Answers
Answer:
A
Step-by-Step Explanation:
We want to find the limit:
[tex]\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}[/tex]
Use direct substitution.
Hence:
[tex]\displaystyle{\Rightarrow 2e^\frac{\pi}{2}\cos(\frac{\pi}{2}})[/tex]
Recall the unit circle. cos(π/2) is simply 0. Hence:
[tex]\displaystyle{\Rightarrow 2e^\frac{\pi}{2}(0)=0[/tex]
Therefore:
[tex]\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}=0[/tex]
So, our answer is A.
Related Questions
There is a line that includes the point (6,–10) and has a slope of –9. What is its equation in point-slope form?
Answers
Answer:
A slope of zero means a horizontal line (parallel to the x axis). So the line is y=-6, which is the y intercept. There is no x term because y=-6 for all x.
Step-by-step explanation:
Answer: y + 10 = -9(x - 6)
Step-by-step explanation:
Use this formula to solve for point-slope form: y - y1 = m(x - x1)
m would be the slope and the given slope is -9
y1 refers to the given y coordinate and x1 refers to the given x coordinate.
y + 10 = -9(x - 6)
A proportion is an equation stating that two ratios are equivalent.
False
True
Answers
Answer:
A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions
Therfore it is true
We can multiply all values by the same amount and still have the same ratio.
The given statement is true.
We have given the statement,
A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions.
We have to determine whether the statement is true or false.
What is the proportion?Proportion is a mathematical comparison between two numbers.
A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions
Therefore it is true.
We can multiply all values by the same amount and still have the same ratio.
To learn more about the proportion of visits:
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Write the equation of the function y=6/x translated 5 units to the left and 4 units up
Answers
Answer:
f(x)= (6/x+5)+4
Step-by-step explanation:
y/x translated 5 units
y/x+5 then 4 units up y/(x+5) +4
IS ANYONE HERE GOOD AT CALCULUS?? IF SO, PLEASEEEE HELP ME!!!! An object’s velocity at time t is given by v(t) = –2 sin t. Let s(t) represent the object’s position at time t. If s(0) = 0, then s(t) = A) 2 cos t. B) –2 cos t. C) 2 cos t – 2. D) –2 cos t + 2.
Answers
Answer: C
Step-by-step explanation:
Since we are given velocity, which is the first derivative, we have to fidn the antiderivative of velocity to get position.
∫-2sint dt
s(t)=2cos(t)+C
Since we are given s(0)=0, we can plug in the values to find C, constant.
0=2cos(0)+C
0=2(1)+C
0=2+C
C=-2
Now that we know our constant, we can find out position.
s(t)=2cos(t)-2
Answer:
Sorry this is not an answer but it wouldn't let me comment go you friend me or something so we can work on calculus together
Step-by-step explanation:
can someone help me please? thanks!
Answers
Answer:
V = 11/21
Step-by-step explanation:
Formula: V = 4/3πr³
Simply plug in r to find volume
V = 4/3π(1/2)³
V = 0.52381
And we have our answer!
A card is drawn at random from a standard pack of playing cards. Then a fair coin is flipped. What is the probability of selecting an Ace and the coin landing on tails?
Answers
Answer:
1/26
Step-by-step explanation:
In a standard pack of cards, there are 52 total cards and 4 aces, two black aces and two red aces.
The probability of selecting an ace is therefore:
4/52 = 1/13
The probability of flipping a coin and it landing on tails is:
1/2
Therefore, the probability of selecting an Ace and the coin landing on tails is:
1/13 * 1/2 = 1/26
Answer this, please. I'm having trouble or I'm just dumb.
Answers
Answer:
f(x)=(5+a)/(a-1)
Step-by-step explanation:
input a+2 for x
f(x)=(a+5)/(a-1)
and no ur not dumb u just need practice :D
Answer:
-4 and 1/7 is your answer.
