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).
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Related Questions
Please help am in class need soon
Find the perimeter of triangle ABC. Found your answer to two decimal places.
Perimeter ABC=
Answers
The Perimeter of a triangle ΔABC is 27.68
Given ABC be triangle having vertices A(-2, -1), B(4, 3), C(-5, 7)
We need to find the perimeter of a triangle as
Perimeter of a triangle ΔABC = AB + BC +CA
Now we need to find distances as
D = √ (x₂ - x₁)² + ( y₂ - y₁ )²
AB = √ (4 - (-2))² + ( 3 - (-1) )²
= √ ( 4 + 2 )² + ( 3+1 )²
= √ (6)² + (4)²
= √ 36 + 16
= √ 52
= 7.21
BC = √ ((-5) - (4))² + ( 7 - (3) )²
= √ (-5 -4 )² + ( 7-3 )²
= √ (-9)² + (4)²
= √ 81 + 16
= √ 97
= 9.84
AC = √ ((-5) - (-2))² + ( 7 - (-1) )²
= √ (-5 -2 )² + ( 7+1)²
= √ (-7)² + (8)²
= √ 49 + 64
= √ 113
= 10.63
Perimeter of a triangle ΔABC = AB + BC +CA
= 7.21 + 9.84 + 10.63
= 27.68
Therefore, the Perimeter of the given triangle ΔABC = 27.68
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A large juice jug holds the equivalent of 10 drinking cups: 4 jugs hold 189 ounces more than 13 drinking cups. How many ounces does a cup hold? Find the given, unknown, known, and solve
Answers
The one cup holds 7 ounces of juice.
According to the statement
We have to find that the How many ounces does a cup hold.
So, For this purpose, we know that the
A quantity is a property of some object or collection of objects that is measurable.
From the given information:
A large juice jug holds the equivalent of 10 drinking cups: 4 jugs hold 189 ounces more than 13 drinking cups.
Let the amount held by a cup be y ounces.
So the large jug holds 10y ounces.
4 jugs hold 189 ounces more than 13 cups
4*10y=189+13y
40y-13y=189
27y=189
y=7
A cup holds 7 ounces.
So, The one cup holds 7 ounces of juice.
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x=b/4 = c solve for x
Answers
To solve for x, the given equation will be transformed as x = c - b/4
What is the equation?
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions in order to express their equivalence. The meanings of the (one or more) word equation and its cognates in various(different) languages can vary slightly. For instance, an equation in French is described as having one or more variables, whereas, in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Finding the values of the variables that result in equality is the first step in solving a variable equation. The variables for which the equation must be solved are known as unknowns, and the unknown values that fulfill the equality are known as the equation's outcomes. Individual equations and conditional equations are the two types of equations.Given that,
x-b/4 = c
To solve for x, the given equation will be transformed as-
x = c - b/4
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What number is under the fraction bar
Answers
Answer:
Denominator
Step-by-step explanation:
The Denominator is under the fraction bar. The numerator is above the bar
Answer:
Denominator
Step-by-step explanation:
Denominator: The number below the fraction bar in a fraction; it tells the total number of equal parts.
I hope this image helps.
URGENTTTT PLEASE ANSWERS Distance between two points whats the distance between the following points?
A. 12
B. 13
C. squareroot of 36
D. squareroot of 97
Answers
Answer: B
Step-by-step explanation:
2/3 miles in 10 mins what distance traveled in an hour
Answers
Answer
4 miles
Step-by-step explanation:
The distance traveled in an hour if a person travels at 2/3 miles in 10 mins is 4 miles.
In order words, the total distance which is travelled in one hour if a person travels a journey of 2/3 miles in 10 mins is 4 miles.
RatioThe ratio of the parameters given from the above is given below:
2/3 miles in 10 mins
Convert hour to minutes:
1 hour = 60 minuteslet
Distance travelled in an hour = xEquate ratio of distance to time taken
2/3 : 10 = x : 60
2/3 ÷ 10 = x / 60
2/3 × 1/10 = x/60
2/30 = x/60
cross product2 × 60 = 30 × x
120 = 30x
divide both sides by 30x = 120 / 30
x = 4 miles
Therefore, the distance traveled or covered in an hour if a person travels at 2/3 miles in 10 mins is 4 miles.
