Lim x>0 (x(e^3x - 1)/(2 - 2cosx))
Evaluating the limand directly at x = 0 yields the indeterminate form 0/0. If L'Hopital's rule is known to you, you can compute the limit by applying it twice:
[tex]\displaystyle\lim_{x\to0}\frac{x\left(e^{3x}-1\right)}{2-2\cos(x)} = \lim_{x\to0}\frac{3xe^{3x}+e^{3x}-1}{2\sin(x)} \\\\\\ = \lim_{x\to0}\frac{9xe^{3x}+6e^{3x}}{2\cos(x)} = \frac62=\boxed{3}[/tex]
Which statement is true about the equations
-3x + 4y = 12 and 1/4x-1/3y = 1
O The system of the equations has exactly one solution at (-8, 3).
O The system of the equations has exactly one solution at (-4, 3).
O The system of the equations has no solution; the two lines are parallel.
O The system of the equations has an infinite number of solutions represented by either equation.
Trigonometric ratio: find an angle measure
Answer:
[tex]T =56.3[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Measure of T
This is calculated as:
[tex]\cos T = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos T = \frac{5}{9}[/tex]
Take arccos
[tex]T = \cos^{-1}{(5/9)}[/tex]
[tex]T =56.3[/tex]
The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x. Find the average value of the cost function over the interval [0, 700).
Answer:
The average value of the cost function over the interval is of $23,500.
Step-by-step explanation:
Average value of a function:
The average value of a function, over an inteval [a,b], is given by:
[tex]A = \frac{1}{b-a} \int_{a}^{b} f(x) dx[/tex]
In this case:
Function [tex]C(x) = 20000 - 10x[/tex], interval with [tex]a = 0,b = 700[/tex]
So
[tex]A = \frac{1}{700} \int_{0}^{700} 20000+10x dx[/tex]
[tex]A = \frac{1}{700} (20000x+5x^2)|_{0}^{700}[/tex]
So
[tex]A = \frac{20000(700)+5(700)^2}{700} = 23500[/tex]
The average value of the cost function over the interval is of $23,500.
A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h and base length b of the box be so as to maximize its volume
Answer:
[tex]b=h=\sqrt{6}[/tex] m
Step-by-step explanation:
Let
Bas length of box=b
Height of box=h
Material used in constructing of box=36 square m
We have to find the height h and base length b of the box to maximize the volume of box.
Surface area of box=[tex]2b^2+4bh[/tex]
[tex]2b^2+4bh=36[/tex]
[tex]b^2+2bh=18[/tex]
[tex]2bh=18-b^2[/tex]
[tex]h=\frac{18-b^2}{2b}[/tex]
Volume of box, V=[tex]b^2h[/tex]
Substitute the values
[tex]V=b^2\times \frac{18-b^2}{2b}[/tex]
[tex]V=\frac{1}{2}(18b-b^3)[/tex]
Differentiate w. r.t b
[tex]\frac{dV}{db}=\frac{1}{2}(18-3b^2)[/tex]
[tex]\frac{dV}{db}=0[/tex]
[tex]\frac{1}{2}(18-3b^2)=0[/tex]
[tex]\implies 18-3b^2=0[/tex]
[tex]\implies 3b^2=18[/tex]
[tex]b^2=6[/tex]
[tex]b=\pm \sqrt{6}[/tex]
[tex]b=\sqrt{6}[/tex]
The negative value of b is not possible because length cannot be negative.
Again differentiate w.r.t b
[tex]\frac{d^2V}{db^2}=-3b[/tex]
At [tex]b=\sqrt{6}[/tex]
[tex]\frac{d^2V}{db^2}=-3\sqrt{6}<0[/tex]
Hence, the volume of box is maximum at [tex]b=\sqrt{6}[/tex].
[tex]h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}[/tex]
[tex]h=\frac{18-6}{2\sqrt{6}}[/tex]
[tex]h=\frac{12}{2\sqrt{6}}[/tex]
[tex]h=\sqrt{6}[/tex]
[tex]b=h=\sqrt{6}[/tex] m
Jamie left home on a bike traveling at 24 mph. Five hours later her brother realized Jamie had forgotten her wallet and decided to take it to her. He took his car and traveled at 64 mph. How many hours must the brother drive to catch Jamie?
Answer:
3 hrs
Step-by-step explanation:
5 * 24 = 120 miles
64x = 120 + 24x
40x = 120
x = 3 hrs
Find the mean of the following data set.
