The limit as a definite integral on the interval [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π , 4π] is [tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex].
What is meant by definite integral?
A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.
Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.
If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.
Let the equation be
[tex]$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$[/tex]
substitute the values in the above equation, we get
= [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π, 4π],
simplifying the above equation
[tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex]
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Which parent functions have a domain of all real values of x? Select all that
apply.
A. Reciprocal
B. Cubic
C. Quadratic
D. Cube root
E. Linear
F. Absolute value
Answer:
A D F
Step-by-step explanation:
The parent functions with a domain of all real values of x are the linear function, the absolute value function, the square root function, and the cube root function.
The linear function is defined by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The domain of this function is all real values of x.
The absolute value function is defined by the equation y = |x|, where |x| is the absolute value of x. The domain of this function is all real values of x.
The square root function is defined by the equation y = √x, where √x is the square root of x. The domain of this function is all nonnegative real values of x.
The cube root function is defined by the equation y = ∛x, where ∛x is the cube root of x. The domain of this function is all nonnegative real values of x.
Therefore, the correct answers are A, D, and F. The reciprocal function, the cubic function, and the quadratic function do not have a domain of all real values of x.
write the equation of the line in slope-int form that is perpendicular to y=-x - 18 and passes through (-6,11)
Answer:
y = x + 17
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x - 18 ← is in slope- intercept form
with slope m = - 1
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1 , then
y = x + c ← is the partial equation of the perpendicular line
to find c substitute (- 6, 11 ) into the partial equation
11 = - 6 + c ⇒ c = 11 + 6 = 17
y = x + 17 ← equation of perpendicular line
Draw the net diagram of the the 3-object below and determine the total surface area
Answer:
see below for the netarea: 168 cm²Step-by-step explanation:
You want the net and total surface area for the triangular prism shown.
NetThe net diagram is attached. It consists of three rectangles with triangles attached to the ends of the widest rectangle. Of course, these parts can be arranged in any order you find convenient, as long as the common edges match the original prism.
AreaThe net shows the area can be computed as the sum of a rectangle 9 cm high and 5+6+5 = 16 cm wide, together with two triangles of base 6 cm and height 4 cm.
A = (9 cm)(16 cm) +2(1/2)(6 cm)(4 cm)
= 144 cm² +24 cm²
= 168 cm²
The total surface area of the prism is 168 cm².
__
Additional comment
The formulas for the area of a rectangle and triangle are ...
A = LW . . . . . area of a rectangle of length L and width W
A = 1/2bh . . . . area of a triangle of base b and height h
data shows that the united states has less intergenerational mobility than germany. that means that:
The data shows that United States has less intergenerational mobility than Germany this data means that the success of the children of United States depends more on the parents income status in comparison to Germany.
Intergeneration mobility is the extent to which the outcomes of the doings of an individual are different in comparison to his or her parents. This basically means the extent to which an individual is gaining something by his own potential.
According to the data United States has less intergeneration mobility in comparison to the intergenerational mobility of Germany.
From this data that outcomes of a children born in United States depends highly on the parents economic and financial status than German kids.
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if you select a random sample of full-time college students, there is an hance that the sample mean is less than how many hours per week?
The sample mean is less than 26.92 hours per week .
What is standard deviation?
Your dataset's average level of variability is represented by the standard deviation. In general, it reveals how far away from the mean each value is.
A low standard deviation denotes that values are grouped closely to the mean, while a high standard deviation denotes that values are typically spread widely from the mean.
Let X~ Normal (26, 4/√16) distribution ie Normal (26, 1) distribution
We want,
P(X<a) = 0.82
Using standard normal approximation,
P(z< (a-26)/1) = 0.82
Using standard normal distribution tables, we get
(a-26)/1 = 0.915
(Since P(z<0.915) = 0.82)
So, a= 26+0.915= 26.915
So the required value is 26.92 (rounded to two decimals)
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Jerry bulit a table with a square top. the perimeter of the tabletop is 18 feet. He knows that the side lentgh of the table is 3, 3 1/4 4 or 4 1/2 use the equation 18 = 4s where s is the side length of the table to determine the side length explain how you found your answer
Answer:
4 1/2 ft
Step-by-step explanation:
18 = 4s
Divide both sides by 4.
