The equation of the tangent line to the curve at the given point is given by: y = x + 1.
What is the equation of a line to the curve?A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Now,
Given:
Equation of line: y = [tex]e^{x}[/tex] cos(x)Given point = (0,1)To find: Equation of a tangent line through the given point.
Finding:
y = [tex]e^{x}[/tex] cos(x)
By product rule of differentiation, y' = [tex]e^{x} sin(x) +e^{x} cos(x)[/tex]
For x = 0, y' (0) = 1 (0) + 1( 1) = 1 = slope of the line
Now, we know: equation of a line is given by:
[tex](y-y_0)=m(x-x_0)[/tex]
For [tex]x_0 = 0 And y_0 = 1[/tex], The equation of the tangent line will be:
=> y - 1 = 1 (x - 0)
=> y - 1 = x
=> y = x + 1
Hence, The equation of the tangent line to the curve at the given point is given by: y = x + 1.
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a bookshelf contains 5 different mathematics textbooks, 4 different engineering textbooks, and 2 different history textbooks. how many different ways are there to arrange the books on a shelf? 39916800 how many different ways are there to arrange them if each book is sorted by category (so all of the books of a type are in a row)? 34560 how many different ways are there to arrange them if only the history books must be next to each other? 725760 how many different ways are there to arrange the books if none of the history books may be adjacent to each other?
Answer:
Step-by-step explanation:
The correct answer is “39916800”. Explanation: No. of mathematics books = 3 No. of Engineering books = 5 No. of history books = 3 Total number of books = 3 + 5 + 3 = 11 Hence, there are 11! ways in which all of these books can be arranged.
I think I may be wrong if someone wants to check this you can
Which graph describes Taco Truck 1?
Which graph describes Taco Truck 3?
Which graph describes Taco Truck 5?
Simplify the ratio 12 to 30.
1/4 x -1/2 =
will give brainest
Hello,
[tex] \frac{1}{4} \times- \frac{1}{2} = \frac{1 \times (-1)}{4 \times 2} = - \frac{1}{8} [/tex]
A graph with hours on the x-axis and height (inches) on the y-axis. A line goes through points (1, 2), (2, 4), and (3, 6).
Which describes the pattern of the data in the graph?
a. The water level increases by 1 inch each hour.
b. The water level increases by 2 inches each hour.
c. The water level increases by a factor of one-half each hour.
d. The water level increases by a factor of 2 each hour.
The water level increases by 2 inches each hour.
How to determine which describes the pattern of the data in the graph?The points on the graph are given as
(1, 2), (2, 4), and (3, 6)
Next, we calculate the slope of the line, as follows:
Slope = [y2 - y1]/[x2 - x1]
So, we have
Slope = [4 - 2]/[2 - 1]
Evaluate the quotient
Slope = 2
The above means that, the water level increases by 2 inches each hour.
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What is the shape of the distribution for the following set of data? x f 5 5 4 3 3 1 2 3 1 5
The shape of the distribution for the following set of data is: symmetrical.
What are distributions?When we study data, one of the major ways to understand it is to think about its general form, such as whether it is symmetrical, has more numbers on one side than the other, or fits a common probability distribution like the normal, binomial, or exponential.
Now,
By looking at how the data are arranged in the table, we can tell that the distribution's form is symmetrical. With 1 item at X=3, it appears that this occurs frequently. The average was calculated using the range of data from X=1 to X=5. In addition, the data contain 5 items at X=5 and X=1, respectively. Both of these occur equally often and at equal intervals from the average. We can also say that there are three items in the data at X=4, three things at X=2, and so on, all of which are equally far from the average. As a result, every piece of data is either averaged out or counterbalanced on the other side of the average. A symmetrical distribution is described here. Therefore, it is neither favorably nor negatively biased. Even though it is symmetrical, the distribution is not normal since a normal distribution contains more data at the average than at the tails, as opposed to fewer.Hence, The shape of the distribution for the following set of data is: symmetrical.
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Complete the sentence.
180g = ___ kg
180g = 0.180 kg or there are 0.180 kilograms in 180 grams.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
The sentence states an equality between a units of weight in grams (g) and kilograms (kg).
