If f ( x ) = 2 x 2 − 7 x + 2 , find f ' ( 2 ) .
Use this to find the linear approximation to f ( x ) at x = 2 . The equation of this linear approximation is L ( x ) =
Use L ( x ) to approximate f ( 2.2 ) . (Compute the actual value of L ( 2.2 ) .) f ( 2.2 ) ≈
Compare this with the actual value of f ( 2.2)=

Answer:

it is 6 I hope that

Step-by-step explanation:

because if division 11 on 759.88

To find the union and intersection of the intervals I₁ = (-2, 2] and I₂ = [1, 5), let’s consider the overlapping values and the combined range.

The union of two intervals includes all the values that belong to either interval. Taking the union of I₁ and I₂, we have:

I₁ U I₂ = (-2, 2] U [1, 5)

To find the union, we combine the intervals while considering their overlapping points:

I₁ U I₂ = (-2, 2] U [1, 5)
= (-2, 2] U [1, 5)

So the union of the intervals I₁ and I₂ is (-2, 2] U [1, 5).

Now let’s find the intersection of the intervals I₁ and I₂, which includes the values that are common to both intervals:

I₁ ∩ I₂ = (-2, 2] ∩ [1, 5)

To find the intersection, we consider the overlapping range between the two intervals:

I₁ ∩ I₂ = [1, 2]

Therefore, the intersection of the intervals I₁ and I₂ is [1, 2].


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Answer:

i was number #173

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

You have to find the lcm, and that is 56!  Hope that helps.

The coordinates of the point S of the line RS having midpoint T are found to be (12, -10).

The points that are given to us are R(8, -4) and T(10, -7). The point T is the mid point of the line segment RS.

If A(a, b) and B(c, d) are the two points then the mid point M of the two points will be,

M = ((a+c)/2), ((b+d/2))

So, using the above modified form of section formula we can find the coordinates of the point S.

Assuming point S to be x and y.  

So, putting all the values,

(10, -7) = ((8+x)/2), ((-4+y/2))

Now, solving further, we get,

8+x/2 = 10

8 + x = 20

x = 12

And,

-4 + y/2 = -7

-4 + y = -14

y = -10

So, the coordinates are (12, -10).

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Answer:

10,-7 (D)

Step-by-step explanation:

I Just Know

Answer:

a) K3050 and b) K1150

Step-by-step explanation:

a) Add all his expenditures

i.e: K300+K150+K100

=K3050

b) Subtract the remaining of his spendings from the total

i.e: K4209 - K3050

=K1150

Answer: 1320 ways.

Step-by-step explanation:

For this problem you should use the formula for variations in combinatorics. You use this when choosing a few objects from a group in which the order of the objects is of importance:

\(P^{12} _{3}=\frac{12!}{(12-3)!}=\frac{12 \cdot 11\cdot 10\cdot ...\cdot 1}{9 \cdot 8 \cdot ... \cdot 1} = 12 \cdot 11 \cdot 10 = 1320\)

where ! stands for factorial.

The head wind is approximately 175 km/h (142.49 km/h - h₂) and the cross wind is approximately 205 km/h.

The speed of an airplane in relation to the air surrounding it is known as airspeed. It may be monitored using an airspeed indicator and is not impacted by the wind or other environmental conditions. The speed of an airplane in relation to the ground is known as groundspeed, on the other hand. It accounts for how the motion of the aircraft is influenced by the wind and other external forces. Usually, groundspeed is calculated using GPS or other comparable technology. The wind component, which is the difference between airspeed and groundspeed, can impact how quickly an aircraft reaches its target.

Let us suppose head wind = h.

Let us suppose the cross wind = c.

Using the aircraft's speed is thus:

275 km/h [295°] = h + c

Dividing the wind vectors into their directional components we have:

h = h₁ + h₂

c = c₁ + c₂

The wind is blowing from West to East, so the horizontal component of the cross wind is 225 km/h.

Vertical component of the cross wind is 0 km/h, since the wind is blowing parallel to the ground.

Thus,

h₁ = h cos θ

h₂ = h sin θ

Here, θ is (295° - 180° = 115°).

The airspeed vector is thus,

275 cos 295° = -228.77 km/h

275 sin 295° = 142.49 km/h

Using vector addition:

-228.77 km/h = h₁ + 225 km/h

142.49 km/h = h₂

We have:

h₁ = -453.77 km/h

h₂ = 142.49 km/h

The actual cross wind is the sum of the horizontal components of the wind and the head wind:

c₁ = -h₁ - 225 km/h ≈ 205 km/h

Hence, the head wind is approximately 175 km/h (142.49 km/h - h₂) and the cross wind is approximately 205 km/h.

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

I think its 4% but I might be wrong so sorry if I am.

