Answers
Answer:
[tex]f(x) = 3 {x}^{2} \\ lim \: \frac{f(x + h) - f(x)}{h} \: \: when \: h - > 0 \\ lim \: \frac{3( x + h)^{2} - 3 {x}^{2} }{h} when \: h - > 0 \\ lim \: \frac{3( {x}^{2} + 2xh + {h}^{2}) - 3 {x}^{2} }{h} when \: h - > 0 \\ \\ lim \: \frac{3 {x}^{2} + 6xh + 3h^{2} - 3 {x}^{2} }{h} when \: h - > 0 \\ lim \: \frac{6xh + 3 {h}^{2} }{h} \: when \: h - > 0 \\lim \frac{6xh}{h} + \frac{3h^{2} }{h}when \: h - > 0 \\ lim \: 6x + 3h \: when \: h - > 0 \\ = 6x + 3(0) \\ = 6x + 0 \\ = 6x \\ \\ or \\ \frac{d(3x^{2}) }{dx} = 2 \times 3x^{2 - 1} \\ = 2 \times 3x^{1} \\ = 2 \times 3x \\ = 6x[/tex]
Related Questions
3. Q3) What is the smallest number of identical squares
that will fit in this rectangle?
Answers
Answer:
Minimum 3 squares.
Step-by-step explanation:
Let the number of identical squares that will fit in the rectangle = x
Sum of the area of the squares = Area of the given rectangle
x(Side length of the square)²= (length of the rectangle × width of the rectangle)
x(S)²= (40 × 90)
x(S)²= 3600 cm²
For the minimum numbers of the squares,
If x = 1,
S = √3600 = 60 cm
But the length of the rectangle is 40 cm, so can't be fitted in the rectangle.
If x = 2,
2S² = 3600
S² = 1800
S = √1800
S = 42.43 cm
Since, length of the rectangle is 40 cm, so the given square can't be fitted in the rectangle.
If x = 3,
3S² = 3600
S² = 1200
S = √1200
= 34.64 cm
Therefore, minimum 3 squares can be fitted in the given rectangle.
The length and width or a rectangular courtyard is 40 feet and 30 feet, respectively. In order to make the courtyard larger, an additional 15 feet is being added to the width
Answers
Answer:
The new area is 1800feet^2
Step-by-step explanation:
Step one:
Given data
The length and width or a rectangular courtyard is 40 feet and 30 feet
we can calculate the area of the courtyard as
Area= 40*30
Area= 1200 feet^2
when the extra 15 feet is added to the width
the new width is= 30+15= 45feet
The new area is
Area= 40*45
Area= 1800 feet^2
in all the area will increase by 1800-1200= 600feet
Eight friends share 64 tickets to the school carnival. Each friend has the same
number of tickets. How many tickets does each friend have?
9
7
6
8
Answers
Answer:
Step-by-step explanation:
What is the first step in solving the inequality. 32≥5−3x
Answers
Answer: Simplify
Step-by-step explanation:
foci of ellipse of 3x2 + y2 =9
Answers
Answer:
x=√-1/3 y^2 +3 or x=-√-1/3 y^2 +3
Step-by-step explanation:
Let's solve for x.
3x2+y2=9
Step 1: Add -y^2 to both sides.
3x2+y2+−y2=9+−y2
3x2=−y2+9
Step 2: Divide both sides by 3.
3x^2/3= -y^2+9/3
x^2=-1/3 y^2 +3
x=√-1/3 y^2 +3 or x=-√-1/3 y^2 +3
Hope it helped!
Write the ratio in simplest form.
Answers
Answer:
1/5
Step-by-step explanation:
Answer:
The answer to the question provided is 3: 15
Helpppp pllzzz & thx
In circle B, find x if m A = 3x + 9 and m B = 8x – 4.
Answers
6x + 18 = 8x - 4
22 = 2x
11 = x
The value of x is 11.
Central Angle Theorem :It states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points.
From given figure, [tex]A=3x+9,B=8x-4[/tex]
[tex]\angle B=2\angle A\\\\8x-4=2(3x+9)\\\\8x-4=6x+18\\\\8x-6x=18+4\\\\2x=22\\\\x=22/2=11[/tex]
Learn more about the central angle of circle here:
https://brainly.com/question/3538263
PLEASE HELP! I NEED THIS DONE BY TOMORROW!
1. In January, a mobile phone shop sold 100 phones. In February, they sold 92 phones. Represent this difference as a percentage change.
2. A piece is cut from a 130cm length of wood so that the remaining length is 104cm. What percentage of the wood has been cut off?
3. There are now 30 boys in a class that originally had 24 boys in it. What was the percentage increase in the number of boys in the class?
4. Last year, there were 300 students in Year 7. This year there are 315 students. Show that this is a 5% increase.
5. A piece of art was bought for £600. Six months later, it was sold for £675. What percentage of profit did the seller make?