From there, we can say that we are asked how many kilograms are there in 180 grams.
Converting grams to kilograms, we must use the conversion
1 g = 0.001 kg
180g = 180 (0.001) kg
180g = 0.180 kg
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i’ll mark brainliest
Answer:
<E
Step-by-step explanation:
The points need to be in order. P is the second to the last on the list and so is E.
A sphere has a diameter of 6 cm.
What is the volume when pi is set to 3?
First, we'll have to find the radius.
Radius is half of the diameter.[tex]\large\boxed{\bold{r= \frac{d}{2}}}[/tex]
[tex]r= \frac {6}{2}[/tex]
[tex]r= 3 \ cm[/tex]
Now, we can workout the volume.
Instead of π, we are asked to use 3.
[tex]\large\boxed{\bold{\red \pi \red = \ \red 3}}[/tex]
[tex]\large\boxed{\bold{V= \ \frac{4}{3} \pi {r}^{3}}}[/tex]
Now, substitute the values according to the formula.
[tex]V= \ \frac{4}{3} × 3 × {3}^{3}[/tex]
[tex]\large\boxed{\bold{V= \ 108 \ {cm}^{3}}}[/tex]
The answer is a whole number so you won't have to round off.
Therefore, the volume of the given sphere is 108 cubic centimeters.
find all parts show work 25 points
HELP
The solution of the system of linear equations behind the geometric system is (x, z) = (29, 13). The measures of the angles RIG and ZIM are 59° and 140°, respectively.
What are the variables behind a geometric system formed by three lines?
In this problem we find a geometric system generated by lines GZ, AM and IR, in which two variables are shown (x, z) and whose values can be found by applying the concepts of complementary and supplementary angles.
A group of angles are complementary if the sum of their measures equals 90°, and supplementary if that sum equals 180°. This system can be represented by the following system of linear equations:
(3 · x - 56) + 90 + (4 · z + 7) = 180 (1)
(4 · z + 7) + (x + 2) = 90 (2)
By (1):
(3 · x - 56) + (4 · z + 7) = 90
3 · x + 4 · z - 49 = 90
3 · x + 4 · z = 139 (1b)
By (2):
x + 4 · z = 81 (2b)
The solution of the system of linear equations behind the geometric system is (x, z) = (29, 13).
Then, the measures of the angles RIG and ZIM are, respectively:
m ∠ RIG = 4 · z + 7
m ∠ RIG = 4 · 13 + 7
m ∠ RIG = 59°
m ∠ ZIM = 360° - (3 · x - 56) - 90° - (4 · z + 7) + (x + 2)
m ∠ ZIM = 360 - 3 · 29 - 56 - 90 - 4 · 13 + 7 + 29 + 2
m ∠ ZIM = 140°
The measures of the angles RIG and ZIM are 59° and 140°, respectively.
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16. <1 and <2 form a linear pair. The
measure
of <2 is six more than twice the
of <1. Find m<2.
The measure of the angle 2 is 122°.
What is referred as the linear pair?When lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are said to be linear. The sum of the angles of the a linear pair will always be 180°. These angles are also referred to as supplementary angles.Given that angles 1 and 2 form a linear pair,
angle 1 + angle 2 = 180 degrees —— (1)
We've also been notified that angle 2 is 6 times the size of angle 1.
That is to say: angle 2 = (2×angle 1) + 6 ———- (2)
Putting the angle 2 value in (1) from (2)
180 = angle 1 + 2×angle 1 + 6
3×angle 1 = 174
1st angle = 58 degrees ———-(3)
(1) and (3) come from:
angle 2 + 58 = 180
2nd angle = 122 degrees
As a result, angle 2 has a measure of 122 degrees.
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If m< ABF=7b-24 and m< ABE = 2b, find m< EBF .
