The tangent line is horizontal whenever [tex]\dfrac{\mathrm dy}{\mathrm d\theta}=0[/tex].
[tex]\dfrac{\mathrm dy}{\mathrm d\theta}=2\cos2\theta=0\implies2\theta=\dfrac{(2n+1)\pi}2\implies\theta=\dfrac{(2n+1)\pi}4[/tex]
where [tex]n[/tex] is any integer.
I'm guessing you're only interested in one complete loop of the lemniscate. In that case, we're restricted to [tex]0\le\theta\le2\pi[/tex]. Then we get 4 points of interest for [tex]n=0,1,2,3[/tex]:
[tex]\theta=\dfrac\pi4,\dfrac{3\pi}4,\dfrac{5\pi}4,\dfrac{7\pi}4[/tex]
Joey runs diagonally across a rectangular field. The field had a width of 15 yards and a length of 36 yards. How far did Joey run
Answer:
Joey ran 39 yards
Step-by-step explanation:
a²+b²=c²
15²+36²=c²
225+1296=c²
1521=c²
√1521=√c²
39=c
Mental break time. What is 1+1?
A) Not this one
B) Still not this one
C) 2
D) You've gone too far, go back to C
C is the correct answer. Appreciate it if you gave me brainliest!
Answer:
C
Step-by-step explanation:
and thank you for this it was funny and a good break from algebra 1! XD
Translate the point (1, 3) to the new origin given ( h , k ). Given center ( h , k ) = (5, 4), find point ( x ', y ').
Answer:
(6,7)
Step-by-step explanation:
To translate a point, move each coordinate the specified amount and direction. Since the origin (0,0) moved to (5,4) or 5 right and 4 up, move (1,3) the same amount and direction. 1 moves right to 6. 3 moves up to 7. The new point is (6,7)
Answer:
(-4,-1)
Step-by-step explanation:
(h,k)=(5,4) and (x,y)=(1,3)
x' = x - h = 1 - 5 = - 4
y' = y -k = 3 - 4 = - 1
Which choices correctly describe reflections in the diagram? Check all that apply.
1)The red triangle A is reflected across the x-axis onto triangle B.
2)The red triangle A is reflected across the y-axis onto triangle D.
3)The blue triangle D is reflected across the x-axis onto triangle C.
4)The blue triangle D is reflected across the line y = x onto triangle B.
5)The green triangle C is reflected across the line y = –x onto triangle A.
Answer:
2
3
5
.................................................
Answer:
2, 3, 4.
I don't have an explanation I just did the test.
V^2-8v=0 solving quadratic equation
Answer:
v = 0, or v = 8
Step-by-step explanation:
The quadratic can be factored, then the zero product rule applied.
v^2 -8v = 0
v(v -8) = 0
A product will be zero when any of the factors is zero. So, the solutions are values of v that make the factors be zero.
v = 0
v -8 = 0 . . . ⇒ . . . v = 8
Express the following rate as a unit rate.
answering 36 questions in 3 minutes
18 questions per minute
12 questions per minute
15 questions per minute
36 questions per minute
The answer is 12 questions per minute as you divide 36 by 3
Answer=12 questions per minute
Answer:
12
Step-by-step explanation:
You are standing 50 meters from a hot air balloon that is preparing to take off. The angle of the elevation to the top of the balloon is 28. Find the height of the balloon
Answer:
27 meters
Step-by-step explanation:
Think of it like a right triangle. One leg is 50m long (the distance you are from the balloon) and the goal is to find the other leg of the triangle. From the place you're standing, the angle is 28°. In relation to that angle, you're given the adjacent side (50m) and need to find the opposite side. Recall SOH-CAH-TOA. You have to use tangent to get the length. Tan = opposite/adjacent. The tan of 28 = x / 50. Use algebra to solve: tan28 (50) = x; aproximately 26.6m = x. So, the height of the hot air balloon is roughly 26.6m or 27m depending on how you round.
