Answers
How: Re-arrange formulae knowing tan(theta) = sin(theta)/cos(theta)
such that it become: cos(theta) -sin(theta)/cos(theta) x cos(theta) = 0.
From there; cos (theta) = sin(theta) (by re-arranging). Now, substitute figures of b), pie/4 = 45 degrees. At 45 degrees, sin(45) = cos(45) = 1/square root of 2. Also, 5pie/4 = 235 degrees. At 235 degrees, sin(235) = cos(235) = -1/square root of 2
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 = 0
cos 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 :)
Related Questions
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
A suitable calculator can show you the number of students having a score in that range is expected to be about 57.
During boot camp, the drill sergeant measured the weight of the men in his unit. he found the average weight of the men to be 142 pounds and the standard deviation 14 pounds. the data is normally distributed. find the interval in which 68% of the data lies. what is the probability that a man picked at random from the unit will weigh more than 170 pounds? that he will weigh less than 128 pounds?
Answers
mean=142
standard deviation=14
a] Find the interval in which 68% of the data lies:
P(x<X)=68%=0.68
the z-score associated with this probability is:
P(z<Z)=0.47
but :
z=(x-mu)/sig
thus;
0.47=(x-142)/14
solving for x we get:
x=148.58
thus 68 percent of the data lie below 148.58
b]what is the probability that a man picked at random from the unit will weigh more than 170 pounds?
x=170
thus
P(x>170) will be:
z=(170-142)/14
z=2
Thus
P(x>170)=1-P(z<2)
=1-0.9772
=0.0228
c] that he will weigh less than 128 pounds?
P(x<128)
z=(128-142)/14
z=(-14/14)=-1
Thus
P(z<-1)=0.1587
To find the interval of 68% of the data, use the empirical rule. The probability a man weighs more than 170 lbs or less than 128 lbs can be found using the normal distribution curve.
Explanation:To find the interval in which 68% of the data lies, we can use the concept of the empirical rule. According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean.
Since the standard deviation is 14 pounds and the mean is 142 pounds, one standard deviation above the mean is 142 + 14 = 156 pounds, and one standard deviation below the mean is 142 - 14 = 128 pounds.
Therefore, the interval in which 68% of the data lies is from 128 pounds to 156 pounds.
The probability that a man picked at random from the unit will weigh more than 170 pounds can be found by calculating the area under the normal distribution curve to the right of 170 pounds.
The probability that a man picked at random from the unit will weigh less than 128 pounds can be found by calculating the area under the normal distribution curve to the left of 128 pounds.
What is a polynomial function in standard form with zeroes 0, 1, 4, and –1?
(Please help and thanks in advance!)
Answers
(x) * (x-1) * (x + 1) * (x-4) = 0
Rescribing we have:
(x) * (x ^ 2-1) * (x-4) = 0
(x) * (x ^ 3 - 4x ^ 2 - x + 4) = 0
(x ^ 4 - 4x ^ 3 - x ^ 2 + 4x) = 0
Therefore, the polynomial in standard form is:
f (x) = x ^ 4 - 4x ^ 3 - x ^ 2 + 4x
Answer:
a polynomial function in standard form with zeroes 0, 1, 4, and -1 is:
f (x) = x ^ 4 - 4x ^ 3 - x ^ 2 + 4x
A tree is 100 feet tall casts a shadow that is 150 feet long . Determine the angle at which the rays of of tge sun hit the ground , to tye nearest degree
Answers
1. You have the following information given in the problem above:
- The tree is 100 feet tall.
- The tree casts a shadow that is 150 feet long.
2. Therefore, you have:
Tan^-1(α)=opposite/adjacent
Where:
- α is the angle.
- opposite=100 feet.
-adjacent=150 feet.
