Find the derivative.
[tex]\dfrac{d}{dx} \left[ \sin^{-1}(\cos e^x)-\cos^{-1}(\sin e^x) \right][/tex]

Answers

Answer 1

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

[tex]\qquad \tt \dashrightarrow \:\dfrac{d}{dx} \left[ \sin^{-1}(\cos e^x)-\cos^{-1}(\sin e^x) \right][/tex]

[tex]\qquad \tt \dashrightarrow \:\dfrac{d}{dx} \sin^{-1}(\cos e^x) - \dfrac{d}{dx}\cos^{-1}(\sin e^x) [/tex]

[tex]\qquad \tt \dashrightarrow \: \bigg(\dfrac{1}{ \sqrt{1 - ( \cos( {e}^{x} ) ) {}^{2} } } \times - \sin( {e}^{x} ) \times {e}^{x} \bigg) - \bigg( - \dfrac{1}{ \sqrt{1 - ( \sin( {e}^{x} )) {}^{2} } } \times \cos( {e}^{x} ) \times {e}^{x} \bigg)[/tex]

[tex]\qquad \tt \dashrightarrow \: \bigg(\dfrac{ - {e}^{x} \sin( {e}^{x} ) }{ \sqrt{1 - ( \cos( {e}^{x} ) ) {}^{2} } } \bigg) - \bigg( - \dfrac{ {e}^{x} \cos( {e}^{x} ) }{ \sqrt{1 - ( \sin( {e}^{x} )) {}^{2} } } \bigg)[/tex]

[tex]\qquad \tt \dashrightarrow \: \dfrac{ - {e}^{x} \sin( {e}^{x} ) }{ \sqrt{1 - \cos {}^{2} ( {e}^{x} ) {}^{} } } + \dfrac{ {e}^{x} \cos( {e}^{x} ) }{ \sqrt{1 - \sin {}^{2} ( {e}^{x} ) {}^{} } } [/tex]

[tex]\qquad \tt \dashrightarrow \: \dfrac{ - {e}^{x} \sin( {e}^{x} ) }{ \sqrt{ { \sin}^{2} ( {e}^{x} ) {}^{} } } + \dfrac{ {e}^{x} \cos( {e}^{x} ) }{ \sqrt{ \cos {}^{2} ( {e}^{x} ) {}^{} } } [/tex]

[tex]\qquad \tt \dashrightarrow \: \dfrac{ - {e}^{x} \sin( {e}^{x} ) }{ { { \sin}^{} ( {e}^{x} ) {}^{} } } + \dfrac{ {e}^{x} \cos( {e}^{x} ) }{ { \cos {}^{} ( {e}^{x} ) {}^{} } } [/tex]

[tex]\qquad \tt \dashrightarrow \: - {e}^{x} + {e}^{x} [/tex]

[tex]\qquad \tt \dashrightarrow \:0[/tex]

I hope this helps, if you find any problem with steps or got a mistake in my explanation then feel free to ask me ~


Related Questions

Evaluate the expression for:
d = 14 and h = 9

Answers

Answer:

5

Step-by-step explanation:

14-9=5

Pls help give brainlest

Answers

Answer:

problem 18=E

problem 20= 135

problem 19= 14

problem 21= -2

problem 22= 0.5

5What is 20% of 50cm

Answers

Answer:

20% of (50 cm)= 10 Centimeters

Step-by-step explanation:

calculator!

Answer:

10 cm

[tex]20 \div 100 \times 50\% = 10cm[/tex]

Select all of the statements that are true, according to the box plots.

A. The weights of the pineapples in Crate 1 were the most variable.

B. The heaviest pineapple was in Crate 1.

C. The lightest pineapple was in Crate 1.

D. Crate 3 had the greatest median weight and the greatest IQR.

E. More than half the pineapples in Crate 1 and Crate 3 were heavier than the heaviest pineapple in Crate 2.

Answers

Answer:

The heaviest pineapple was in Crate 1.

More than half the pineapples in Crate 1 and Crate 3 were heavier than the heaviest pineapple in Crate 2.

Step-by-step explanation:E.

PLEASE HELPPP!!! ILL GIVE BRAINLIEST!!!

Answers

Answer:

240 ft²

the explanation is in the picture

25 millas
5 millas
…………………

Answers

Answer:

11.5 degrees.

Step-by-step explanation:

[tex]using sinx = \frac{opposte}{hypothenus} \\ sinx = \frac{5}{25} \\ sinx = 0.2 \\ x = sin {}^{ - } (0.2) \\ x = 11.5 \: degrees[/tex]

What is the volume to a rectangular prism when it has 9.3cm, 4cm and 4 cm

Answers

Given Dimension :-

9.3 cm , 4cm , 4cm

To find :-

The volume of rectangular prism

Solution :-

Volume of rectangular prism=L × W × H

Volume :- 9.3 × 4 × 4 cm³

Volume = 148.8 cm³

Answer:

Volume of rectangular prism is 148.8 cm³

Step-by-step explanation:

In the question we have .