If a fair die is tossed, find the probability that the uppermost face displays a(n):
if a fair dice is tossed the probability is (T, H) (H, T) ( T, T) (H, H)
A fair, six-sided die has six equally likely outcomes. The probability of any one face showing up when the die is tossed is 1/6 or approximately 0.1667. Probability is a long term expectation under ideal theoretical conditions.
Explanation:The question is asking about the probability of each face showing up when a six-sided die is tossed. A fair, six-sided die has six possible outcomes: the faces are numbered 1, 2, 3, 4, 5, or 6. Each face is equally likely to be the uppermost face when the die is tossed. Therefore, the probability of any one face showing up is 1 out of 6, or approximately 0.1667.
Probability is a theoretical concept that tells us how likely an event is to occur. It does not describe the short-term results of an experiment. Rather, it gives information about what can be expected in the long term. Thus, if you were to toss a fair, six-sided die many times, you would expect that each face would come up about one-sixth of the time. This expectation is based on the assumption of ideal theoretical conditions where the die is fair.
Probability is a key concept in statistics and is used in many different areas of life, including in decision making, prediction, risk management, and games of chance.
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Our goal is to make add-on sales during 85% of sales. If you make 35 sales, how many add-on sales do.You need to make to meet the goal?
Answer:
30 add-on sales to make the goal
Step-by-step explanation:
multiply 35*85% (or 0.85)
35*0.85 = 29.75
Since you can't make 0.75 of a goal, round up to the next highest number = 30
A car travels 2 5/8 miles in 3 1/2 minutes at a constant speed. Which equation represents the distance, d, that the car travels in m minutes?
Answer:
[tex]d=0.75m[/tex]
Step-by-step explanation:
Let
d------> the distance in miles
m----> the time in minutes
we know that
The speed is equal to divide the distance by the time
so
[tex]speed=d/m[/tex]
we have
[tex]d=2\frac{5}{8}\ miles=\frac{2*8+5}{8}=\frac{21}{8}\ miles[/tex]
[tex]m=3\frac{1}{2}\ minutes=\frac{3*2+1}{2}=\frac{7}{2}\ minutes[/tex]
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
so
In this problem the speed is the constant of proportionality
[tex]d=km[/tex]
Find the value of k
[tex]k=\frac{(21/8)}{(7/2)} =0.75\frac{miles}{minute}[/tex]
[tex]d=0.75m[/tex] ----> linear equation that represent the distance, d, that the car travels in m minutes
What is the are of a triangle (picture provided)
Answer:
Area Δ = 102.3 units² ⇒ The answer is (d)
Step-by-step explanation:
* Use the formula of the area:
∵ Area of the triangle = 1/2 (a)(b) sin(C)
∵ We have the length of the 3 sides
∴ Use cos Rule to find the angle C
∵ cos(C) = (a² + b² - c²)/2ab
∵ a = 25 , b = 13 , c = 17
∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650
∴ m∠C = 39°
∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²
∴ The answer is (d)
Answer:
Area Δ = 102.3 units² ⇒ The answer is (d)
Step-by-step explanation:
Use the formula of the area:
∵ Area of the triangle = 1/2 (a)(b) sin(C)
∵ We have the length of the 3 sides
∴ Use cos Rule to find the angle C
∵ cos(C) = (a² + b² - c²)/2ab
∵ a = 25 , b = 13 , c = 17
∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650
∴ m∠C = 39°
∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²
∴ The answer is (d)
The expression 2x(3x^2+4) can be simplified into which of the following?
a. 6x^3+4
b. 5x^3+6x
c. 6x^2+8x
d. 6x^3+8x
Answer:
[tex]\large\boxed{d.\ 6x^3+8x}[/tex]
Step-by-step explanation:
[tex]2x(3x^2+4)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(2x)(3x^2)+(2x)(4)\\\\=6x^3+8x[/tex]
An example of dependent events is drawing a blue marble out of one jar and then drawing a
blue marble out of the another jar.
red marble out of the same jar, after replacing the first marble.
red marble out of the same jar, without replacing the first marble.
red marble out of another jar.
Answer:
red marble out of the same jar, without replacing the first marble.
