Step-by-step explanation:
You will have to use the limit defition of the derivative. Brainly does not have calculus symbols, which is very unfortunate, so I can only use my words. Take the limit as the change in 'x' approaches zero. You will have:
[tex] \frac{sin(x + {x}^{.} ) - sin(x)}{ {x}^{.} } [/tex]
If you let "x dot" equal zero as the limit requires, you will get 0/0 which is indeterminate. Break up the first term using the formula for the sine of a sum. You get:
[tex] \frac{sin(x)cos( {x}^{.} ) + sin( {x}^{.})cos(x) - sin(x) }{ {x}^{.} } [/tex]
Factor a sin(x) from the first and third term to get:
[tex] \frac{sin(x)(cos( {x}^{.}) - 1 ) + sin( {x}^{.})cos(x) }{ {x}^{.} } [/tex]
Use the linearity to break the limit into two parts:
[tex] \frac{sin(x)(cos( {x}^{.}) - 1 )}{ {x}^{.} } + \frac{sin( {x}^{.} )cos(x)}{ {x}^{.} } [/tex]
First term converges to zero, second term converges to cosine. Therefore proving the derivative of sine is cosine
During its grand opening sale, a local electronics store gave customers a chance to win a new flat screen TV. Customers only had to fill out a card with their name, address, and telephone number and drop it into a box. One winner would be chosen at random. This is an example of a
Using sampling concepts, it is found that this is an example of a random sample.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, one winner is chosen at random from all the participants, hence random sampling is used.
More can be learned about sampling concepts at https://brainly.com/question/25122507
please help!! very important!!
Answer:
d
Step-by-step explanation:
Hardware store:
4 bulbs = $20
1 bulb = $20 / 4 = $5
Grocery store:
6 bulbs = $24
1 bulb = $24 / 6 = $4
The difference in price = $5 - $4 = $1
The grocery store sells at the lesser price.
So, the grocery store charges $1 less per light bulb than the hardware store.
If you spin the spinner 9 times, what is the best prediction possible for the number of times it will land on yellow?
Answer:
0? There's no yellow.
Step-by-step explanation:
arrange in ascending order. : 5/8, 3/4, 7/12, 1/2
Answer:
1/2, 7/12, 5/8, 3/4.
Step-by-step explanation:
I did that in ascending order.
URGENT HELP 20 POINTS
Answer:
[tex]ab( {a} ^{2} + {b)}^{2} \\ [/tex]
[tex] {a}^{ 3} b + a {b}^{3} [/tex]
Can Some1 Please Help Me!!!
The ratio of men to women working for a company is 4 to 3. If there are 161 employees total, how many men work for the company?
Answer:
i dont know
Step-by-step explanation:
hope you find you answer
If you travel 60 feet in 4 seconds, how fast are you going in yards per minute?
Answer:
approximately 300 yards per minute
Step-by-step explanation:
What is 180-90-37 as a degree?
Answer:
53 degrees
Step-by-step explanation:
since 180 is a straight line and 90 is half of that, all you need to do is take 37 away from 90 and you get 53
The equivalent degree of the of the expression is 53 degrees .
Given,
180° - 90° - 37°
Now,
The equivalent value of the expression :
180° - 90° - 37°
Firstly compute the like terms,
-90° - 37°
= -127°
Now,
180° - 127°
= 53°
Know more about degrees,
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Need this asap first gets brainliest
Answer:
Step-by-step explanation:
5a)→Solution,
[tex]\hookrightarrow 46+90=x[Sum\: of\: interior \:angle\: is\: equal\: to \:exterior\:angles]\\\\\hookrightarrow x=136[/tex]
5b)→Solution,
77+x=180
x=180-77
x=103
Help help help help math math
Answer:
[tex]x = \geqslant 34[/tex]
Step-by-step explanation:
x is greater than or equal to 34, because the illustration shows, that it can go beyond 34. The filled in dot also means that x can also be equal to 34. (i hope i explained it in a good way)
a circular wall clock with a circumference of 94.2 cm is mounted on a wall. How much area of the wall did it occupy
please i reallly need help right now 25 points
Answer:
D) all real numbers except x = 6
Step-by-step explanation:
If there is a solid line or dot at an x value, then it is included in the domain. Since there are open dots at x = 6, that means it is not included in the domain. With that being said, the domain can be written as:
(-∞, 6)∪(6, ∞)
Hope this helps!
