So, theta = arctan(sqrt(500^2-d^2) / d) would give us the angle between the ground and the ladder where d is distance from the base of the ladder to the building.
The angle between the ground and the ladder can be found using the inverse tangent function (also known as arctan) and the Pythagorean theorem.
First, we need to find the ratio of the height of the ladder to the distance from the base of the ladder to the building. This ratio is known as the tangent of the angle between the ground and the ladder.
Let h be the height of the ladder and d be the distance from the base of the ladder to the building.
tan(theta) = h/d
Next, we can use the Pythagorean theorem to find the value of h:
d^2 + h^2 = 500^2
Now we can substitute the value of h in the first equation.
tan(theta) = sqrt(500^2-d^2) / d
To find the angle between the ladder and the ground, you can use the inverse tangent function on the above equation.
theta = arctan(sqrt(500^2-d^2) / d)
To find the exact value of the angle, you would need to know the value of d (distance from the base of the ladder to the building).
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Can anyone tell me the answer . Sorry if it’s hard to see please just zoom
Answer:
WXUV
Step-by-step explanation:
Well, you see, think of it as a reflection.
Drivers pay a toll to pass over a busy bridge, and there are many toll booths that collect money. The city manager counted the total number of cars waiting to pay their tolls at 15-minute intervals during two different days, once on a weekday and once on a weekend. The histograms below show the results.
Using the histograms, which of the following is the correct comparison of the distributions?
A-The 10–20 interval contains the most observations on both days.
B-The two distributions for number of cars in line are both skewed right.
C-The median number of cars for both distributions lies in the 20–30 interval.
D-There were more than 40 cars in line more often on the weekend than the weekday.
IT IS B GOT IT RIGHT
B-The two distributions for number of cars in line are both skewed right.
Which of the following is the correct comparison of the distributions?The histograms compare the number of cars waiting to pay their tolls at 15-minute intervals during two different days, once on a weekday and once on a weekend.The histograms reveal that the two distributions for the number of cars in line are both skewed right, meaning that the majority of observations are concentrated on the left side of the distribution, with fewer observations on the right side.The 10–20 interval contains the most observations on both days, and the median number of cars for both distributions lies in the 20–30 interval.There were fewer than 40 cars in line more often on the weekend than the weekday.This type of comparison is known as a distribution comparison, which is used to compare the shape and spread of two or more distributions.
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I don’t understand, someone please help
a)
The rate of change is of 3, hence the hourly cost is of $3.The initial value is of 3.50, hence the skate rental fee is of $3.50.b) The slope-intercept definition of the linear function is given as follows:
y = 3x + 3.50.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the intercept, representing the value of y when x assumes a value of zero.Two points on the linear function in this problem are given as follows:
(2, 9.50) and (5, 18.50).
The slope is given by the division of the change in y by the change in x, hence:
m = (18.50 - 9.5)/(5 - 2)
m = 9/3
m = 3.
Representing the hourly charge.
Hence:
y = 3x + b.
When x = 2, y = 9.50, hence the intercept b, representing the rental fee, is given as follows:
9.5 = 3(2) + b
b = 3.50.
Meaning that the function is defined as follows:
y = 3x + 3.5.
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How do you use table formulas?
There are different tables used in mathematics i.e. logarithmic tables, semi-logarithmic tables, exponential tables, trigonometric function tables, etc.
The tables are provided with data that is needed for the calculations. For example: if the value of Sin 45° needs to be found then we have to move to the table of Sin Θ and then follow the rows of angles where the value of Sin 45° can be obtained. Similarly, the values of other functions can be found in this way. However, the trigonometric table also provides the relation between two functions like Tan Θ= [tex]\frac{SinΘ}{CosΘ}[/tex].
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Which statement are true about xyz
Is Dawn or Denise correct?
Answer:
Dawn is correct maybe because -3 is less than 4
correct if I'm wrong
If U and T are the midpoints and the distance between S and R is 56 miles, what is the distance from U to T ?