Step-by-step explanation:
Dependant events means one depends on the other. If you don't replace the first marble then the chance of drawing any other marble is changed. To better see it try giving them numbers, how many blue and red marbles start in the jar and calculate probability before and after removing a blue marble.
Dependent events are those in which the outcome of one affects others. Drawing a marble from a jar and then drawing another without replacing the first one is an example of dependent events. Independent events don't affect each other, as when drawing marbles from different jars or replacing a marble before drawing another from the same jar.
The question you've asked pertains to the concept of dependent and independent events in probability theory. Dependent events are events in which the outcome of one affects the outcome of the others.
If we draw a blue marble from the jar and then, without replacing the first marble, we draw another marble, these are dependent events because the second event is affected by the outcome of the first.
On the other hand, if we draw a blue marble from one jar and then draw a marble from another jar, these are independent events because they do not affect each other.
Similarly, if we draw a marble from a jar, replace it, and then draw another, these are also independent events because putting the first marble back makes the second draw unaffected by the first one.
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Bart works 36 hr a week and makes $612.Charles worked 34hr a week and makes$663.Who makes more per he how do you know
Answer:
Charles
Step-by-step explanation:
Bart worked for 36 hours, and earned $612.
$612 / 36 = $17 is what he earned per hour
Charles worked for 34 hours, and earned $663.
$663 / 34 = $19.5 is what he earned per hour
You don't even need to solve for anything actually. Just looking at the given values, you will see that Charles earned more money despite working less hours compared to Bart.
How do i solve for X
2x+4-7x+9x= -2
What is X?
Answer:
x = -3/2 or -1.5
Step-by-step explanation:
You have to get X on one side by itself.
2x + 4 - 7x + 9x = -2
Subtract the 4
2x - 7x + 9x = -6
Combine like terms
-5x + 9x = -6
Combine like terms
4x = -6
Divide by 4
x = -6/4
Simplify
x = -3/2 or -1.5
What is SIN A?
Question 4 options:
3/4
4/3
3/5
4/5
Final answer:
The value of sin A cannot be determined without knowing the value of angle A.
Explanation:
The question is asking for the value of sin A. In mathematics, sin A represents the sine of angle A. The sine function is a mathematical function that relates the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right triangle.
The correct answer to the question is 3/5. To find this value, you need to know the value of angle A. Without that information, we cannot determine the exact value of sin A.
Final answer:
The correct value of SIN A from the given options cannot be determined without additional context. SIN A refers to the ratio of the side opposite to angle 'A' to the hypotenuse in a right triangle or the y-coordinate on the unit circle at angle 'A'. Possible values are within the range of -1 to 1.
Explanation:
The question 'What is SIN A?' is seeking the trigonometric value of the sine function at a particular angle denoted by 'A'. When presented with options like 3/4, 4/3, 3/5, and 4/5, we need additional information regarding angle 'A' or the context of a right triangle or unit circle to determine the correct value. Without this information, we cannot definitively answer which option is correct.
Generally, in a right triangle, SIN A would represent the ratio of the length of the side opposite to angle 'A' to the length of the hypotenuse. Therefore, it is a value between -1 and 1. The options 3/4 and 3/5 could potentially be correct since they are within this range, but 4/3 cannot be because it exceeds this range. In a unit circle context, sin A would represent the y-coordinate of a point on the circle's circumference at an angle 'A' from the x-axis.
A Farmer divisids 20acre sections into 1-4 Acer sections into how many sections does the farmer divide her land
Answer:
80 - 1/4 acre sections
Step-by-step explanation:
If the farmer is dividing her land into 1/4 acre sections...
