Answer:
cos theta = adj / hyp is positive (+/+)
Step-by-step explanation:
In this open interval, the hypotenuse (radius) is always positive, whereas the adjacent side is positive and the opposite side negative.
in this interval:
sin theta = opp / hyp is neg (-/+)
cos theta = adj / hyp is positive (+/+)
tan theta = opp / adj = (-/+) : negative
The function ƒ(x) = (x − 1)^2 + 5 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an inverse function.
The restricted domain for ƒ is ?
Answer:
f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.
Step-by-step explanation:
The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.
* if x>1, then x-1>0.
* Also since the parabola opens up, then y>5.
So let's solve y=(x-1)^2+5 for x.
Subtract 5 on both sides:
y-5=(x-1)^2
Take square root of both sides:
Plus/minus sqrt(y-5)=x-1
We want x-1>0:
Sqrt(y-5)=x-1
Add 1 on both sides:
Sqrt(y-5)+1=x
Swap x and y:
Sqrt(x-5)+1=y
x>5
y>1
Which of the following statements are correct? Select ALL that apply!
Select one or more:
O a. -1.430 = -1.43
O b. 2.36 < 2.362
O c.-1.142 < -1.241
O d.-2.33 > -2.29
O e. 2.575 < 2.59
O f. -2.25 -2.46
Translate the triangle. Then enter the new coordinates. A(-3, 4) A'([?], [?]) B'([ ], [ ] C([],[]) B(0, 1) C(-4,1)
or
Answer:
The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].
Step-by-step explanation:
Vectorially speaking, the translation of a point can be defined by the following expression:
[tex]V'(x,y) = V(x,y) + T(x,y)[/tex] (1)
Where:
[tex]V(x,y)[/tex] - Original point.
[tex]V'(x,y)[/tex] - Translated point.
[tex]T(x,y)[/tex] - Translation vector.
If we know that [tex]A(x,y) = (-3,4)[/tex], [tex]B(x,y) = (0,1)[/tex], [tex]C(x,y) = (-4,1)[/tex] and [tex]T(x,y) = (6, -4)[/tex], then the resulting points are:
[tex]A'(x,y) = (-3, 4) + (6, -4)[/tex]
[tex]A'(x,y) = (3, 0)[/tex]
[tex]B'(x,y) = (0,1) + (6, -4)[/tex]
[tex]B'(x,y) = (6, -3)[/tex]
[tex]C'(x,y) = (-4, 1) + (6, -4)[/tex]
[tex]C'(x,y) = (2, -3)[/tex]
The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].
PLEASE HELP ME PLEASE AND BE CORRECT
Answer:
12 cm²
Step-by-step explanation:
area = L *B
a = 6 * 2
a = 12cm²
A bank records deposits as positive numbers and withdrawals as negative numbers.
Mike withdrew $60 from his bank account 3 times.
what is the change in mikes account balance after all 3 withdrawals?
use the figure to find y
Answer:
y = 3
Step-by-step explanation:
6sin(30) = 3
Hi, help with question 18 please. thanks
Answer:
See Below.
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle y^2 = 1 + \sin x[/tex]
And we want to prove that:
[tex]\displaystyle 2y\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right) ^2 + y^2 = 1[/tex]
Find the first derivative by taking the derivative of both sides with respect to x:
[tex]\displaystyle 2y \frac{dy}{dx} = \cos x[/tex]
Divide both sides by 2y:
[tex]\displaystyle \frac{dy}{dx} = \frac{\cos x}{2y}[/tex]Find the second derivative using the quotient rule:
[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{(\cos x)'(2y) - (\cos x)(2y)'}{(2y)^2}\\ \\ &= \frac{-2y\sin x-2\cos x \dfrac{dy}{dx}}{4y^2} \\ \\ &= -\frac{y\sin x + \cos x\left(\dfrac{\cos x}{2y}\right)}{2y^2} \\ \\ &= -\frac{2y^2\sin x+\cos ^2 x}{4y^3}\end{aligned}[/tex]
Substitute:
[tex]\displaystyle 2y\left(-\frac{2y^2\sin x+\cos ^2 x}{4y^3}\right) + 2\left(\frac{\cos x}{2y}\right)^2 +y^2 = 1[/tex]
Simplify:
[tex]\displaystyle \frac{-2y^2\sin x-\cos ^2x}{2y^2} + \frac{\cos ^2 x}{2y^2} + y^2 = 1[/tex]
Combine fractions:
[tex]\displaystyle \frac{\left(-2y^2\sin x -\cos^2 x\right)+\left(\cos ^2 x\right)}{2y^2} + y^2 = 1[/tex]
Simplify:
[tex]\displaystyle \frac{-2y^2\sin x }{2y^2} + y^2 = 1[/tex]
Cancel:
[tex]\displaystyle -\sin x + y^2 = 1[/tex]
Substitute:
[tex]-\sin x + \left( 1 + \sin x\right) =1[/tex]
Simplify. Hence:
[tex]1\stackrel{\checkmark}{=}1[/tex]
Q.E.D.
