What is the average rate of change for the function f(x) = –4x2 + 1 over the interval –3/2 ≤ x ≤ 0?

Answer:

number of black pencils is 17

Answer:

Step-by-step explanation:

SecA - TanA

= 1/CosA - SinA/CosA

= 1 - SinA/CosA

We know that Sin2A = 2SinACosA  and Cos2A = Cos²A - Sin²A

Thus SinA = Sin2(A/2) = 2Sin(A/2)CosA/2

       CosA = Cos2(A/2) = Cos²A/2 - Sin²A/2

Now substituting the values back,

=> 1 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)

// we know that Sin²θ + Cos²θ = 1

=> Sin²(A/2) + Cos²A/2 -  2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)

//We know that numerator is of form a² + b² - 2ab which is (a - b)².

//Similarly denominator is of form a² - b² which is (a - b)(a + b)

=> [Sin(A/2) - Cos(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]

=> [ - {Cos(A/2) - Sin(A/2)}]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]

=> [Cos(A/2) - Sin(A/2)]² /  [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]

=> [Cos(A/2) - Sin(A/2)] / [Cos(A/2) + Sin(A/2)]

= R.H.S

Hence proved.

Answer:

Đáp án:

60km

Step-by-step explanation:

30 phút

=

1

2

giờ

Ô tô đi từ A đến B rồi từ B về A mất số thời gian là:

10

−

6

−

1

2

=

3

,

5

giờ (không tính thời gian nhận hàng)

Gọi độ dài quãng đường AB là

x

(km)

Ta có:

Thời gian đi từ A đến B là

x

40

(quãng đường chia vận tốc)

Thời gian đi từ B đến A là

x

30

Ta có phương trình:

x

40

+

x

30

=

3

,

5

⇔

x

=

60

(km)

Vậy quãng đường AB là 60km.

The equation of the circle whose center is (0, 0) and whose radius 5 is x² + y² = 25.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x-a)²+(y-b)² = r²

Where (a, b) is the centre and 'r' is the radius

We have a circle with centre (0, 0) and radius of 5.

Now, Substituting these value into the equation form, we have

(x-0)²+(y-0)² = 5²

x² + y² = 25

Hence, the equation of the circle whose center is (0, 0) and whose radius 5 is x² + y² = 25.

Learn more about equation of a circle here:

https://brainly.com/question/10165274

#SPJ2

Answer:

96 dollars and 50 cents

Step-by-step explanation:

Answer:

6.52 x 10^3 is just basically 6.52 × 1000, which is 6520. But 652,000 ÷ 10^2 is just 652000 ÷ 100, which is 6520. That's why they have the same answer.

Answer: x= 6 +/- root of 7

Step-by-step explanation:

1. Expand the left hand side: e.g, 3^2 = 3×3 =9

(x-6)(x-6) = 7

2. Multiply the brackets first by "separating" one of them, and take 7 to the left hand side:

x(x-6) - 6(x-6) =7

x^2 - 6x -6x +36-7=0

Simplify by adding like terms

x^2 -12x +29=0

3.Now your equation is in the form ax^2+bx + c =0, it means you can use the quadratic formula which is x= [-b +/- root of (b^2 - 4ac)]÷ 2a

Then SUBSTITUTE where:

a=1

b= -12

c=29

Therefore, x should be 6+ root of 7 OR 6- root of 7

Answer:

uhhhh okay thank you for removing my answer

Step-by-step explanation:

Answer:

A

Giải thích:

f(1)=f(x)

f(-1) và f(-2)= f(-x)

=> f(1)=f(-1) =A. f(x)=f(-x)

Answer:

32

Step-by-step explanation:

If n represents the amount of flowers they sold, then the correct answer should be 32. The cost for each flower they sold would be 3 x 4 and then add $20 for advertising.

Answer:

70

Step-by-step explanation:

we have the angle of vertex in the isosceles triangle = 180-2*bottom coner= 180-65/2=50

3 angles in the equilateral triangle are equal to 60

we have 50 + 60 +h =the angle of PQR =180

h=70

Answer: h = 70°

In the triangle with Angle R = 65

It is a isoceles triangle as two sides are equal

So base angles will be equall too

Then the third angle will which is the q one will be

65+65+q = 180

q = 180 - 130

q = 50

In the other triangle with all sides equal will be equilateral triangle which means all angles equal = 60

So

Now ATQ

60 + 50 + h = 180

h = 180 - 110 (Angles on a straight line adds upto 180)

h = 70

Must click thanks and mark brainliest

Answer:

3x + 11

Step-by-step explanation:

1) Remove Parentheses:

x + 4 + 2x + 7

2) Combine Like Terms:

(2x + x) and (4 + 7)

3) Simplify:

3x + 11

Hope this helps, good luck! Have a good day. :)

[tex]\\ \sf\longmapsto 2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48} \\\\ \sf\longmapsto 2 \sqrt{25 \times 3} - \sqrt{36 \times 3} + 5 \sqrt{16 \times 3} \\ \\ \sf\longmapsto 2 \times 5 \sqrt{3} - 6 \sqrt{3} + 5 \times 4 \sqrt{3} \\ \\ \sf\longmapsto 10 \sqrt{3} - 6 \sqrt{3} + 20 \sqrt{3} \\ \\ \sf\longmapsto (10 - 6 + 20) \sqrt{3} \\ \\ \sf\longmapsto 24 \sqrt{3} [/tex]

Answer:

24aprtment3

Step-by-step explanation:

Answer:

At 2

Step-by-step explanation:

I think it is because it slants down instead of going up. That is the reason why I say my answer is at 2.

