Help help help ASAP math math

(a) Since u = cos(x) gives du = -sin(x) dx, we have

∫ sin(x) cos(x) dx = - ∫ (-sin(x)) cos(x) dx

= - ∫ cos(x) d(cos(x))

= - ∫ u du

= - 1/2 u² + C

= -1/2 cos²(x) + C

(b) Now u = sin(x) gives du = cos(x) dx, so

∫ sin(x) cos(x) dx = ∫ sin(x) d(sin(x))

= ∫ u du

= 1/2 u² + C

= 1/2 sin²(x) + C

(c) Since sin(2x) = 2 sin(x) cos(x), we have

∫ sin(x) cos(x) dx = 1/2 ∫ sin(2x) dx

Substitute u = 2x, so that du = 2 dx, and

∫ sin(x) cos(x) dx = 1/2 ∫ sin(2x) dx

= 1/4 ∫ 2 sin(2x) dx

= 1/4 ∫ sin(u) du

= -1/4 cos(u) + C

= -1/4 cos(2x) + C

(d) Integrate by parts, setting

u = sin(x)          ==>  du = cos(x) dx

dv = cos(x) dx  ==>  v = sin(x)

Then

∫ sin(x) cos(x) dx = sin²(x) - ∫ sin(x) cos(x) dx

2 ∫ sin(x) cos(x) dx = sin²(x) + C

∫ sin(x) cos(x) dx = 1/2 sin²(x) + C

The solutions in (b) and (d) are identical, but all 4 are equivalent, and this follows from the identities,

sin²(x) + cos²(x) = 1

cos(2x) = cos²(x) - sin²(x)

Answer:

10

Step-by-step explanation:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let [tex](x_1,y_1)[/tex] = (-4, 2)

Let [tex](x_2,y_2)[/tex] = (2, -6)

Substituting given points into the formula:

[tex]\implies d=\sqrt{(2-(-4))^2+(-6-2)^2}[/tex]

[tex]\implies d=\sqrt{(6)^2+(-8)^2}[/tex]

[tex]\implies d=\sqrt{36+64}[/tex]

[tex]\implies d=\sqrt{100}[/tex]

[tex]\implies d=10[/tex]

Answer:

26 inches

Step-by-step explanation:

You need to add 3+5+7+7+4= 26 because you need to find the area of the figure which the inches are area to add and get how many inches in the figure. Sorry if you don't get it but the answer is 26 inches.

Answer:

all real numbers.

Step-by-step explanation:

9x - 8y = 1

18x - 16y = 2

if you look at the first equation, you can figure out what y equals.

9x - 8y = 1

add 8y to both sides

9x = 1 + 8y

subtract 1 from both sides

9x - 1 = 8y

divide both sides by 8

[tex]\frac{9x - 1}{8}[/tex] = y

now, substitute y in the second equation.

18x - 16y = 2

18x - 16([tex]\frac{9x - 1}{8}[/tex]) = 2

18x - 2(9x - 1) = 2

18x - 18x +2 = 2

2 = 2

the answer is all real numbers, because regardless of what x equals, 2 will always equal 2.

Answer:

Length = 8

Breadth = 12

Step-by-step explanation:

Since Area = length * breadth

96 = (x+2)(x-2)

Since (a+b)(a-b) = a^2-b^2

(x+2)(x-2) = x^2-4

Therefore

x^2-4 = 96

x^2 = 100

x = +-10

Since x > 0

x = 10

Answer:

1664 cards

Step-by-step explanation:

416 divided by 8 is 52 and 52 times 32 is 1664.

Answer:

[tex]b=3[/tex]

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation.

[tex]2*(b+3)-(12)=0[/tex]

Then solve!

Answer:

I need to know the equation, but if you have to cube them then you will find your answer right away if you google how to cube numbers.

Step-by-step explanation:

Sorry for the bad answer.

Answer:

slope=2 y-intercept=4

Answer:

Step-by-step explanation:

The fraction will represent the number of shaded squares over the total number of squares. You have correctly identified it as 98/100. That fraction can be reduced, if you like, to 49/50.

The pronunciation of your fraction is "ninety-eight hundredths." The decimal number with that same pronunciation is 0.98.