2. When you substitute these values, you obtain:
Tan^-1(α)=100/150
α=34º
The answer is: 34º
Which is the correct simplified form of the expression ?(4m-2n8/9m-6n-8)1/2
Answers
Answer:
[tex]\frac{2m^2n^8}{3}[/tex]
Step-by-step explanation:
The given expression is:
[tex](\frac{4m^{-2}n^8}{9m^{-6}n^{-8} })^{\frac{1}{2}}[/tex]
Upon simplifying the above equation, we get
Move [tex]m^{-6}[/tex] to teh numerator and Using the negative exponent rule, we get
=[tex](\frac{4m^{-2}n^8m^6}{9n^{-8} })^{\frac{1}{2}}[/tex]
Move [tex]n^{-8}[/tex] to teh numerator and Using the negative exponent rule, we get
=[tex](\frac{4m^{-2}n^8m^6n^8}{9})^{\frac{1}{2}}[/tex]
=[tex](\frac{4m^{4}n^{16}}{9})^{\frac{1}{2}}[/tex]
=[tex](\frac{(2)^2(m^2)^2(n^8)^2}{(3)^2})^{\frac{1}{2}}[/tex]
=[tex]\frac{2m^2n^8}{3}[/tex]
which is the correct simplified form of the given expression.
Two consecutive positive odd integers have a product of 63. what is the smaller number
Answers
Through trial and error, you can find that 7*9 = 63 so we see that 7 is the smaller number. Or you can factor 63.
-----------------------------------
The way your teacher probably wants you to do it is through algebra
x = smaller number
x+2 = next highest number
x*(x+2) = 63
x^2+2x = 63
x^2+2x-63 = 0
At this point, we can use the quadratic formula or factor. Factoring may be easier
x^2+2x-63 = 0
(x+9)(x-7) = 0
x+9=0 or x-7 = 0
x = -9 or x = 7
Toss out x = -9 because the instructions state that the integers must be positive.
The only valid answer is x = 7.
If x = 7, then x+2 = 7+2 = 9
So,
x*(x+2) = 63
7*9 = 63
where 7 is the smaller factor.
Please help me find the value of x in the triangle in the link!
Answers
The sum of the interior angles of all triangles is 180 degrees; you can find x by setting the sum of the two unknown angles, x, and 98 equal to 180 and solving algebraically.
180 = 98 + x + x
180 = 98 + 2x
82 = 2x
41 = x
Answer:
x = 41
Solve d = c π for π. A) π = cd B) π = c d C) π = d c D) π = c − d
Answers
Answer:
The answer is B
Step-by-step explanation:
Which equation shows 2x – y = 6 converted to slope-intercept form? y = x – 3 y = 2x – 6 y = –2x + 6
Answers
so you would subtract the 2x over to get -y=-2x+6 then you would divide by -1 to get y=2x-6
so y=2x-6 is the answer
If SAT scores are normally distributed with a mean of 1518 and a standard deviation of 325, find the probability that a randomly selected SAT score is between 1550 and 1575.
A.
0.5714
B.
0.9684
C.
0.0316
D.
0.5398
Answers
Standard deviation, sigma = 325
Range required: 1550 ≤ X ≤ 1575
Z = (X - x_bar)/sigma
Z1 = (1550-1518)/325 ≈ 0.1
Z2 = (1575-1518)/325 ≈ 0.18
From Z tables,
P(Z1) = 0.5398
P(Z2) = 0.5714
P(1550≤X≤1575) = P(Z2) - P(Z1) = 0.5714 - 0.5398 = 0.0316
The correct answer is C.
Answer:
C.
0.0316
Step-by-step explanation:
What is 12.5(18/6)+5³
Answers
Final answer:
To solve the expression 12.5(18/6) + 5³, divide 18 by 6 to get 3. Multiply 12.5 by 3 to get 37.5. Then, calculate 5³, which equals 125. Adding the results, you get 162.5.
Explanation:
To solve the expression 12.5(18/6) + 5³, follow the order of operations (PEMDAS/BODMAS). First, divide 18 by 6, which equals 3. Next, multiply 12.5 by 3, which equals 37.5. Finally, calculate 5³, which equals 125. Adding the results, 37.5 + 125 = 162.5.
Twenty different statistics students are randomly selected. for each of them, their body temperature ( degrees °c) is measured and their head circumference (cm) is measured. if it is found that r=0, does that indicate that there is no association between these two variables?
Answers
An r-value, or correlation coefficient, goes from -1 to positive 1. -1 indicates a perfect decreasing match and 1 indicates a perfect increasing match. 0 indicates no relationship between the variables.
Computer amount of interest earned and the following simple interest from a deposit of 5500 at 6% for three years equals?