Step-by-step explanation:
substitute 19 for x in the equation.[tex]f(x)=\frac{3}{19+2} -\sqrt{19-3}[/tex]
do the processes.[tex]f(x)=\frac{3}{21} -\sqrt{16}\\f(x)=-\frac{1}{7} -4\\f(x)= -4\frac{1}{7}[/tex]A line which intersects one of two parallel lines intersects the other also.
A. Always
B. Sometimes
C. Never
(I put always, but that turned out to be incorrect)
Answers
Answer:
Sometimes
Step-by-step explanation:
When a line intersects one of two parallel lines, it will sometimes intersect the other also.
Ex. If one of the parallel lines was at y=2, the intersecting line could be y=2.
The correct answer is- B. sometimes
A line which intersects one line need not necessarily intersect other line also , also the two parallel lines never intersect.
What is transversal?
A transversal is a line that passes through two lines in the same plane at two distinct points. Its a line that crosses other lines.
here, in the question its not mentioned about transversal so its not necessary that line which intersects one parallel line also intersect other. Hence, its sometimes either or situation that depends upon the probability of the situation that a line will intersect or not.
hence, the correct answer is- B. Sometimes.
learn more about "transversal" here
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Which functions graph is a translation of the graph of f(x)= 3x^2 + 4 seven units down?
A. F(x)= -4x^2 +4
B. F(x)= 10x^2+4
C. F(x)= 3x^2-3
D. F(x)= 3x^2 +11
Answers
Answer:
Option C
Step-by-step explanation:
Consider the function f ( x ) = 3x^2 + 4;
[tex]f ( x ) = 3x^2 + 4,\\\\4 = vertex ( y - intercept ),\\\\\\[/tex]
Now if this graph were to be translated 7 units down, considering the function was f ( x ) = 3x^2, the new graph would be f ( x ) = 3x^2 - 7. The same concept is applied to the graph f ( x ) = 3x^2 + 4;
[tex]4 - 7 = - 3,\\f ( x ) = 3x^2 - 3\\\\Solution - Option C[/tex]
* Note that a translation doesn't effect the rate with which the graph changes, it only effect's it's position on the coordinate plane
Hope that helps!
IM STUCK ON THIS QUESTION! PLEASE HELP FAST
Answers
Answer:
The function has point discontinuity (a hole in fancy terms)
Step-by-step explanation:
If you factor out the top, you will get x(x + 2)(x + 5). You can right away cross out the (x + 5)'s. When you do so, you will create a hole in the graph, because x ≠ 5. Therefore, your answer is the 1st option.
Write a quadratic function that has an axis of symmetry of x=7
Answers
Answer:
If a function has an axis of symmetry x = a,
Step-by-step explanation:
then f (x) = f (- x + 2a). The following graph is symmetric with respect to the origin. In other words, it can be rotated 180o around the origin without altering the graph. Note that if (x, y) is a point on the graph, then (- x, - y) is also a point on the graph.The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
On the right triangle shown below, calculate the height of the traffic
light. Round your answer to the nearest whole number. Enter the
value without units.
Answers
Answer:
x = 14
Step-by-step explanation:
Tan 25 = [tex]\frac{opposite}{adjacent}[/tex]
Where opposite = x, Adjacent = 30 m
=> 0.466 x 30 = x
=> x = 14
Answer:
[tex]\Huge \boxed{\mathrm{14 \ meters}}[/tex]
Step-by-step explanation:
We can use trigonometric functions to solve for the problem.
[tex]\displaystyle \sf tan( \theta )=\frac{opposite \ side}{adjacent \ side}[/tex]
Plug in the values and evaluate.
[tex]\displaystyle \sf tan( 25\° )=\frac{x}{30}[/tex]
Multiply both sides by 30.
[tex]\displaystyle \sf 30 \cdot tan( 25\° )=x[/tex]
[tex]\sf x=13.98922974...[/tex]
The height of the traffic light is 14 meters (rounded to nearest whole number).