8, 5, 15, 12, 10
A. 12.5
B. 10
C. 14
D. 50
Answer:
10
Step-by-step explanation:
the sum of 8,5,15,12,10 is 50 and there are 5 numbers so 50 divided by 5 is 10 and it's mean is also 10
hope this helps !
Gemma recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was 16 miles per hour faster than on her way home. If Gemma spent a total of 1 hour bicycle, find the two rates.
first speed --- x mph
return speed -- x+16 mph
6/x + 6/(x+16) = 1
times each term by x(x+16)
6(x+16) + 6x = x(x+16)
x^2 + 4x - 96 = 0
(x-8)(x+12) = 0
x = 8 or x is a negative
her first speed was 8 mph
her return speed was 24 mph
check:
6/8 + 6/24 = 1 , that's good!
Find the distance between the two points in simplest radical form. (-6,1) and (−8,−4)
Answer: 5
Step-by-step explanation: I think it is 5
The quadrilateral KLMN is dilated with the center of dilation located at point M. Which statement is accurate?
1. The scale factor is 3, which means the length of the image of segment KL will be 1/3 times as long.
2. The scale factor is 1/3, which means the length of the image of segment KL will be 1/3 times as long.
3. The scale factor is 3, which means the length of the image of segment KL will be 3 times as long.
4. The scale factor is 1/3, which means the length of the image of segment KL will be 3 times as long.
Answer:
3. The scale factor is 3, which means the length of the image of segment KL will be 3 times as long.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure. If a point A(x, y) is dilated about the center of dilation located at O(a, b), the new point is at A'[k(x - a) + a, k(y - b) + b].
Quadrilateral KLMN has vertices at K(2, 1), L(-1, -5), M(6, -5) and N(6, 1). If it is dilated by 3, about the center M(6, -5), the new points are:
K' = (3(2 - 6) + 6, 3(1 - (-5)) + (-5)) = (-6, 13)
L' = (3(-1 - 6) + 6, 3(-5 - (-5)) + (-5)) = (-15, -5)
M' = (3(6 - 6) + 6, 3(-5 - (-5)) + (-5)) = (6, -5)
N' = (3(6 - 6) + 6, 3(1 - (-5)) + (-5)) = (6, 13)
Therefore the image of segment KL will be 3 times long.
Andrew wants to build a square garden and needs to determine how much area he has for planting the perimeter of the garden is between 12 and 14 feet what is the range if the possible areas
Answer:
9 ft^2 and 12.25 ft^2
Step-by-step explanation:
We need to figure out the area for a square with a perimeter of 12 feet and 14 feet.
A square has four sides that are all equal in length, therefore:
12/4 = 3
14/4 = 3.5
3 and 3.5 are the individual side lengths of the garden, so to find the area, we just multiply those numbers by themselves (since it is a square garden).
3*3 = 9
3.5*3.5 = 12.25
Therefore, the answer is 9 ft^2 and 12.25 ft^2
andrea uses 3.12 cups of flour in a recipe that makes 8 key lime cupcakes. Corey uses 2.52 cups of flour in a recipe that makes 7 key lime cupcakes. How much more flour per cupcake is needed for corey's recipe
Answer:
0.03 more flour per cupcake
Step-by-step explanation:
3.12/8 = 0.39
2.52/7 = 0.36
0.39 - 0.36 = 0.03
Hope this helps c:
A researcher believes that 5% of pet dogs in Europe are Labradors. If the researcher is right, what is the probability that the proportion of Labradors in a sample of 806 pet dogs would be greater than 4%
Answer:
0.9036
Step-by-step explanation:
Calculation to determine the probability that the proportion of Labradors
P(Proportion greater than 4%)
= P(z> 0.04 -0.05 /√0.05 * 0.95/806
= P(z > -1.30)
=0.9036
Thereforethe probability that the proportion of Labradors is =0.9036
The probability that a 38-year-old white male will live another year is .99813. What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy
Answer:
The insurance company should charge $1,873.5.
Step-by-step explanation:
Expected earnings:
1 - 0.99813 = 0.00187 probability of the company losing $1 million(if the client dies).
0.99813 probability of the company earning x(price of the insurance).
What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy?