Answers
1 year = $330
3 years = $330 x 3 = $990
Answer: $990
Wright a real world problem that involves classifying a quadrilateral. Then solve the problem.
Answers
The shape of quadrilateral ABCD changes as the moving platform swings around, but its side lengths do not change. Both pairs of opposite sides are congruent, so ABCD is a parallelogram by Theorem 8.7.By the definition of a parallelogram, AB DC . Because DC is parallel to line l, AB is also parallel to line l by the Transitive Property of Parallel Lines. So, the moving platform is parallel to the ground.
Write the equation of the given circle.
center (-2, -2)
radius of 6
Answers
(x + 2)² + (y + 2)² = 36
A quadrilateral has angles that measure 90°, 46°, and 120°. What is the measure of the fourth angle?
Answers
The sum of the internal angles of a quadrilateral is equal to 360 degrees
so
Let
x--------> the measure of the fourth angle
90+46+120+x=360
x=360-(90+46+120)
x=104 degrees
the answer is
the measure of the fourth angle is 104 degrees
what is the best approximation of the volume, in cubic units, of a cone of diameter 20 and height 13
Answers
to solve this, use the following equation:
divide the diameter by 2 to get the radius
π[tex] r^{2} [/tex][tex] \frac{h}{3} [/tex]
and you will have:
1361.36 cubic units
I hope this helps, and have a nice day!
The best approximation for the volume of the cone in cubic units is 1361.357 units³.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
Diameter of the cone = 20
Radius of the cone, r = Half of diameter
= 20/2 = 10
Height of the cone, h = 13
Volume of the cone = 1/3 π r² h
= 1/3 π (10)² (13)
= 1361.357 units³
Hence the volume is 1361.357 units³.
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This week, sandy was out sick on monday and tuesday. Last week, Jared was out sick on Thursday and Friday. The week before, Elisa was out sick on Wednesday and Thursday. What generalization can you make about these three students absents? Can you make a second generalization?
Answers
A generalization is a broad statement or an idea that is applied to a group of people or things. Most often, generalizations are not entirely true, because usually, the pattern they see in the relationship of a certain group of individuals or situations does not apply. In our example, where Elisa, Sandy, and Jared got sick and were absent from school for two days straight, within the 3 week period, we can make the following generalizations patterns:
1) There is an outbreak of sickness in the school for 3 consecutive weeks.
2) The said sickness lasts for two days.
Look at the cylinder below. which of these could not be a cross section of the cylinder? a circle b square c triangle d rectangle
Answers
If you sliced horizontally across a cylinder standing up, you would have a circle.
If you sliced vertically down a cylinder standing up, you could have either a rectangle or a square.
You would never have a triangle.
Final answer:
A square cannot be a cross section of a traditional circular cylinder when sliced perpendicular to its height. However, circles, rectangles, and triangles can be cross sections depending on the shape of the cylinder and the slicing.
Explanation:
When considering the cross sections of a cylinder, it is important to remember that the cross-sectional shape remains consistent along the height of the cylinder. A cross section made perpendicular to the height of a traditional circular cylinder is always a circle. Therefore, the correct answer to which shape could not be a cross section of a cylinder is a square, option b. Circles, rectangles, and triangles can all be cross sections of a cylinder depending on the shapes of the top and bottom faces of the cylinder and how the cross section is sliced.
If the cylinder is a right circular cylinder, the only possible perpendicular cross-sectional shape is a circle. A square cross section can occur in a cylinder if the top and bottom faces are square and the cylinder is not circular. Similarly, a rectangular cross section can occur if the cylinder has a rectangular type of cross-section to start with. However, for a circular cylinder, a triangle cannot be a cross section because slicing it will always yield a circular shape due to the round nature of its base.
What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)squared + 4?
Answers
Answer:
x = 3/2
Step-by-step explanation:
That is quite long and drawn out, so we have to get it down to a single quadratic equation, set equal to 0.
Begin by expanding the right side to get
[tex]y+3x-6=-3(x^2-4x+4)+4[/tex]
then multiplying in the -3 to get
[tex]y+3x-6=-3x^2+12x-12+4[/tex]
Now we will combine all the like terms and get everything on one side of the equals sign, and set it equal to 0:
[tex]-3x^2+9x-2=0[/tex]
In order to find the equation of the axis of symmetry we have to put it into vertex form, which is accomplished by completing the square on this quadratic.