The symbol % and the symbol /100 have identical meaning. This makes them essentially interchangeable.

  98/100 = 98%

Your numbers are ...

  98/100 (or 49/50), 0.98, and 98%.

_____

Additional comment

We have shown you that % is a shorthand way to write /100. There is another similar symbol: ‰ is shorthand for /1000.

1/100 is one percent. 1/1000 is one mil.

The equation of any straight line can be written as in slope intercept form as -

[tex]\green{ \underline { \boxed{ \sf{y=mx+c}}}}[/tex]

where,

Given equation:-

[tex]\begin{gathered}\\\implies\quad \sf 5x+y = 10 \\\end{gathered} [/tex]

Arranging it in slope intercept form by transposing 5x to RHS

[tex]\begin{gathered}\\\implies\quad \sf y = 10 -5x \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf y = -5x +10\\\end{gathered} [/tex]

[tex]\leadsto[/tex]Comparing the equation y = -5x +10 with the standard form of the equation, we get -

[tex]\quad \bull\: \sf m= -5[/tex]

[tex]\quad \bull \: \sf c= 10[/tex]

Thus , 5 is our required answer.

Answer:

[tex]\displaystyle y = -5x + 10[/tex]

Step-by-step explanation:

5x + y = 10

- 5x - 5x

_________

[tex]\displaystyle \boxed{y = -5x + 10}[/tex]

I am joyous to assist you at any time.

Answer:

4 1/3 feet

Step-by-step explanation:

11 3/8 - 3 1/8 = 8 2/3

8 2/3 / 2 = 4 1/3

Answer:

y(x) = 1/2 (x - sqrt(5 x^2 + c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 + c_1))

Step-by-step explanation:

Solve 2 x + y(x) + (dy(x))/(dx) (x - 2 y(x)) = 0:

Let P(x, y) = 2 x + y and Q(x, y) = x - 2 y.

This is an exact equation, because (dP(x, y))/(dy) = 1 = (dQ(x, y))/(dx).

Define f(x, y) such that (df(x, y))/(dx) = P(x, y) and (df(x, y))/(dy) = Q(x, y).

Then, the solution will be given by f(x, y) = c_1, where c_1 is an arbitrary constant.

Integrate (df(x, y))/(dx) with respect to x in order to find f(x, y):

f(x, y) = integral(2 x + y) dx = x^2 + x y + g(y) where g(y) is an arbitrary function of y.

Differentiate f(x, y) with respect to y in order to find g(y):

(df(x, y))/(dy) = d/(dy) (x^2 + y x + g(y)) = x + (dg(y))/(dy)

Substitute into (df(x, y))/(dy) = Q(x, y):

x + (dg(y))/(dy) = x - 2 y

Solve for (dg(y))/(dy):

(dg(y))/(dy) = -2 y

Integrate (dg(y))/(dy) with respect to y:

g(y) = integral-2 y dy = -y^2

Substitute g(y) into f(x, y):

f(x, y) = x^2 - y^2 + y x

The solution is f(x, y) = c_1:

x^2 - y^2 + y x = c_1

Solve for y:

y(x) = 1/2 (x - sqrt(5 x^2 - 4 c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 - 4 c_1))

Simplify the arbitrary constants:

Answer:  y(x) = 1/2 (x - sqrt(5 x^2 + c_1)) or y(x) = 1/2 (x + sqrt(5 x^2 + c_1))

For Sofia:-

So

For Flynn:-

Now

difference

for A (xa ; ya) and B (xb ; yb)

the slope is (yb - ya) / (xb - xa)

here :

slope = - 3/4 = (4 - r) / (-3 - (-7))

(4 - r) / 4 = - 3/4

so 4 - r = - 3

then r = 7

check

points (-7 ; 7) and (-3 ; 4)

slope = (4 - 7) / (-3 - (-7) = -3/4

Answer:

1/9

Step-by-step explanation:

First turn all the negative exponents into positive by flipping the fractions then plug in the given values.