6. In a sale, trainers originally costing £70 are reduced to £49. Calculate the percentage change.
7. Josh invests £3500. When his investment matures, he receives £4200. Work out the percentage
increase in his investment.
8. A car company bought a car for £8000. Two years later they sold the car for £7200. Calculate their
percentage loss.
Answers
Answer
down below
Step-by-step explanation:
i did it on your last post
please give me a brainliest!!
5/7-1/2= show work PLZZZZZZZZZZ HELPPPP
Answers
Answer:
3/14
Step-by-step explanation:
We need to line up the fractions. 5/7 on top, 1/2 on the bottom. We need to find common denominator so, 7 x 2 (denominators) gives us 14. 14 is now the denominator we will use. Solve for numerator: Starting at bottom fraction. 2 goes into 14 7 times, 7 times original numerator (1) 35. Theres your new numerator. Now, the top fraction: 7 goes into 14 2 times. 2 x original numerator (5) = 10. Now subtract both numerators (10 - 7 = 3) Plug in the denominator and your answer is: 3/14
What is the simplified form of the following expression?
5 V8 - V18 -2 V2
Answers
Answer:
B) 5V2
Step-by-step explanation:
5√2 is the simplified form of the 5 √8 - √18 -2√2. Therefore, the correct option is option B.
What is mathematical expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. In order to help determine the sequence of operations and other features of logical syntax, mathematical symbols can be used to represent numbers, variables, operations, function, brackets, punctuation, or grouping.
Expressions are syntactic devices. It must be properly constituted, which means that the permissible operators have to include the right amount of inputs in the right places, legal characters for these inputs, a clearly defined sequence of operations, etc.
5 √8 - √18 -2√2
10√2-3√2 -2√2
√2(10-3-2)
5√2
Therefore, the correct option is option B.
To know more about mathematical expression, here:
https://brainly.com/question/29176690
#SPJ7
20 points!!
What are the next three terms of the arithmetic sequence -18, -13, -8, -3,…?
Answers
Answer:
3, 8, 13, 18
Step-by-step explanation:
please help me?!!
a motorboat takes 5 hours to travel 150 Miles going Upstream. the return trip takes 3 hours going Downstream .what is the rate of the boat in still water and what is the rate of the current ?
Answers
Answer:
The the rate of the motorboat in still water is 40 km/h; the rate of the current is 10 km/h.
Step-by-step explanation:
Let u be the rate of the motorboat in still water (in kilometers per hour),
let v be the rate of the current.
Then the rate of the motorboat going downstream is u+v km/h,
while its rate going upstream is u-v km/h.
From the other side, the rate of the motorboat going downstream is 150/3=50km/h = 30 km/h.
Thus you have these two equations
u + v = 50 (1) (for the rate downstream), and
u - v = 30 (2) (for the rate upstream).
To solve the system, add equations (1) and (2). You will get
2u = 50 + 30 = 80; hence,
u = 80/2 = 40 km/h.
Then from the equation (1), v = 50 - u = 50 - 40 = 10 km/h.
ANSWER. The the rate of the motorboat in still water is 40 km/h; the rate of the current is 10 km/h.
Isaiah leaves one city at noon. He has to be at another city at 186 km away at 3:00 P.M. The speed limit the entire way is 65 km/h. Can he arrive at the second city on time? Explain your reasoning using mathematical evidence.
Answers
Answer:
From noon to 3 pm, there are three hours so the average speed Isaiah will need to arrive in another city in 3 hours is 186/3 = 62 km/h. Since this is less than the speed limit, Isaiah can go an average speed between 62 km/h to 65 km/h to arrive at the second city on time.
Step-by-step explanation:
The difference of H.C.F. and L.C.M. of the numbers 12 and 16 is:
Pls help
Answers
Step-by-step explanation:
the hcf of numbers 12and16 is 12
the lcm of numbers 12and 16 is 4
hcf is divide
lcm is multiply by prime factorization
The following system of linear equations has
-3x + 7y = 10
3x + 7y = -8
Answers
For trapezoid JKLM A and B are midpoints of the legs. Find AB.
19
B
M
L
27
C.
23
a
h
35
46
Answers
Can you please help with both? :)
Answers
Answer:
12, 20
Step-by-step explanation:
Don't worry I just know
Help please! worth a lot of points! Screenshot included
Answers
Answer:
x=44444444444444444444444444444444
Step-by-step explanation:
Answer:
.2
Step-by-step explanation:
Sin x = - 1/2
where (-360 < x < 360)
Answers
Answer:
-30, 210 and 330 degrees
Step-by-step explanation:
Given the expression Sin x = - 1/2
x = arcsin(-1/2)
x = -30 degrees
Since sin is negative in the third and fourth quadrant
x = 180 + 30
x = 210 degrees
In the fourth quadrant
x = 360 - 30
x = 330
Hence the value of x within the interval -360 < x < 360 are -30, 210 and 330 degrees
-2•f(-6)-7•g(-7) help
Answers
Answer:
11
Step-by-step explanation:
-2 • f(-6) -7 • g(-7) = ?
