simplify (sin^4(x) - cos^4(x)) / (sin^2(x) - cos^2(x))

Answer:

63

Step-by-step explanation:

∫₂⁴ f(x) g"(x) dx

Integrate by parts.

If u = f(x), then du = f'(x) dx.

If dv = g"(x) dx, then v = g'(x).

∫ u dv = uv − ∫ v du

= f(x) g'(x) − ∫ g'(x) f'(x) dx

f'(x) is constant at 3, so:

= f(x) g'(x) − ∫ 3 g'(x) dx

= f(x) g'(x) − 3 g(x)

Evaluate from x=2 to x=4.

[f(4) g'(4) − 3 g(4)] − [f(2) g'(2) − 3 g(2)]

[(13) (7) − 3 (9)] − [(7) (1) − 3 (2)]

64 − 1

63

The required value of [tex]\int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex] is 63.

Given that,

The table above gives selected values of twice-differentiable functions f and g,

The first two derivatives of g. If f′ (x) = 3 for all values of x.

We have to determine,

What is the value of [tex]\int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex].

According to the question,

To obtain the value of given function, integrating the function,

[tex]= \int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex]

Integrating by using by-parts.

[tex]= \int\limits^4_2 {f(x)g"(x)} \, dx (1)\\\\if\ u = f(x), \ then \ du = f'(x)dx\\\\if \ dv = g"(x)dx, \ then \ v = g'(x)\\\\[/tex]

Then,

[tex]\int u\ dv = uv\ - \ \int v \ du\\\\= f(x) \ g'(x) - \int g'(x) f'(x) \ dx\\[/tex]

if f'(x) is constant at 3,

Then,

[tex]= f(x) g'(x) - \int g'(x)\dx\\\\= f(x) g'(x) -3g(x)[/tex]

Substitute from x = 2 to x = 4 then evaluate,

[tex]= [f(4)\ g'(4) - 3 \ g (4)]- [f(2)\ g'(2) - 3 \ g (2)]\\\\= [(13).(7) - 3.(9)] - [7.(1)- 3.(2)]\\\\= [91-27} - {7-6}\\\\= 64-1\\\\= 63[/tex]

Hence, The required value of [tex]\int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex] is 63.

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Answer:

Step-by-step explanation:

[tex]7\cdot \:3\\\mathrm{Multiply\:the\:numbers:}\:7\cdot \:3=21\\=21\\[/tex]

Answer:

21

Step-by-step explanation:

Answer:

Jamie will have covered a distance of 45.08 km while Cori will be 4.8 km away

Step-by-step explanation:

Here, we want to know how far will each of both riders be in 2 hours time.

Jamie is riding 14 mph

This means the number of miles covered in two hours will be 14 mph * 2 = 28 miles

For comparison purposes, let’s convert this to kilometer.

Since 1 mile = 1.61 km, then 28 miles will be 28 * 1.61 km = 45.08 km

For Cori, he is riding at 0.04 km per minute

1 hour = 60 minutes

so 2 hours = 2 * 60 = 120 minutes

Since the speed is 0.04 km in a minute

Then the distance in 120 minutes will be 0.04 * 120 = 4.8 km

Answer:

The answer is B.

Step-by-step explanation:

0.40 km to miles 0.248548

Then 0.248548 x 120=2 hours

Answer:

5544 cm²

Step-by-step explanation:

Radius of circle = r

Circumference = 2πr

2πr = 264

22/7*r = 132

r = 132*7/22

 = 42 cm

Area = πr²

        = 22/7*42*42

        = 5544 cm²

Answer:

Each crate can contain 288 baseballs.

Step-by-step explanation:

Since one baseball takes up 1 × 1 × 1 space, and each box has 6 × 6 × 2 units of space, then the number of baseballs in one box is 6 × 6 × 2 ÷ 1 × 1 × 1 = 72 baseballs.

So, 72 baseballs can be contained in one box.

Now, since each crate contains 4 boxes, the number of balls contained in each crate is 1 × 4 boxes = 1 × 4 × 72 baseballs = 288 baseballs.

So each crate can contain 288 baseballs.

Answer:

no

Step-by-step explanation:

I think it is 128.77 cm. Because it has the most numbers, and it is presice.

Answer:

The answer is B. and D.

Step-by-step explanation:

if you solve the equation, you will find that X=18. Since his sister's sales are X, his sister sold 18. You multiply by 2.5 to find Robert's sales.