In order to complete the square, the leading coefficient has to be a +1. Ours is a -3, so we will factor that out. First, though, now that it is set to equal 0, we will move the constant, -2, over to the other side, isolating the x terms.
[tex]-3x^2+9x=2[/tex]
Now we can factor out the -3:
[tex]-3(x^2-3x)=2[/tex]
The rules for completing the square are as follows:
Take half the linear term, square it, and add it to both sides. Our linear term is 3. Half of 3 is 3/2, and squaring that gives you 9/4. We add into the parenthesis on the left a 9/4, but don't forget about that -3 hanging around out front that refuses to be ignored. We didn't add in just a 9/4, we added in (-3)(9/4) = -27/4:
[tex]-3(x^2-3x+\frac{9}{4})=2-\frac{27}{4}[/tex]
In the process of completing the square we created a perfect square binomial on the left. Stating that binomial and simplifying the addition on the right gives us:
[tex]-3(x-\frac{3}{2})^2=-\frac{19}{4}[/tex]
We can determine the axis of symmetry at this point. Because this is a positive x-squared polynomial, the axis of symmetry is in the form of (x = ) and what it equals is the h coordinate of the vertex. Our h coordinate is 3/2; therefore, the axis of symmetry has the equation x = 3/2
Factor this expression.
4x – 20
A. 4(x – 16)
B. 4(x – 6)
C. 4(x – 5)
D. 4(x – 10)
Answers
Answer: C. 4(x – 5)
Which function has an inverse that is also a function?
Answers
Option C gives us such a function, all x values are different and all y values are different. So inverse of function given in option C will result in a relation which will also be a function.
In all other options, y values are being repeated, which means they are not one to one functions.
So, the answer to this question is option C
{ ( -1 , 3 ) , ( 0,4 ), ( 1 , 14 ) , ( 5, 6 ) , ( 7, 2 )}
Further explanationFunction is a relation which each member of the domain is mapped onto exactly one member of the codomain.
There are many types of functions in mathematics such as :
Linear Function → f(x) = ax + bQuadratic Function → f(x) = ax² + bx + cTrigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan xLogarithmic function → f(x) = ln xPolynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...If function f : x → y , then inverse function f⁻¹ : y → x
Let us now tackle the problem!
According to the definition above, it can be concluded that a function cannot have the same x value.
Of the four tables available in choices, table option C has an inverse that is also a function. This is because x values and y values are all different.
[tex]\{(-1,3) , ( 0,4} ) , ( 1,14 ) , ( 5, 6) , ( 7, 2) \}[/tex]
Option A doesn't have inverse because there is the same value of y i.e 4
[tex]\{(-1,-2) , ( 0,\boxed{4} ) , ( 1,3 ) , ( 5, 14) , ( 7, \boxed {4}) \}[/tex]
Option B doesn't have inverse because there is the same value of y i.e 4
[tex]\{(-1,-2) , ( 0,\boxed{4} ) , ( 1,5 ) , ( 5, \boxed {4}) , ( 7, 2) \}[/tex]
Option D doesn't have inverse because there is the same value of y i.e 4
[tex]\{(-1,\boxed {4}) , ( 0,\boxed{4} ) , ( 1,2 ) , ( 5, 3) , ( 7, 1) \}[/tex]
Learn moreInverse of Function : https://brainly.com/question/9289171Rate of Change : https://brainly.com/question/11919986Graph of Function : https://brainly.com/question/7829758Answer detailsGrade: High School
Subject: Mathematics
Chapter: Function
Keywords: Function , Trigonometric , Linear , Quadratic
find the height of the triangle
Answers
We'll do the sine trig. identity, as it is the most effective.
Given an angle '[tex] \alpha [/tex]' in a right triangle, '[tex]sin( \alpha )[/tex]' is defined as the opposite side of the triangle to the given angle, over the triangle's hypotenuse.
So, for this setup:
[tex]sin(20)= \frac{x}{10} [/tex]
Now, we solve for x:
[tex]x=10sin(20)=3.42[/tex]
So, answer is 3.4
sin theta = opposite / hypotenuse ; where theta =20 ; h = 10
sin (20) = x / 10
x = 3.42
The answer is the fourth one, 3.42
Can someone please help me with this!!