Answer:
∠ EBF = 16°
Step-by-step explanation:
note that EB is the angle bisector of ∠ ABF , then
∠ ABE = ∠ EBF = 2x and
∠ ABF = ∠ ABE + ∠ EBF , that is
7b - 24 = 2b + 2b
7b - 24 = 4b ( subtract 4b from both sides )
3b - 24 = 0 ( add 24 to both sides )
3b = 24 ( divide both sides by 3 )
b = 8
Then
∠ EBF = 2x = 2(8) = 16°
x+20)4x²+10x+2(
PLEASE SOLVE AND ANSWER.
Answer:
4x[tex] \sf {}^{3} [/tex] +80x²+10x+2
Step-by-step explanation:
(x+20)4x²+10x+2
Let's simplify step-by-step.
(x+20)(4)x²+10x+2
Distribute:
=4x[tex] \sf {}^{3} [/tex] +80x²+10x+2
Solve: 5x - 7x + 6 = -2(x - 3).
A 0
B 3/4
C 2
D no solution
E infinitely many solutions
I will give 80 points
Answer: E: Infinitely many solutions
Step-by-step explanation:
Starting with 5x - 7x + 6, let's combine like terms.
5x - 7x is -2x.
Thus, we have -2x + 6 = -2(x-3)
Using the distributive property for the right side, we multiply -2 * x, and get -2x, and -2 * -3 and get +6.
Now we have -2x + 6 = -2x + 6. We have the same equation here, and know that there is infinitely many solutions here off the bat.
For sake of computations, let's solve and show our work.
Subtracting 6 from both sides, we have -2x = -2x.
Adding 2x to both sides, we get 0 = 0.
Thus, we have infinitely many solutions.
The football team is selling gift cards in increments of
$25 and $50. If they sold $6,000 worth of gift cards
which equation could be used to determine how many
$50 gift cards, g, were sold if 180 gift cards were sold in
the $25 amount?
Answer: 4,500+50g=6,000
Step-by-step explanation:
write the index notation of 6*6*6
Step-by-step explanation:
6×6×6 can be written as 6^3...
Answer:
6^3
Step-by-step explanation:
6 x 6 x 6 is equal to 6^3
7. The John G. Riley Center and Museum in
Tallahassee is open for tours year-round.
Admission is $5.00. If 283 tour tickets are sold
each month, how many tickets would be sold
in 1 year?
3396 Tickets would be sold in one year. If 283 tickets are sold each month you need to do 283 (tickets) x 12 (months) and that will get you 3396 Tickets per every 12 months.
The value of y varies inversely with the square of x, and y = 4, when x = 5. What is y when x=10
Answer:
Step-by-step explanation:
[tex]y=k/x^{2}[/tex]
when y=4, x=5. Therefore:
[tex]4=k/5^2[/tex]
[tex]k=100\\[/tex]
If [tex]k=100, x=10 \\[/tex]
then [tex]y=100/10^2[/tex]
y=1
Answer:
The value of x when y = 9 is x = 2 or x = -2
Step-by-step explanation:
Given that value of y varies inversely as the square of x, and y=4, when x=3.
Therefore the initial statement is:
[tex]y x \frac{1}{x^{2} }[/tex]
A recipe for homemade modeling clay includes cup of salt for every cup of water. If there are 6 cups of salt, how many gallons of water are needed?
Answer:
0.375
Step-by-step explanation:
see above
Vertex (-2,-5) passes through (4,4) in vertex form
The equation of parabola is [tex]y=1/4x^{2}+x/2-4\\\\[/tex].
What is parabola?A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape. A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.
Given:
The equation of parabola in vertex form is
[tex]y=a(x-h)^{2} +k[/tex]
Being vertex here
h=-2
k=-5
According to given question we have
∴
Equation of parabola in vertex form is
[tex]y=a(x+2)^{2} -5[/tex]
. The parabola passes through point (4,4) So the point (4,4) will satisfy the equation .
[tex]4=a(4+2)^{2} -5\\\\4=a*36-5\\\\9=a*36\\\\a=9/36\\\\a=1/4[/tex]
Hence the equation of parabola is
[tex]y=1/4(x+2)^{2} -5\\\\y=1/4(x^{2} +4+2x)-5\\\\y=1/4x^{2} +1+x/2-5\\\\y=1/4x^{2}+x/2-4\\\\[/tex]
Therefore, the equation of parabola is [tex]y=1/4x^{2}+x/2-4\\\\[/tex].
