Answer:
[tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}[/tex]
Step-by-step explanation:
Notice that [tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=\frac{12(0)e^{0}-12(0)}{cos(5(0))-1}=\frac{0}{0}[/tex], which is in indeterminate form, so we must use L'Hôpital's rule which states that [tex]\lim_{x \to c} \frac{f(x)}{g(x)}=\lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]. Basically, we keep differentiating the numerator and denominator until we can plug the limit in without having any discontinuities:
[tex]\frac{12xe^x-12x}{cos(5x)-1}\\\\\frac{12xe^x+12e^x-12}{-5sin(5x)}\\ \\\frac{12xe^x+12e^x+12e^x}{-25cos(5x)}[/tex]
Now, plug in the limit and evaluate:
[tex]\frac{12(0)e^{0}+12e^{0}+12e^{0}}{-25cos(5(0))}\\ \\\frac{12+12}{-25cos(0)}\\ \\\frac{24}{-25}\\ \\-\frac{24}{25}[/tex]
Thus, [tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}[/tex]
Help help help help help help help
Answer:
14 :)
Step-by-step explanation:
28/2 = 14
Have an amzing day!!
Please rate and mark brainliest!!
Adam is purchasing a new television that costs $2,187.96 after tax. He borrowed the money from his parents and must pay back the full amount plus simple interest at the rate of 3.5%. What is the interest he will pay if he takes 2 years to pay his parents back? (Include Decimal with the cents; No Commas)
Using simple interest, considering the parameters stated in the exercise, it is found that he will pay an interest of $153.16.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of interest after t years in is modeled by:
I = Prt
In which:
P is the initial amount.r is the interest rate, as a decimal.In this problem, the parameters are given as follows:
P = 2187.96, r = 0.035, t = 2.
Hence, the interest paid will be of:
I = Prt = 2187.96 x 0.035 x 2 = $153.16.
More can be learned about simple interest at https://brainly.com/question/25296782
Write the equation of the trigonometric graphs.
Answer:
[tex]2 \cos(4x) [/tex]
Step-by-step explanation:
The highest and lowest value is 2 and -2 respectively so the amplitude is 2.
That also means the vertical translation is 0.
The graph is reaches it max every pi/2 units so the period is
pi/2.
Since the graph intersects a non zero value at 0, it will be the cosine function.
Step 2: A cosine function is
[tex]a \cos(b(x - c)) + d[/tex]
where a is the amplitude
[tex] \frac{2\pi}{ |b| } [/tex]
is the period
C is the horinzontal shift
d is the vertical shift
We know a is 2
D is 0.
To find b,
[tex] \frac{2\pi}{b} = \frac{\pi}{2} [/tex]
[tex]b = 4[/tex]
So as of right now we have
[tex]2 \cos(4x) [/tex]
Answer(s):
[tex]\displaystyle y = 2sin\:(4x + \frac{\pi}{2}) \\ y = 2cos\:4x[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{8}} \hookrightarrow \frac{-\frac{\pi}{2}}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 2[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2sin\:4x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{8}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{8}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{8}} = \frac{-\frac{\pi}{2}}{4}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2sin\:(4x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [\frac{5}{8}\pi, 0],[/tex]from there to [tex]\displaystyle [\frac{\pi}{8}, 0],[/tex]they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
A square is inscribed in a circle. How much larger is the area of the circle than the area of the square?
ratio form
Answer:
π/2 : 1 or π : 2
Step-by-step explanation:
In the attachments I have a picture of a square inscribed in a circle.
Call the side of the square a. Therefore, the area of the square is a^2.
We can also see that the diagonal of the square is the circle's diameter.
Using the Pythagorean Theorem we find that the diagonal/diameter of the circle is a√2. Thus the radius is that divided by 2, which is (a√2)/2.
We also know that the formula for a circle's area is πr^2, so the area of the circle is π((a√2)/2)^2 --> π(a^2)(2)/4 --> π(a^2)/2.
Hence the ratio of the circle to the square is π(a^2)/2 to a^2 which is π/2 to 1 or π to 2.
Richard and Teo have a combined
age of 23. Richard is 2 years older than twice Teo's age. How old are Richard and
Teo?
