[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2)~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^3-125=0\implies x^3-5^3=0\implies (x-5)(x^2+5x+5^2)=0 \\\\[-0.35em] ~\dotfill\\\\ x-5=0\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula}[/tex]
[tex]\bf \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{+25} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{-5\pm\sqrt{5^2-4(1)(25)}}{2(1)}\implies x=\cfrac{-5\pm\sqrt{25-100}}{2} \\\\\\ x=\cfrac{-5\pm\sqrt{-75}}{2}~~ \begin{cases} 75=&3\cdot 5\cdot 5\\ &3\cdot 5^2 \end{cases}\implies x=\cfrac{-5\pm\sqrt{-3\cdot 5^2}}{2}[/tex]
[tex]\bf x=\cfrac{-5\pm 5\sqrt{-3}}{2}\implies x=\cfrac{-5\pm 5\sqrt{-1\cdot 3}}{2}\implies x=\cfrac{-5\pm 5\sqrt{-1}\cdot \sqrt{3}}{2} \\\\\\ x=\cfrac{-5\pm 5i\sqrt{3}}{2}\implies \boxed{x= \begin{cases} \frac{-5+ 5i\sqrt{3}}{2}\\\\ \frac{-5-5i\sqrt{3}}{2} \end{cases}}[/tex]
To solve the complex number equation x^3-125=0, we rearrange to x^3=125 and apply the rule for cube roots in the complex system. This yields three solutions: x = 5, x = 5*omega, and x = 5*omega^2.
Explanation:The given equation is x^{3}-125=0. It belongs to the category of complex number equations within the complex system. We can solve this equation step-by-step by using the cube root of unity in the complex number system.
Firstly, move '125' to the right side of the equation: x^{3}=125. We find that x is the cube root of 125. The solutions to this kind of equation are given by a rule in the complex number system that the cube roots of a number a are given by [a^(1/3), a^(1/3)*omega, a^(1/3)*omega^2], where omega is a cube root of unity and equals -1/2+sqrt(3)i/2 and omega^2=-1/2-sqrt(3)i/2 .
Therefore for x^{3}=125, we get x = 5, 5*omega, and 5*omega^2. These are the solutions in the complex number system.
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If three points are collinear they are also coplanar truth or false
Answer:
TRUE
Step-by-step explanation:
APE-X
The statement is true. Three points are collinear if they lie on the same line. Since a line exists within a plane, those points would also exist within that plane, making them coplanar.
Explanation:The statement 'If three points are collinear they are also coplanar' is indeed true.
Here's why: Points are said to be collinear if they lie on the same line. A line, by definition, exists within a plane, so any points on that line would also exist within that same plane, which means they are coplanar.
For example, imagine a piece of paper. This paper represents a plane. Draw a line across the paper and mark three points on that line. The three points are collinear because they are on the same line. Since the line is on a plane (the paper), the points are also coplanar.
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Solve the expression for x: (4 – 2) (x – 2) = 4x – 8 A. x = –2 B. x = 0 C. x = 6/5 D. x = 2
Answer:
Option D) x = 2
Step-by-step explanation:
(4-2)(x-2) = 4x - 8
Distribute and simplify 4-2
2(x-2) = 4x - 8
2x-4 = 4x -8
Subtract 2x on both sides and add 8 on both sies
4x - 8 = 2x-4
2x= 4
Divide 2 on both sides
x = 2
Please mark for Brainliest!! :D Thanks!!
For more questions or more information, please comment below!
Write a recursive sequence that represents the sequence defined by the following explicit formula:
Answer:
0,-2,-4,-6,-8, ...
Step-by-step explanation:
In order to find the sequence represented by the given explicit formula we have to plug in the values of n
Given formula is:
[tex]a_n=2-2n\\a_1=2-2(1)\\=2-2=0\\a_2=2-2(2)\\=2-4\\=-2\\a_3=2-2(3)\\=2-6\\=-4\\a_4=2-2(4)\\=2-8\\=-6\\a_5=2-2(5)\\=2-10\\=-8[/tex]
So the explicit sequence is:
0,-2,-4,-6,-8,..........
Answer:
kmkmlklm
Step-by-step explanation:
The Millers drove 150 miles in 3 hours. At this rate, how long will it take them to drive 400 miles?
Answer:
It will take 8 hours to drive 400 miles
Step-by-step explanation:
The millers drive 50 miles an hour. So we can write the proportion 1/50 = x/400. Then we solve for x and get 8 hours.