Answer:

x = (8-6i)/10

x = (8+6i)/10

Step-by-step explanation:

The wholesale cost $423

The merchant increases the wholesale cost by 35%

The washer sells it for $571.05

The wholesale cost can be calculated as follows

y + 35/100= 571.05

y + 0.35= 571.05

1.35y= 571.05

y= 571.05/1.35

y= 423

Hence the wholesale cost is $423

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Answer:

A

Step-by-step explanation:

Answer:

yes I guess a rectangle has opposite sides parallel parallelogram has opposite sides parallel a trapezium has opposite sides parallel a rhombus has opposite sides parallel if I'm wrong please connect me right away thank you.

Answer:

1.Yes, 2 pairs

2.Yes, 2 pairs

3.Yes, 1 pair

4.Yes, 2 pairs

Step-by-step explanation:

1.Each pair of co-interior angles are supplementary, because two right angles add to a straight angle, so the opposite sides of a rectangle are parallel. This means that a rectangle is a parallelogram, so: Its opposite sides are equal and parallel. Its diagonals bisect each other.

2.A parallelogram is a four sided figure where the opposite sides are parallel.

3.A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

4.Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides.

Mendelian genetics uses probability pedigrees and chi-square statistics to study the patterns of inheritance of traits. Probability pedigrees are diagrams to calculate chance of inheritance, while chi-square statistics is a test to compare observed data to expected results.

Mendelian genetics is the study of inheritance patterns of traits from parent to offspring. It is based on the work of Gregor Mendel, a 19th century monk and scientist who studied the inheritance of traits in pea plants. Probability pedigrees are diagrams that can be used to calculate the chance of a certain trait being passed down from generation to generation. These diagrams represent the relationships between family members, and the likelihood of a trait being inherited from a parent. Chi-square statistics is a statistical test used to compare observed data to expected results. This is often used to determine the likelihood that an observed trait is inherited from a parent. The chi-square test is used to measure the amount of deviation from the expected, and can help to identify patterns of inheritance. By using probability pedigrees and chi-square statistics, researchers can gain a greater understanding of the patterns of inheritance in a population. This knowledge can be used to develop strategies to prevent or treat diseases that have a genetic component.

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Answer:

6x+19

Step-by-step explanation:

Since it is parallel it is has the same slope. So, make it 6x+b. After doing this, plug in the coordinates and you would get b=19. Hope it helps u :)

Let ages of Seema and her mother be “5x” years and “12x” years respectively.

Difference between ages is 21 years

Hence,

12x - 5x = 21

7x = 21

x = 3

Therefore,

Age of Seema = 5 × 3 = 15 years

Age of her mother = 12 × 3 = 36 years

Ratio of ages after three years = ( 15+3 ) / (36+3 )

= 18 / 39

= 6 / 13

= 6 : 13

Step-by-step explanation:

the answer is the third one

hope it helps and if u need a explanaton I can help

Answer:

A

Step-by-step explanation:

1-0.045=0.955

Answer:

it 480

Step-by-step explanation:

if your k 12 this is right

Answer:

The Answer is A. 480, I picked 525 and got it wrong because I was doubting that it wasnt 480 but it was. well good luck

The lengths of the diagonals or "hips" of the trapezoid are:

d1 = 10 cm

d2 = 4 cm

In an inscribed trapezoid, the opposite angles are supplementary, meaning they add up to 180 degrees. Since one of the angles in the trapezoid is 120 degrees, the opposite angle will be 180 - 120 = 60 degrees.

Now, let's label the trapezoid. Let A and B be the endpoints of the longer base, with AB = 10 cm, and let C and D be the endpoints of the shorter base, with CD = 4 cm. Let E be the intersection point of the diagonals, creating two triangles within the trapezoid.

Since the opposite angles at the intersection point of the diagonals are equal, we have angle AEC = angle BDE = 60 degrees.

Since the sum of the angles in a triangle is 180 degrees, we can find angle AED by subtracting the sum of angles AEC and BDE from 180 degrees:

angle AED = 180 - (angle AEC + angle BDE)

angle AED = 180 - (60 + 60)

angle AED = 60 degrees

Now, let's consider triangle AED. It is an isosceles triangle since AE = ED (both are radii of the circle). Thus, angle ADE = angle AED = 60 degrees.

We have angle AED = angle ADE = 60 degrees, and angle AEB = 120 degrees. Therefore, angle ABE = 180 - (angle AED + angle AEB) = 180 - (60 + 120) = 0 degrees.

Angle ABE being 0 degrees means that line AB is parallel to line CD. Hence, the trapezoid is actually a rectangle.

In a rectangle, the diagonals are equal in length. Let's denote the length of the diagonals as d1 and d2.

Since AB and CD are the bases of the trapezoid, d1 is equal to the longer base AB, and d2 is equal to the shorter base CD:

d1 = 10 cm

d2 = 4 cm

Therefore, the lengths of the diagonals or "hips" of the trapezoid are:

d1 = 10 cm

d2 = 4 cm

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The dimensions of a different sector with the same area and perimeter are An alternative sector's radius is 6.42 inches. An alternative sector has an arc length of 16.52 inches.

