Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for x=-3 and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?
Never mind I got it. mtan=6x+4. Sub in x values, for x=-2, take 6(-2)+4 = -8, and for x=1.5. 6(1.5)+4=13.
Answers
Complete Question
Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for [tex] x = 3[/tex] and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?
Answer:
The generally expression for the slope of [tex]y = 2x^2 + 4x[/tex] is [tex]y' = 4x +4[/tex]
The graph is shown on the first uploaded image
The generally expression for the slope of [tex]y=2x^2+4[/tex] is [tex]y' = 4x[/tex]
Step-by-step explanation:
From the question we are told that
The equation of the curve is [tex]y = 2x^2 + 4x[/tex]
First we differentiate the equation
So
[tex]y' = 4x +4[/tex]
Therefore the generally expression for the slope tangent to the curve [tex]y=2x^2+4x[/tex] is [tex]y' = 4x +4[/tex]
The next step is to substitute for x = 3 and x = 0.5
So for [tex]x_1 = 3 [/tex]
[tex]y' = 4(3) +4[/tex]
[tex]y' =m_1= 16[/tex]
And for [tex]x_2 = 0.5[/tex]
[tex]y' = 4(0.5) +4[/tex]
[tex]y' =m_2= 6[/tex]
Here m_1 and m_2 are slops of the curve
Next we obtain the coordinates of the tangent lines
So at [tex]x_1 = 3 [/tex]
[tex]y_1 = 2(3)^2 + 4(3)[/tex]
[tex]y_1 = 21[/tex]
So the coordinate for the first tangent line is
[tex](x_1 , y_1 ) = (3 , 21)[/tex]
At [tex]x_2 = 0.5 [/tex]
[tex]y_2 = 2(0.5)^2 + 4(0.5)[/tex]
=> [tex]y_2 = 2.5[/tex]
So the coordinate for the second tangent line is
[tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex]
Next we obtain the equation for the tangent lines
So generally the slope is mathematically represented as
[tex]m = \frac{y - y_1 }{x-x_1}[/tex]
For [tex](x_1 , y_1 ) = (-3 , 21)[/tex] and [tex]y' =m_1= 16[/tex]
[tex] 16 = \frac{y -21 }{x-3)}[/tex]
=> [tex]y = 16x - 27[/tex]
For [tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex] and [tex]y' =m_2= 6[/tex]
[tex] 6 = \frac{y -2.5 }{x-0.5}[/tex]
[tex]y = 6x -0.5[/tex]
Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating y=2x^2+4 as follows
[tex]y' = 4x[/tex]
Related Questions
If the length of a box of Milk Duds box is tripled, how much longer will the box be?
Answers
Answer:
3x
Step-by-step explanation:
x = original length of the box.
~theLocoCoco
MATH
Please heeeeeeeeeeeeeeelp
Answers
1. 5mn
2. -125p^3q^6
Step by Step:
1. 15m^2n^2/3mn
=5mn^2/n
=5mn
2. (-5q^2p)^3
=(-5pq^2)^3
=-125p^3q^6
If f(2) = 12 and f '(x) ≥ 3 for 2 ≤ x ≤ 5, how small can f(5) possibly be?
Answers
Answer:
21
Step-by-step explanation:
From our previous knowledge, if f'(x) = m ,
Then f(x) = mx+c
For a smaller value of f(5), m should be the smallest possible integer if m = 3
i.e. f(x) = 3x+c
replacing the value of x with 2 given from the question to get the value of c, we have:
f(x) = 3x+c
f(2) = (3×2)+c
where; f(2) = 12
12 = 6+c
- c = -12 + 6
- c = - 6
c = 6
Now, f(x) can now be;
f(x) = 3x + 6
f(5) = (3×5)+6
f(5) = 15 + 6
f(5) = 21
Therefore, smallest possible value of f(5) is 21
A road map is drawn to the scale of 1 inch equals 20 miles. How far apart in miles are two towns which are 2 1/2 inches apart on the map?
Answers
50
Step-by-step explanation:
You set this up with a ratio, 1:20 or 1 equals 20 miles. So i'm multiplying by 20 regardless. Now I have 2 and a half inches or you can say 2.5. Multiply 2.5 (on paper..) and 20 and there you go. 20 times 2 equals 40 and 20 times a half is 10, 40 + 10= 50.