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help asap question in picture
Answers
[tex] \: \Large \mathbb{SOLUTION:}[/tex]
[tex] \: \: \rm{ \bigg( - \frac{5}{3} \bigg) {}^{2} } \\ [/tex]
[tex] \: \: \text{Determine the sign for exponential or radical expreasions}[/tex]
[tex] \: \: \rm{ \bigg( \frac{5}{3} \bigg) {}^{2} } \\ [/tex]
[tex] \: \: \text{Calculate the power}[/tex]
[tex] \: \: \rm \boxed{ \frac{25}{9} } \\ [/tex]
[tex] \frac{25}{9} \\ [/tex]
Solution:Determine the sign
[tex]( -\frac{5}{3} ) {}^{2} [/tex]
[tex]( \frac{5}{3} ) {}^{2} [/tex]
[tex] \frac{5 {}^{2} }{3 {}^{2} } \\ [/tex]
[tex] \frac{25}{3 {}^{2} } \\ [/tex]
[tex] \frac{25}{9} \\ [/tex]
Enter your answer as a proper fraction, or mixed number.
Answers
Answer:
3/14
Step-by-step explanation:
Answer:
3/14
Step-by-step explanation:
. The sides of a rectangle are (x+1) and (2x +5). If the perimeter is 36m, Find the value of x
Answers
3x+6=18
3x=12
x=4
if a number is divided by an d minused from an another number
Answers
This process required 3 to be subtracted 5 consecutive times, so again we see that 15 ÷ 3 = 5. The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient.
Division is a simple operation in which a number is divided. It's easiest to think of it as a number of objects being divided among a certain number of people.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
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The regular pentagon shown is rotated clockwise about center point P.
●P
Choose all degrees of rotation that will carry the regular pentagon onto itself.
A. 72°
B. 90°
C. 108°
D. 144°
E. 216°
Answers
Answer:
A. 72°
D. 144°
E. 216°
Step-by-step explanation:
are you tempted to calculate the internal angles ?
that is, I guess, the trap set by your teacher here, and it would be the wrong approach.
nevertheless, quickly just as a reminder :
the sum of all internal angles in a polygon is
(n - 2)×180°
n being the number of sides.
in our case that is
(5 - 2)×180 = 3×180 = 540°
so, each internal angle is 540/5 = 108°.
but we are not turning at an edge or vertex. no, we are turning the pentagon around is central point.
we are running each vertex along a circle arc. the center of that circle being P.
after every 1/5 of the circle arc there is a vertex of the pentagon.
and whenever we rotate one vertex on top of the next one, we carry the pentagon visually onto itself.
so, instead of a full circle rotation we need only 1/5 of that :
360 / 5 = 72°
and with every additional 1/5 of the circle arc (or 72°) we get it again.
that means at
72°
144°
216°
288°
360°
the pentagon carries onto itself.
therefore, A, D and E are correct.
Given that the curves are formed from
quarter circles,
find the area of the shaded region.
Give your answer in terms of TT.
4m
4m
The diagram is not drawn to scale
Answers
The area of the shaded region is 8π-16.
The side of the square is 4 m. Imagine a diagonal of the given square, which divides the shaded region into two equal parts due to symmetry. The radius of the quarter circle formed by one of the arcs and the two sides of the square is 4 m. The area of the quarter circle = 1/4πr²The area of the quarter circle = 1/4π4²The area of the quarter circle is 4π m². The diagonal and the two adjacent sides of the square form a right-angled triangle with a base of 4 m and a height of 4 m. The area of the triangle is 1/2*base*height. The area of the triangle is 1/2*4*4. The area of the triangle is 8 m². The area of the shaded region bisected by the diagonal = Area of quarter circle - Area of triangleThe area of the shaded region bisected by the diagonal = 4π-8 m²The area of the shaded region is twice the area of the shaded region bisected by the diagonal. The area of the shaded region = 2 * (4π-8)The area of the shaded region is 8π-16 m².To learn more about area, visit :
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I need help with number 5
Answers
If you had 3 apples and 2 bananas the total would still equal 5, etc.
ƒ(x) = −3x² + 3x
Find f (8)
Answers
Answer:
-168
Step-by-step explanation:
-3(8)^2+(3)(8)
(-3)(64)+(24)
-192+24
-168
A person can order a new car with a choice of 12 possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?
Answers
Answer:
96
Step-by-step explanation:
12 colors times 2 possibilities of with or without air conditioning is 24.
24 times two possibilities of with or without automatic transmission is 48.
48 times two possibilities of with or power windows is 96.
96 times two possibilities of with or CD player is 192.
Solve for n.
n = 3
8 x n = 32
nx 8 = 32
n = 4
32+8= n
32+ n = 8
n = 5
n = 6
Answers
Answer:
n = 4
Step-by-step explanation:
8 * n = 32
Solve for n
Divide each side by 8
8*n/8 = 32/8
n = 4
Can someone solve just the c problem
Answers
Applying the distributive property, the solution of x for item c is given as follows:
x = (3a - 8 - b)/(a - b).