The correct statements are (B) and (D).

Two or more expressions with an equal sign are defined as an equation.

The given equation is x + 2.5x = 63.

Note that Robert's sales are 2.5 times his sister's sales, therefore, if his sister's sales is x then his sales are 2.5x

Hence, option (A) is incorrect, as Robert's sales are 2.5x.

Solve the equation as follows:

x + 2.5x = 63

3.5x = 63

x = 63/3.5

x = 18

Hence, option (B) is correct.

Since x=18, Robert's sales are:

2.5 × 18

= 45

Hence, option (C) is incorrect, as Robert's sales are $45, not $25.20.

Option (D) is already shown to be correct.

Option (E) is also incorrect, as option (D) is correct.

Hence, the correct statements are (B) and (D).

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Answer:

Step-by-step explanation:

(2n - 1) and (2n + 1) So, 2n -1 + 2n + 1 = 72. 4n = 72.

n = 18. So, The odd numbers are.

(2n - 1) = ((2 x 18) - 1) = 35. and,

(2n + 1) = ((2 x 18) + 1) = 37.

Step-by-step explanation:

[tex]\text{Hi there! :]}[/tex]

[tex]\large\boxed{y = 8}[/tex]

[tex]3y + 8 = 1/2y + 28\\\\\text{Subtract 8 from both sides:}\\\\3y + 8 - 8 = 1/2y + 28 - 8\\\\3y = 1/2y + 20\\\\\text{Subtract 1/2y from both sides:}\\\\3y - 1/2y = 1/2y - 1/2y+ 20\\ \\\text{Convert 3y to 6/2y to make subtracting easier:}\\5/2y = 20\\\\\text{Divide both sides by 5/2 (Multiply by reciprocal, or 2/5):}\\\\\\5/2y * 2/5 = 20 * 2/ 5\\\\y = 8[/tex]

Answer:

16

Step-by-step explanation:

Step-by-step explanation:

M=9 so m+n becomes 9+n.

N=7 so 9+n becomes 9+7.

9+7=16

Answer:

I'm pretty sure y=mx+b is standard form, unless I'm reading the question wrong.

Step-by-step explanation:

Answer:

z=-[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Answer:

i think its 9, i dont exactly know

Step-by-step explanation:

The answer is D.

Turning fractions into decimals will help you eliminate answers!!

How I got D:

-2 3/4 can be turned into -2.75 by dividing 3/4.

-2 3/4 is the smallest number out of all of them so it has to be first.

-2.67 is the second smallest value.

3/5 is .60 making it the third smallest value.

4 is the second largest value.

17/4 is 4.25, which is the largest.

A is not correct because -3/5 is not the smallest number.

B Is not correct because the largest number is 17/4.

C is not correct because -2.67 is not the smallest number.

Answer:

56mph

Step-by-step explanation:

If d=rt,

then s=d/t,

so if d=67.2 and t=1.2,

then 67.2/1.2=56

Answer:

Rotation

Step-by-step explanation:

If you were to translate it, it wouldn't match up because it needs to be turned around. translation just involves moving the shape without rotating it. a dilation means that you're changing the size, and you're not supposed to do that for this problem. a reflection means that if you were to fold in between these two shapes, they would match up. They Don't in this case so that won't work. A rotation is the only way to get it so that all of the areas match up.

Answer: Train 2 is traveling 4 miles per hour faster than train 1.

Step-by-step explanation:

Answer:

Train 2 is traveling 4 miles per hour faster than train 1.

Step-by-step explanation

:)))))

Step-by-step explanation:

y = -4(x+6)(x-8)

= -4[x²-2x-48]

= -4x²+8x+192

Answer:

c!

Step-by-step explanation:

have a great day! (sorry this was late!)

Answer:

.

Step-by-step explanation:

Answer:

8+3/4w

Step-by-step explanation:

The value of x will be equal to -1 when the value of h(x) is -2.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that  h(x) = -3x – 5, and the value h(x) = -2. The value of x will be calculated as below:-

h(x) = -3x – 5,

-2=-3x -5

3=-3x

x=-1

Therefore, the value of x will be equal to -1 when the value of h(x) is -2.

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Answer:

165

Step-by-step explain:

1=60

2 times 60 is 120

.75=3/4

3/4 of 60 is 45

add 120 and 45

= 165