As per graph:
f(-6) = 5
g(-7) = -3
Calculation:
-2 • f(-6) -7 • g(-7) =
-2(5) - 7(-3) =
-10 + 21 =
11
What is m∠P? There is a five sided polygon PQRST in which the measure of angle PQR is 132 degrees, the measure of angle QRS is (4x-10) degrees, the measure of angle RST is (5x-11) degrees, the measure of angle STP is 128 degrees and the measure of angle TPQ is (4x+2) degrees.
Answers
Answer:
94°
Step-by-step explanation:
There is a five sided polygon PQRST in which the measure of angle PQR is 132 degrees, the measure of angle QRS is (4x-10) degrees, the measure of angle RST is (5x-11) degrees, the measure of angle STP is 128 degrees and the measure of angle TPQ is (4x+2) degrees.
Sum of angles in a pentagon = 540°
Hence:
PQR + QRS + RST +STP + TPQ = 540 °
132 + (4x-10)° + (5x-11)° + 128° + (4x+2) degrees = 540°
132 + 4x - 10 + 5x - 11 + 128 + 4x + 2 = 540
132 - 10 - 11 + 128 + 2 + 4x + 5x +4x = 540°
241 +13x = 540
13x = 540 - 241
13x = 299
x = 299/13
x = 23
What is m∠P?
m∠P in Pentagon PQRST = TPQ
TPQ = 4x + 2
= 4 × 23 + 2
= 94°
3/5 ÷ 1/4 – 2/5 ^2 (these are fractions and ^2 this is a exponent)
Answers
Answer:
The answer is 7/100
Pls help and SHOW WORKINGS..
Answers
3x = 45
x = 15
plug 15 into
5(15) + 55
75 + 55 = 130
130 + angle 2 = 180
angle 2 = 50
Think for a situation or application in which proportion is evident/useful
Answers
Answer:
Dieting (?) since proportions of the food can affect you're diet and it's also useful to stay on track.
Antoine Purchase 1.8 kg of apples and 315 dekagrams of oranges This was 1350 g more than the weight of bananas bridges what was the way of the bananas Antonio purchased in grams
Answers
Answer: 3600 grams
Step-by-step explanation:
A dekagram means 10 grams.
1 kilogram = 1000 grams
Therefore the total number of grams when Antoine Purchase 1.8 kg of apples and 315 dekagrams of oranges will be:
= (1.8 × 1000) + (315 × 10)
= 1800 + 3150
= 4950 grams
Since this was 1350g more than the weight of bananas, the weight of the bananas Antonio purchased in grams will be:
= 4950 - 1350
= 3600 grams
Please help. I need a smart person to help :)
Answers
Answer:
quadrant 2!
Step-by-step explanation:
PLS HELP MEEEEEE ( I don’t need to know the first one )
Answers
Answer:
k=27
Step-by-step explanation:
Answer:
direct variation is y = kx
k is the slope of the line y = mx + b
i don't know that last one, sorry
Step-by-step explanation:
Tickets to a play cost $4 in advance and $5 at the door. The theater club president wants to raise at least $400 from the ticket sales. If the club sells 40 tickets in advance, what is the least number of tickets the club needs to sell at the door to reach the president’s goal?
Least number of tickets =
Answers
Answer:
x≥48
Step-by-step explanation:
4×40 = 160
400-160 = 240
240÷5 = 48
I'm so confused............................................
Answers
Answer:
Step-by-step explanation:
a is not less than 0 because it is to the right of 0 on the number line, so the first statement is false. The second statement is true. The absolute value of positive a is positive a, and since a is to the right of 0 on the number line, it is greater. The third statement is false. The absolute value of positive a is positive a, not 0.
How many solutions does this equation have?
–4s = –10 − 5s
does it have 1 solution or zero or infinity many solutions
Answers
[tex] - 4s = - 10 - 5s \\ - 4s + 5s = - 10 \\ s = - 10[/tex]
Answer Check by substituting s = -10 in the equation.[tex] - 4( - 10) = - 10 - 5( - 10) \\ 40 = - 10 + 50 \\ 40 = 40 \: \: \tiny \boxed{ \green \checkmark}[/tex]
SolutionsNo Solutions
When both sides of equation are different. For example, 3 = 4 which makes the equation false. That means the equation is false for all real numbers, thus having no solutions.
One Solution
A common type solution because you see this type of solution a lot. If you can solve the equation for a variable like x = 2 or s = 0. That's one solution.
Infinitely Many Solutions
When both sides are same like 3 = 3 or 7 = 7. That means the equation is true for all real numbers. You can see this type of solution by solving the equation with same both sides like 3x+2 = 3x+2.
AnswerBecause we can solve the equation for s-term. Therefore the answer is one solution