Use the quadratic formula to find the solutions to the quadratic equation below. x^2 - 6x - 5 = 0
Step-by-step explanation:
We know the quadratic formula, which is :
[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }}} \\ \\ [/tex]
Here,
a = 1b = -6c = -5So,
[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ - ( - 6) \pm \sqrt{ {( - 6)}^{2} - 4(1)( - 5) } }{2(1)} }}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 36 - 4( - 5) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 36 + 20 } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 56 } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(28) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(2)(14) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(2)(2)(7) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2} . \sqrt{2} . \sqrt{2 . 7} }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm 2 \sqrt{14} }{2} }}} \\ \\ [/tex]
Now, Separating the solutions :
[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ 6 + 2 \sqrt{14} }{2} }}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{x = 3 + \sqrt{14}}}}\\ \\ [/tex]
[tex]\\ {\longrightarrow \qquad{ \sf{x = \frac{ 6 - 2 \sqrt{14} }{2} }}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{x = 3 - \sqrt{14}}}}\\ \\ [/tex]
Solve the equation for x.
-2x = 14
-
Enter the number that belongs in the green box.
x = [?]
Enter
I
Answer:
[tex]\displaystyle -7[/tex]
Explanation:
[tex]\displaystyle \boxed{-7} = \frac{14}{-2}[/tex]
I am joyous to assist you at any time.
Answer:
[tex]\boxed{\sf{x=-7}}[/tex]Step-by-step explanation:
To solve this problem, you have to find the value of x to isolate it on one side of the equation.
-2x=14First, you divide by -2 from both sides.
-2x/-2=14/-2
Solve.
Divide these numbers from left to right.
14/-2=-7
x=-7
Therefore, the final answer is x=-7.Identify the elements for each problem
find circumference of the circle whose parameter is 14 cm
Find the circumference of a circle with diameter 14 cm
Mr. Chau is planting a circular flower garden in his backyard. If the diameter of his garden is 12 feet, what is the area of the garden?
Answer:
A = 113.04 ft² or 36π ft²
Step-by-step explanation:
Area of a circle: πr²
radius: d/2 (12/2 = 6 ft)
π (pi) = 3.14
Solve:
A = πr²
A = 3.14(6)²
A = 3.14(36)
A = 113.04 ft² or 36π ft²
Hope this helps!
In each circle, find the value of x. Please help
In a circle, angles subtended by the same arc at the circumference are equal. This means that angles in the same segment are equal.
Using this equation, we can create the following equation:
[tex]4x=3x+10[/tex]
For which we can solve to get:
[tex]x=10[/tex]
Hope this helps!
Pls help me
Pls show your answer pls and thank you
Answer:
Step 1
According to given details
Number of delivered pizzas at the weekly meeting=5
Number of slices in one pizza =8
(a)
Now evaluate total number of slices
Number of slices in one pizza =8
Total slices =8x5
=40 slice
(b)
Yes, we can find more than one way
= 5 ÷ 1/8
= 5x8/1
=40/1
A roller coaster's height is given by the equation h = -0.067t^2 + 7t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0
A. 13.40 seconds
B. 50.07 seconds
C. 52.24 seconds
D. 111.19 seconds
The time it take riders to pass over the hill and reach ground level is 111.19seconds
Functions and valuesGiven the roller coaster's height expressed by the function below;
h = -0.067t^2 + 7t + 50
where
t is the time in seconds
The driver will hit the ground at the point where h = 0
Substitute
-0.067t^2 + 7t + 50 = 0
Multiply through by -1
0.067t^2 - 7t +-50 = 0
Factorize
On factorizing, the positive value of "t" is 111.19 seconds
Hene the time it take riders to pass over the hill and reach ground level is 111.19seconds
Learn more on functions here: https://brainly.com/question/25638609
Answer:
D) 111.19
Step-by-step explanation:
Step 1:
set h = 0
0 = -0.067t^2 + 7t + 50
Step 2:
multiply by -1
0 = 0.067t^2 - 7t - 50
Step 3:
My way may differ than your way but my is plug in all answer choices as t. If the answer choice equal to 0 meaning the answer.
