Answers
The equation to the tangent line to [tex]y = e^{(x^2)}[/tex] at point (1,0) is given by:
y = 2e(x - 1).
What is the equation to the tangent line of a function of a point?Supposing that we have a function f(x) at a point [tex](x_0, y_0)[/tex], the equation of the tangent line to this function is given by:
[tex]y - y_0 = f^{\prime}(x_0, y_0)(x - x_0)[/tex]
In which f' is the derivative.
In this problem, the function is:
[tex]f(x) = e^{(x^2)}[/tex]
Applying the chain rule, the derivative is:
[tex]f^{\prime}(x) = 2xe^{(x^2)}[/tex]
At x = 1, the derivative is:
[tex]f^{\prime}(1) = 2(1)e^{((1)^2)} = 2e[/tex]
Hence the tangent line at point (1,0) is given by:
y = 2e(x - 1).
More can be learned about the equation of a tangent line at https://brainly.com/question/8174665
#SPJ1
Related Questions
What’s the distance between A and B
A= (-3,-4)
B= (4,5)
A) square root of 256
B) square root of 130
C) Square root of 82
D) square root of 32
Answers
Answer:
C
bacause the root is 82 and it's not that far
pls help i have no clue what this is
Answers
Answer:
³√729 = 9
Step-by-step explanation:
The given information is,
→ ³√729
Prime factorization of 729 is,
→ 3 × 3 × 3 × 3 × 3 × 3
We know that,
→ ³√27 = 3
Let's solve the problem,
→ ³√729
→ ³√{(3 × 3 × 3) × (3 × 3 × 3)}
→ ³√(27 × 27)
→ 3 × 3 = 9
Hence, the answer is 9.
Negative 16/72 in simplest form
Answers
Answer:
Negative 2/9 I believe
Step-by-step explanation:
sorry if i am wrong
Answer:
-2/9
Step-by-step explanation:
-16/72
Simplify
We can divide the top and bottom by 8
16 divided by 8 = 2
72 divided by 8 = 9
-2/9
3.What is the official language of cape verd
Answers
Answer:
Portuguese
Step-by-step explanation:
My brother-in-law lived in Cape Verde for 2 years, and he is fluent in Portuguese as a result.
Answer:
Portuguese is the official language of Cape Verde
Which classifications within the real number system decribe all numbers in the set -1, 1, 0, 14/2, square root 25
Answers
The classification within the real number system that describes all numbers in the set -1, 1, 0, 14/2, square root 25 is; Rational Numbers
How to classify real numbers?
Real numbers can be defined as the union of both rational and irrational numbers.
Rational numbers are numbers that can be represented by fractions, such as exact roots and repeating decimals.
Irrational numbers cannot be represented by fractions, such as non-repeating decimals and non-exact roots.
Now;
-1 is a rational number
1 is a rational number
14/2 is a rational number
The square root of 25 is equal to 5 as 25 is a perfect square of 5. Hence, as 5 is an integer and can be expressed in the form of p/q root, then we say that 25 is rational number
Read more about Real Numbers at; https://brainly.com/question/19941539
#SPJ1
what is the surface area of triangular pyramid?
Answers
Answer:
223.5 in²
Step-by-step explanation:
The surface area of a triangular pyramid comprises:
Area of the base triangle.Area of 3 congruent side triangles.Area of a triangle
[tex]\sf A=\dfrac{1}{2}bh[/tex]
where:
b = baseh = heightFrom inspection of the diagram:
Base triangle: b = 10 in, h = 8.7 inSide triangles: b = 20 in, h = 12 in[tex]\begin{aligned}\implies \textsf{Area of the base triangle} & = \sf \dfrac{1}{2} \cdot 10 \cdot 8.7\\& = \sf 5 \cdot 8.7\\& =\sf 43.5\:in^2\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{Area of a side triangle} & = \sf \dfrac{1}{2} \cdot 10 \cdot 12\\& = \sf 5 \cdot 12\\& =\sf 60\:in^2\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{S.A. of the triangular pyramid} & = \textsf{base triangle}+\textsf{3 side triangles}\\& = \sf 43.5 + 3(60)\\& = \sf 43.5 + 180\\& = \sf 223.5\:in^2\end{aligned}[/tex]
Therefore, the surface area of the given triangular pyramid is 223.5 in².