18/4 = 4s/4
9/2 = s
4 1/2 = s
The side of the table is 4 1/2 ft.
How do you write 3/4 as a percent?
Answer:
0.75 or 75%
Step-by-step explanation:
I know that 2/4 is 0.5 or 50% and 1/4 is 0.25 or 25% so it goes by 25. One more than 2/4 is 3/4, which is what you are trying to find, so it would be 0.75, or 75%.
Solve the equation for a. K = 4a + 9ab a = K(4 + 9b) a = 4(K + ...
The equation K = 4a + 9ab solved for a is a = K /(4 + 9b). (Option D)
In mathematics, an equation refers to a formula that expresses the equality of two mathematical expressions by connecting them with the equals sign =.
The given equation is K = 4a + 9ab.
In order to solve for a, the a variable must be isolated at one side of the equation and the other variables must be collected on the other sides.
On the right-hand side, as both terms contain the variable a, hence factoring it,
K = a(4 + 9b)
Dividing both sides by (4 + 9b) to isolate a,
a = K /(4 + 9b)
Note: The question is incomplete. The complete question probably is: Solve the equation for a in K = 4a + 9ab. A) a = K(4 + 9b) B) a = 4(K + 9b) C) a = (4 + 9b)/K D) K /(4 + 9b)
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radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute. what is the rate of change of the surface area when the radius is 6 inches and the height is 18 inches?
The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.
Given:
radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.
we are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.
we have dr/dt = 6 in/min and dh/dt = -4 in/min
Volume, V = πr²h
Differentiate the above expression to get:
dV/dt = 2πrh dr/dt + πr² dh/dt
SUbstitute the value we get:
dV/dt = 2π(6)(18)(6) + π(6)²(-4)
= 4069.44 - 452.16
= 3617.28 in³ per minute.
The volume is increasing at a rate of 3617.28 in³ per minute.
Area = 2πr(h+r)
Differentiate the above expression:
dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}
dA/dt = 2π {(18+6)(6) + 6(-4+6)}
= 2π(144 + 12)
= 312π
= 979.68 in² per minute.
The area is increasing at a rate of 979.68 in² per minute.
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The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.
Given:
The radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.
We are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.
We have dr/dt = 6 in/min and dh/dt = -4 in/min
In geometry, it is defined as a three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
Volume, V = πr²h
Differentiate the above expression to get:
dV/dt = 2πrh dr/dt + πr² dh/dt
Substitute the value we get:
dV/dt = 2π*6*18*6 + π*6² * -4
= 4069.44 - 452.16
= 3617.28 in³ per minute.
The volume is increasing at a rate of 3617.28 in³ per minute.
Area = 2πr(h+r)
Differentiate the above expression:
dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}
dA/dt = 2π {(18+6)(6) + 6(-4+6)}
= 2π(144 + 12)
= 312π
= 979.68 in² per minute.
The area is increasing at a rate of 979.68 in² per minute.
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In 1846 the depth of the river was 5 feet deep. In 1847 it dropped to 3.5 feet. This year, 1848, it rose to 5.3 feet.
What is the percentage change
Answer:
From 1846 to 1847 there was a 30% decrease and from 1847 to 1848 it increased by 51.4%
Step-by-step explanation:
How it decreased by 30%
V2-V1/V1x100
V2=3.5 V1=5
=(3.5−5)|5|×100
=−1.55×100
=−0.3×100
=−30%change
=30%decrease
How it increased by 51.4%
V2-V1/V1x100
V2=5.3 V1=3.5
=(5.3−3.5)|3.5|×100
=1.83.5×100
=0.514286×100
=51.4286%change
=51.4%increase
How many solutions are there to the inequality x₁ + x₂ + x₃ ≤ 11, where x₁, x₂, and x₃ are nonnegative integers?