Pedro predicted that he would sell 128 novels. He actually sold 150 novels. What are the values of a and b in the table below? Percent Error Item Approximate value Exact value Error Absolute error Ratio Percent error Novels 128 150 a b a = Negative StartFraction 22 over 128 EndFraction; b = negative 17.2 percent a = Negative StartFraction 22 over 150 EndFraction; b = negative 14.7 percent a = StartFraction 22 over 150 EndFraction; b = 14.7 percent a = StartFraction 22 over 128 EndFraction; b = 17.2 percent
Answers
Answer:
C)
AKA
a= 22/150; b= 14.7%
AKA
a = StartFraction 22 over 150 EndFraction; b = 14.7 percent
__________________________________________________
I am very sorry if this was wrong for you, but it was correct for me.
Brainliest would be apreaciated, but if not thats completley ok.
Sorry I dont have an explaination im not very good at those.
Sorry abt my spelling i know i suck.
And sorry I could not help earlier.
hope it helped :)
Answer: C)
AKA
a= 22/150; b= 14.7%
AKA
a = StartFraction 22 over 150 EndFraction; b = 14.7 percent
What is the length of Line segment B C? Round to the nearest tenth. Triangle A B C is shown. Angle B C A is a right angle and angle C A B is 65 degrees. The length of hypotenuse B A is 16 centimeters and the length of B C is x. 6.8 cm 7.5 cm 14.5 cm 17.7 cm
Answers
Answer:
14.5 =x
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opposite side/ hypotenuse
sin A = BC / AB
sin 65 = x /16
Multiply each side by 16
16 sin 65 =x
14.50092459 =x
14.5 =x
Answer:
C on edge
Step-by-step explanation:
Which of the following are square roots of the number below check all that apply 144
Answers
The square root of 144 is ± 12
The correct answer choice is option C.
What is square root?Square root refers to a number which, when squared, yields another number.
For instance, the square root of 4 is ± 2
the square root of 9 is ± 3
the square root of 16 is ± 4
the square root of 25 is ± 5
Therefore, square root of 144 = ±12
that is, (12 × 12) or (-12 × -12)
Read more on square root:
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Complete question:
Which of the following are square roots of the number below check all that apply 144 a. ±14 b. ±44 c. ±12 d. ±41
Find the 75th term of the arithmetic sequence -21, -10,1, ...
Answers
Answer:
a(75) = 793
Step-by-step explanation:
Arithmetic Explicit Formula: an = a1 + (n-1)d
Step 1: Find equation
d = (1-(-10)) = 11
a1 = -21
an = -21 + 11(n-1)
Step 2: Plug in 75 as n
a(75) = -21 + 11(75-1)
a(75) = 793
And we have our final answer!
Factorize x^3-10x^2-53x-42
Answers
Answer:
(x+1)(x-14)(x+3)
Step-by-step explanation:
The first step in factorising polynomials is to find the smallest factor first. The way to do this is with trial and error. Lets see if x+1 is a factor.
According to the factor theorem, (x-a) is a factor of P(x) if and only when P(a) = 0
In this case we will use f(x) = ((x)^3)-((10x)^2)-53x-42
f(-1) = 0
Therefore (x+1) is a factor of the polynomial.
Now we divide the polynomial with (x+1) via long division to get (x^2)-11x-42.
We now factorise (x^2)-11x-42 using whatever method you would like. I'm going to use the AC method, where we find a number that multiplies to AC and adds to B, In this case AC = -42, and B = -11.
Therefore (x^2)-11x-42 factosied is (x-14)(x+3)
Now merge (x+1) with (x-14)(x+3)
The final answer is (x+1)(x-14)(x+3)
If this has helped, please consider making this the Brainliest answer!