10.
7
TR
Connect to Everyday Life Compare
the door's height to the desk's height
using multiplication and addition.
8 ft
2 ft
Answers
Using proportions and multiplication, it is found that the door's height is 4 times greater than the desk's height.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The ratio between two amounts a and b is the proportion of a to b, that is, the division of a by b.
For this problem, we have that:
The door's height is of 8 ft.The desk's height is of 2 ft.8/2 = 4, hence, the door's height is 4 times greater than the desk's height.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Please hurry
Solve for c.
a = 11+4b- 4c
i think c is correct
Answers
Answer:
I'm not sure, but what I got as my answer was c= -a/4 + 11/4 + b
Step-by-step explanation:
A school district receives a donation of 15,000 pencils. At one of the middle school in the district, there are 4 math classes. At each of the other three middle schools in the district, there are 6 math classes each. Each math class gets the same number of pencils. How many pencils does each math class get?
Answers
Hence , the number of pencil's each math class get 1500 .
A numerical expression in arithmetic are often a mixture of numbers, and integers combined mistreatment mathematical operators like addition, subtraction, multiplication, or division.Let the number of pencil's each math class have be "x".
It is given that one middle school have 4 math classes and other three middle school have e 6 math classes .
Then number of pencil's 4 math classes get = 4x
The number of pencil's 6 math classes get = 6x
Total number of pencil's = 15,000
According to question
4x + 6x = 15000
10x = 15000
x = 15000/10
x = 1500
Learn more about numerical expression here :
https://brainly.com/question/4344214
#SPJ1
Determine the value of c in the diagram. C 50°
Answers
Answer: 10
Step-by-step explanation:
The value of C is 10, because if 50° was in half, it would been 10 and 5.
2. Which statement correctly describes the
perpendicular bisector construction below?
Answers
The statement correctly describes the perpendicular bisector construction below The construction of JK to bisect GH: Option D is the correct answer
What is perpendicular bisector?The term perpendicular bisector refers to the line that divides another line into two equal parts, making an angle of 90 degrees. The term is made up of two words, perpendicular and bisector.
Perpendicular refers to angle 90 degrees, while the bisector refers to dividing into two equal parts.
In the picture, the main line is GH while JK is the line constructed to bisect the main line
Read more on perpendicular bisector here: https://brainly.com/question/11006922
#SPJ1
Translate the sentence into an equation.
Six more than the quotient of a number and 4 is equal to 8.
Use the variable x for the unknown number.
Answers
Answer:
(n ÷ 4) + 6 = 8
Step-by-step explanation:
Quotient means The answer when you divide' So we are working in the division.
n ÷ 4 is the division part
It says 'and' which can also mean addition. So we add 6. So far our equation is: (n ÷ 4) + 6 (Brackets are needed as we are dividing n by 4 and not dividing n by 4+6)
Lastly it says the answer must be 8 so we add that at the end. So the answer is:
(n ÷ 4) + 6 = 8
Simplify : p^2-p-12/p^2-10p+24
Answers
Step-by-step explanation:
[tex] = \frac{ {p}^{2} - p - 12 }{ {p}^{2} - 10 + 24} \\ [/tex]
[tex] = \frac{ {p}^{2} - (4 - 3)p - 12 }{ {p }^{2} - (6 + 4)p + 6 \times 4} \\ [/tex]
[tex] = \frac{ {p}^{2} - 4p + 3p - 4 \times 3 }{ {p}^{2} - 6p - 4p + 6 \times 4 } \\ [/tex]
[tex] = \frac{p(p - 4) + 3(p - 4)}{p(p - 6) - 4(p - 6)} \\ [/tex]
[tex] = \frac{(p + 3)(p - 4)}{(p - 4)(p - 6)} \\ [/tex]
[tex] = \frac{p + 3}{p - 6} \\ [/tex]
☘️☘️☘️...
Whats 9,999 - 999 x (12 - 9) divided by 10?
Answers
Answer: 9699.3
Step-by-step explanation:
?
Find a + b, 9a + 3b, |a|, and |a − b|. a = 9i − 4j + 3k, b = 6i − 9k
Answers
1) a + b = ?