There are 66 solutions to the inequality x₁ + x₂ + x₃ ≤ 11, where x₁, x₂, and x₃ are nonnegative integers.
To solve this inequality, we must find all the possible combinations of nonnegative integers x₁, x₂, and x₃ that add up to 11 or less. This can be done by breaking down the problem into a series of nested loops. The outermost loop will iterate through all possible values of x₁, while the two inner loops will iterate through all possible values of x₂ and x₃ that add up to the remaining value of 11 minus x₁. We know that the maximum value of x₁ is 11, so the outermost loop will run from 0 to 11. For each value of x₁, the inner loops will run from 0 to (11 - x₁), incrementing by 1 each time. This will ensure that all possible combinations of x₂ and x₃ that add up to 11 minus x₁ are tested. Once we have all the combinations, we can count them to get the total number of solutions. In this case, there are 66 solutions to the inequality.
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8010005 in international number system
Answer:
8,010,005
Step-by-step explanation:
eight million ten thousand and five
hope this helps
1. After a pay raise, Kate's monthly salary increased from $3500 to $3780. Find the percentage increase in her pay raise.
Answer:
8%
Step-by-step explanation:
1. Subtract the larger number from the smaller:
3780 - 3500 = 280
2. Divide the result from step 1 by the FIRST salary amount:
280 ÷ 3500 = 0.08 NOTE: Order Matters!!!
3. Change the decimal to a percent
(GEOMETRY) PLEASE HELP ME WRITE A TWO COLUMN PROOF FOR THIS PROBLEM!!!!
If right triangle ABC with right angle ACB and altitude CD then
ΔABC ~ ΔACD
ΔABC ~ ΔCBD
ΔACD ~ ΔCBD
What is Angle-Angle Similarity (AA~) Theorem?
If two angles of one triangle and two corresponding angles of another triangle are congruent, then the triangles are similar.
According to the given question:
A right triangle is given with its altitude drawn from the right angle to its hypotenuse.
Consider the triangled ABC and ACD
By the reflexive property of angle congruence, it follows that:
∠A ≅ ∠A
Since the angles B and D are right angles, from the right angles congruence theorem, it also follows that:
∠C ≅ ∠D
Hence, by the Angle-Angle Similarity (AA~) Theorem, it follows that triangles ABC and ACD are similar. Similarly triangle ABC is similar to triangle CBD
Consider triangles ACD and CBD:
Triangles ABC and ACD are similar. Also triangle ABC is similar to triangle CBD
Therefore, Triangle CBD is similar to triangle ACD as both of them are similar to triangle ABC.
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Light travels at about 186,000 miles per second.
Which shows an equivalent speed?
(A)
(В)
O
D
1.86x103 miles per second
1.86x104 miles per second
1.86x105 miles per second
1.86x106 miles per second
Answer:
The answer is 1.86x10 6
Step-by-step explanation:
10x6 is 100k and the speed light travels is 186k so to get the answer you need to find the one that gets to 100k and then multiply it by 1.86
aspurpinion has 17 teeth and a diametral pitch of 8 teeth/in. it runs at 1120 rpm and drives a gear at 544 rpm. find the number of teeth on the gear and the distance between the centers of the pinion and gear
Theoretical centre-to-centre distance (C)=3.25 which is the distance between the centers of the pinion and gear
Given data:
No. of teeth on the pinion(TP)=17.
Diametral pitch(pd)=8 teeth/in.
The rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.
The rotational speed of the gear(NG)=544 rev/min or 544 rpm.
To calculate:
No. of teeth on gear(TG) & theoretical centre-to-centre distance(C).
We know that;
Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear
For pinion,
pd=TP/DP
Pittiong the values in above eq.