Answer:
The answer is 8!
Step-by-step explanation:
It will take 8 hours to drive 400 miles
The millers drive 50 miles an hour. So we can write the proportion 1/50 = x/400. Then we solve for x and get 8 hours.
What equation results from completing the square and then factoring? X 2 + 4x = 7 A. (x + 4)2 = 3 B. (x + 2)2 = 3 C. (x + 4)2 = 11 D. (x + 2)2 = 11
Mary invests £12000 in a savings account
the account pays 1.5% compound interest per year
Work out the value of her investment after 2 years
PLEASE HELP AND SHOW ALL YOUR WORKING BRAINLIEST
Answer:
First of all , 12000 multiply with 1.5 percent and with the answer times it with 2 and with the answer add with 360
#hope it helps
Step-by-step explanation:
12000×1.5%
=180
180×2
=360
12000+360
= 12360
#hope it helps
Explain the difference between function and relation and the relationship between the domain and the range of a function.
Given two sets X and Y, a relation between X and Y freely associates elements of X with elements of Y, with no restrictions.
A function is a relation with some restrictions: there must be exactly one element of Y connected with each element of X.
The set X is called the domain of the function, and it represents all the possible inputs that we can feed the function with. As we just said, every element of the domain must have a correlated element in Y.
The set Y is called the range of the function, and it represents all the possible outputs that the function can return.
The difference between function and relation and the relationship between the domain and the range of a function is discussed below
What is domain and range?The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
Let there be an X set and a Y set. An ordered pair (x,y) is called a relation in x and y. The first element in an ordered pair is called the domain, and the set of second elements is called the range of the relation.
A function is a particular kind of relation between sets. A function takes every element x in a starting set, called the domain, and tells us how to assign it to exactly one element y in an ending set, called the range.
For example, each person is in the following table is paired with a number representing his or her height:
Alex → 180 Claudia → 165 Gilbert → 204 Judith → 165
The given relation {(Alex, 180), (Claudia, 165), (Gilbert, 204), (Judith, 165)} is a function as every person is pairs with exactly one number, their height. The domain is (Alex, Claudia, Gilbert, Judith). The range is (165, 180, 204).
The domain is the input, the independent value—it's what goes into a function. The range is the output, the dependent value—it's what comes out. Domain and range may be limited to a few discrete values, or they may include all numbers everywhere, to infinity and beyond.
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The slope of diagonal AB is? And it’s equation is? Please help!
Answer:
0
y = -2
Step-by-step explanation:
The formula for the slope is (in general) Δy / Δx Since the value of y does not change (I'm assuming we are talking about AB), the slope is (-2 - - 2) / (2 - -2) = 0/4 = 0
So the equation of the line is
y = mx + b
m = 0
y = 0*x - 2
y = - 2 <<<< Equation
Answer:
Slope = 0
Equation:
[tex]y = -2[/tex]
Step-by-step explanation:
Note that the diagonal AB is a horizontal line parallel to the x axis. The Slope m of a line is a measure of how the function f(x) changes when x increases or decreases.
Note, however, that horizontal lines such as segment AB do not change and their value of y does not depend on the value of x. Therefore all horizontal lines have slope m = 0.
Finally, the equation of line AB is
[tex]y = -2[/tex]
19. Find the current in a circuit if the power is 500 W (watts) and the resistance is 25 ohms. Round off your answer to two decimal places. Use the formula .
A. 4.47 A
B. 0.22 A
C. 20 A
D. 0.05 A
For this case we have by definition, that the electrical power is given by:
[tex]P = I ^ 2 * R[/tex]
Where:
P: It's the power
I: It's the current
R: It's the resistance
Clearing the current:
[tex]I ^ 2 = \frac {P} {R}\\I = \pm \sqrt {\frac {P} {R}}[/tex]
We choose the positive value:
[tex]I = \sqrt {\frac {500} {25}}\\I = \sqrt {20}\\I = 4.47A[/tex]
ANswer:
Option A
NEED ANSWER ASAP! 50 PTS!
Which of the following would best represent a sine function with an amplitude of 7, a period of pi over 4 , and a midline at y = 3? (1 point)
f(x) = 7 sin 8x + 3
f(x) = 3 sin 8x + 7
f(x) = 7 sin( pi over 4 x) + 3
f(x) = 3 sin( pi over 4 x) + 7
Answer:
f(x) = 7 sin 8x + 3 ⇒ 1st answer
Step-by-step explanation:
* Lets revise the trigonometry translation
- If the equation is y = A sin (B x + C) + D
* A is the amplitude
- The amplitude is the height from highest to lowest points and
divide the answer by 2
* The period is 2π/B
- The period is the distance from one peak to the next peak
* C is the horizontal shift
- The horizontal shift is how far the function is shifted to left
(C is positive) or to right (C is negative) from the original position.