The distance between two places along a segment of a curve is known as the arc length.

Sector radius, r = 8.26 inches

Sector arc length = 12.84 inches

Sector perimeter = 2r + length of the arc

The specified sector's perimeter is equal to 2 x 8.26 x 12.84 x 29.36 inches.

The circle's circumference is 2 + 8.26 + 16.52.

The specified circle's area is A = 8.262 * 68.2276.

Sector area, A = 53.0292 inch2

Consequently, we have;

2R plus A equals 29.36 inches

A·R = 53.0292 × 2

that provides;

R² + 53.0292 = 14.68·R

R² - 14.68·R + 53.0292 = 0

using a graphing calculator to factor yields;

(R - 6.42)·(R - 8.26) = 0

R = 6.42 or R = 8.26

R = 8.26 is the measurement for the first sector.

Due to the distinctions between the sectors, we have;

R = 6.42 inches is the radius of the other sector.

The length of the arc, A = 29.36 - 2R

∴ A = 29.36 - 2 × 6.42 = 16.52

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Answer:

4 years

Step-by-step explanation:

Given data

Simple interest= $400

Principal= $2000

Rate= 5%

The simple interest formula is given as

SI=PRT/100

substitute and solve for T

400=2000*5*T/100

cross multiply

400*100= 10000*T

40000=10000T

T= 40000/10000

T= 4 years

Hence the time taken is 4 years

The THREE true statements regarding the graph of B(w) are;

A) Based on the zeros of the function, the number of boxes of cereal sold is 0 after 0 weeks.

C) Based on the end behavior of the function, the number of boxes of cereal sold will keep falling after reaching the maximum.

E) Based on the asymptote of the function, the number of boxes of cereal sold will never reach 0 after the cereal is introduced in the store.

We are given the graph represented by the quadratic function;

B(w) = 120w/(150 + w²) for w ≥ 0 that models;

the number of boxes, B, in thousands, of the cereal sold after w weeks

From the graph, we can see that at the origin which is the coordinate (0, 0) that it remains so and as such the number of boxes of cereal sold is 0 after 0 weeks. Thus, option A is correct

Secondly, from the given graph, we see that the graph starts rising from zero to a maximum after which it keeps falling. Thus, we can say that option C is correct

Lastly, we see that the graph asymptote approaches 500 thousand boxes but never gets to zero and as such we can say that option E is correct.

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The shape of the graph changes qualitatively at k = ± 2 and

\(k=\sqrt{(2)\).

The given function is f(x,y) = y-x²+y²+kxy.

The critical points of the function are found by taking the partial derivatives and equating them to zero:

∂f/∂x = -2x + ky = 0

y = 2x/k

∂f/∂y = 2y + kx = 0

y = -kx/2

Substituting y from the first equation into the second equation gives

x = k²x/4, so k² = 4 and k = ± 2.

Therefore, the critical points are (0,0), (2,4), and (-2,4)

We will now examine the critical points to see when the shape of the graph changes qualitatively.

There are two cases to consider:

Case 1: (0,0)At (0,0), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2 0;0 2].

The determinant of the Hessian matrix is -4, which is negative.

Therefore, (0,0) is a saddle point and the graph changes qualitatively as k increases for all values of k.

Case 2: (±2,4)At (2,4) and (-2,4), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2k 2k;2k 2].

The determinant of the Hessian matrix is 4k²+8, which is positive when k is greater than √(2).

Therefore, the critical points (2,4) and (-2,4) are local minima when

k > √(2).

Thus, the shape of the graph changes qualitatively at k = ± 2 and

k = √(2).

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32 Km is  the distance between these two places.

What is distance?

let the  distance = x

75 % of x

75 × x/100 = 24

75x= 240

x = 2400/75

x= 32

The distance between two places is 32 km

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Answer:

by divisibility rule of 3 for a no. to be divisible by 3 there is necessary condition that sum of all digit is divisible by 3.

so ans is 2 (smallest digit)

Answer:

volume=12п

Step-by-step explanation:

circumference =2пr

2пr=18п

r=18п:2п

r=9

volume of sphere= (4/3)*п*r

volume=(4/3)*п*9

volume=4*п*3

volume=12п

Answer: i need to see a picture or sum , i have to go off of

Step-by-step explanation:

Answer:

Option (D)

Step-by-step explanation:

If a function f(x) is represented on a graph and we follow the transformation as,

f(x) → \(k.f(x)\)

1). If k ≥ 1, graph of the parent function f(x) will be stretched vertically by a factor k.

That means the transformed graph will be narrower.

2). If 0 < k < 1, graph will be vertically compressed or the transformed function will show a wider graph.

Following this rule,

f(x) → \(\frac{1}{2}.f(x)\) shows k = \(\frac{1}{2}\) [Since 0 < \(\frac{1}{2}\) < 1]

Therefore, transformed form will be wider.

Option (D) will be the answer.