1. there will be 4 sections in one acre (4/4 = 1)
2. multiply 4 (sections) by 20 (acres)
4*20 = 80
Consider the function below. x -1 0 1 2 f(x) -2 3 8 13 Which of the following functions could be the inverse of function f? A. x 1 0 -1 -2 s(x) -2 3 8 13 B. x -2 3 8 13 q(x) -1 0 1 2 C. x -2 -3 -8 -13 r(x) 1 0 -1 -2 D. x -1 0 1 2 p(x) 2 -3 -8 -13
Answer: B
x q(x)
-2 -1
3 0
8 1
13 2
Step-by-step explanation:
An inverse of a function is a reflection across the y=x line. This results in each (x,y) point becoming (y,x).
x f(x)
-1 -2
0 3
1 8
2 13
So the inverse becomes:
x Inverse
-2 -1
3 0
8 1
13 2
Answer:
The correct option is B.
Step-by-step explanation:
The table of values of a function is given below:
x : -1 0 1 2
f(x) : -2 3 8 13
If a function is defined f:R→R
[tex]f(x)=\{(x,y):x\in R,y\in R\}[/tex]
them the inverse of function is defined as
[tex]f^{-1}(x)=\{(y,x):x\in R,y\in R\}[/tex]
The table of values of inverse function is
x : -2 3 8 13
f⁻¹(x): -1 0 1 2
We can say that q(x) is the inverse function of f(x). Therefore the correct option is B.
Evaluate arccsc sqrt 2.
Answer:
{π/4 +2πn, 3π/4 +2πn}
Step-by-step explanation:
csc = 1/sin, so when csc(θ) = √2, sin(θ) = 1/√2. Then θ = π/4 or 3π/4.
This means arccsc(√2) will be the set of angles shown above.
___
Once you recognize that π/4 is one of the angles, you can eliminate all but the correct answer choice.
Of course this is much easier if you have memorized the short list of trig function values:
sin(π/6) = cos(π/3) = 1/2
sin(π/4) = cos(π/4) = 1/√2 = (√2)/2
sin(π/3) = cos(π/6) = (√3)/2
tan = sin/cos
sec = 1/cos
csc = 1/sin
Answer:
the above answer is correct
A non toxic furniture polish can be made by combining vinegar and oil. The amount of oil should be five times the amount of vinegar. How much of each ingredient is needed in order to make 27 oz of furniture polish?
There should be 4.5 oz of vinegar and 22.5 oz of oil
-5x+y=0
x+y=27
-6x=-27
Which is the definition of a ray?
A.a part of a line that has one endpoint and extends indefinitely in one direction
B.the set of all points in a plane that are a given distance away from a given point
C.lines that lie in the same plane and do not intersect
D.a part of a line that has two endpoints
The correct answer is (A)!
Pham's annual salary is $78,000. Pham gets paid each month. Find Pham's monthly gross salary?
Answer:
Pham earns 6,500 per month.
Step-by-step explanation:
To get the monthly salary, divide the yearly salary by 12.
78,000/12 = 6,500
Answer:
78,000 / 12 = 6,500
Step-by-step explanation:
Pham's annual salary is $78,000
To find Pham's month salary
Divide 78,000 by 12
Thus 6,500
Given the figure, what is x?
A) 216
B) 144
C) 96
D) 72
D) x = 72
If this helps, please mark brainliest
Answer:
if ur doing usa test prep it’s D) 72
Step-by-step explanation:
A recent survey by the cancer society has shown that the probability that someone is a smoker is P(S)=0.19. They have also determined that the probability that someone has lung cancer, given that they are a smoker is P(LC|S)=0.158. What is the probability (rounded to the nearest hundredth) that a random person is a smoker and has lung cancer P(S∩LC) ?
0.35
0.03
0.02
0.83
Answer:
0.03
Step-by-step explanation:
The given question uses the concept of Conditional Probability. The general formula of conditional probability in terms of two events A and B is:
[tex]P(A|B) = \frac{P(A \cap B}{P(B)}[/tex]
In the given case, the two events are:
LC = Event that someone has lung cancer
S = Event that someone is smoker
The formula in terms of these events will be:
[tex]P(LC | S)=\frac{P(S \cap LC)}{P(S)}[/tex]
Using the given values, we can find the probability that a random person is a smoker and has lung cancer P(S∩LC).