What is the distributive property?The distributive property is when the outside term multiplies each of the inside terms of an expression.
For example, in this problem:
a(x - 3) = ax - 3a.b(x - 1) = bx - b.Hence the solution for x of the expression is found as follows:
a(x - 3) + 8 = b(x - 1).
ax - 3a + 8 = bx - b
ax - bx = 3a - 8 - b
x(a - b) = 3a - 8 - b
x = (3a - 8 - b)/(a - b).
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If the number 12,345x is divisible by 11, the lest digit of x must be....
Answers
Answer:
The last digit you multiplied by.
Step-by-step explanation:
It's not that hard, but here you go :)
If you multiplied 12 by 11 you would get 2 as your last digit, because 2 is the last digit of 12. (12x11=132)
So for 123 by 11, following this pattern, 3 is the last digit of 123 so the answer must end in 3. (123x11=1353)
If you still don't get the pattern I'll give you a few more examples here:
If you multiply 1234 by 11 you would get a number ending in 4 because the last digit of 1234 is 4! (1234x11=13574)
So what would be the last digit of 12345?
Hope this was helpful!
(The answer was 5 btw)
Question:
Given the demand equation p=190/q+10 where 10<0<85, for what value of q is | n | a maximum? For what value is it minimum?
Answers
The maximum and minimum value of η at q = 10 and q = 85 respectively.
The demand equation is p = 190/ (q + 10) where 10 < 0 < 85.
η is the elasticity of demand.
Then, the elasticity of demand is given as:
η = ( dq/ dp) × ( p / q )
Now, we have p = 190/ (q + 10)
Therefore,
p ( q + 10 ) = 190
pq + 10p = 190
q = ( 190 - 10p ) / p
Now,
dq / dp = ( d/dp ) ( ( 190 - 10p ) / p )
dq / dp = ( -190/ p² )
Substituting these values in the elasticity demand,
η = ( dq/ dp) × ( p / q )
η = ( -190/ p² ) × ( p / q )
η = ( -190/ pq )
η = ( -190/ [190 / (q + 10 ) ]q )
η = [ - ( q + 10 ) / q ]
| η | = | - ( q + 10 ) / q |
η = ( q + 10 ) / q = 1 + 10/q
The critical point is when | η' | = 0.
η' = ( d / dq ) ( 1 + 10/q )
η' = - 10/ q²
- 10/ q² = 0
Hence, - 10/ q² is not defined.
Therefore, the function is not defined at q = 0.
Therefore, q = 0 is not a solution.
We have 10 ≤ q ≤ 85
The value of functions at the endpoint,
At q = 10,
η = ( 1 + 10/q )
η = ( 1 + 10/10 )
η = 1 + 1 = 2
At q = 85,
η = ( 1 + 10/q )
η = ( 1 + 10/85 )
η = 1.11764
Therefore, the absolute value of the elasticity of demand is maximum at q = 10.
The absolute value of the elasticity of demand is minimum at q = 85.
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Grady's father is building a 15-meter fence with the start of the fence at coordinates(8, 5) and the midpoint of the fence at coordinates(3.5, -1) . What are the coordinates of the other end of the fence?
Answers
Based on the calculations, the coordinates of the other end of the fence are equal to (-1, -7).
What is a line segment?A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.
How to determine the coordinates of the other end of the fence?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint on x-coordinate is given by:
xm = (x₁ + x₂)/2
3.5 = (8 + x₂)/2
Cross-multiplying, we have:
7 = 8 + x₂
x₂ = 7 - 8
x₂ = -1.
Midpoint on y-coordinate is given by:
ym = (y₁ + y₂)/2
-1 = (5 + y₂)/2
Cross-multiplying, we have:
-2 = 5 + y₂
y₂ = -2 - 5
y₂ = -7.
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A bowl weighs 11/40 pound.
a. Express this weight as a decimal.
b. Explain how you can find the decimal by thinking of the denominator as a 4 and using mental math.
Answers
The weight as a decimal will be 0.275.
The way to fins the decimal using mental maths is to believe that it's 1/4.
How to compute the value?It should be noted that the information given is that we should convert 11/40 t decimal.
This simply means to divide and the answer is 0.275.
Also, the way to find the decimal using mental maths is to believe that it's 1/4.
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A movie company spent $12,000,000 making a feature film. If tickets to see the movie cost $8.00 each, determine the number of tickets that must be sold in order for the company to break even
Answers
Answer: They will need to sell 1,500,000 to break even.
12,000,000 / 8 is 1,500,000
40 divided by 20? I’m really confused I did the math and got 21 but the calculator say 2.