I need help on. this question. (3x^6)^3 the answer must have one exponent
Answers
Answer:
[tex]27x^{18}[/tex]
Step-by-step explanation:
[tex]\left(3x^6\right)^3[/tex]
Separate [tex]3x^6[/tex]:
[tex]3^3\times\left(x^6\right)^3[/tex]
[tex]27\times\left(x^6\right)^3[/tex]
[tex]27x^{6\times3}[/tex]
[tex]27x^{18}[/tex]
the quotient of 15 and y
Answers
Answer:
Because we are working with a variable (y) and we don't know what number it represents, we can only write down what the calculation would be, but we can't get the actual number answer.
15/y
Step-by-step explanation:
A quotient is the answer to a division.
The statement "the quotient of 15 and y" can be written as 15/y
We have,
The statement "the quotient of 15 and y".
This can be written as,
15/y
The expression "15/y" represents the quotient of 15 and y.
When you divide 15 by y, you are calculating the quotient or the result of the division.
The numerator (15) represents the dividend, which is the number being divided, and the denominator (y) represents the divisor, which is the number by which you divide.
Thus,
The statement "the quotient of 15 and y" can be written as,
15/y
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
-5, -6, 0,6
Which pair of numbers has a sum of zero? (5 points)
-6,0
-5,6
6, -6
-5,0
Answers
Answer:
6,-6
Step-by-step explanation:
6+(-6)=6-6=0
The answer is 6,-6
3.60 rounded to the nearest tenth
Answers
Answer:
3.6 its already rounded just take off the 0
The requried when rounding 3.60 to the nearest tenth is given as 3.60.
When rounding a number to the nearest tenth, we consider the digit immediately to the right of the tenth place. In this case, the number is 3.60.
The digit in the hundredth place is 0. Since it is less than 5, we do not need to round up. When rounding to the nearest tenth, if the digit in the hundredth place is 5 or greater, we would round up by increasing the digit in the tenth place by 1. However, if the digit in the hundredth place is less than 5, we leave the digit in the tenth place as it is.
In this case, since the digit in the hundredth place is 0, we simply keep the digit in the tenth place, which is 6. Therefore, rounding 3.60 to the nearest tenth results in 3.6.
Learn more about round-off here:
https://brainly.com/question/12051621
#SPJ6
PLEASE HELP A cylinder with radius 6 feet and height 6 feet has its radius doubled. How many times greater is the volume of the larger cylinder than the smaller cylinder? How many times greater is the volume of the larger cylinder than the smaller cylinder?
Answers
Answer:
16 Times Greater
Step-by-step explanation:
Smaller cylinder:
radius = 6 inches
height = 8 inches
area = (pi)r^2h
area = (3.14)6^2(8)
radius = 24 inches
height = 8 inches
area = (pi)r^2h
area = (3.14)24^2(8)
.
[(3.14)6^2(8)] / [(3.14)24^2(8)]
[6^2(8)] / [24^2(8)]
[6^2] / [24^2]
[36] / [576]
16 times greater
Answer:
Step-by-step explanation:
Smaller cylinder:
h = 6 ft
r = 6 ft
Volume of smaller cylinder = πr²h
= π * 6 * 6 * 6 cubic ft
Bigger cylinder:
r = 6 * 2 = 12 ft
h = 6 ft
Volume of bigger cylinder = π * 12 * 12 * 6 cubic ft
Volume of bigger cylinder = π * 12 * 12 * 6
Volume of smaller cylinder π * 6 * 6 * 6
= [tex]\frac{2 * 2}{1*1}\\[/tex]
= 4 : 1
The volume of greater cylinder is 4 times than the smaller cylinder.
A student has some $1 and $5 bills in his wallet. He has a total of 14 bills that are worth 50$. How many of each type of bill does he have?
Answers
Answer:
3.5$
Step-by-step explanation:
Nine 5's and five 1's. Nine five-dollar bills hit $45 dollars, and the remaining $5 can only be paid in 1's to reach 14 bills.
2 lines intersect. Where the 2 lines intersect, 4 angles are created. Labeled clockwise, from uppercase right: angle 1 (3 x minus 1) degrees, angle 2 is blank, angle 3 (2 x + 9) degrees, and angle 4 is blank. What are the numerical measures of each angle in the diagram? ∠1 and ∠3 measure degrees. ∠2 and ∠4 measure degrees.