* D is the vertical shift
- The vertical shift is how far the function is shifted vertically up
(D is positive) or down (D is negative) from the original position.
- The equation of the mid-line is y = D
* Now lets solve the problem
∵ f(x) = A sin(Bx + C) + D
∵ The amplitude is 7
∴ A = 7
∵ The period is 2π/B
∵ The period is π/4
∴ 2π/B = π/4 ⇒ divide both sides by π
∴ 2/B = 1/4 ⇒ Use cross multiplication
∴ B × 1 = 2 × 4
∴ B = 8
∵ The equation of the mid-line is y = D
∵ The equation of the mid-line is y = 3
∴ D = 3
- There is no mention for C
∴ C = 0
∴ f(x) = 7 sin 8x + 3
What number must you add to complete the square?
x^2 + 12x = 16
Answer: B. 36
The complete square is (x+6)^2. It's missing the third term, which is 36 because 6 x 6 is 36.
ANSWER
B. 36
EXPLANATION
The given quadratic expression is:
[tex] {x}^{2} + 12x = 16[/tex]
To complete the square we add the square of half the coefficient of x.
The coefficient of x is 12.
Half of it is 6.
The square of 6 is 36.
Therefore we add 36 to both sides of the equation to complete the square.
The correct answer is B.
A research company is looking at the correlation between the years since 1970 and the average amount of years that couples stay married. Use complete sentences to explain how the data below indicates a non-linear model.
Time (in years) since 1970: 0, 10, 20, 30, 40
Average age of a marriage (yrs.): 10, 11.2, 13.9, 17.2, 29
Answer and Step-by-step explanation:
Since we have given that
Time Average age of a marriage
0 10
10 11.2
20 13.9
30 17.2
40 29
We need to show that the above data indicated a non linear model.
For this it is enough to show that slope is different:
So, we consider the slope for first 2 points:
(0,10) and (10,11.2)
So, slope becomes
[tex]m_1=\dfrac{y_2y_1}{x_2-x_1}=\dfrac{11.2-10}{10-0}=\dfrac{1.2}{10}=0.12[/tex]
and similarly, (10,11.2) and (20,13.9)
[tex]m_2=\dfrac{y_2-y_}{x_2-x_1}\\m_2=\dfra{13.9-11.2}{20-10}=\dfrac{2.7}{10}=0.27[/tex]
so, [tex]m_1\neq m_2[/tex]
So, it becomes non linear model.
Solve the equation by graphing.
m^2 = 2m + 8
Answer:
m= 4, -2
Step-by-step explanation:
move everything to one side.
m^2-2m-8=0
then factor
(m-4)(m+2)
then
m= 4, -2
hope this helps!
Answer:
Step-by-step explanation:
Forest covers an area of 3400 km^2. Each year this area decreases by 7.25%. What will the area be after 13 years
Area of 3400 decreases by 7.25%.
Rewrite 7.25% as a decimal.
This leads to 0.0725.
So, (3400)(0.0725) = 246.5.
Now (246.5)(13 years) = 3,276.
The area after 13 years will be
3,276 km^2.
URGENT PLEASE HELP ME WITH THIS MATH QUESTION
Answer:4
Step-by-step explanation: 6 times 6 divide by 9
Multiply the denominators across and Multiply the numerators across
x/6= 6/9
9x= 36
x= 4
Check answer by using substitution method
x/6= 6/9
4/6= 6/9
Divide by 2 for 4/6
Divide by 3 for 6/9
2/3= 2/3
Answer is x= 4
Identify whether the figure has plane symmetry, symmetry about an axis, or neither. HELP ASAP!!
Answer: B) plane symmetry and symmetry about an axis
Step-by-step explanation: Please see the image below!
The figure has plane symmetry and symmetry about an axis option second “plane symmetry and symmetry about an axis” is correct.
What is a line of symmetry?It is defined as the line which will make exactly two halves with similar shape and size in the geometry. For two-dimensional shape there is a line of symmetry, and for the three-dimensional shapes there is a plane of symmetry. In other words, if we make a mirror image of the shape around the line of symmetry, we will get exactly the same half portion.