→ (9i − 4j + 3k) + (6i − 9k)
→ 15i - 4j - 6k
2) 9a + 3b = ?
→ 9(9i − 4j + 3k) + 3(6i − 9k)
→ (81i - 36j + 27k) + (18i - 27k)
→ 99i - 36j
3) |a| = ?
→ |9i − 4j + 3k|
→ 9i + 4j + 3k
4) |a − b| = ?
→ |(9i − 4j + 3k) - (6i − 9k)|
→ |3i - 4j + 12k|
→ 3i + 4j + 12k
Answer:
[tex]a+b=15i-4j-6k[/tex]
[tex]9a+3b=99i-36j[/tex]
[tex]|a| = 9i+4j+3k[/tex]
[tex]|a-b| = 3i+4j+12k[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}a = 9i-4j+3k\\b=6i-9k\end{cases}[/tex]
[tex]\begin{aligned}a+b & = (9i-4j+3k)+(6i-9k)\\& = 9i-4j+3k+6i-9k\\& = 9i+6i-4j+3k-9k\\& = 15i-4j-6k\\\end{aligned}[/tex]
[tex]\begin{aligned}9a+3b & = 9(9i-4j+3k) + 3(6i-9k)\\& = 81i-36j+27k+ 18i-27k\\& = 81i+ 18i-36j+27k-27k\\& = 99i-36j\end{aligned}[/tex]
[tex]\begin{aligned}|a| & = |9i-4j+3k|\\& = 9i+4j+3k\end{aligned}[/tex]
[tex]\begin{aligned}|a-b| & = |(9i-4j+3k)-(6i-9k)|\\& = |9i-4j+3k-6i+9k|\\& = |9i-6i-4j+3k+9k|\\& = |3i-4j+12k|\\& = 3i+4j+12k\end{aligned}[/tex]
A. Write the FF sets using the roster method:
B. Complete the FF by writing each set in three defferent ways :
Answers
The roster form of the given sets will be S = { 1, 2, 3, 4, 5, 6, 7, 8, 9}, S = { blue, red, green } and S = { Math, Science, English, Hindi, SST, Computer }.
We are given some sets in descriptive form.
We have to write it in the roster form.
The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.
1 ) The set of all counting numbers less than 10.
Roster form will be:
S = { 1, 2, 3, 4, 5, 6, 7, 8, 9}
2) The set of primary colors.
Roster form will be:
S = { blue, red, green }
3 ) The set of all subjects in grade 7 level:
Roster form will be:
S = { Math, Science, English, Hindi, SST, Computer }
Therefore, the roster form of the given sets will be S = { 1, 2, 3, 4, 5, 6, 7, 8, 9}, S = { blue, red, green } and S = { Math, Science, English, Hindi, SST, Computer }.
Learn more about roster form here:
https://brainly.com/question/2166579
#SPJ9
Justin says that the equation for the circle is (x−2)2+(y+1)2=4 . What is his error?
Answers
Justin says that the equation for the circle is (x−2)^2+(y+1)^2=4 . The error is in RHS there should be a square of radius like 16 should be come in RHS instead of 4.
A line that is bent such that its ends meet and all of its points are equally spaced from the middle. We gathered in a circle around the hearth. 2: something shaped like or like a circle.
Dimensional terms include circumference, diameter, radius, chord, segment, tangent, point of contact, arc, angles on major and minor arcs, angle of center, and sectors. A circle's circumference is the distance that surrounds it.
Learn more about circle here
https://brainly.com/question/24375372
#SPJ9
What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
O all real numbers greater than or equal to -2
O all real numbers greater than or equal to -3
Answers
The domain of the function given on the graph is basically all numbers which are real and greater than or equal to -3.
Given a graph of a function.
We are required to choose the correct domain of the function from the options.
Function is basically a relationship between two or more variables that are expressed in equal to form. The values that we enter in the function are known as part of domain of that function and the values that we get from the function are known as part of range of that function.
Because the lowest point on x axis on which the curve starts is -3 and it continuously increases, so the domain of the function given on the graph is basically all real numbers which are greater than or equal to -3.
Hence the domain of the function given on the graph is all real numbers which are greater than or equal to -3.