8 teeth/in =17/DP =>DP=17/8 in.
or DP=2.125 in.
Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)
(NP/NG)=(TG/TP)
1120/544 =TG/17 =>TG=35
therefore No. of teeth the gear(TG)=35 {Ans}
Also from gear ratio formula,
(NP/NG)=(DG/DP)
1120/544=DG/2.125
DG=4.375 in.
In figure I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre-to-centre distance(C)
From fig.,
centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}
C=(DP+DG)/2 {\large \because Diameter =2*radius}
C=(2.125+4.375)/2 in. =3.25 in.
therefore Theoretical centre to centre distance (C)=3.25
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Which of the following pair of linear equations is inconsistent?
A. x - 2y = 6; 2x + 3y = 4
B. 9x - 8y = 17; 18x -16y = 34
C. 2x + 3y = 7; 4x + 6y = 5
D. 5x - 3y =11; 7x + 2y =13
A ladder is leaning against a vertical wall makes an angle of 20° with the ground. The foot of the ladder is 3 m from the wall. Find the length of ladder (Round to the nearest whole number).
If you choose the 20 degree acute angle, the distance between the foot of the ladder and the wall represents the [Select] leg. Since we are given the [Select] leg and solving for the hypotenuse, we need to use [Select] to solve for the length of the ladder. The length of the ladder when solved is [Select] meters.
Options for blank #1: adjacent, opposite, hypotenuse
Options for blank #2: adjacent, opposite, hypotenuse
Options for blank #3: sine, cosine, tangent
Options for blank #4: 3, 1, 9, 4
The length of the ladder is approximately 3 m. The correct option is the first option 3
Calculating the length of a ladderFrom the question, we are to calculate the length of the ladder.
From the given information,
The ladder makes an angle 20° with the ground
and
The foot of the ladder is 3 m from the wall
This scenario gives a right triangle where the hypotenuse is the ladder and the adjacent is the distance of the foot of the ladder from the wall.
Let the length of the ladder be x
Thus,
Using SOH CAH TOA
We can write that
cos 20° = 3 / x
x = 3/(cos 20°)
x = 3.19
x ≈ 3 m
Hence, the length is approximately 3 m
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What is the best unit to measure the capacity of a washing machine.
A) milliliter
B) liter
Answer:
Liter
Step-by-step explanation:
Milliliters are used for much smaller amounts of liquid.
Question 11
Erica recorded the number of sales she made during each of the first 4 months when she began her new career. Erica plotted the data on a coordinate grid, and she noted that the data correlate to an exponential equation, as shown What is the domain of the function shown in the graph?
The domain of the graph is {1, 2, 3, 4}
What is Domain?"All the values" that are input into a function are referred to as the domain of a function. The set of all potential inputs for a function is its domain.
Given:
As, we know domain of a function is the set of all possible inputs for the function.
from the Graph, we can find the coordinates ( 1, 10), (2, 20), (3, 40) and ( 4, 80)
So, the domain of the graph is {1, 2, 3, 4}
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Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. No less than 4 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
The required graph of the inequality has been shown and the solution is; 8 Nickels and 12 dimes.
How to solve a system of inequalities?
Inequality can be defined as the relation of the equation possessing the symbol of ( ≤, ≥, <, >).
Let the number of nickels be x and let the number of dimes be y,
We are told that Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. Thus, we can generate the equations as;
x + y = 20
x = 20 - y - - - - (1)
0.05x + 0.10y ≤ 1.60 - - - -(2)
We are also told that no less than 4 of the coins are dimes. Thus;
x ≥ 4
From the graph, one solution is given as 8 Nickels and 12 dimes.
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a new vaccination is being used in a laboratory experiment to investigate whether it is effective. there are 273 subjects in the study. is there sufficient evidence to determine if vaccination and disease status are related?vaccination statusdiseasednot diseasedtotalvaccinated5762119not vaccinated8371154total140133273step 2 of 8: find the expected value for the number of subjects who are vaccinated and are diseased. round your answer to one decimal place.