The final distance from U to T is 112 miles.
Since U and T are the midpoints of SR and ST respectively, we know that SU and RT are congruent and have the same length.
We need to find the overall displacement of U&T.
Also, we know that the distance between S and R is 56 miles.
Therefore, the distance from U to T is equal to twice the distance from S to U which is 2 * (distance from S to R) = 2 * 56 = 112 miles.
Therefore, The final distance from U to T is 112 miles.
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Insert parentheses in the Expression so that it has a value of 19. Then show why your expression has a value of 19.
5+4*2+6-2*2-1
The expression 5+4*2+6-2*2-1 has a value of 14 using order of operations
How to simplify an expression using order of operation?
The order of operations are the rules that tell the sequence in which the multiple operations in an expression should be solved. A way to remember the order of the operations is PEMDAS, where each letter stands for a mathematical operation
Parenthesis ( )
Exponent a⁷
Multiplication x
Division ÷
Addition +
Subtraction -
Let's use PEMDAS:
Remember, multiplication comes before addition and subtraction, thus, we have:
5+4×2+6-2×2-1 = 5 + (4×2) + 6 - (2×2) - 1
= 5 + 8 + 6 - 4 - 1
= 14
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mariela took out a mortgage and purchased a house located in the v zone of an nfip participating community. what does that mean for mariela?
Mariela's purchase of a house located in the V Zone of an NFIP participating community means that the house is located in a high amount of risk flood zone and that she is required to purchase flood insurance if she has a mortgage. This insurance will help to protect her investment in the event of a flood.
Mariela must purchase flood insurance if she has a mortgage on her house, which is located in a high amount of risk flood zone in an NFIP participating community. This insurance will help to protect her investment in the event of a flood.
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Review the table of values showing the mass of a radioactive isotope over time.
Which statement best describes the explanatory and response variables in the regression model?
In the logarithmic regression model, the explanatory variable is time and the response variable is the remaining mass.
In the logarithmic regression model, the explanatory variable is the remaining mass and the response variable is time.
In the exponential regression model, the explanatory variable is time and the response variable is the remaining mass.
In the exponential regression model, the explanatory variable is the remaining mass and the response variable is time.
In the exponential regression model, the explanatory variable is time and the response variable is the remaining mass. thus it is the correct option.
What is the regression model?Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.
The response variable (or the dependent variable) always belongs on the y-axis (represented as the second column of the table).
Since the explanatory variable (or the independent variable) always belongs on the x-axis (represented as the first column of the table).
According to the table of values showing the mass of a radioactive isotope over time.
Based on explanation above the correct choice is C which could be In the exponential regression model, the explanatory variable is time and the response variable is the remaining mass.
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A car is traveling at a speed of 60 miles. How far can the car travel in 2 1/2 hours
Answer: 150 miles
Step-by-step explanation: the car goes 30 miles every half hours, therefore, in five half hours it goes 150 miles.
The Math Club is selling shirts as a fund-raiser. The company charges a set-up fee plus a certain cost for each shirt. The function rule C = 9n + 45 represents the Math Club's cost, with C representing the total cost of the order, and n representing the number of shirts. What could the numbers in the function represent? Select all that apply.
Responses
45 is the minimum number of shirts
45 is the minimum number of shirts
9 is the price per shirt.
9 is the price per shirt.
9 is the initial set-up fee charged to design the shirts.
9 is the initial set-up fee charged to design the shirts.
45 is the price per shirt.
45 is the price per shirt.
45 is the initial set-up fee charged to design the shirts.
45 is the initial set-up fee charged to design the shirts.
Answer: The function rule C = 9n + 45 represents the cost of the shirts that the Math Club is selling. The variable C represents the total cost of the order and the variable n represents the number of shirts.
The number 9 in the function represents the price per shirt, this is because as the number of shirts increases by 1, the total cost increases by 9. This tells us that the cost of each shirt is $9.