Answer:
Richard= 16 years old
Teo= 7 years old
Step-by-step explanation:
Let Richard's and Teo's age be R and T years old respectively.
[tex]\textcolor{steelblue}{\text{Form 2 equations based on given information:}}[/tex]
R +T= 23 -----(1)
R= 2T +2 -----(2)
[tex]\textcolor{steelblue}{\text{Solving by substitution:}}[/tex]
Substitute (2) into (1):
(2T +2) +T= 23
3T +2= 23
3T= 23 -2
3T= 21
T= 21 ÷3
T= 7
Substitute T= 7 into (2):
R= 2(7) +2
R= 14 +2
R= 16
Thus, Richard is 16 years old and Teo is 7 years old.
z varies jointly with x and y. If x = 2, y = 3, and z = 4, write the variation equation and find z when x = −6 and y = 2.
Step-by-step explanation:
that means
z = k×x×y
4 = k×2×3 = k×6
k = 4/6 = 2/3
so, when x = -6 and y = 2, we get
z = 2/3 × -6 × 2 = 2 × -2 × 2 = -8
I need HELP with this question!
Answer:
It will be C
Step-by-step explanation:
Because it says least to greatest and C says 1/2 3/8 5/16 7/16 9/32 15/32 and that is least to greatest there you go
Fastest answer gets brainliest (must provide an explanation and steps for proof)
Answer:
[tex]\sf g(x+5) = \dfrac{x+6}{4x+17}[/tex]
explanation:
g(x + 5) || this function refers to x = x + 5
solving steps:
[tex]\sf g(x) = \dfrac{1+x}{-3+4x}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{1+(x+5)}{-3+4(x+5)}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{6+x}{-3+4x+20}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{x+6}{4x+17}[/tex]
Answer:
Given function:
[tex]g(x)=\dfrac{1+x}{-3+4x}[/tex]
To find [tex]g(x+5)[/tex], substitute [tex]x+5[/tex] into the function in place of [tex]x[/tex]:
[tex]\implies g(x+5)=\dfrac{1+(x+5)}{-3+4(x+5)}[/tex]
[tex]=\dfrac{1+x+5}{-3+4x+20}[/tex]
[tex]=\dfrac{x+6}{4x+17}[/tex]
Kiara and Mia went to a county fair. They each paid the same admission fee but they were in a different number of rides. Each ride costs the same the total amount they each spent is shown in the table
let's take admission fee= z
8z+11z=17.50+21.25
19z=38.75
z=38.25/19
z=2.4 (aprox)
Or In case of Kiara 17.50 amount paid in 8 rides
.so 1 ride=17.50/8
=2.1875
same In case of mia
so 1 ride=21.25/11
=1.9318.
but, they are not match so there is problem in your Questions.
Brainliest if correct
Answer:
6.1291 < 8.3 < 8.308 < 8.38
Step-by-step explanation:
Start by looking at the whole numbers.
6 < 8
Since the only whole numbers are 6 and 8, we can rule out that the smallest number, or with the least value, is 6.
Next, look at the tens place.
Since they are all 8.3--, we cannot find the next one until we look at the hundredths place.
Next, look at the hundredths place.
Keep in mind that 8.3 is the same as 8.300
There is 8.30 < 8.38 and 8.308 <8.380
Now we know the lowest value and the highest value! (6.1291 and 8.38)
Between the last two, let's figure out where they place
Look at the thousandths place.
8.300 < 8.308
Hence, the answer provided above!
6.1291 < 8.3 < 8.308 < 8.38
Hope this helps! :)
What is the total height of the plants that measured 1
1/8 and
1/4?
The temperature at 1:00 p.m. The temperature at 1:00 p.m. on Tuesday was -13°C. There was an increase of 6º per
hour starting at 1:00 p.m. Which of the following best represents the Celsius
temperature n hours after 1:00 p.m. on Tuesday?
A. -13 + bn
B. -13 - 6n
C. -13n + 6
D. -13n - 6
So
Equation in slope intercept form
y=mx+by=6n+(-13)y=6n-13Option A
Kevin made 4 identical necklaces each having beads and a pendant. The total cost of the beads and pendants for all 4 necklaces was $23.60. If the beads cost a total of 9.20 how much did each pendant cost
Write the Equation of the conic.