A choice
0 = 0.067(13.40)^2 - 7(13.40) - 50
0 = 12.03 - 94.5 -50
0 = - 132.47
It doesn't equal to 0 meaning this choice is wrong answer
B choice
0 = 0.067(50.07)^2 - 7(50.07) - 50
0 = 167.96 - 350.49 - 50
0 = - 232.53
It doesn't equal to 0 meaning this choice is wrong answer
C choice
0 = 0.067(52.24)^2 - 7(52.24) - 50
0 = 182.84 - 365.68 - 50
0 = - 232.84
It doesn't equal to 0 meaning this choice is wrong answer
D choice
0 = 0.067(111.19)^2 - 7(111.19) - 50
0 = 828.33 - 778.33 - 50
0 = 0
It does equal to 0 meaning this choice is right answer
The answer is D) 111.19
Pls give me brainiest (I worked hard for this)
The volume of a tree stump can be modeled by considering it as a right cylinder. Justin measures its circumference as 84 in and its volume as 20214 cubic inches. Find the height of the stump in feet. Round your answer to the nearest tenth if necessary.
The height of the stump tree which can be modeled by considering it as a right cylinder is 35.9 inches.
What is a cylinder?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Since the base of a cylinder is circular in shape, the circumference is expressed as;
C = 2πr
Given that the circumference of the base is 84 in, we can now calculate the radius r.
C = 2πr
84in = 2 × 3.14 × r
84in = 6.28 × r
r = 84in / 6.28
r = 13.4in
Now, the Radius of the cylinder r = 13.4in and its volume = 20214in³, we substitute this values into the expression for volume of cylinder above to find the height h.
V = π × r² × h
20214in³ = 3.14 × ( 13.4in)² × h
20214in³ = 3.14 × 179.56in² × h
20214in³ = 563.8in² × h
h = 20214in³ / 563.8in²
h = 35.9in
Therefore, the height of the stump tree which can be modeled by considering it as a right cylinder is 35.9 inches.
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Kevin is an auto mechanic. He spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He works no more than 36 hours a week. He routinely completes at least 2 shocks replacements and 3 brake replacements a week. If he charges $400 for labor replacing shocks and $200 in labor for replacing brakes, how many jobs of each type should he complete a week to maximize his income?
Answer:
See below ....question is a bit unclear
Step-by-step explanation:
He makes 133.33 per hour with shocks and only 100 per hour with brakes.
he should only do 36/3 = 12 shock jobs per week and no brakes.
if he HAS to do at LEAST 3 brake jobs
then he should do 3 brakes and 10 shocks
What is the measure, in degrees, of
Answer:
Hi good job
Step-by-step explanation:
Two vertices of a rectangle are located at (6, 1) and (8, 1). The rectangle has an area of 18 units2 and is entirely in the first quadrant. What are the other two vertices?
The two other two vertices will be (6, 10) and (8, 10)
How to calculate the area of a rectangle?A rectangle is a 2-dimensional shape with equal opposite sides. The formula for calculating the area is given as:
Area = length * width
Given;
Area = 18 square units
Length = x2 -x1 = 8 -6
length = 2 units
Determine the width
Width = A/l
Width = 18/2
Width = 9 units
Hence the two other two vertices will be (6, 10) and (8, 10)
Learn more on area of rectangle here: https://brainly.com/question/2607596
Find the slope of the line shown in the graph below.