The number 45 in the function represents the initial set-up fee charged to design the shirts. This is because even if no shirts are ordered, there is still a cost of $45. This represents a fixed cost that the Math Club must pay to have the shirts designed.
Step-by-step explanation:
Please answer this question with a decent explanation.
Answer:
b
Step-by-step explanation:
sr =
[tex] \sqrt[10]{3} [/tex]
Caleb is going to invest in an account paying an interest rate of 6% compounded daily. How much would Caleb need to invest, to the nearest cent, for the value of the account to reach $1,900 in 5 years?
Caleb would need to invest $1,764.69 to the nearest cent, for the value of the account to reach $1,900 in 5 years with an interest rate of 6% compounded daily.
What is compound interest?
Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is different from simple interest, which is calculated only on the initial principal.
To find out how much Caleb needs to invest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal or initial investment
r = the annual interest rate (expressed as a decimal)
n = the number of times per year that interest is compounded
t = the number of years the investment will be held
We know that Caleb wants the future value of the investment to be $1,900 in 5 years and interest is compounded daily with an annual rate of 6%. So we can set up the equation as:
A = P(1 + r/n)^(nt)
1900 = P(1 + 0.06/365)^(365*5)
To solve for P, we can use a calculator to get the result:
P = $1,764.69
Hence, Caleb would need to invest $1,764.69 to the nearest cent, for the value of the account to reach $1,900 in 5 years with an interest rate of 6% compounded daily.
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help D: !!!!!!!!!!!!!
Answer: x is 90 and y is 41
Step-by-step explanation: Since angle C is equal to 49 degrees, and angle D is noticeably 90, we can do the following:
90 + 49 = 139
180 - 139 = 41
Therefore, our answer is x = 90 and y = 41
Khan academy
After a certain medicine is injected, its concentration in the bloodstream changes exponentially
over time.
The graph describes the medicine's concentration (in milligrams per liter) over time (in hours).
concentration
(mg/l)
100
90-
80-
70-
60
50-
40-
30-
20-
10.
←
1 2 3
4
5 6 7
time
(hours)
How does the medicine's concentration change over time?
A?
B?
C?
D?
The Medicine Concentration drops 70 % each hour .
What is a graph ?
graph can be defined as a visual indicator in which we can represent the data.
Given,
A certain medicine is injected, its concentration in the bloodstream changes exponentially over time as shown in graph
Concentration of medicine when it was injected
=> at t = 0
Hence 100 mg/l was concentration when medicine was injected
Nt = No [tex]e^{-kt}[/tex]
N₀ - initial Quantity = 100 mg/l
at t = 1 Concentration is 70 mg/l
=> 70 = 100 [tex]e^{-kt}[/tex]
=> k = 0.3567
Decay Constant = 0.3567
T = Half life period
50 = 100 [tex]e^{-kt}[/tex]
=> -0.693 = -kT
=> 1.943 hr
Hence , Medicine Concentration drops 70 % each hour .
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A watering can dispenses water at the rate of 0.3 gallon per minute. The original volume of water in the can was 7 gallons. Which set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water
The set of ordered pairs depicts the volume of water in the can in gallons (y) as a function of time in minutes (x), beginning with the first minute after the can begins distributing water and ending with {(1, 6.7) , (2, 6.4) , (3, 6.1)}.
What is ordered pairs?An ordered pair is a pair of objects in mathematics. The order of the objects in the pair is important: the ordered pair differs from the ordered pair unless a = b. Ordered pairs are also known as 2-tuples or 2-length sequences. An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair's numeric values can be integers or fractions.
Here,
A watering can dispenses water at the rate of 0.3 gallon per minute.
The original volume of water in the can was 7 gallons.
If you plot a graph of volume of water in the can (gallons) against time (minutes),
The set of points on the graph will be:
After 1 minute: (1, 7 - 0.3) = (1, 6,7)
After 2 minutes: (2, 7 - 0.6) = (2, 6.4)
After 3 minutes: (3, 7 - 0.9) = (3, 6.1)
i.e the set {(1, 6.7) , (2, 6.4) , (3, 6.1)}
The set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water is {(1, 6.7) , (2, 6.4) , (3, 6.1)}.