Answer:
(x+1)(x+3)(x-14)
Step-by-step explanation:
=> x³-10x²-53x-42
We'll break 10x² and -53x into parts
=> x³+x²-11x²-11x-42x-42
Taking common
=> x²(x+1)-11x(x+1)-42(x+1)
Taking x+1 as common will make it
=> (x+1)(x²-11x-42)
Using mid term break formula
=> (x+1)(x²-14x+3x-42)
=> (x+1)[x(x-14)+3(x-14)]
Taking (x-14) as common
=> (x+1)(x+3)(x-14)
This is the required factorized form.
Hope it helps :)
the interior angles of a Pentagon are (y+13°),(y+15°),(y+23°),(y+29°), and(y+40°) a.Find the value of y b. Find the value of each interior angles
Answers
Answer:
y=84
first : 84+13=97
second : 84+15=99
third : 84+23=107
fourth: 84+29=113
fifth : 84+40 =124
97+99+107+113+124 = 540
Step-by-step explanation:
sum of interior angles of a pentagon=540 degreas
y+13+y+15+y+23+y+29+y+40=540
5y=540-(13+15+23+29+40)
y=84
first : 84+13=97
second : 84+15=99
third : 84+23=107
fourth: 84+29=113
fifth : 84+40 =124
97+99+107+113+124 = 540
Let A = {1, 2, 3, 4, 5} and B = {2, 4}. What is A ∩ B? (1 point)
A. {2, 4}
B. {1, 2, 3}
C. {1, 2, 3, 4}
D. {1, 2, 3, 4, 5}
Answers
Answer:
{2, 4}.
Step-by-step explanation:
A = {1, 2, 3, 4, 5} and B = {2, 4}.
A ∩ B?
This means intersection or what is in common
A ∩ B = {2, 4}.
Can anyone help me i am really confused
Answers
Answer:
125 cm³
Step-by-step explanation:
The volume (V) of a cube = s³ ( s is the length of the sides )
Since the shape is a cube then all sides are congruent, thus
V = 5³ = 5 × 5 × 5 = 25 × 5 = 125 cm³
Answer:
v=l×w×h 5×5×5=125cubedcm
Step-by-step explanation:
you see a cube has an equal length, width and height
1/6 converted to a decimal rounded to 3 dp?
Answers
Answer:
0.83?
Step-by-step explanation:
Step-by-step explanation:
1/6 or 1÷6 =
0.1666666r
What is the nth term rule of the quadratic sequence below -4,1,12,29,52,81,116
Answers
Step-by-step explanation:
29-12 is a 17 difference
52-29 is a 23 difference (adding 6 to the number 17)
81-52 is a 29 difference (adding 6 to the number 23)
116-81 is a 35 difference (adding 6 to the number 29)
Answer:
29-12 is a 17 difference
52-29 is a 23 difference (adding 6 to the number 17)
81-52 is a 29 difference (adding 6 to the number 23)
116-81 is a 35 difference (adding 6 to the number 29)
Step-by-step explanation:
which equation has no solution?
Answers
Answer:
Equation 5 + 2(3 + 2x) = x + 3(x + 1) has no solution.
Step-by-step explanation:
We are looking at two lines.
4(x + 3) + 2x = 6(x +2)
4x + 12 + 2x = 6x + 12
6x + 12 = 6x + 12
These are two identical lines, with an infinite number of solutions. (All points on the lines are the exactly the same).
5 + 2(3 + 2x) = x + 3(x + 1)
5 + 6 + 4x = x + 3x + 3
4x + 11 = 4x + 3
Both lines have the same gradient but have a different incline with the y axis. By definition, they are parallel to each other and there fore have zero solutions. Equation 5 + 2(3 + 2x) = x + 3(x + 1) has no solution, which is the answer we are looking for.
5(x + 3) + x = 4(x +3) + 3
5x + 15 + x = 4x + 12 + 3
6x + 15 = 4x + 15
These are two different lines with exactly one solution.
4 + 6(2 + x) = 2(3x + 8)
4 + 12 + 6x = 6x + 16
6x + 16 = 6x + 16
These are two identical lines, with an infinite number of solutions. (All points on the lines are the exactly the same).