Identify the domain of the function shown in the graph.
A. -5
B. x> 0
C. 0
D. x is all real numbers.
PLEASE HELP please I need this done now
The total cost of a truck rental, y, for x days, can be modeled by y = 35x + 25.
What is the rate of change for this function?
Answers
A- 35$
B-25$
C-60$
D-10$
Answer:
35
Step-by-step explanation:
y = 35x+23 is in the form
y = mx+b where m is the slope and b is the y intercept
The slope can also be called the rate of change
35 is the slope
Taree fourts of the 64 books were math books. determine the percent of the books that were math books.
Answer: 75% - these are books on mathematics.
Step-by-step explanation:
[tex]\dfrac{3}{4} \cdot 64 = 48\\[/tex]
64 - 100%
48 - x%
[tex]\dfrac{64}{100} =\dfrac{48}{x}\\\\x=\dfrac{48 \cdot 100}{64} \\\\x=75 \%[/tex]
Santos flipped a coin 300 times. The coin landed heads up 125 times. Find the ratio of heads to total number of coin flips. Express a simplified ratio
Answer:
5:12
Step-by-step explanation:
125:300 simplified = 5:12
I hope this helps
Find the value of x in each case and give an explanation plzzz, thank youu :)
Answer:
Step-by-step explanation:
the arrows from the picture tells us that TV is parallel to RS
since TS is a transversal that cuts the 2 parallel lines TV and RS than ∠S =x
(alternate interior angles)
sum of angles in a Δ is 180° so x+x+2x = 180°, 4x =180°, x= 45°
2x = 45*2 = 90°
Two workers finished a job in 12 days. How long would it take each worker to do the job by himself if one of the workers needs 10 more days to finish the job than the other worker
Two workers finished a job in 7.5 days.
How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?
let t = time required by one worker to complete the job alone
then
(t+8) = time required by the other worker (shirker)
let the completed job = 1
A typical shared work equation
7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1
multiply by t(t+8), cancel the denominators, and you have
7.5(t+8) + 7.5t = t(t+8)
7.5t + 60 + 7.5t = t^2 + 8t
15t + 60 = t^2 + 8t
form a quadratic equation on the right
0 = t^2 + 8t - 15t - 60
t^2 - 7t - 60 = 0
Factor easily to
(t-12) (t+5) = 0
the positive solution is all we want here
t = 12 days, the first guy working alone
then
the shirker would struggle thru the job in 20 days.
Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15
Step-by-step explanation:
graph a circle with General form.x^2 +y^2+8x-12y+24=0
Answer:
jhshejwjabsgsgshshsnsjs
Answer:
Step-by-step explanation:
Put the equation into center-radius form.
x² + y² + 8x - 12y + 24 = 0
x² + y² + 8x - 12y = -24
(x²+8x) + (y²-12y) = -24
(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24
(x+4)² + (y-6)² = 28
Center: (-4,6)
radius: √28
So for this problem, I almost got it however my rounding is off causing my answers to be wrong. Can someone please help me with the two that are wrong. Thank you for your help!
Answer:
it 94x26.2 i think it right if not sorry :/
Step-by-step explanation:
Select the correct answer.
Each statement describes a transformation of the graph of y=x. Which statement correctly describes the graph of y= x - 13?
OA. It is the graph of y= x translated 13 units to the right.
OB. It is the graph of y=xwhere the slope is decreased by 13.
It is the graph of y= x translated 13 units to the left.
OD. It is the graph of y= x translated 13 units up.
ОС.
minus sign ironically makes it go to the right
because the function crosses the y axis at -13
It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of transformation, we have to compare the two equations and look for changes.
In the equation y = x - 13, we subtract 13 from the value of x.
This means that the graph of y = x is shifted 13 units downwards,
since every point on the graph has 13 subtracted from its y-coordinate.
Hence, It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
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Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
d^2y/ dx^2 − 6 dy/dx + 9y = 0; y = c1e3x + c2xe3x When y = c1e3x + c2xe3x,
y'' - 6y' + 9y = 0
If y = C₁ exp(3x) + C₂ x exp(3x), then
y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))
y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))
Substituting these into the DE gives
(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))
… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))
… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))
= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))
… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))
… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)
= 0
so the provided solution does satisfy the DE.
A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)
Answer:
A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum.
Step-by-step explanation:
according to the fundemental theorem of algebra, how many roots exist for the polynomial function? f(x) = (x^3-3x+1)^2
Answer:
6
Step-by-step explanation:
First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.
Expanding, we get
(x³-3x+1)² = (x³-3x+1)(x³-3x+1)
= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1
= x^6 - 6x^4 + 2x³ +9x²-6x + 1
In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots
which transformation of the red triangle on the graph maps it into the missing peice of the square?