Learn more about domain at https://brainly.com/question/26098895
#SPJ9
Question is incomplete as it should include the attached figure.
Solve for c.
2c 12c + 13c = 12
Answers
The value of c is 4.
Here, we are given an equation
2c - 12c + 13c = 12
Since, all the terms on the left hand side have a c in them, we can take it common outside the bracket as follows-
c (2 - 12 + 13) = 12
or c (2 + 13 - 12) = 12
Firstly, we add the positive terms in the bracket which will give us
c (15 -12) = 12
Now, we subtract 12 from 15 to get
c (3) = 12
or 3c = 12
Dividing by 3 on both sides we get
c = 12/3
c = 4
Thus, the value of c is 4.
Learn more about linear equations here-
https://brainly.com/question/13729904
#SPJ9
Your question was incomplete. Find the full content below-
Solve for c.
2c-12c+13c=12
Find the area and perimeter.
The figure shows a rectangle. The length of the rectangle is given by 9 x units. The width of the rectangle is given by 2 x plus 7 units.
18x2 + 63x; 22x + 14
63x2 + 16; 22x + 14
18x2 + 63x; 16x + 2
63x2 + 18; 11x + 7
Answers
The area and the perimeter are 18x^2 + 63x and 22x + 14
How to determine the area and the perimeter?The given parameters are
Length = 9x
Width = 2x + 7
The area is calculated as
Area = Length * Width
So, we have
Area = 9x * (2x + 7)
This gives
Area = 18x^2 + 63x
The perimeter is calculated as
P = 2 * (Length + Width)
So, we have
P = 2 * (9x + 2x + 7)
Evaluate
P = 22x + 14
Hence, the area and the perimeter are 18x^2 + 63x and 22x + 14
Read more about area and perimeter at:
https://brainly.com/question/19819849
#SPJ1
Guys I don’t know the answer tell me the remainder too
Answers
Answer:
119 R5
divide divide divide divide
The answer is
.119 R 12.........................................
(x³- 3x²+2x+1)/x²-4x+4 dx (dx/dy) + (x²+4y-y²)/(²√4y+y²)
Answers
Answer:
y=1 x=1
×[[×[+[[+[+[+[+[+[+[+[+[+[[
(A) Find the slope of the line that passes through the given points_
(B) Find the point-slope form of the equation of the line.
(C) Find the slope-intercept form of the equation of the line.
(D) Find the standard form of the equation of the line.
(4,2) and (11,8)
Answers
a) The slope of the line is 6 / 7.
b) The point-slope form of the equation of the line is y - 2 = (6 / 7) · (x - 4).
c) The slope-intercept form of the equation of the line is y = (6 / 7) · x - 17 / 7.
d) The point-slope form of the equation of the line is - 6 · x + 7 · y + 17 = 0.
How to find the equation of the line in three different forms
There are three different forms of the equation of the line:
Point-slope
y - y' = m · (x - x') (1)
Slope-intercept
y = m · x + k (2)
Standard
a · x + b · x + c = 0 (3)
Where:
m - Slopek - y-Intercepta) The slope that passes through the two given points is found by secant line formula:
m = [8 - 2] / [11 - 4]
m = 6 / 7
b) The point-slope form of the equation of the line is:
y - 2 = (6 / 7) · (x - 4)
c) The slope-intercept form of the equation of the line is:
y - 2 = (6 / 7) · x - 24 / 7
y = (6 / 7) · x - 17 / 7
d) The standard form of the equation of the line is:
7 · y = 6 · x - 17
- 6 · x + 7 · y + 17 = 0
To learn more on equations of the line: https://brainly.com/question/2564656
#SPJ1
Find PD if the coordinate of P is -7 and the coordinate of D is -1.
Answers
The length of PD is 6 units given that he coordinate of P is -7 and the coordinate of D is -1.
We are given that the coordinate of point P is - 7 and the coordinate of point D is - 1
We need to find the distance between the point P and point D.
The length of PD is the distance between point P and point D which will be calculated as:
PD = | P + D |
Substituting the values, we get that:
PD = | - 7 + - 1 |
PD = | - 6 |
PD = 6 units.
Therefore, the length of PD is 6 units given that he coordinate of P is -7 and the coordinate of D is -1.