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a senate committee has 8 republicans and 6 democrats. in how many ways can we form a subcommittee with 3 republicans and 2 democrats?
840 ways can we form a subcommittee with 3 republicans and 2 democrats
Given that
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical. (It is not important how each set's members are arranged.) If there are n elements in the set, then C kn is the number of k-combinations.
a senate committee has 8 republicans and 6 democrats.
now, we need to find how many ways can we form a subcommittee with 3 republicans and 2 democrats
= 8[tex]C_{3}[/tex] × 6[tex]C_{2}[/tex]
=[tex]\frac{8!}{5!3!}[/tex] × [tex]\frac{6!}{4!2!}[/tex]
=56 × 15
=840
840 ways can we form a subcommittee with 3 republicans and 2 democrats
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Segment $s_1$ has endpoints at $(4,1)$ and $(-8,5)$. Segment $s_2$ is obtained by translating $s_1$ by $2$ units to the right and $3$ units up. Find the midpoint of segment $s_2$. Express your answer as $(a,b)$ with $a$ and $b$ integers.
The midpoint [tex]s_{2}[/tex] is = (0,4).
Midpoint refers to a point that is in the middle of the line connecting two points. The two mentioned points are the endpoints of a line and the midpoint is lying in between the two points. The midpoint divides the line connecting these two points into two equal halves
According to the question,
The endpoints [tex]s_{2}[/tex] are 2 units to the right and 3 units up from the endpoints [tex]s_{1}[/tex].
[tex]s_{1}[/tex] has endpoints at (4, 1) and (-8, 15).
[tex]s_{2}[/tex] has endpoints at (4+2, 1+3) and (-8+2, 1 +3)
[tex]s_{2}[/tex] has endpoints at (6, 4) and (-6, 4).
The midpoint of [tex]s_{2}[/tex] = [tex](\frac{6-6}{2} , \frac{4 + 4}{2} )[/tex] = ( 0, 4)
So, the midpoint [tex]s_{2}[/tex] is = (0,4).
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working at their respective constant rates, machine 1ii makes 240 copies in 8 minutes and machine 2iiii makes 240 copies in 5 minutes. at these rates, how many more copies does machine 2iiii make in 4 minutes than machine 1ii makes in 6 minutes?
On solving the provided question we can say that by unitary method number of extra copies made by machine 2 = 192 – 180 = 12
What is unitary method ?
The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen.
In 8 minutes, Machine 1 produces 240 copies. In 5 minutes, machine 2 produces 240 copies. The rates of operation for each machine are constant.
machine 1 makes 240 = 8 mins
[tex]1 min = 240/8 = 30\\6 min = 3 X 6 = 180[/tex]
In 5 minutes, machine 2 produces 240 copies.
[tex]1 min = 240/5 = 48\\4 min = 192[/tex]
number of extra copies made by machine 2
[tex]= 192 – 180\\ = 12[/tex]
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Find the slope of the line that passes through these two points
Step-by-step explanation:
your teacher gave you even the formula. so, what is still not clear ?
in regular words, the slope of a line is the ratio
y coordinate difference / x coordinate difference
when going from one point on the line to another.
so, we have here (-2, 1) and (3, 2).
x changes by +5 (from -2 to 3).
y changes by +1 (from 1 to 2).
so, the slope is +1/+5 = 1/5
Can you construct a triangle using line segments 12 cm 7 cm and 5 cm?
For the given line segments 12cm ,7cm and 5cm , a triangle cannot be constructed as the sum of two sides is not greater than third side .
What is a Triangle ?
a Triangle is closed figure joined by three line segments .
The condition for the sides to form a triangle , is :
the sum of any two sides of triangle should be greater than the third side of the triangle :
the given side lengths are : 12cm ,7cm and 5cm ;
on adding the two sides of triangle ,
we get ;
⇒ 12+7 = 19 > 5 ; True
⇒ 12+5 = 17 > 5 ; True
⇒ 7+5 = 12 > 12 ; False
The third condition is not met .