A. a translation 16 units right
B. a reflection across the y-axis
C. a 90° counterclockwise rotation about the origin
D. a 90° clockwise rotation about the origin
E. a 180° rotation about the origin
Answer:
D
The missing piece (triangle) is facing right side up but the red triangle has its point facing left
TO get it facing up, turn it by 90 degrees clockwise
Triangles P Q R and S T U are shown. Angles P R Q and T S U are right angles. The length of P Q is 20, the length of Q R is 16, and the length of P R is 12. The length of S T is 30, the length of T U is 34, and the length of S U is 16.
Using the side lengths of △PQR and △STU, which angle has a sine ratio of Four-fifths?
∠P
∠Q
∠T
∠U
Answer:
[tex]\angle P[/tex]
Step-by-step explanation:
Given
[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]
[tex]PQ = 20[/tex] [tex]QR = 16[/tex] [tex]PR = 12[/tex]
[tex]ST = 30[/tex] [tex]TU = 34[/tex] [tex]SU = 16[/tex]
See attachment
Required
Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]
Considering [tex]\triangle PQR[/tex]
We have:
[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse
So, we have:
[tex]\sin(P) = \frac{16}{20}[/tex]
Divide by 4
[tex]\sin(P) = \frac{4}{5}[/tex]
Hence:
[tex]\angle P[/tex] is correct
Answer:
A or <P
Step-by-step explanation:
on edge 2021
What is the answer to this? Is it d?
Answer:
Step-by-step explanation:
yeah of course..your answer is true.. it's part d and there is no solution for that system...w and v both of them remove in solution of system and we don't have any unknown variable for solving.
9514 1404 393
Answer:
D. no solutions
Step-by-step explanation:
The first equation can be simplified to standard form:
0.5(8w +2v) = 3
4w +v = 3 . . . . . . . eliminate parentheses
__
The second equation can also be simplified to a comparable standard form:
8w = 2 -v +4w
4w +v = 2 . . . . . . add v -4w
__
Comparing these two equations, we find the variable expressions to be the same, but the constants to be different. If any set of variable values were to satisfy one of these equations, it could not satisfy the other equation. There are no solutions to the system.
Answer ASAP
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More information pleaseeeeeeee
A friend wants to buy a pool and has two places she wants to purchase the pool with the largest volume which pool should she buy a rectangular pool that is 20' x 15' in 54 inches deep or a cylindrical pool that has a 3.3 m radios and is 1.8 m deep
Answer:
20'×15 in 54 inches
Step-by-step explanation:
The Best as a pool should be rectangular in shape and 54inches deep for safety of life's
The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.
What is the volume of a cylinder?The volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = [tex]\pi r^{2}[/tex]h
The volume of the cylindrical pool that has a 3.3 m radius and is 1.8 m deep is;
= [tex]\pi r^{2}[/tex]h
[tex]= 3.14 (3.3)^2 (1.8)\\\\= 61.55 m^3[/tex]
The volume of the rectangular pool that is 20' x 15' in 54 inches deep ;
V = 20 x 15 x 54
V = 16,200 cubic meter.
The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.
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a+b=60000
[tex]\frac{a}{b}=\frac{4}{1}[/tex]
a=?
b=?
Answer: a = 25.67
Step-by-step explanation:
X = The set of months in a year?
there are 12 set of months in a year
The elevation E, in meters, above sea level at which the boiling point of a certain liquid ist degrees Celsius is given by the function shown below. At what elevation is the boling point 99.5*7 100°?
E() - 1200(100-1) • 580(100 - 1)
At what elevation is the boiling point 99.5?
E (90.5*)=. meters
At what elevation is the boiling point 100"?
E(100*)-meters
Answer:
Given E(t)=1100(100-t)+580(100-t)^2
Put t = 99.5, we get
E(99.5)=1100(100-99.5)+580(100-99.5)^2
E(99.5)=1100(0.5)+580(0.5)^2
E(99.5)=1100(0.5)+580(0.25)
E(99.5)=550+145
E(99.5)=695m
Step-by-step explanation:
It can be concluded that -
E(99.5) = 695
E(100) = 0
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the function as follows -
E(t) = 1100(100 - t) + 580(100 - t)²
The given function is -
E(t) = 1100(100 - t) + 580(100 - t)²
At → E(99.5)
E(99.5) = 1100(100 - t) + 580(100 - t)²
E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²
E(99.5) = 1100(0.5) + 580(0.5)²
E(99.5) = 550 + 145
E(99.5) = 695
At → E(100)
E(100) = 1100(100 - t) + 580(100 - t)²
E(100) = 1100(100 - 100) + 580(100 - 100)²
E(100) = 0
Therefore, it can be concluded that -
E(99.5) = 695
E(100) = 0
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How many tens are in 6 hundreds
Answer:
60
Step-by-step explanation:
10 x 6 = 60
Hope this helped! :)
HELP ME WITH THIS MATHS QUESTION
PICTURE IS ATTACHED
Answer:
In picture.
Step-by-step explanation:
To do this answer, you need to count the boxes up to the mirror line. This will give us the exact place to draw the triangle.
The picture below is the answer.
please help, it’s urgent !!!
D
A
B
C
for more explanation please don't hesitate to just respond