Answers
Answer:angle 1 and 3 measure 29 degrees.
angle 2 and 4 measure 151 degrees.
Step-by-step explanation:
Answer:
29 and 151
Step-by-step explanation:
Please answer this question
Answers
Answer:
I think it would be B but im not completly sure.
Which expression is equivalent to –3 – 3x – 1 + x?
2x – 4
–2x + 4
–2x – 4?
4 – 2x
Answers
Answer:
-2x-4
Step-by-step explanation:
-3-1-3x+x
-4-2x
Answer:
-2x-4?
Step-by-step explanation:
Assignment on Edge 2021
⊂(®ω®)⊃
Prasha has five blocks of wood The total weight of all five blocks of wood is 3 kilograms. 4 of the blocks of wood each have a weight of 650 grams. Work out the weight, in grams, of the other block of wood. Step by step please :).
Answers
650 * 4 = 2600 grams. This is the total weight of the 4 blocks.
To find the weight of the final block, 3000 - 2600 = 400 grams
The weight of the other block of wood is 400 grams.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Prasha has five blocks of wood the total weight of all five blocks of wood is 3 kilograms.
4 of the blocks of wood each have a weight of 650 grams.
∴ (4×650) = 2600 grams is the total weight.
So, the weight of the other block of wood is (3000 - 2600) grams.
= 400 grams.
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ2
What is the value of the expression 2.58 x - 53?
Answers
Answer:
-136.74
Step-by-step explanation:
Find the derivative of the function. g(x) = ∫5 x 4 x u2 − 1u2 +1 dug'(x) = g
Answers
Answer:
[tex]\mathbf{g'(x) = 5 \times \dfrac{(25x^2-1)}{(25x^2+1)}- 4 \times \dfrac{(16x^2-1)}{(16x^2+1)}}[/tex]
Step-by-step explanation:
The question can be better structured and represented as :
[tex]g(x) = \int ^{5x}_{4x} \dfrac{u^2-1}{u^2+1} \ du[/tex]
now the derivative of the function of g(x) is g'(x) which is equal to:
[tex]g'(x) = \dfrac{(5x)^2-1}{(5x)^2 +1 }\dfrac{d}{dx}(5x) - \dfrac{(4x)^2-1}{(4x)^2 +1 }\dfrac{d}{dx}(4x)[/tex]
[tex]\mathbf{g'(x) = 5 \times \dfrac{(25x^2-1)}{(25x^2+1)}- 4 \times \dfrac{(16x^2-1)}{(16x^2+1)}}[/tex]
I need this right now please
Answers
The age of Noelle’s dad is 6 less than 3 times Noelle’s age. The sum of their ages is 74. Find their ages
Answers
Where in real life do you work with radical expressions and functions? Give an example of your own.
Answers
Answer: Radical expressions are utilized in financial industries to calculate formulas for depreciation, home inflation and interest. Electrical engineers also use radical expressions for measurements and calculations.
Step-by-step explanation: Example: √x+y
√16
12+√x
√3*x²
parallel to y = 3x – 1 and passes through the point ( – 4, – 11)
Answers
Using the format y= mx + b, plug in your x and y values to find b (m is the slope)
-11 = 3(-4) + b
-11= -12 + b
b = 1
You now have all the needed values to write the equation in slope-intercept form:
y = 3x + 1
23,500 rounded to the nearest thousand?
Answers
Answer:
24,000
Step-by-step explanation:
is simple just 3500 is closer to 4000 than 3000
Answer:
24,000
Step-by-step explanation:
3. Jackie played the drums in the band. If he beat the drum at a rate of
110 beats per minute, how many beats would he play in 4 minutes
Answers
Answer:440 beats
Step-by-step explanation:
The minutes cancel when you multiply.
Which phrase should be inserted in the line to make a true statement? 2/3 is _____ 8/12 A. Is greater than B. Less than C. Cannot be compared.D.is equal to (HELP I NEED THIS HURRYY PLSSSS)
Answers
Answer:
the answer is equal because 8/12=2/3 so 2/3=8/12 (2/3)
Step-by-step explanation:
What number is 7 unit to the leaft of -1
Answers
Answer:
-8
Step-by-step explanation:
Since its going left I’m assuming it means negative. So you’re adding -7 to -1.