Therefore , the line segments 12 , 7 and 5 do not form a triangle .
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Melissa purchased a new car. the car had a list price of $20,540. melissa made a down payment of $3,900 and financed the rest, paying 8.6% interest compounded monthly over a payment period of 5 years. if melissa also had to pay 8.25% sales tax, a $995 vehicle registration fee, and a $57 documentation fee, what is her monthly payment?
Melissa's monthly payment is $450 if the down payment is $3,900.
To calculate the monthly payment, we first need to calculate the total amount financed. This is done by adding the list price of the car ($20,540), the sales tax (8.25% of $20,540 = $1,690.35), the registration fee ($995), and the documentation fee ($57) for a total of $23,282.35.
We then need to calculate the total amount of interest that Melissa will pay over the 5-year loan period. This is done by multiplying the interest rate (8.6%) by the total amount financed ($23,282.35) and multiplying that by the number of years (5).
This gives us a total interest payment of $7,634.84. We then add the total amount financed ($23,282.35) and the total interest payment ($7,634.84) and subtract the down payment ($3,900), which gives us the total amount that Melissa will pay over the 5-year loan period: $27,016.99.
We then divide this total amount by the number of months in the loan period (60) to get the monthly payment: of $450
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any one good at math that can help here
So on n solving the provided question, we can say that the value of the slope intercept is 2x - 3y -12 =0
what is slope intercept?In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.
Given, x - intercept of a line is 6
so,
The line will pass through the point (6, 0)
Also given. the y - intercept ofthe line is —4 c = —4
So, the line will pass through the point (0, —4)
Now,
Slope, m = y2 - y1/x2 - x1
m = -4-0/0-6 = 2/3
y = mx + c
y = 2x/3 - 4
3y = 2x - 12
2x - 3y -12 =0
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Hi. would you please help me? I don't understand how use the numbers (answer choices) in possible factors and sum of the factors
Factors of polynomial x²+5x+6 are -2,-3.
What are polynomials?Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.
The expression is categorised as monomial based on how many terms are included in it:
An expression with just one term is referred to as a monomial. A monomial expression must have a single term that is not zero in order to qualify. A Monomial examples include 5x and 3.
Binomial:-
An expression of a polynomial with exactly two terms is called a binomial. Examples of binomials are:
– 5x+3, 6a^4 + 17x.
Trinomial:-A trinomial is an expression which is composed of exactly three terms. A Examples of trinomial expressions are:
– 8a^4+2x+7, 4x^2 + 9x + 7.
Now Given polynomial is x^2+5x+6
To find factors put it equal to zero
x^2+3x+2x+6=0
x(x+3)+2(x+3)=0
x+3=0, x+2=0
x=-2,-3
Hence, The factors of the given polynomial are -2,-3.
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A mattre tore i having a ale all mattree are 30 % off nate want to know the ale price of a mattre that i regulary 1000
Sale price of the mattress is $700.
What is a sales price in math?
The price after the original price has been reduced by a discount.
The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
Mattress that is of $1000 is sold at discount 30%.
Original price of mattress = $1000
Percentage of discount on mattresses = 30%
So,
Amount of discount on mattresses
= [ 30 / 100 ] × 1000
= $300
sale price of the mattresses = $1000 - $300 = $700
Therefore, the sale price of the mattresses is $700.
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Use a double integral to find the area of the region. The region inside the circle (x − 2)2 + y2 = 4 and outside the circle x2 + y2 = 4
The area of the region inside the circle (x − 2)^2 + y^2 = 4 and outside the circle x^2 + y^2 = 4 is given by
Area = ∬R dA where R is the region we're trying to find the area of.
We can find the area of the region by subtracting the area of the smaller circle from the area of the larger circle.