We have a three-dimensional figure shown in the figure.
If a plane can divide a three-dimensional figure into two congruent mirrored halves, the figure possesses plane symmetry.
As a result, there are two plane symmetries in the provided figure.
If there is a line around which a three-dimensional figure may be rotated by an angle higher than 0° but less than 360° so that the image coincides with the preimage, the figure has symmetry at that axis.
As a result, the following figure displays axis symmetry. As a result, the figure features plane symmetry as well as axis symmetry.
Thus, the figure has plane symmetry and symmetry about an axis option second “plane symmetry and symmetry about an axis” is correct.
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Please answer this multiple choice question correctly for 30 points and brainliest!!
Answer:
A
Step-by-step explanation:
it has to do with the people's ethnics or standard or values.
The statement is not ambiguous so it has no language barrier
Answer:
C. use of language
Step-by-step explanation:
The descriptor "childish" will likely influence results. Most Grade 9 students prefer not to be thought of as "childish."
Need help with translating and reflection
Answer:
I think it's -5, 3
Step-by-step explanation:
since it's four units down that would be 5, 3
next, since you need to reflect on the other side of the y axis, it would be -5, 3
hope this helps :)
Answer:
(-5, 3)
Step-by-step explanation:
We are given a point [tex] ( 5 , 7 ) [/tex].
When we translate this given point four units down, it means that its x coordinate will remain the same while 4 units will be subtracted from the y coordinate to get:
[tex] ( 5 , 7 ) \times (5, 3) [/tex]
Now this point [tex] ( 5 , 3 ) [/tex] is to be reflected over the y axis so the y coordinate will remain the same but the x coordinate will change its sign.
So we get:
(-5, 3)
Find the slope of a line given the following points
Answer:
-6/5
Step-by-step explanation:
The slope is computed from ...
slope = (change in y)/(change in x)
= (-2 -4)/(3 -(-2)) = -6/5
Answer:
[tex]-\frac{6}{5}[/tex]
Step-by-step explanation:
Pre-SolvingWe are given the points (-2,4) and (3, -2).
We want to find the slope (m) of this line.
SolvingThe slope can be found using the following formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points.
Even though we are already given the points, we can label the values of them to avoid confusion and mistakes.
[tex]x_1=-2\\y_1=4\\x_2=3\\y_2=-2[/tex]
Now, substitute the values of the points into the formula. Remember that we have negative numbers.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-2-4}{3--2}[/tex]
[tex]m=\frac{-6}{3+2}[/tex]
[tex]m=\frac{-6}{5}[/tex]
The slope of the line is [tex]-\frac{6}{5}[/tex].
You dug a hole that was 8 feet deep. After taking a short break, you dug down 3 more feet in the same hole. When finished digging, a tractor accidentally filled the hole with 4 feet of dirt. How deep is your hole now?
The hole which was initially 8 feet deep and then extended by 3 more feet got partially filled by 4 feet of dirt by a tractor, resulting in a total remaining depth of 7 feet.
Explanation:Your question is a simplifying numerical values scenario. First, you dug a hole that was 8 feet deep. Next, you dug an additional 3 feet, so you would add these two values together to get a total depth of 11 feet (8 + 3). Finally, a tractor accidentally filled 4 feet of the hole with dirt. Subtracting this from the total depth of the hole means your hole is now 7 feet deep (11 - 4).
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PLease help! timedd
Find the angle between u = sqr5i-8J and v = sqr5i+j. Round to the nearest tenth of a degree. (the square root is only on the 5i in both)
A.65.9
B.98.5
C.90.4
D33.3
Use the dot product to find [v] when v =(-2,-1)
A.-1
b.-3
c;sqr5
dsqr3
Answer:
98.5 degrees
Step-by-step explanation:
To find the angle measurement between two vectors use: cos(theta)=(u dot v)/(|u|*|v|)
The vectors are u=sqrt(5)i-8j and v=sqrt(5)i+1j .
So find the dot product of u and v. u dot v=sqrt5*sqrt(5)+(-8)*(1)=5-8=-3.
Second step: Find the magnitude of both vectors. So to find the magnitude of a vector, let's call it t when t=ai+bj, you just do |t|=sqrt(a^2+b^2).
|u|=sqrt(5+64)=sqrt(69) and |v|=sqrt(5+1)=sqrt(6)
Now multiply your magnitudes of your vectors: sqrt(69)*sqrt(6)=sqrt(414).