Will give brainliest!!
Answers
Kristin decides to spend at most $50 for a birthday dinner at a restaurant, including a 15% tip.,
Write an inequality in one variable to represent this situation.
What is the most that her meal can cost before a tip?
Answers
Where x is the meal's cost (no tip included)
50 - 15% = 42.5.
x >(or equal to) 42.50.
(nothing is copied content, I copy pasted a number into the right position, feel free to check it mods)
The representation of this situation as an inequality is 1.15x ≤ 50. To find the maximum possible cost of Kristin's meal before the tip, the inequality is solved for x, which results in the value of $43.48.
Explanation:In this scenario, the cost of Kristin's meal before the tip can be represented by the variable x. The tip is 15% of the cost of the meal, which can be represented as 0.15x. The total cost of the meal, including the tip, is therefore x + 0.15x, which is 1.15x. Given that the total cost cannot exceed $50, we can write the following inequality to represent this situation: 1.15x ≤ 50.
To find the most that her meal can cost before a tip, we need to solve this inequality for x. So, we divide both sides by 1.15: x ≤ 50/1.15. After calculation, we find that x (the cost of the meal before the tip) must be ≤ about $43.48.
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Under the normal curve, approximately what percent of scores fall between and -1 to +1 standard deviations around the mean?
Answers
You can use a calculator to get a more approximate answer. If you have a TI calculator, you can use the "normalcdf" function to type in normalcdf(-1,1)
Solve this inequality: 3q + 11 + 8q > 99. A. q > 8 B. q > 1/8 C. q > 88 D. q > 11
Answers
To solve this problem we must first group like terms.
Original Equation :
3q + 11 + 8q > 99
New Equation {Grouped Like Terms} :
3q + 8q + 11 > 99
Now, we'll add our similar elements.
Old Equation :
3q + 8q + 11 > 99
New Equation {Added Similar Elements} :
11q + 11 > 99
Next, we'll have to change the equation. To do this we'll add minus eleven to both sides of the equation. This will give us eleven q on its own.
Old Equation :
11q + 11 > 99
New Equation {Added Subtract 11 to Both Sides} :
11q + 11 - 11 > 99 - 11
Now we simplify.
Old Equation :
11q + 11 - 11 > 99 - 11
New Equation {Old Equation Simplified} :
11q > 88
Now, we'll have to divide both sides by eleven. We do this so as to get the variable ( q ) on its own.
Old Equation :
11q > 88
New Equation {Added Divide Both Sides by 11} :
[tex] \frac{11q}{11} [/tex] > [tex] \frac{88}{11} [/tex]
Once again, we now have to simplify.
Old Equation :
[tex]\frac{11q}{11}[/tex] > [tex]\frac{88}{11}[/tex]
New Equation {Old Equation Simplified} :
q > 8
So, this means that the solution to the inequality given is q > 8.
Hope this helps!
- Lindsey Frazier ♥
The volume of an oblique pyramid with a square base is V units3 and the height is h units.
Which expression represents the area of the base of the pyramid?
A)3v/h units
B)(3V – h) units
C)(V – 3h) units
D)V/3H units
Answers
V = (1/3) * (Ab) * (h)
Where,
Ab: base area
h: height
Clearing the area of the base we have:
Ab = (3 * V) / (h)
Answer:
An expression that represents the area of the base of the pyramid is:
A) 3v / h units
Answer: A. 3V/ h units^2
Step-by-step explanation:
Anja collected data about the number of dogs 9th-grade students own. She created this histogram to represent the data and determined that it is skewed right. Which statement is true about Anja’s claim?
Answers
A regular octagonal pyramid has a base edge of 3m and a lateral area of 60m^2. Find its slant height.
Answers
Find area of 1 triangle:
Area of one side triangle = 60 ÷ 8 = 7.5 m²
Given area and length, find height:
Area of each triangle = 7.6 m²
Length of each triangle = 3m
Area = 1/2 x base x height
7.5 = 1/2 x 3 x height
Heigth = 5m
Answer: Slanted Height = 5 m
The slant height is 5 m