[tex]0.158=\frac{P(S \cap LC)}{0.19} \\\\ P(S \cap LC) = 0.158 \times 0.19\\\\ P(S \cap LC) = 0.03[/tex]
Therefore, the probability (rounded to the nearest hundredth) that a random person is a smoker and has lung cancer P(S ∩ LC) is 0.03
Answer:
P (S∩LC) = 0.03
Step-by-step explanation:
It is known that the probability if someone is a smoker is P(S)=0.19 and the probability that someone has lung cancer, given that they are also smoker is P(LC|S)=0.158.
So using the above information, we are to find the probability hat a random person is a smoker and has lung cancer P(S∩LC).
P (LC|S) = P (S∩LC) / P (S)
Substituting the given values to get:
0.158 = P(S∩LC) / 0.19
P (S∩LC) = 0.158 × 0.19 = 0.03
Find the length of the arc shown in brown. Leave your answer in terms of pi.
Answer:
The length of the arc is [tex]8\pi\ ft[/tex]
Step-by-step explanation:
we know that
The measure of the arc shown in brown is equal to
[tex]180\°-60\°=120\°[/tex] -----> by central angle
Remember that
The length of the arc of the complete circle (360 degrees) is equal to the circumference
[tex]C=\pi D[/tex]
we have
[tex]D=24\ ft[/tex]
substitute
[tex]C=\pi (24)=24 \pi\ ft[/tex]
so
by proportion
Find the length of the arc for a measure of [tex]120\°[/tex]
[tex]\frac{24\pi }{360} \frac{ft}{degrees} =\frac{x }{120} \frac{ft}{degrees}\\ \\x=120*(24\pi )/360\\ \\ x= 8\pi\ ft[/tex]
Anita earns 60 points every time she shops at a grocery store.She needs a total of 2,580 points to receive a free prize.So far she has earned 480 points.How many more times will Anita have to shop at the grocery store in order to earn the additional points she needs for a prize?
Answer: 43 more times
2580÷60=43.
Step-by-step explanation: 43×60 =2580
This proves that 43 times is correct.
Answer:
c 43
Step-by-step explanation:
Laura sold 3/4 of a case of Girl Scout cookies. Anna sold 2/3?Of a case. Witch girl sold more cookies?
we can simply put both fractions with the same denominator, and thus then we can just compare which numerator is larger.
we can do so by multiplying each fraction by the other's denominator, let's proceed.
[tex]\bf \stackrel{Laura}{\cfrac{3}{4}\cdot \cfrac{3}{3}}\implies \cfrac{9}{12}~\hfill \stackrel{Anna}{\cfrac{2}{3}\cdot \cfrac{4}{4}}\implies \cfrac{8}{12} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{Laura}{\cfrac{9}{12}}~>~\cfrac{8}{12}~\hfill[/tex]
Which statement about function F and Function G is true?
Answer:
C. Both functions have a y-intercept of -2
Step-by-step explanation:
A. Function F in decreasing then increasing, therefore it's incorrect
B. Function F is symmetrical about the y-axis, but Function G is not
C. Both functions intercept the y-axis at (0,-2) so it's correct
D. Only function G shows a linear relationship.
To look at a picture of what Function G looks like. Press y= on your Ti-84 calculator (top left) put the function in, and then press graph (top right)
This is 100% correct. I took algebra 1 last year.
The temperature at 8:00am is 5 degrees Celsius and increases 2 degrees per hour. Does this equal y=2x+5
Answer:
no
got correct on algebra nation
Charles rolled a ball across the floor and noticed that it stopped before reaching the other side of the room. A force applied to the ball in the opposite direction in which it was rolling caused this to happen. What is the name of this force? A. Friction B. Gravity C. Electricity D. Magnetism
Answer:
Friction
Step-by-step explanation:
Because friction between the floor and the ball made the ball stopped from rolling.
Answer:
Friction
Step-by-step explanation:
The force that acts in opposite direction to the motion of the ball thereby causing it to stop is the force of friction.
This frictional force is a force of opposition that causes bodies moving in a particular direction to come to an halt. The force always acts in the opposite direction to the moving force acting on a body.