(3/1)^2 * (1/x)^4 * y^2

Simplify to:

9 * 1/(x^4) * y^2

Plug in:

9 * 1/(3^4) * -1^2

Simplify:

9 * 1 * 1/(3^4) = 9/(3^4) = 9/81 = 1/9

Answer:

h =12

Step-by-step explanation:

[tex]In\: \triangle ABC, \: \angle ABC = 90\degree \: \&\:\\ BD\perp AC[/tex]

Therefore, by geometric mean property:

[tex]BD = \sqrt {AD\times CD} \\

h = \sqrt {(AC-CD) \times CD} \\

h = \sqrt {(25-16) \times 16} \\

h = \sqrt {9 \times 16} \\

h = \sqrt {144} \\

\huge \red {\boxed {h = 12}} \\

[/tex]

Answer:

Step-by-step explanation:

12

Answer:

1.2

Step-by-step explanation:

Answer:

$17

Step-by-step explanation:

So first

The total money John have is $20

then he earned $5 which means $20+$5 = $25

After that he spent $10 = $25- $10 = $15

Again earned $5 = $15+$5=$20

At last spent $3 = $20-$3=$17

Hence the total money he owe or have left is $17

Step-by-step explanation:

8 cups total a day

1 bottle holds 2 cups (Celeste drinks 4 bottles a day = 8 cups) 

If she drank 1.5 bottles already, she needs to drink 2.5 bottles 

Let x be the number of bottles she needs to drink to have at least 8 cups 

The inequality is x >= 2.5 bottles

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

3.9

That's the question????

Using translation concepts, it is found that a 90º clockwise rotation of the triangle around the origin took place.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, considering the points on triangles ABC and A'B'C', the change is modeled by:

(x,y) -> (y, -x).

Which is a 90º clockwise rotation of the triangle around the origin.

More can be learned about translation concepts at https://brainly.com/question/4521517

80 >= -8(w-8)

Use distributive property:

80 >= -8w + 64

Subtract 64 from both sides:

16 >= -8w

Divide both sides by -8:

-2 >= w

Because the division was done using a negative value the inequality gets reversed:

w >= -2

Answer : w >= -2

First, you want to find the area of the entire thing first.

The length adds up to 14, the width to 10. Multiply and you get 140 as the total area.

Now to get rid of the flower bed is simple, 8 Multiply to 3 which makes 24, then divide by 2 which is 12. Substract 12 to 140 and you get 128.

The formula for a trapezoid is Area= (base1 +base2)/2 times height. Following this, and 5 and 7 which gets 12. divide 12 to 2 and you get 6. 6 times 10 is 60.

Subtract 60 to 128 and you get 68.

Mark best if possible please.

Answer:

Step-by-step explanation:

First, you want to find the area of the entire thing first.

The length adds up to 14, the width to 10. Multiply and you get 140 as the total area.

Now to get rid of the flower bed is simple, 8 Multiply to 3 which makes 24, then divide by 2 which is 12. Substract 12 to 140 and you get 128.

The formula for a trapezoid is Area= (base1 +base2)/2 times height. Following this, and 5 and 7 which gets 12. divide 12 to 2 and you get 6. 6 times 10 is 60.

Subtract 60 to 128 and you get 68.

.

The building should be 1.024 meters high and unfortunately there are no buildings with such height in the world.

In this question we must use definition of geometric progression to predict initial height ([tex]h_{o}[/tex]), in meters, in terms of current height ([tex]h[/tex]), in meters, and number of bounces experimented by the ball ([tex]n[/tex]). The expression is described below:

[tex]h = h_{o}\cdot \left(\frac{1}{2} \right)^{n}[/tex]   (1)

If we know that [tex]n = 10[/tex] and [tex]h = 1\,m[/tex], then the initial height is:

[tex]1 = h_{o}\cdot \left(\frac{1}{2} \right)^{10}[/tex]

[tex]h_{o} = 2^{10}[/tex]

[tex]h_{o} = 1024\,m[/tex]

The building should be 1.024 meters high and unfortunately there are no buildings with such height in the world. [tex]\blacksquare[/tex]

The statement is incomplete, complete form is shown below:

A ball falls from the roof of a building and bounces half as high each time. How tall would a building have to be if, after hitting the ground ten times, the ball bounces to 1 meter? Is there a building this tall?

To learn more on geometric series, we kindly invite to check this verified question: https://brainly.com/question/15130111