Break even means that the earnings are 0, so:
[tex]0.99813x - 0.00187(1000000) = 0[/tex]
[tex]0.99813x = 0.00187(1000000)[/tex]
[tex]x = \frac{0.00187(1000000)}{0.99813}[/tex]
[tex]x = 1873.5[/tex]
The insurance company should charge $1,873.5.
Identify the effect on the graph of replacing f(x) by A f(x)
Answer:
See explanation
Step-by-step explanation:
Required
Effect of replacing [tex]f(x)[/tex] with [tex]f(x - h)[/tex]
f(x) is represented as: (x,y)
While
f(x - h) is represented as (x - h, y)
Notice the difference in both is that, the x value in f(x - h) is reduced by a constant h while the y value remain unchanged.
This means that the graph of f(x) will shift horizontally (i.e. along the x-axis) to the left by h units
(x-1)/(x-1)=1, what is the answer and explenation
2/9 divided by 5/6
help pleaseee
Hey there!
[tex]\mathsf{\dfrac{2}{9}\div\dfrac{5}{6}}[/tex]
[tex]\mathsf{= \dfrac{2\times6}{9\times5}}[/tex]
[tex]\mathsf{2\times 6 = \bf 12}[/tex]
[tex]\mathsf{9\times5 = \bf 45}[/tex]
[tex]\boxed{\mathsf{=\bf \dfrac{12}{45}}}[/tex]
[tex]\large\textsf{BOTH NUMBERS has the Greatest Common Factor (GCF) of 3}[/tex]
[tex]\mathsf{= \dfrac{12\div3}{45\div3}}[/tex]
[tex]\mathsf{12\div3=\bf 4}[/tex]
[tex]\mathsf{45\div3=\bf 15}[/tex]
[tex]\boxed{\mathsf{=\bf \dfrac{4}{15}}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{4}{15}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\~\frak{Amphitrite1040:)}}[/tex]
The greatest number of elements possible in
Answer:
4
9
Step-by-step explanation:
If X has 5 elements, and Y has 4 elements, and all 4 of Y's elements are the same as 4 of X's elements, then the intersection of the sets has 4 elements.
If X has 5 elements and Y has 4 elements, and they are all different, then the union of the sets has 9 elements.
Answer:
4
9
What is the value of k?
K=?
9514 1404 393
Answer:
k = 2
Step-by-step explanation:
The geometric mean theorem for the altitude tells you ...
ON = √(OL·OM)
ON² = OL·OM . . . . . square both sides
4² = 8·k . . . . . . . . substitute values
k = 16/8 = 2 . . . . divide by the coefficient of k
_____
Additional comment
The geometric mean theorem for the legs tells you ...
MN = √(MO·ML) ⇒ l = 2√5
LN = √(LO·LM) ⇒ m = 4√5
These relations come from the fact that corresponding sides of the right triangles are proportional. (All of the triangles are similar.)
Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x = 0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.
I error l ≤
Answer:
upper bound for the error, | Error | ≤ 0.0032
Step-by-step explanation:
Given the data in the question;
[tex]e^{0.4[/tex] < e < 3
Using Taylor's Error bound formula
| Error | ≤ ( m / ( N + 1 )! ) [tex]| x-a |^{N+1[/tex]
where m = [tex]| f^{N+1 }(x) |[/tex]
so we have
| Error | ≤ ( 3 / ( 3 + 1 )! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 3 / 4! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 3 / 24 ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 0.125 ) [tex]|[/tex] -0.0256 [tex]|[/tex]
| Error | ≤ ( 0.125 ) 0.0256
| Error | ≤ 0.0032
Therefore, upper bound for the error, | Error | ≤ 0.0032
Type the correct answer in each box. Use numerals instead of words.
Multiply the expressions.
If a = 1, find the values of b, c, and d that make the given expression equivalent to the expression below.
Answer:
a=1, b=9, c=-2, d=4
Step-by-step explanation:
20 and 1/2 feet times 13 and 1/8 feet is what total
Answer:
269 and 1/16 feet total (or 269.0625 feet to be precise)
Step-by-step explanation:
20 and 1/2 = 20.5
13 and 1/8 = 13.125
20.5 * 13.125 = 269.0625 feet = 269 and 1/16 feet
Please help:
Given: ∠4 is congruent to ∠2
Prove: ∠3 and ∠1 are supplementary
Statements and Reasons
Answer:
See Below.
Step-by-step explanation:
We can write a two-column proof.