So now we have:
cos(theta)=-3/sqrt(414)
Now arccos( ) or cos^(-1) to find the angle theta.
theta=cos^(-1)[-3/sqrt(414)] which is approximately 98.5 degrees.
Answer:
Ans 1) The correct option is B) 98.5
Ans 2) The correct option is C) [tex]\sqrt{5}[/tex]
Step-by-step explanation:
The angle measurement between two vectors by:
[tex]cos(\theta)=\frac{(u.v)}{(|u|\times |v|)}[/tex]
Magnitude of vector t=ai+bj, calculated by:
[tex]|t|=\sqrt{a^{2}+b^{2}}[/tex]
The given vectors are [tex]u=\sqrt{5}i-8j[/tex] and [tex]v=\sqrt{5}i+1j[/tex]
First find the dot product of u and v;
[tex]u.v=(\sqrt{5}i-8j)(\sqrt{5}i+1j) = 5-8= - 3[/tex]
Now, Find the magnitude of both vectors u and v.
[tex]|u|=\sqrt{(\sqrt{5})^{2}+8^{2}}[/tex]
[tex]|u|=\sqrt{5+64}[/tex]
[tex]|u|=\sqrt{69}[/tex]
and
[tex]|v|=\sqrt{(\sqrt{5})^{2}+1^{2}}[/tex]
[tex]|v|=\sqrt{5+1}[/tex]
[tex]|v|=\sqrt{6}[/tex]
Now, put the all values in [tex]cos(\theta)=\frac{(u.v)}{(|u|\times |v|)}[/tex]
[tex]cos(\theta)=\frac{-3}{\sqrt{69} \times \sqrt{6}}[/tex]
[tex]=\frac{-3}{414}[/tex]
take arc cos both the sides,
[tex]\theta=cos^{-1} \frac{-3}{\414}[/tex]
[tex]\theta=98.5 \degree[/tex] (approx)
Therefore, the correct option is B) 98.5
Ans 2) calculate IvI by
If t= ai +bj then magnitute is [tex]\sqrt{a^{2}+b^{2}}[/tex]
Given : v = (-2,-1)
it means v = -2i -1 j
[tex]|v| =\sqrt{(-2)^{2}+(-1)^{2}}[/tex]
[tex]|v| =\sqrt{4+1}[/tex]
[tex]|v| =\sqrt{5}[/tex]
Therefore, the correct option is C) [tex]\sqrt{5}[/tex]
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
y= -6x + 6
y= 3x - 3
Answer:
one solution: (x, y) = (1, 0)
Step-by-step explanation:
See below for a graph with the one solution identified.
Answer:
The system has one solution at (1,0).
Step-by-step explanation:
Consider the provided system of equations
y=-6x+6
Substitute x = 0 in above equation.
y=-6(0)+6
y=6
The coordinate is (0,6)
Now substitute y=0 in the above equation.
0=-6x+6
-6=-6x
x=1
The coordinate is (1,0)
Now use the coordinates (0,6) and (1,0) in order to draw the graph.
The graph of y= -6x + 6 is shown in figure 1.
Similarly, consider the second equation y= 3x - 3
Substitute x = 0 in above equation.
y=3(0)-3
y=-3
The coordinate is (0,-3)
Now substitute y=0 in the above equation.
0=3x-3
3=3x
x=1
The coordinate is (1,0)
The graph of y= 3x - 3 is shown in figure 2.
Now draw the graph of both equation as shown in figure 3.
By observing the graph it can be concluded that the system has one solution at (1,0)
Hence, the system has one solution at (1,0).
which is an equation of the line containing the points (2, 5) and (4, 4) in standard form?
-2x+5y=12
2x+y=12
x+2y=12
-x+2y=8
Answer:
x +2y = 12
Step-by-step explanation:
Try the given points in the given equations and see what works.
-2x + 5y at (2, 5) is -2(2) +5(5) = 21 ≠ 12
) +) 2x + y at (2, 5) = 2(2) +(5) = 9 ≠ 12
x + 2y at (2, 5) = 2 +2(5) = 12 . . . . . goes through first point
x + 2y at (4, 4) = 4 + 2(4) = 12 . . . . goes through second point
__
You know the answer at this point, so the next check is just for "completeness." It is not necessary to properly answer the question.