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the equation of parabola is missing
How do you write 0.63 as a percentage
Answer:
63%
Step-by-step explanation:
To write a decimal as a percentage, you simply multiply it by 100. 0.63 * 100 is 63, so your final answer would be 63%.
FINAL ANSWER: 63%
(4y+1)x0=0 property
The property represented by the expression is the property of zero.
We are given an expression:
(4 y + 1) × 0 = 0
We need to tell which property is this.
The property that is used is called the property of zero. In this, it states that whenever a number is multiplied by 0, the answer or the result will always be zero.
For example: 3 × 0 = 0, 4 × 0 = 0, M × 0 = 0 or P × 0 = 0.
It does not matter whether a constant or a variable is multiplied with it, the result of the multiplication will always be zero.
Therefore, the property represented by the expression is the property of zero.
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Evaluate the expression.
Answer: 1
Step-by-step explanation:
4^(-1) / 4^(-1)=
1/4 / 1/4=
1/4 * 4/1= ==> Dividing by a number is basically multiplying its reciprocal
1*4/(4*1)=
4/4=1
A group of students visited the zoo café for lunch. Each student received a bacon cheeseburger
and milkshake, and the total bill was $104.00. How many students were in the group? Please show your work.
Sandwiches Sides Beverages
Hamburger $3.25
Bacon Cheeseburger $4.75
Chicken Fajita Taco $3.50
French Fries, Small $1.55
French Fries, Large $1.90
Onion Rings $2.40
Cole Slaw $1.45
Soft Drink, Small $1.30
Soft Drink, Large $1.65
Milkshake $3.25
Juice $1.80
Answer:
13
Step-by-step explanation:
Use with problems 11 and 12. Round to the nearest hundredth place.
C-3,1)
D(0, -6)
Answer:
7.6. Good luck
What’s the slope of the line?
Answer:
slope = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (2, - 1)
m = [tex]\frac{-1-1}{2-(-2)}[/tex] = [tex]\frac{-2}{2+2}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
you are employed at a grain processing plant that sells cornmeal for $1.28 per pound. if a sack of cornmeal weighs 4 pounds 12 ounces, how much does it cost?
Answer:
$6.08
Step-by-step explanation:
16 ounces = 1 pound
4 pounds 12 ounces = 4 12/16 pounds OR 4 ¾ pounds
4¾ ≈ 4.75
4.75 pounds x $1.28 = $6.08
Write the number five million four thousand three hundred in standard form.
Answer:
5,004,300
Step-by-step explanation:
just copy and paste the one on the bottom 5,004,300
. An architect is designing a new windmill with four sails. In her
sketch, the sails' center of rotation is the origin, (0,0), and the tip of one of the sails,
point
S, has coordinates (2,4). She wants to make another sketch that shows the windmill
after the sails have rotated 270° clockwise about their center of rotation. What would
be the coordinates of S?
The coordinates of S are (-4,2) .
The sails' center of rotation = Origin (0,0)
Coordinates of S on the top of one of the sails, = (2,4)
Rotation :The action or process of rotating on or as if on an axis or center.
Centre of Rotation :The center of rotation is a point about which a plane figure rotates. This point does not move during the rotation.
It is given that sails have rotated 270° clockwise.
So, When we rotate a figure of 270 degree clockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.
So, the point turn (2, 4) into (-4, 2).
Thus, the coordinates of S are (-4,2).
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Assume you are working with population of n= 16 scores. the sum of all of the scores is equal to 96. what is the population mean?
The population mean of the data is 6.
How to find the population mean?The population has n = 16 scores.
The sum of all of the scores is equal to 96.
Therefore, the population mean can be found as follows:
The population mean is the mean or average of all values in the given population.
The population mean is represented mathematically as follows:
population mean = sum of terms / number of terms
Therefore,
sum of terms = 96
number of terms = 16
Hence,
population mean = = 96 / 16
population mean = 6
Therefore, the population mean of the data is 6.
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