Statements: Reasons:
[tex]\displaystyle 1)\, \angle 4\cong \angle 2[/tex] Given
[tex]\displaystyle 2)\, \angle 3 \cong \angle 4[/tex] Vertical Angles are Congruent
[tex]\displaystyle 3) \, \angle 1 + \angle 2 = 180[/tex] Linear Pair
[tex]\displaystyle 4)\, \angle 1 + \angle 4 = 180[/tex] Substitution
[tex]\displaystyle 5) \, \angle 1 + \angle 3 = 180[/tex] Substitution
[tex]\displaystyle 6) \, \text{$\angle 3$ and $\angle 1$ are supplementary}[/tex] Definition of Supplementary Angles
What is the value of 3 minus (negative 2)?
A number line going from negative 5 to positive 5.
Answer:
5
Step-by-step explanation:
3-(-2) will become positive 5. so number line will go towards positive 5.
PLEASE HELP!!! I have been adding and multiplying many different ways however my answer are wrong. How do I go about solving the perimeter then?
Answer:
66 m
Step-by-step explanation:
First, lets add up the numbers you know. It should be:
16, 8, 17, and 7.
Add them all up, and you will get:
48.
For the last two sides, subtract 7 from 16 to get 9.
For the last slide, subtract 8 from 17 to get 9.
Add them all up, and get 66.
ANSWER ASAP IM BEING TIMED
IF I GET AN A ON THIS I WILL DO ANOTHER POINT FREE DROP, PLEASE SHOW YOUR WORK
The lengths of three sides of a quadrilateral are shown below:
Side 1: 1y2 + 3y − 6
Side 2: 4y − 7 + 2y2
Side 3: 3y2 − 8 + 5y
The perimeter of the quadrilateral is 8y3 − 2y2 + 4y − 26.
Part A: What is the total length of sides 1, 2, and 3 of the quadrilateral? (4 points)
Part B: What is the length of the fourth side of the quadrilateral? (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)
Answer:
Part A
(1y^2+3y-6)+(4y-7+2y^2)+(3y^2-8+5y)
6y^2+12y-21
insert a digit in place of each ... to make a number that is divisible by 6
4 . . . 6
Answer:
2
Step-by-step explanation:
3x+4 number of terms
9514 1404 393
Answer:
2
Step-by-step explanation:
In this expression, the terms are the parts of the sum. They are 3x and 4. There are 2 terms.
What is the gradient of the blue line?
5
4
3
2
1
-5 -4 -3 -2 - 1 0 1. 2. 3. 4. 5
- 1
- 2
- 3
- 4
- 5
The line starts at (-5,3) and finishes (5,0.5)
Answer:
The gradient is -0.25
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-5,3)[/tex]
[tex](x_2,y_2) = (5,0.5)[/tex]
Required
The gradient (m)
This is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{0.5-3}{5--5}[/tex]
[tex]m = \frac{-2.5}{10}[/tex]
[tex]m = -0.25[/tex]
Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)
The x y-coordinate plane is given.
The function enters the window in the second quadrant, goes up and right becoming less steep, crosses the y-axis at approximately y = 3.2, changes direction at the approximate point (0.7, 3.3), goes down and right becoming more steep, and stops at the closed point (2, 3).
The function starts again at the open point (2, 1), goes up and right becoming more steep, goes up and right becoming less steep, passes through the open point (4, 4), changes direction at the approximate point (4.2, 4.1), goes down and right becoming more steep, and exits the window in the first quadrant.
(a) lim x → 2− f(x)
(b) lim x → 2+ f(x)
(c) lim x → 2 f(x)
(d) f(2)
(e) lim x → 4 f(x)(f) f(4)
Answer:
Hence the answer is given as follows,
Step-by-step explanation:
Graph of y = f(x) given,
(a) [tex]\lim_{x\rightarrow 2^{-}}f(x)=3[/tex]
(b) [tex]\lim_{x\rightarrow 2^{+}}f(x)=1[/tex]
(c) [tex]\lim_{x\rightarrow 2}f(x)= DNE \left \{ \therefore \lim_{x\rightarrow 2^{-}} f(x)\neq \lim_{x\rightarrow 2^{+}}f(x) \right.[/tex]
(d) [tex]f(2)=3[/tex]
(e) [tex]\lim_{x\rightarrow 4}f(x) = 4[/tex]
(f) [tex]f(4)= DNE.[/tex]{ Hole in graph}
Hence solved.