The expected value for the number of subjects who are vaccinated and are diseased is 56.7
Since we are given the information that a new vaccination is being used in a laboratory experiment to investigate whether it is effective. there are 273 subjects in the study. We can calculate this by taking the total number of subjects who are vaccinated (119) and multiplying it by the proportion of subjects who are diseased
(47/273). 119 x (47/273) = 56.7
which is the expected value for the number of subjects who are vaccinated and are diseased
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what is another name for a chord that passes through the center of the circle? A) Diameter B) Circumference C) center D) radius
Answer:
A
Step-by-step explanation:
diameter
The another name for the chord that passes through the center of the circle is the diameter.
The correct option is (A).
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
As per the given data:
We have to find out the alternate name for a chord that passes through the center of a circle out of the given options.
Diameter:
It's a chord that passes through the center and touches the ends of the circumference of the circle.
Hence, this is correct.
Circumference:
It's the length of the boundary of a circle, hence this cannot be a chord.
This is incorrect.
Center:
It's a point and a chord is a line, hence this cannot be true.
Radius:
A radius is not a chord, as it does not touch the endpoints on the circumference of the circle.
The another name for the chord that passes through the center of the circle is the diameter.
Hence, The another name for the chord that passes through the center of the circle is the diameter.
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what is the value of tan a?
The value of tanA is always less than 1.
What is a number's tan of?
Tangent is the ratio of the side opposite the angle we know or want to know over the side next to that angle, and is sometimes abbreviated as T-A-N.
Describe tan angle A.
The trigonometric ratio between the opposite and adjacent sides of a right triangle that contains an angle is its tangent.
Tangent is the mathematical term for the length of the leg that faces the angle and is often abbreviated as "tan." For instance, in the triangle above, tan(A) = 68 or 34 and tan(B) = 86 or 43.
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( 3x^2 - 5x + 7) (2x^2 + 6x - 4) Try solving this one on your own first! What is the coefficient of the x3 term in the final polynomial? 8 -10 6 18
On solving the provided question, by multiplying the give polynomials, we got to know that - [tex]( 3x^2 - 5x + 7) X (2x^2 + 6x - 4)[/tex] = [tex]6x^4 + 8x^3 - 28x^2 + 62x - 28[/tex], the coefficient of x3 is 8
what are polynomials?An mathematical expression known as a polynomial requires that all of the variables' exponents be integers. Each polynomial variable's exponent must be an integer that is not negative. Although a polynomial is made up of a constant and a variable, it cannot be divided by a variable.
Given polynomials are -
[tex]( 3x^2 - 5x + 7) and (2x^2 + 6x - 4)[/tex]
By multiply the given polynomials, we got -
[tex]( 3x^2 - 5x + 7) X (2x^2 + 6x - 4)[/tex]
= [tex]6x^4 + 8x^3 - 28x^2 + 62x - 28[/tex]
So, the coefficient of x3 is 8
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select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x 5)4 2x2 5 = 0 6(2x 4)2 = (2x 4) 2 6x4 = -x2 5 8x4 2x2 – 4x = 0
An equation is quadratic if the greatest power of the coefficients is 2. Hence, for the given equations, only 6(2x + 4)2 = (2x + 4) + 2 is quadratic in nature.
What in mathematics is a quadratic equation?
A quadratic equation is a second-order polynomial equation with one variable that goes like this: x ax2 + bx + c = 0. with a ≠ 0 .
The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. The answer could be simple or complicated.
Why it is called quadratic equation?
In mathematics, a quadratic issue is any problem that involves multiplying a variable by itself, often known as "squaring."
This vocabulary is based on the fact that a square's area is equal to the product of its side length and itself. The Latin word quadratum, which means square, is where the word "quadratic" derives.