-x +2y at (2, 5) = -(2) +2(5) = 8 . . . . goes through first point
-x +2y at (4, 4) = -(4) + 4(4) = 4 ≠ 8 . . . does not go through second point
Please help me with this
Answer:
7. B) 26–35
8. C) 31/77
Step-by-step explanation:
7. It's a matter of writing the fractions in a way that lets you compare their values. It is usually convenient to convert them to decimal:
(age group, healthy fraction)
(18–25, 9/48 = 0.1875)
(26–35, 16/98 ≈ 0.1633)
(36–45, 19/94 ≈ 0.2021)
(> 45, 12/60 = 0.2000)
The group with the smallest percentage of healthy blood sugar is 26–35.
__
8. There are 94+60 = 154 study participants who are at least 36. Of those, 35+27 = 62 are at risk for diabetes. That ratio is ...
62/154 = 31/77
A _____ is accepted to be true without proof, while a _____ is an assertion that can be proven using the rules of logic.A.theorem; problemB.given; postulateC.postulate; theoremD.theorem; postulate
Answer:
C. postulate; theorem
Step-by-step explanation:
While a "given" is taken as true without proof, and a "problem" sometimes involves an assertion that can be proven, the answer choices involving these terms are not correct here.
The dictionary definitions of "postulate" and "theorem" apply. It is useful to learn the meaning of these terms so you can understand problems and descriptions that use them.
Find three consecutive even integers such that the sum is of the least and the middle is 48 more than the greatest
Answer:
50, 52, and 54
Step-by-step explanation:
The three even integers are x, x+2, and x+4. The sum of the least two is 48 more than the greatest:
x + x+2 = x+4 + 48
2x + 2 = x + 52
x = 50
So the three integers are 50, 52, and 54.
3. As the angle θ increases to 90° the value of tan(θ)
A. approaches +1.
B. decreases rapidly.
C. increases rapidly.
D. approaches –1.
Answer:
C. increases rapidly.
Step-by-step explanation:
tan(θ) = sin(θ)/cos(θ)
Now, when sin 90 = 1
and cos 90 = 0
so, tan(90) = 1/0 = not defined.
(1/0 is infinity and its value is not defined)
So, when angle θ increases to 90°, then the value of tan(θ) increases rapidly, as shown in the figure below.
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The graph below shows two normal distributions.
What is the difference of the means of the distributions?
Answer:
15
Step-by-step explanation:
The mean of the first graph comes to be the point at which the graph reaches its highest point.
The mean of the blue graph is: μ = 30
The mean of the blue graph is: μ = 45
The difference of the means of the distributions is: 45 - 30 = 15
Answer:
15
Step-by-step explanation:
Given the following: f(a) = x2 - 8x + 4; g(x) = 4x – 3; and h(x) = x + 2.
Complete the following:(h.g)(x)
4x2 + 5x – 6
-22 + 12x - 7
22 – 12x +7
4x3 – 35x2 + 403 - 1
Answer:
(h.g)(x) = 4x^2 + 5x - 6
Step-by-step explanation:
Given the following: f(a) = x^2 - 8x + 4; g(x) = 4x – 3; and h(x) = x + 2.
(h.g)(x) = (4x – 3)(x + 2)
(h.g)(x) = 4x^2 + 8x - 3x - 6
(h.g)(x) = 4x^2 + 5x - 6
The value of (h . g)(x) is 4x² + 5x - 6.
What is composite function?A function whose values are found from two given functions by applying one function to an independent variable and then applying the second function to the result and whose domain consists of those values of the independent variable for which the result yielded by the first function lies in the domain of the second.
Given:
f(x) = x² - 8x + 4; g(x) = 4x – 3; and h(x) = x + 2.
Now,
(h . g)(x) = (4x – 3)(x + 2)
(h . g)(x) = 4x² + 8x - 3x - 6
(h . g)(x) = 4x² + 5x - 6
Hence, (h . g)(x)= 4x² + 5x - 6.
Learn more about composite function here:
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Write an equation that can be used to find the atmospheric temperature T, at an altitude A.
The Table
Altitude- 0 2000 4000 6000 8000
Temp. - 88 81 74 67 60
Answer:
T = 88 -(7/2000)A
Step-by-step explanation:
The table values have a constant difference of +2000 ft and -7 degrees, so the slope of the linear equation is -7/2000 degrees per ft. The temperature is 88 at an altitude of 0, so we can write the requested equation in slope-intercept form as ...
T = 88 -(7/2000)A
_____
The slope-intercept form of the equation for a line is ...
y = mx + b
where m is the slope and b is the y-intercept. In this equation, y is the dependent variable and x is the independent variable. For our temperature equation, the dependent variable is T, and the independent variable is A.