That gives you -8.
Please please help fast
Answers
Answer:
no I'm pretty sure. hope it helps
Answer: No
Step-by-step explanation:
First convert 10 feet to yards and also 20 inches to yards.
10 feet to yards is 3.3 and 20 inches to yards is 0.55
Now add them to see if they equal to 4 or greater than.
0.55 + 3.33= 3.88
3.88 is less than 4 so Anis will not be able to make a fence
Divide 2.9 x 107 by 6.9 x 103 by using scientific notation. Round your answer to one decimal place in scientific notation with no spaces
Answers
someone please help me with #63! WILL MARK BRAINLIEST
Answers
Answer:
cos60=b/h
1/2= b/3
b= 3/2=1.5
again
sin60=p/h
[tex]\sqrt3[/tex]/2= p/3
p =3[tex]\sqrt3[/tex]/2
Step-by-step explanation:
Answer:
1.5 in. and [tex]\frac{3\sqrt{3} }{2}[/tex]in.
Step-by-step explanation:
easier method:
angle opp. to 30 degrees is 1/2 of hypotonuse:
3/2=1.5 inches
angle opp. to 60 degrees is [tex]\sqrt{3}[/tex] of 30 degree angle:
3/2*[tex]\sqrt{3}[/tex]=3[tex]\sqrt{3}[/tex]/2
A serving of small frozen casserole is 1/3 of the pan. If you eat 1/4 of the pan, what fraction of a serving have you eaten
Answers
Answer:
If the portion of frozen casserole occupies 1/3 of the pan, it can be affirmed that it occupies 0.333 of it. Thus, if someone eats 1/4 of the pan, it could be stated that they are eating 0.25 of it.
Therefore, to determine the fraction of the portion that has been eaten, the following calculation must be performed:
33 = 100
25 = X
(25 x 100) / 33 = X
2500/33 = X
75.75 = X
25/33 = X
Therefore, the fraction of the serving that was eaten is 25/33, or 76% of the serving.
Can someone help me with 4?
Answers
Answer:
ok so the answer is 343
Step-by-step explanation:
so for 4) you first use PEMDAS(Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction), and you do what's in the parenthesis first, so 7^4= 2401, that is inside the parenthesis, next you do the exponent outside the parenthesis, so is (2401)^2=5764801, and then you divide the 7^5=16807, so it looks like 5764801/16807=343
hope it helps
Answer:
The Answer is 343.
Step-by-step explanation:
First- We do the parenthesis first according to PEMDAS which is 7 x 7 x 7 x 7 equals 2401.
Next- We do 2401 x 2401 which equals 5764801.
Then- We do the bottom exponent which is 7 x 7 x 7 x 7 x 7 equals 16807.
Last- We divide 5764801 by 16807 and we get 343.
Hope this helps!
Which are true regarding the statement "A quadrilateral having exactly one pair of parallel opposite sides is a trapezoid”? Check all that apply. It is a conditional statement that can be written as “If a quadrilateral has exactly one pair of parallel opposite sides, then it is a trapezoid.” The hypothesis is: a quadrilateral having exactly one pair of parallel opposite sides. The hypothesis is: it is a trapezoid. The conclusion is: a quadrilateral having exactly one pair of parallel opposite sides. The conclusion is: it is a trapezoid.
Answers
Answer: A,B,E
Step-by-step explanation:
The statement is "The conclusion is: it is a trapezoid." the correct option is D.
What is a quadrilateral?Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.
That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
We are given that;
The statement "A quadrilateral having exactly one pair of parallel opposite sides is a trapezoid”
Now,
The following statements are true regarding the statement "A quadrilateral having exactly one pair of parallel opposite sides is a trapezoid":
It is a conditional statement that can be written as “If a quadrilateral has exactly one pair of parallel opposite sides, then it is a trapezoid.”
The hypothesis is: a quadrilateral having exactly one pair of parallel opposite sides.
The conclusion is: it is a trapezoid.
Therefore, by quadrilaterals the answer will be "The conclusion is: it is a trapezoid."
Learn more about quadrilaterals here :
brainly.com/question/8181188
#SPJ7