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The complete question is -
Select all of the following equation(s) that are quadratic in form.
x4 – 6x2 – 27 = 0
3x4 = 2x
2(x + 5)4 + 2x2 + 5 = 0
6(2x + 4)2 = (2x + 4) + 2
6x4 = -x2 + 5
8x4 + 2x2 – 4x = 0
How do you evaluate [(1/(x)−(1/x^(2)+x))] as x approaches 0?
As x approaches 0, the denominator of the expression [(1/(x)−(1/x^(2)+x))] approaches infinity and the numerator approaches 0. Therefore, the expression approaches 0 as x approaches 0.
1. Evaluate the denominator of the expression [(1/(x)−(1/x^(2)+x))] as x approaches 0.
2. The denominator of the expression [(1/(x)−(1/x^(2)+x))] approaches infinity as x approaches 0.
3. Evaluate the numerator of the expression [(1/(x)−(1/x^(2)+x))] as x approaches 0.
4. The numerator of the expression [(1/(x)−(1/x^(2)+x))] approaches 0 as x approaches 0.
5. Therefore, the expression [(1/(x)−(1/x^(2)+x))] approaches 0 as x approaches 0.
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How do you write 0.85 as a percent?
Answer: 85%
Step-by-step explanation:
Since percentages are numbers/ratios expressed as a fraction of 100, 85/100 becomes 85%
Consider the graph of the line y = 1//2x – 4 and the point (−4, 2). The slope of a line parallel to the given line is . A point on the line parallel to the given line, passing through (−4, 2), is . The slope of a line perpendicular to the given line is . A point on the line perpendicular to the given line, passing through (−4, 2), is ✔ (–2, –2) .
For the given line y = 1/2x - 4,
The slope of the line parallel to the given line is m = 0.The point on the line parallel to the given line, passing through (-4, 2) is (0, 4) and its equation is x - 2y + 8 = 0.The slope of the line perpendicular to the given line is m = -2.The point on the line perpendicular to the given line, passes through (-4, 2) is (-2, -2) and its equation is y = -2x - 6.How to calculate the slopes and equations of parallel and perpendicular lines of a line?Consider a line with the equation ax+by+c=0
The slope of the line is m = -b/a.The slope of the line parallel to the given line is m = 0.The slope of the line perpendicular to the given line is m = a/b or the product of their slopes equal to -1.The equation of the line parallel to the given line and passing through the point (x1, y1) is a(x - x1) + b(y - y1) = 0.The equation of the line perpendicular to the given line and passing through the point (x1, y1) is b(x - x1) - a(y - y1) = 0.Calculation:It is given that, the equation of a line is given as y = 1/2x - 4.
The slope of the given line is m = 1/2; (since it is in the form of y=mx+c)
Then, the slope of the line parallel to the given line is m = 0.
And the equation of the parallel line passing through the point (-4, 2) is
a(x - x1) + b(y - y1) = 0; where a = 1; b = -2 (y = 1/2x-4 ⇒ 2y = x - 8)
⇒ 1(x + 4) - 2(y - 2) = 0
⇒ x + 4 -2y + 4 = 0
⇒ x - 2y +8 = 0
So, the point on the parallel line is (0, 4).
The slope of the line perpendicular to the given line is m = -1/1/2 = -2.
And the equation of the perpendicular line passing through the point (-4, 2) is
b(x - x1) - a(y - y1) = 0; where a = 1; b = -2;
⇒ -2(x + 4) - 1(y - 2) = 0
⇒ -2x - 8 - y +2 = 0
⇒ y = -2x - 6
So, the point on the perpendicular line is (-2, -2).
All of these are shown in the graph below:
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=99(1.04)^4
The percentage rate of increase or decrease of the function y=99(1.04)^4 is 4%
What is an exponential function?This is a type of function that are of 3 main parts
the starting or initial value
base function
the exponents
Considering the given problem, y=99(1.04)^4
the starting = 99
the base = 1.04
the exponents = x
The base is what determines increase or decrease with a base of 1.04 shows a percentage increase is 4%
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