Answer: The slope is 1
Step-by-step explanation:
We can see that between the two points it goes up 2 units (rise) and right 2 units (run).
Since slope is [tex]\frac{rise}{run}[/tex] we can sub in the values to find the answer
[tex]\frac{rise}{run}=\frac{2}{2} =1[/tex]
Find the amount of work W done by a force F = 115i +350j
in moving an object in a straight line given by the displacement vector D = -13i+15j.
The work is equal to the dot product of the force and displacement vectors:
W = (115 i + 350 j) • (-13 i + 15 j)
W = 115 × (-13) + 350 × 15
W = 3755
aitlyn has $2500 in a saving account.
She collects 3% annual simple interest.
How many years will it take to collect
$150 in interest?
Answer:
2 yearsStep-by-step explanation:
The interest amount per year is
3% of $2500 = 3*2500/100 = 75Number of years is
150/75 = 2Answer:
2 years
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = total interest earnedP = principalr = interest rate (in decimal form)t = time (in years)Given:
P = $2500r = 3% = 0.03I = $150Substitute the given values into the formula and solve for t:
⇒ 150 = 2500(0.03)t
⇒ 150 = 75t
⇒ t = 150 ÷ 75
⇒ t = 2
Therefore, it will take 2 years to collect $150 in interest.
Please HELP NEED ASAP>
Tyrone conducted an experiment with a spinner. He spun the arrow on the spinner 20 times and recorded the results in the table shown. Which statement below is a true statement based on the statement above. Please no links.
Answer:
A)
Step-by-step explanation:
The experimental probability on 'A' is higher than the theoretical probability of landing on 'A'.
Find the volume of the triangular prism to the right.
5 ft
10 ft
The volume of the prism is ? ft^3
Answer:
rectangular is 114ft and triangular is 112ft
Step-by-step explanation:
Let the volume of a rectangular prism be VR and that of right triangular prism be VT. If The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism, then VR = 32 + VT
Since VR = length * width and height
VR = 6*x*3
VR = 18x ft³
Also VT = Length *width * Height/2
VT = (7 * x * 4)/2
VT = 28x/2
VT = 14xft³
Since VR = 32 + VT
18x = 32+(14x)
collect like terms
18x-14x = 32
4x = 32
divide both sides by 4
4x/4 = 32/4
x = 8
Volume of the rectangular prism = 18x
Volume of the rectangular prism = 18*8
Volume of the rectangular prism = 144ft³
Volume of the right triangular prism = 14x
Volume of the rectangular prism = 14*8
Volume of the rectangular prism = 112ft³
the three sides of a triangle are 11/3 cm , 15/4 cm and 26/9 cm . find it's perimeter .
[tex] \sf\longmapsto \: \frac{371}{36} [/tex]
☘︎ Solution :- Given : Three sides are 11/3 cm , 15/4 cm and 26/9 cm To find : perimeter of the trianglePerimeter of a triangle = Sum of the length of the three sides
perimeter of the given triangle = 11/3 + 15/4 + 26/9
Make the denominator same by taking the LCM of the denominators .( LCM of 3 , 4 and 9 is 36 )
[tex]\sf\longmapsto \: \frac{132 \: + \: 135 \: + \: 104}{36} \: \: \: [/tex]
[tex]\sf\longmapsto \: \frac{371}{36} \: cm \: [/tex]
♧ Therefore, the perimeter of a triangle is 371/36 cm
The temperature in Denver, Colorado this
morning was -7°. In the afternoon, the
temperature rose to 16º.
What does this mean?
A. The temperature is 16° below zero
B. The temperature is 16° above zero
PLEASE HELP!!