12. A circle with endpoints of a diameter at(1, -3) and (1,3).
Need help please thanks
Answer:
(x² -1) + y² = 9
Step-by-step explanation:
diameter=6 so radius means 6/2=3 (thus,radius²=3²=9)
centre (1 and midpoint of diameter is at y=0, so 1,0)
Jason measured rainfall for a science project. Last week it rained 3 1/8 inches in all. This week it rained 1 7/8 inches on one day and 2 3/4 inches on another. How many more inches did it rain this week than last week? Explain how you found your answer.
Answer:
1 1/2 inches
Step-by-step explanation:
To find how much more a second number is than a first number, the first is subtracted from fhe second. Here, we want to know how much more the second week total is than the first, so we subtract the first week's total from the second week's total.
__
We find the second week's total by adding up the values associated with the different days in the second week.
second week's total = 1 7/8 +2 3/4 = (1 +2) +(7/8 +6/8) = 3 13/8 = 4 5/8
Then the difference is ...
second week's total - first week's total
= 4 5/8 -3 1/8 = (4 -3) +(5/8 -1/8) = 1 4/8 = 1 1/2
It rained 1 1/2 inches more this week than last week.
A garden table and a bench cost $668 combined. The garden table costs $82 less than the bench. What is the cost of the bench?
Step-by-step explanation:
let the cost of the bench = x
the cost of the garden table = x + 82
x + (x + 82) = 668
2x + 82 = 668
2x = 586
x = 293
The bench costs $293 and the garden table costs 293 + 82 = $375
can you mark me as brainliest, it will help me a lot. thank you in advance
What's the area of this figure?
Answer:
58.5
Step-by-step explanation:
the area for a square is l x l so 9
the area for a rectangle is l x w so 33
the area for a rectangle is l x w /2 so 33 /2 = 16,5
so after adding them all up you get 58.5
Joe spins a spinner with a 1, 2, 3, and 4. He also flips a coin with heads and tails. what is the probability of Joe spinning a 1 and landing on heads?
Answer:
The probability of Joe spinning a 1 is a 1 out of 4 chance and the probability of him flipping heads is a 50/50 chance
Step-by-step explanation:
The spinner only has 4 numbers therefore getting any number out of those four would be a 1/4th probability. As for the coin, the coin only has 2 sides so there is a 50% chance it lands on heads or a 50% chance it lands on tails.
5. Gavin makes a homemade cleaner using į cup vinegar
for every 2 quarts of water.
Answer:
For every 2 quarts of water, ¹/₂ cup of vinegar is used.
⇒ To find the amount of vinegar, divide the number of quarts by 4.
⇒ To find the number of quarts, multiply the amount of vinegar by 4.
4 qt water = 4 ÷ 4 = 1 cup vinegar
1¹/₂ cups vinegar = 1¹/₂ x 4 = 6 qt water
8 qt water = 8 ÷ 4 = 2 cup vinegar
Plot the points on the graph (see second attached image).
Draw a line through the points.
Find 3 along the x-axis and trace up to the line. Trace along to the y-axis.
Therefore, Gavin would need to use 12 quarts of water with 3 cups of vinegar.
Help me plssssssssssss
Answer:
DC=12, AD=5, DB=13, 90 degrees
Step-by-step explanation:
Hope this helps!!!
Let me know if you want an explanation!
cos(theta)+1 / tan^2(theta) = cos(theta) / sec(theta) - 1
The total cost f(x), in dollars, for renting a bowling lane for x hours is shown:
f(x) = 2x + 12
What does f(14) represent?
A. The number of dollars it costs to rent the bowling lane for 14 hours
B. The number of games you can bowl for a cost of $14
ting
C. The number of games you can bowl in 14 hours
D. The number of hours the bowling lane can be rented for a cost of $14
find the measure of mousing angle and justify your answer with postulates and theorems.
Answer:
Step-by-step explanation:
By the same-side interior angles theorem,
If you spend 1.5 hours a week studying for English and 5 hours studying for math what is the ratio of time spent studying in math to studying for English?
Answer:
1.5/5
Step-by-step explanation:
For every 1.5 hours your spend studying English, you spend 5 hours studying Math.