The area of the larger circle is:
Area = ∬R dA = ∬((x − 2)^2 + y^2 <= 4) dA = π*4 = 4π
The area of the smaller circle is:
Area = ∬((x^2 + y^2) <= 4) dA = π*4 = 4π
Therefore, the area of the region inside the circle (x − 2)^2 + y^2 = 4 and outside the circle x^2 + y^2 = 4 is
Area = 4π - 4π = 0
The area of the region is 0 square units.
Answer:
I agree with kiddobreeze08
Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X.
The measure of angle ∠CXA is 134°
What is the Isosceles triangle?
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Triangle ABC is an isosceles triangle where AB = BC
∵ AB = BC
- The base angles in the isosceles triangle are congruent
∴ m∠BAC = m∠BCA
∵ m∠ BCA = 46° ⇒ given
∴ m∠ BAC = 46°
- The sum of the measures of the interior angles in any triangle is 180°
∵ m∠BAC + m∠BCA + m∠ABC = 180°
- Substitute the values of angle BAC and BCA in the equation above
∴ 46 + 46 + m∠ABC = 180
∴ 92 + m∠ABC = 180
- Subtract 92 from both sides
∴ m∠ABC = 88°
- BF, AD, and CE are bisectors segments of angles B, A, and C and they are intersected at point X
∵ CE bisects ∠BCA
∵ X ∈ CE
∴ m∠XCA = 1/2 m∠BCA
∴ m∠XCA = 1/2 (46) = 23°
∵ AD bisects ∠BAC
∵ X ∈ AD
∴ m∠XAC = 1/2 m∠BAC
∴ m∠XAC = 1/2 (46) = 23°
- In Δ AXC
∵ m∠XAC = 23° ⇒ proved
∵ m∠XCA = 23° ⇒ proved
∵ m∠CXA + m∠XAC + m∠XCA = 180° ⇒ interior angles of Δ
Substitute the values of angles XAC and XCA
∴ m∠AXC + 23 + 23 = 180
∴ m∠CXA + 46 = 180
- Subtract 46 from both sides
∴ m∠CXA = 134°
Hence, The measure of angle ∠CXA is 134°.
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The complete question is:
Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X. triangle ABC with diagonals BF, AD, and EC that intersect at point X If segment BA is congruent to segment BC and m∠BCA = 46°, what is m∠CXA?
find an equation of the tangent line to the curve at the given point. y =√ x , (81, 9)
An Equation of the tangent line to the curve is 18y=x+81
Given equation
y²=x
This is an equation of a parabola. graph{y^² = x [-10, 10, -5, 5]}
For finding the tangent to the equation, we first differentiate it.
The goal here is to find the value of dy/dx which will give the slope of the tangent to the parabola.
So,
[tex]\frac{d}{dy}(y^2)=\frac{dx}{dy} \\\\2y=\frac{dx}{dy} \\\\\frac{1}{2y} =\frac{dx}{dy} \\\\[/tex]
Now, we want to evaluate the slope at the given point. So substituting y we get,
[tex]\frac{1}{18} =\frac{dx}{dy}[/tex]
This is the slope of the tangent.
It passes through (81,9) [as per in the question]
The general equation of a line is y=mx+c
m is the slope of the line.
For the line/tangent that we got
[tex]m=\frac{dy}{dx}[/tex]
[tex]y=\frac{x}{18} +C[/tex]
The point should satisfy the equation of the line/ tangent. So,
[tex]9=\frac{x}{18} +C[/tex]
So, c=9/2
Finally, substitute the value in our equation of the line/tangent:
[tex]y=\frac{x}{18} +\frac{9}{2}[/tex]
18y=x+81
Therefore, the equation of the tangent line to the curve at the given point, y =√ x, (81, 9) is 18y=x+81
To know more about the equation of the tangent:
https://brainly.com/question/7252502
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Whats the explicit equation for the sequence: 8000, 4000, 2000, 1000?
Answer:
V÷ 2
Step-by-step explanation:
Get peevious number and divide by half.