Learn more about coordinate here:
https://brainly.com/question/11337174
#SPJ9
3x + 6y = 9 solve for x
Answers
Answer:
x= -2y+3
Step-by-step explanation:
First move the variable to the right: 3x= 9-6y
Next divide both sides of the equation by 3: x=3-2y
Lastly reorder the numbers, the variable should be placed first: x= -2y+3
4. — 1+4= + 12 10 1 2 3 4 5 can you answer this?
Answers
Answer:
7=37
Step-by-step explanation:
no solution problem
a = 18t + 5 4) Leo made an initial deposit to a savings account. Each week thereafter, he deposited a fixed amount into the account. The equation above models the amount, a, in dollars, that Leo has deposited after t weekly deposits. According to the model, how many dollars was Leo's initial deposit? (Disregard the $ sign when gridding your answer.) 5 6 8 9
Answers
According to the model, Leo's initial deposit was $0
According to the model, how many dollars was Leo's initial deposit?The model is given as
a = 18t + 5
When he makes his initial deposit, the value of t is
t = 0
i.e. this represents his balance before he starts saving on a weekly basis
Substitute 0 for t in the equation a = 18t + 5
So, we have
a = 18 * 0 + 5
Evaluate
a = 5
Hence, Leo's initial deposit was $0
Read more about linear functions at:
https://brainly.com/question/15602982
#SPJ1
f(x) = 4x³ + 5x² 3x6
g(x) = 4x - 5
Find (f - g)(x).
Answers
The value of (f-g)(x) is 4x3+5x2-7x-1.
Real- or complex-valued functions defined on the set Z+ of positive integers are arithmetic functions. They explain arithmetic characteristics of numbers and are frequently applied in number theory. For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-" Multiplication (Identifying the result; "" Finding the quotient in division (")Mathematical branch known as arithmetic deals with the study and use of numbers, relationships between numbers, and observations on numbers.
f(x)=4x3+5x2-3x-6
g(x)=4x-5
Therefore,
(f-g)(x)=f(x)-g(x)
=(4x3+5x2-3x-6) – (4x-5)
= 4x3+5x2-3x-6-4x+5
=4x3+5x2-(4+3)x-(6-5)
=4x3+5x2-7x-1
Hence, the value of (f-g)(x) is 4x3+5x2-7x-1
To learn more about value of x visit:
brainly.com/question/21481562
#SPJ9
Consider Line 2, which has the equation: y = = - 1/3x + 14, Give the equation of the line parallel to Line 2 which passes through: (-7,4).
Answers
The equation of teh second line is y = -1/3x + 5/3
How to determine the equation?The first equation is given as
y = -1/3x + 14
The slope of the above equation is
m = -1/3
Parallel lines have equal slope
So, the slope of the other line is
m = -1/3
The equation is then calculated as
y = m(x - x1) + y1
So, we have
y = -1/3(x + 7) + 4
Expand
y = -1/3x - 7/3 + 4
Evaluate
y = -1/3x + 5/3
Hence, the equation of teh second line is y = -1/3x + 5/3
Read more about linear equation a:
https://brainly.com/question/14323743
#SPJ1
Let f(X)=3√x
if g(x) is the graph of the f(x) shifted down 1 units and left 5 units write a formula for g(x)
g(x)=
Answers
g(x) = 3√(x-5) -1
The process of altering a graph to produce a different version of the preceding graph is known as graph transformation. The graphs can be moved about the x-y plane or translated. They may also be stretched, or they may undergo a mix of these changes.
Horizontal stretching: It means the graph is elongated or shrink in x direction.
Vertical stretching : It means the graph is elongated or shrink in y direction
Vertical translation : It means moving the base of the graph in y direction
Horizontal translation : It means moving the base of the graph in x direction
According to rules of transformation f(x)+c shift c units up and f(x)-c shift c units down.
Therefore, in order to move the graph down 1 units, we need to subtract given function by 1 , we get
g(x) = 3√x -1
According to rules of transformation f(x+c) shift c units left and f(x-c ) shift c units right.
Therefore, in order to move the graph left by 5 units, we need to add given function by 5 , we get
g(x) = 3√(x-5) -1
To learn more about graphical transformation, refer to https://brainly.com/question/4025726
#SPJ9