Brainliest please?
In the adjoining figure, the parallel lines are marked by arrow lines. The value of angle 1 is:
Answer:
20°
Step-by-step explanation:
40°, 70° and 90° are the measures of the three angles of the quadrilateral.
Measure of fourth angle of the Quadrilateral
= 360° - (40° + 70° + 90°)
= 360° - 200°
= 160°
Measure of angle 1 will be equal to the measure of the linear pair angle of 160° as they are corresponding angles.
Thus,
[tex]m\angle 1 = 180\degree- 160\degree[/tex]
[tex]\implies\huge\purple{\boxed{ m\angle 1 = 20\degree}}[/tex]
Alternate method:
[tex]m\angle 1 = 180\degree- [360\degree-(40\degree+70\degree+90\degree)][/tex]
[tex]\implies m\angle 1 = 180\degree- [360\degree-200\degree][/tex]
[tex]\implies m\angle 1 = 180\degree- 160\degree[/tex]
[tex]\implies m\angle 1 = 20\degree[/tex]
Answer:
m∠1 = 20°
Step-by-step explanation:
Alternate interior angle theorem (z-angles): when two parallel lines are cut by a transversal, the resulting alternate interior angles are equal.
Therefore, because of the parallel lines, angle 1 is equal to the missing angle in the quadrilateral (see attached diagram - alternate angles marked in red).
Let x = unknown angle in the quadrilateral (marked in blue on attached diagram)
Sum of interior angles of a quadrilateral = 360°
⇒ x + 40° + 70° + 90° = 360°
⇒ x + 200° = 360°
⇒ x = 160°
Angles on a straight line add up to 180°
⇒ x + m∠1 = 180°
⇒ 160° + m∠1 = 180°
⇒ m∠1 = 20°
Match the angle measures with its equivalent.
Answer:
From top to bottom:
11π/12
-18 degrees
210 degrees
-5π/3
Step-by-step explanation:
Equation to change from radians to degrees:
(Radian number) x (180/π)
The trick is to remember that you want to cancel out the π when converting to degrees
Equation to change from Degrees to radians:
(degree number) x (π/180)
Bring in the π when converting to radians
So for the top one, you want to multiply 165 by π/180 to get
11π/12
Then the second one is -π/10 by 180/π to get
-18 degrees
and so forth
Answer:
Step-by-step explanation:
let be π=180 degrees.
165 degrees have to be 11π/12.
-π/10 will be -18 degrees.
7π/6 will be 210 degrees.
-300 degrees will be -5π/3
Write an equation of the line that passes through the points (1, -6) and
(5, -6).
Answer:
Step-by-step explanation:
Hello ;
y= -6
Find the measure of ∠b.
Answer:
B. 38°
Step-by-step explanation:
The angles of a triangle add up to 180.
So, 62 + 80 + b will add up to 180.
First, we add 62 =80, which gives us 142.
The we subtract 142 from 180, which gives us 38.
mark must at least 32 units of vitamin a 10 units of vitamin b and 55 units of vitamin c daily he can choose between pill #1 which contains 8 units of a 1 unit of b and 2 units of c or pill #2 which contains 2 units of a and 1 unit of b and 7 units of c pill #1 cost $0.15 and pill #2 cost $0.35 how many of each pill should he buy in order to minimize his cost?
He buys blank of pill #1 and blank of pill #2
the minimum cost of $
PLEASE HELP ASAP!!! IM STUCK ON THIS
Answer:
Pill 1 costs 25e, and pill 2 costs 75e. Complete parts a and below. An a. How many of each pill should he buy in order to minimize his cost? What is the minimum?
Step-by-step explanation:
Mrs. Reynolds has $153. She buys a bicycle for $105.
Then, she finds $20 at the bottom of her purse.
How much money does she have now? Use the bar diagrams to help you.
Step 1:
Step 1: a bar diagram shows 105 and m, the money left after buying a bike. Together 105 and m are equal to 153.
Step 2:
Step 2: a bar diagram shows that 20 and m is equal to s, the money now.
Enter your answer in the box.
Mrs. Reynolds has $
now.
Answer:
$68
m=48 s=68
Step-by-step explanation:
153-105=48+20=68