Ashley and Beth drove from city A to city B in exactly 5 hours, not taking rest stops. Ashley drove up to the area located halfway between the two cities at the average speed of 40 miles per hour and then Beth drove the other half at an average speed of 60 miles per hour. How many hours did Beth drive on their trip?
Answers
Answer:
2 hours
Step-by-step explanation:
Time= 5 hrs
Ashley's speed= 40 mph
Beth's speed= 60 mph
Beth's time in travel= x
Since they drove the same distance, we have this equation:
60x=40(5-x)60x=200-40x100x=200x=200/100x=2 hoursIdentify the recursive formula for the following sequence. 8, 16, 32, 64, ...
Answers
Answer:
The recursive formula for the given sequence
[tex]t_{n}= (2)^{n+2}[/tex]
Step-by-step explanation:
Explanation:-
Given sequence is 8 , 16, 32, 64 ,.....
First term is a = 8
common ratio [tex]r = \frac{16}{8} =2[/tex]
[tex]r = \frac{32}{16} =2[/tex]
[tex]r = \frac{64}{32} =2[/tex] and so on..
Given sequence of the common ratio 'r' is equal
The [tex]n^{th}[/tex] term of the sequence
[tex]t_{n} = a r^{n-1}[/tex]
[tex]t_{n}= 8 (2)^{n-1}[/tex]
[tex]t_{n}= (2)^{(3+n-1)}[/tex]
[tex]t_{n}= (2)^{n+2}[/tex]
This is recursive formula for the given sequence
[tex]t_{n}= (2)^{n+2}[/tex]
Verification:-
[tex]t_{n}= (2)^{n+2}[/tex]
put n=1 ⇒ t₁ = 8
put n=2 ⇒ t₂ = 16
put n=3 ⇒ t₃ = 32
put n=4 ⇒ t₄= 64
and so on..
The sequence 8 ,16 , 32 , 64 ....
if z (3,-1) is the midpoint of line segment of coordinate x (5,2) and y (a,b) then find the value of a and b. I need it fast if u tell fast I'll mark ur Brainliest. It's a deal
Answers
Answer:
the coordinates of y are (1,-4)
Step-by-step explanation:
by using midpoint formula
z(x,y)=([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
putting the values of coordinates
(3,-1)=[tex]\frac{5+a}{2}[/tex],[tex]\frac{2+b}{2}[/tex]
separating the coordinates
3=[tex]\frac{5+a}{2}[/tex] and -1=[tex]\frac{2+b}{2}[/tex]
3×2=5+a and -1×2=2+b
6=5+a and -2=2+b
6-5=a and -2-2=b
1=a and -4=b
so the actual coordinates of y are (1,-4)
i hope it will help you
A flower shop normally orders 18 3/5 pounds of roses each week. The shop is planning on ordering four times as much during the week of Valentine's Day. For how many pounds of roses should the order be?
Answers
Answer:
74 2/5 pounds
Step-by-step explanation:
They usually order 18 3/5 pounds of roses.
They want to order 4 times this amount:
4 * 18 3/5
= 4 * 93/5
= 74 2/5 pounds
They should order for 74 2/5 pounds
What is the answer in these boxes
Answers
Answer:
I found that the answer is (5,1)
Step-by-step explanation:
4 times x(5) is 20
3 times y(1) is 3
20 + 3 = 23
bottom equation:
x(5) -- 5y(1) = 0
Help me compleate the sentance
Answers
Answer:half
Step-by-step explanations:
Please check photo below
Answer:
Half :D
Step-by-step explanation:
Also hello brother
how big is New York city
Answers
Answer:Land area: 302.6 mi²
Population: 8.399 million
Step-by-step explanation:
New York City can be described as very big and it has actually been ranked as the 24th biggest city in the United States in terms of land area it ...
Answer:
Land area: 783.8 km²
Population: 8.399 million
Step-by-step explanation: