That is your radius. Now we plug it in.
(x - 2)² + (y - 4)² = (√34)²
Your final answer is:
(x - 2)² + (y - 4)² = 34
Doug can paint the living room in 4 hours. it would take elaine 6 hours to paint the same room. how long would it take doug and elaine, working together, to paint the living room?
Answers
You can get this by setting up the equation:
x/4 + x/6 = 1
Where x is equal to the amount of hours spent working. In this equation x/4 would be Doug. In 4 hours he would paint on room. x/6 would be Elaine. When you add them together using common denominators, you can find x.
How is the interquartile range calculated? HELP WITH APEX PLEASE!
Answers
By definition the interquartile range or IQR is obtained when the 25th percentile or [tex] Q_{1} [/tex] is subtracted from the 75th percentile or [tex] Q_{3} [/tex].
Thus, from the above definition, the formula for IQR is:
[tex] IQR=Q_{3}-Q_{1} [/tex]
As we can see from the provided options that the definition of IQR matches the expression provided in Option A and thus, Option A is the correct answer.
Quartile 3 (Q3) minus quartile 1 (Q1) is right for apex.
A summer camp manager wants to order 500 bag lunches for a field trip. Each lunch will have a piece of fruit. The manager is deciding on ordering apples, oranges, bananas, or plums. The camp manager surveys 50 random campers, and the results are given in this table.
Based on the results, which fruit should the manager order?
A- Apples
B- Oranges
C- Plums
D- Bananas
Answers
What is the surface area of a square pyramid with a height of 12 mm and a base that measures 10 mm on each side? Round to the nearest tenth if necessary.
Answers
AS = Ab + Al
Where,
Ab: base area
Al: lateral area
We have then:
The area of the base is:
Ab = (10) * (10) = 100 mm ^ 2
The lateral area is:
Al = (4) * (1/2) * (10) * (root ((12) ^ 2 + (5) ^ 2))
Al = 260 mm ^ 2
The surface area is:
AS = 100 + 260
AS = 360 mm ^ 2
Answer:
The surface area of a square pyramid is:
AS = 360 mm ^ 2
The surface area of the square pyramid is [tex]\(360 \, \text{mm}^2\)[/tex]
To calculate the surface area of a square pyramid, we need to find the area of its base and the area of its four triangular faces. Given the following:
The base side length [tex](\(s\))[/tex] is [tex]10\ mm[/tex].
The height of the pyramid [tex](\(h\))[/tex] is [tex]12 \ mm[/tex]
Step-by-Step Calculation:
1. Area of the base:
The base is a square with side length [tex]\(s = 10\) mm.[/tex]
[tex]\[\text{Area of the base} = s^2 = 10^2 = 100 \, \text{mm}^2\][/tex]
2. Slant height of the pyramid:
To find the slant height [tex](\(l\))[/tex], we need to use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle where one leg is half the side length of the base [tex](\(\frac{s}{2} = \frac{10}{2} = 5\) mm)[/tex] and the other leg is the height of the pyramid [tex](\(h = 12\) mm)[/tex].
[tex]\[l = \sqrt{\left(\frac{s}{2}\right)^2 + h^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \, \text{mm}\][/tex]
3 Area of the four triangular faces:
Each triangular face has a base of [tex]10\ mm[/tex] and a slant height of [tex]13 \ mm[/tex].
[tex]\[\text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 10 \times 13 = 65 \, \text{mm}^2\][/tex]
Since there are four triangular faces:
[tex]\[\text{Total area of the four triangular faces} = 4 \times 65 = 260 \, \text{mm}^2\][/tex]
4. Total surface area:
The total surface area of the square pyramid is the sum of the area of the base and the area of the four triangular faces:
[tex]\[\text{Total surface area} = \text{Area of the base} + \text{Total area of the four triangular faces} = 100 + 260 = 360 \, \text{mm}^2\][/tex]
If Michael and imani add an 18% tip to the bill,what does their lunch cost in total
Answers
Answer:
X + (0.18 * X)
where X is the price of the bill without the tip
Step-by-step explanation:
The first thing you have to do is convert the percentage to a decimal value. For example, if it is 30%, its decimal value is 0.30. As simple as dividing that 300 by 100. Repeat the previous step with all the percentages you have to add.
In this case it is 18% therefore the decimal value will be 0.18. As we do not have the value of the account, we will call this value X .
Therefore the total price of the account, that is, with the addition of the tip is as follows:
X + 18% de X =
X + (0.18 + X)
The sales tax in the city of Taxemalot is 8.1%. What is the growth factor for any item purchased at your local Tarmart? a.8.1 c.1.081 b.0.81 d.81
Answers
PLEASE HELP will give brainiest if correct
Answers
b. [tex] \frac{ \pi }{4} or \frac{5 \pi }{4} [/tex]
Explanation:
Before we begin, remember that:
tan α = [tex] \frac{sin \alpha }{cos \alpha } [/tex]
Now for the given, we have:
cos θ - tan θ * cos θ = 0
cos θ - [tex] \frac{sin (theta)}{cos (theta)} [/tex] * cos θ = 0
cos θ - sin θ = 0cos θ = sin θ
Now, divide both sides by cos θ, we get:
1 = tan θ
Following the ASTC rule, we know that the tan function is positive in the first and third quadrants.
This means that:
either θ = [tex] \frac{ \pi }{4} [/tex]
or θ = π + [tex] \frac{ \pi }{4} [/tex] = [tex] \frac{5 \pi }{4} [/tex]
Hope this helps :)
What is the center of the circle with the equation (x-1)2 + (y-3)2= 9?
Answers
[tex](x-a)^2+(y-b)^2=r^2[/tex]
[tex]\text{a and b are the x and y coordinates of the center of the circle; r is a length of a radius}[/tex]
We have:
[tex](x-1)^2+(y-3)^2=9\\\\\text{therefore coordinates of the center of the circle are (1; 3) and a radius is equal 3}[/tex]
x - 1 means that x coordinate is 1 and y - 3 gives the y coordinate which is 3
Center is at ( 1, 3) answer
If I get 3 problems wrong on a 12 question math paper, what grade would I get?
Answers
If you got 3 questions wrong on a 12 problem math paper, to figure out how many you got right you must subtract the number you got incorrect (3) from the total number (12).
12-3=9
To figure out your grade, you have to divide how many you got correct (9-see above) by the total number of questions (12).
9/12 = 0.75
If you multiply this decimal by 100, you get the equivalent percentage of 75%.
Therefore, you would have gotten a 75% on the paper.
Hope this helps!
Which shapes have rotational symmetry that occurs at 180°?
Check all that apply.
regular octagon regular pentagon regular hexagon square right isosceles triangle
Answers
- Regular Hexagon
- Square
It should be regular octagon, regular hexagon, and square
An ice chest contains 88 cans of apple juice, 44 cans of grape juice, 55 cans of orange juice, and 66 cans of mango juice. suppose that you reach into the container and randomly select three cans in succession. find the probability of selecting three cans of appleapple juice.
Answers
Determine if the following data set follows a linear, quadratic, or exponential model. (0, 1), (1,3), (2, 9), (3, 19), (4, 33)
show your work
PLEASE SOMEONE HELP!
Answers
I think that it would be a linear model.
Answer:
Step-by-step explanation:
quadratic C
At sea, the distance to the horizon is directly proportional to the square root of the elevation of the observer. if a person who is 36 feet above the water can see 7.4 miles, find how far a person 64 feet above the water can see.
Answers
The square root of 36 feet (the elevation) is 6 feet.
Equation for direct proportion: y=kx (y is directly proportionate to x, k is the amount of proportion)
7.4 miles = 6 feet * k
7.4mi = 6feet* (1.233 * whatever the conversion rate is between feet and miles)
The same applies to 64: the square root of it will be directly proportionate to the distance.
√64 = 8
8feet*k = [thenumber_we_don't_know]miles
8*1.233 = {??}
= 9.84
The answer is 9.84.
The person 64 feet above the water can see 9.84 miles.
It is given in the question that the distance to the horizon is directly proportional to the square root of the elevation of the observer.
if the elevation of the observer be h and distance to the horizon be x then:
[tex]x=k\sqrt{h}[/tex] where k is the constant of proportionality
from the given data:
[tex]7.4= k\sqrt{36}\\\\7.4=6k\\\\k=1.23[/tex]
So, if h = 64 feet then,
[tex]x=k\sqrt{h}\\\\x=1.23\sqrt{64}\\\\x=9.84 miles[/tex] is how far the person 64 feet above the water can see.
Learn more:
https://brainly.com/question/16998607
simplify: 10(6y+x)=4
Answers
10(6y) + 10x = 4 Simplify the 10 times 6y
60y + 10x = 4
PLEASE HELP!!!Which pair of angles are corresponding? Two horizontal lines cut by a diagonal transversal. Angles 1, 3, 5, and 7 are located on the left-hand side of the transversal starting from the top. Angles 2, 4, 6 and 8 are located on the right-hand side of the transversal starting at the top. Question 2 options: 1 and 3 1 and 4 4 and 8 1 and 8
Answers
______________________________________________________
Answer:
According to the description of the case, the angles should be named after this picture.
The congruents angles among each other are:
Blue: 1,4,5,8
Purple: 2,3,6,7
Therefore the three possibilities are:
a. 1 and 4
b. 4 and 8
c. 1 and 8
Step-by-step explanation:
Which group of values makes the expression 3x2y−2z UNDEFINED? A) x = –1; y = 0; z = 3 B) x = –1; y = 3; z = 0 C) x = 0; y = −1; z = 3 D) x = 0; y = 3; z = −1 E) x = –1; y = 2; z = 1
Answers
Which group of values makes the expression 3x/2y−2z UNDEFINED?
we know that
So that the expression is defined, the denominator in (3x/2y) can not be zero
hence
the value of y = 0 makes the expression UNDEFINED
therefore
the answer is
the option A) x = –1; y = 0; z = 3
Answer:
The answer is A
Step-by-step explanation:
sadly i dont have the work of it just by looking it up you can get the answer tho. Answer is A
write a polynomial function of nth degree that has the given zeros
Answers
A polynomial function of nth degree with given zeros, use the form f(x) = a (x - x1)(x - x2)...(x - xn), which is [tex]f(x) = x^3 - 2x2 - 5x + 6[/tex]
To write a polynomial function of the nth degree with given zeros, you can use the fact that a polynomial function f(x) with zeros at x1, x2, ..., xn can be expressed as:
f(x) = a (x - x1)(x - x2)...(x - xn)
Where 'a' is the leading coefficient, which can be any non-zero real or complex number, and (x - xi) are factors for each zero of the polynomial. If the polynomial is supposed to have a specific coefficient for the highest power term, then 'a' is that coefficient; otherwise, 'a' can be chosen freely to define the polynomial.
To illustrate with an example, if we had a polynomial of degree 3 with zeros at 1, -2, and 3, and we want the leading coefficient to be 1, our polynomial would be:
f(x) = (x - 1)(x + 2)(x - 3)
Expanding this product, we would get:
[tex]f(x) = x^3 - 2x2 - 5x + 6[/tex]
This polynomial of third degree has the specified zeros and a leading coefficient of 1.
Given that b=8,a=3,and b=65,find the measure of
A. 19.9 or 160.1
B.19.9
C160.1
D not a triangle
Answers
Answer: B. 19.9
Step-by-step explanation: Set up an equation where sin and the degree angle is in the numerator, and the side length is in the denominator.
Sin65/8 = Sinx/3
Plug Sin65 into your calculator and you will get 0.9063. Divide this number by 8.
0.9063/8 = 0.1133
Your equation is now 0.1133 = sinx/3
Multiply by 3 on each side.
0.3399 = sinx
Put sin on the left side. It will look like:
Sin^-1(0.3399) = x
Press enter on your calculator. You will get
X = 19.9.
The number of tropical fish that an aquarium can hold depends on the volume of the fish tank. the interior dimensions of the fish tank are 25 cm, 30 cm, and 39 cm. each fish requires 10,000 cubic centimeters of water. how many tropical fish will this fish tank hold?
Answers
What is the greatest common factor of 60x4y7, 45x5y5and 75x3y?
Answers
Answer:
15x^3·y
Step-by-step explanation:
The numbers 60, 45, 75 are all multiples of 15, so 15 is their greatest common factor.
The least power of the factor x is 3; the least power of the factor y is 1, so the GCF is ...
GCF = 15·x^3·y
Urgent!! Need an answer ASAP!
Professor Scott has 84 students in his college mathematics lecture class. The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive a score between 63.4 and 81.2? Express the answer to the nearest student.
Answers
=====================================================
Explanation:
Convert each raw score to a z score
If x = 63.4, then
z = (x-mu)/sigma
z = (63.4-72.3)/8.9
z = -1
if x = 81.2, then
z = (x-mu)/sigma
z = (81.2-72.3)/8.9
z = 1
So P(63.4 < x < 81.2) is the same as P(-1 < z < 1)
Through the empirical rule (aka the 68-95-99.7 rule), we know that roughly 68% of the data values are within one standard deviation of the mean. In other words
P(-1 < z < 1) = 0.68 approximately (see note below)
Multiply 0.68 by the total 84 to get
0.68*84 = 57.12
which rounds to 57 people
Note: we can use a calculator to get a more accurate result of 0.68268949; a data table works as well but it won't be as accurate. For the purposes of this problem, the value 0.68 is good enough
Answer: 57
=====================================================
Explanation:
Convert each raw score to a z score
If x = 63.4, then
z = (x-mu)/sigma
z = (63.4-72.3)/8.9
z = -1
if x = 81.2, then
z = (x-mu)/sigma
z = (81.2-72.3)/8.9
z = 1
So P(63.4 < x < 81.2) is the same as P(-1 < z < 1)
Through the empirical rule (aka the 68-95-99.7 rule), we know that roughly 68% of the data values are within one standard deviation of the mean. In other words
P(-1 < z < 1) = 0.68 approximately (see note below)
Multiply 0.68 by the total 84 to get
0.68*84 = 57.12
which rounds to 57 people
Note: we can use a calculator to get a more accurate result of 0.68268949; a data table works as well but it won't be as accurate. For the purposes of this problem, the value 0.68 is good enough
please help compare these integers by typing the symbol that would make the statement true
12 ________ - 18
Answers
Positive integers are always greater.
A bag of uninflated balloons contains 10 red, 12 blue, 15 yellow and 8 green balloons. A balloon is drawn at random, what is the probability of drawing a red balloon?
Answers
(28.57%)
We have been given that a bag of uninflated balloons contains 10 red, 12 blue, 15 yellow and 8 green balloons.
We need to find the probability of drawing a red balloon.
We know that probability is given by
[tex]\\ \text{Probability =} \frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Since we know that there are 10 red balloons. Therefore, our number of favorable outcomes is 10.
In order to find the total number of outcomes, we will add balloons of all colors.
Therefore, total outcomes are = [tex]10+12+15+8 = 45[/tex]
We can now substitute the values of favorable outcomes and total outcomes in order to find the required probability.
[tex]\\ \text{Probability =} \frac{\text{10}}{\text{45}} = \frac{2}{9}[/tex]
Which quadratic equation is equivalent to (x+2)2+5(x+2)-6=0
Answers
The volume of a solid gold statue can be approximated as 1000 cm3. If the density of gold is about 20/cm3, what is the mass of the statue?
Answers
Rewrite for mass
M=d x v
M= 1000 x 20
Mass is 20,000 grams