Answers
The calculated division of the numbers 40 divided by 20 is 2
How to calculate the division of the numbersFrom the question, we have the following parameters that can be used in our computation:
40 divided by 20
When represented as an equation, we have
40 divided by 20 = 40/20
Divide 40 by 20
So, we have the following result
40 divided by 20 = 2
Using the above as a guide, we have the following:
the result is 2
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your hourly wage of $15 differs from the average by less than or equal to $5
Answers
The mathematical expression of the statement is x - 15 <= 5
How to determine the mathematical expression?The statement is given as:
Hourly wage of $15 differs from the average by less than or equal to $5
Let the average hourly wage be x
So, we have:
Hourly wage of $15 differs from the average = x - 15
less than or equal to $5 => <=5
So, the expression is
x - 15 <= 5
Hence, the mathematical expression of the statement is x - 15 <= 5
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(a)-534° is found in quadrant
Answers
Answer: Quadrant 3
Step-by-step explanation:
Hard to explain.
For each of the right triangles, determine the measure of the missing side. Leave the measures in
exact form if irrational.
(if u can please show the work so i can get a better understanding)
Answers
Using the Pythagorean theorem, the missing sides are:
1. 5
2. 13
3. √15
4. 3
How to Apply the Pythagorean Theorem?The Pythagorean theorem is given as: c² = a² + b², where c is the longest side and a and b are the other two legs.
1. Missing side = √(3² + 4²) [Pythagorean theorem]
Missing side = 5
2. Missing side = √(12² + 5²) [Pythagorean theorem]
Missing side = 13
3. Missing side = √(4² - 1²) [Pythagorean theorem]
Missing side = √15
4. Missing side = √((√10)² - 1²) [Pythagorean theorem]
Missing side = √(10 - 1) = √9
Missing side = 3
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Side KN of figure KLMN is parallel to side LM. Figure KLMN is rotated 90 degress clockwise about Point P to produce Figure RSTU. Based on this information, select all statement that are true.
Answers
The figure KLMN is being rotated by 90°, which is a rigid transformation, the true statements are therefore;
(D) Figure RSTU is congruent to figure KLMN
(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
How can the similarities between the two figures following the rotation be found?The given parameters are;
In KLMN, KN||LM
The transformation applied to figure KLMN = A 90° clockwise rotation about point P.
The image of KLMN following the rotation transformation is Figure RSTU.
Please find attached a drawing of the possible diagram in the question obtained from a similar question online.
The options from the question are;
(A) [tex] \overline{ST}[/tex] is parallel to [tex] \overline{RU}[/tex]
(B) [tex] \angle R[/tex] is the same measure as [tex] \angle N[/tex]
(C) [tex] \overline{RS} [/tex] is the same length as \overline{MN}
(D) Figure RSTU is congruent to figure KLMN
(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
A rotation transformation is a rigid transformation, therefore;
The distances between any two points on the pre–image is the same as the distance between corresponding points on the image, which gives;
Figure KLMN [tex] is congruent to [/tex] Figure RSTU
Figure KLMN [tex] \cong [/tex] Figure RSTU
According to the postulate, Corresponding Angles of Congruent Figures are Congruent, we have;
[tex] \angle T \cong \angle M[/tex]
Which gives;
[tex] \angle T[/tex] = [tex] \angle M[/tex]
[tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
The correct options are therefore;
(D) Figure RSTU is congruent to figure KLMN
(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
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Set B = {a,b,c,d} and Set C = { b,d,f,g}. Find B u C.
Answers
Answer:
do ur best
Step-by-step explanation: somebody else might can help u
Bob mows lawns for 5 weeks during summer break. He mows 2 lawns every day. By the end of 5 weeks, how many lawns has Bob mowed?
Answers
Answer: 70
Step-by-step explanation:
7 days a week x 2 lawns = 14
14 lawns x 5 weeks = 70 lawns
Answer:
70 lawns
Step-by-step explanation:
If Bob mows lawns every day for 5 weeks this is how the equation would work:
2 * 7 = 14
14 * 5 = 70
I got the 7 because there's seven days per week.
For the equation, find three ordered pair solutions by completing the table. Then use any two of the ordered pairs to graph the equation.
Answers
For the linear function y = 0.5x. three ordered pairs are given as follows:
x = 0, y = 0.x = 2, y = 1.x = -2, y = -1.Using points (-2,-1) and (2,1), the graph of the function is given at the end of the problem.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the function is:
y = 0.5x.
Hence three pairs of points are given as follows, replacing the value of x in the equation to find y.
x = 0, y = 0.x = 2, y = 1.x = -2, y = -1.The graph of the function is given at the end of the answer.
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