HOPE THIS HELPED

Answer: y=80/5x+80

Step-by-step explanation:

At one point graph goes from (0,400) to (25,800). So the y intercept is 400 because that’s where the line was at x=0. 0 to 25 is 25. 400 to 800 is 400. So the equation would be y=400/25x+400. But you can divide all of it by 5 to get y=80/5x+80.

Answer:

Its c

Step-by-step explanation:

Answer:

Approximately 17 stars

Answer:

1 significant figure: 50,000 2 significant figures: 52,000 3 significant figures: 51,800

Step-by-step explanation:

FIrst, a significant figure is basically a non-zero digit (at least in your case). Basically, the 1 significant figure in your case would be to the nearest 10 thousand, which would be 50,000. Now, for 2 significant figures. This would be the nearest thousand, 52,000. Finally, 3 significant figures is to the nearest hundred, aka 51,800. Note: If you find a problem like this again 0 in between two digits that aren't 0 is a significant digit, aka the 0 in 51809. Hope this helped!

Answer:   -80

Step-by-step explanation:

Answer:

140.625

Step-by-step explanation:

1125 books, placed into 8 per boxes, 1125/8=140.625

Answer:

2/5m - 1/5

Step-by-step explanation:

Given the equation :

2(1/5m - 2/5) + 3/5

First step:

Open the bracket by multiplying values in the bracket by 2

2/5m - 4/5 + 3/5

-4/5 + 3/5 = (-4 + 3) / 5 = - 1 / 5

Hence,

2/5m - 4/5 + 3/5 = 2/5m - 1/5

= 2/5m - 1/5

Answer:

37.5%

Step-by-step explanation:

Calculation to determine the theoretical probability that the tree is not within the acres of apple trees

Using this formula

P=(Number of all orchard acres - Apple acres)/(Total orchard acres)*100

Where,

P represent Probability

Let plug in the formula

P=(40 acres- 25 acres)/40 acres

P=15 acres/40 acres *100

P=3/8*100

P=.375*100

P=37.5%

Therefore the THEORETICAL PROBABILITY that the tree is not within the acres of apple trees is 37.5%

Answer:

the answer is 37.5

Step-by-step explanation:

it is

Answer:

9. Hypotenuse = √(19.1²+11.3²) = √492.5 = 22.2 m²

10. Area = (34×40)/2 + (17²×π/2)

= 680 + 453.96

= 1133.96 cm²

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

The basic 30-60-90 triangle ratio is:

Side opposite to 30° angle is : x

Side opposite to 60° angle is : x √3

Side opposite to 90° angle is : 2x

From the diagram we learn that

x√3 = 10

[tex]x = \frac{10}{\sqrt{3}}=\frac{10*\sqrt{3} }{\sqrt{3}*\sqrt{3}}\\\\x=\frac{10\sqrt{3}}{3}= 5.77\\[/tex]

∠T = 30°, Side opposite to ∠T is AC = 5.77

∠A = 90°, side opposite to ∠A is TC = 2x = 2*5.77 = 11.54

Answer:

3x+ 7 =49

Step-by-step explanation:

49-7= 42

42 divided by 3 = 14

her daughter is 14 years old

I truly hope this helped, it makes sense to me. I wasn't sure whether or not you needed a more detailed equation, but that's one.

have a great day!

Answer:

A = 96 inches ^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 ( b1+b2)h  where b1 and b2 are the bases and h is the height

A = 1/2( 14+10)*8

A = 1/2(24)*8

A = 12*8

A = 96 inches ^2

The area of trapezoid is given

A = 1/2 (b1+b2)h where b1 and b2 is base and h is height

A = 1/2 (14+10)*8

A = 1/2 (24)*8

A = 12 * 8

Answer:

Gloves = 11 pairs

Socks = 4 pairs

Step-by-step explanation:

Given that :

Time taken to knit pair of socks = 3 hours

Time taken to knit pair of gloves = 7 hours

Total time taken to knit 15 pairs of gloves and socks = 89 hours

Let :

number of socks = x and number of gloves = y

x + y = 15 - - - - (1)

3x + 7y = 89 - - - (2)

From (1):

x = 15 - y

Put x = 15 - y in (2)

3(15 - y) + 7y = 89

45 - 3y + 7y = 89

45 + 4y = 89

4y = 89 - 45

4y = 44

y = 44/4

y = 11

From :

x = 15 - y

x = 15 - 11

x = 4

Answer:

Step-by-step explanation:

The central angle of a hexagon is 60 degrees. Drop a line from the center to the middle of the side marked 7.

Use the  tan of the angle so formed (which is 30 degrees)

Tan(30)= opposite / height (which is the line you just drew).

Tan(30) = 3.5 / h

Tan(30) = 0.5774

Tan(30) = 3.5 / h                multiply both sides by h

h*Tan(30) = 3.5                  Divide by tan30

h = 3.5 / Tan(30)

h = 3.5 / 0.5774

h = 6.062

Now from both ends of the given side, draw 2 lines to the center. Find the area of that triangle.

Area of 1 triangle = 1/2 * b * h

area of 1 triangle = 1/2 * 7 * 6.062

Area of 1 triangle = 21.2176

There are 6 such triangles so multiply that number by 6

Answer:  6 * 21.2176

Answer:  127.31