Length of prism = 9.3 cm

Width of prism = 4 cm

Height of prism = 4 cm

And we are asked to find the volume of rectangular prism . We know that ,

[tex] \quad \pink{ \boxed{ \sf{Volume _{ (Rectangular\: Prism) } = L × W × H }}}[/tex]

Where ,

L = Length of rectangular prism

W = Width of rectangular prism

H = Height of rectangular prism

Solution : -

[tex] \quad \: \longmapsto \: 9.3 \times 4 \times 4[/tex]

Calculating further :

[tex] \quad \: \longmapsto \:9.3 \times 16[/tex]

We get :

[tex] \quad \: \longmapsto \: \purple{ \underline{\boxed{\frak{148.8 \: cm {}^{3} }}}}[/tex]

Therefore , volume of rectangular Prism is 148.8 cm³

#Keep Learning

i need help with my math homework what is 234234x3432

Answers

The answer is: 803,891,088, just multiply.

Ted used a $150 check to pay for some books. Where in his checkbook register should he write this amount?
A. in the PAYMENT or WITHDRAWAL AMOUNT column
B. in the DEPOSIT AMOUNT column
C. in the BALANCE column
D. in the FEE column

Answers

C
Because you are balancing how much you have left in your bank

could someone help me super fast? no fake answers please
optionally could someone help me too with any of the other questions on my profile they are worth 50 points each too

Answers

Answer:

(a)  graph iii)

(b)  graph v)

(c)  graph ii)

(d)  graph iv)

Step-by-step explanation:

All given equations are in vertex form:  y = (x - h)² + k

where (h, k) is the vertex of the parabola

The vertex is the turning point of the parabola, so the minimum point for parabolas that open upward, and the maximum point for parabolas that open downward.

Vertices of the given graphs:

i) (-3, 2)

ii) (-3, -2)

iii) (2, 3)

iv) (3, 2)

v) (-2, -3)

vi) (2, -3)

Part (a)

Given equation:  y = (x - 2)² + 3

Therefore, the vertex is (2, 3) → graph iii)

Part (b)

Given equation:  y = (x + 2)² - 3

Therefore, the vertex is (-2, -3) → graph v)

Part (c)

Given equation:  y = (x + 3)² - 2

Therefore, the vertex is (-3, -2) → graph ii)

Part (d)

Given equation:  y = (x - 3)² + 2

Therefore, the vertex is (3, 2) → graph iv)

Vertex form of parabola having vertex (h,k)

y=a(x-h)²+k

#1

y=a(x-2)²+3

Vertex (2,3)

Graph III

#2

y=(x+2)²-3

Vertex (-2,-3)

Graph V

#3

y=(x+3)²-2

Vertex (-3,-2)

Graph II

#4

y=(x-3)²+2

Vertex (3,2)

Graph IV

At the Madison Ski Resort, it snowed 5 feet yesterday and 2/3 of a foot today. How much more did it snow yesterday than today?

Write your answer as a fraction or as a whole or mixed number.

Answers

Answer:

4 1/3

Step-by-step explanation:

this is just a subtraction problem. What you know is that it snowed 5ft yesterday and 2/3ft today. So that means that the amount of more snow yesterday can be calculated with 5 - 2/3ft (this will show how much more snow there was yesterday). The result of this expression would be 4 1/3. Hope this helps!

please help giving branliest

Answers

Answer:

7

Step-by-step explanation:

since it's a right triangle we can use the pythagorean theorem.

hence, sqrt(25^2 - 24^2) = the answer = 7

make sure to ask if you need any further guidance.

A cuboid with a volume of 374cm^3 has dimensions 2cm,(x+3)cm and (x+9)cm
Please help me get the full 7 marks

Answers

Answer:

x² + 12x - 160 = 0

x = 8 or x = -20

The dimensions are 2 cm, 11 cm, 17 cm.

Step-by-step explanation:

The volume of the cuboid is the product of the three dimensions.

volume = 2(x + 3)(x + 9)

volume = 2(x² + 12x + 27)

volume = 2x² + 24x + 54

We are told the volume equals 374 cm³.

2x² + 24x + 54 = 374

2x² + 24x - 320 = 0

x² + 12x - 160 = 0

(x - 8)(x + 20) = 0

x - 8 = 0 or x + 20 = 0

x = 8 or x = -20

We do not use x = -20 because it would cause two dimensions to be negative which cannot be.

x = 8

x + 3 = 8 + 3 = 11

x + 9 = 8 + 9 = 17

The dimensions are 2 cm, 11 cm, 17 cm.

What is the approximate volume of the sphere shown?
r= 13 inches
o 527 cubic inches
o 7327 cubic inches
o 2,9297 cubic inches
0 2,1977 cubic inches
< Previous

Answers

Answer:

2,197 is D

Explanation:

4/3 * 3.14 * 13^3 =

2,197

Find the area of the figure.EXPLAIN THE STEPS!!!!!

Answers

Answer:

Explanation:

So you want to start by finding the area of the big square.

We know the width of the big square is 60cm. The length of the big square is

19

+

24

+

13

=

56

Big square

A

r

e

a

=

L

W

=

56

60

=

3360

Now let’s find the little square inside the bigger square. We see from the picture that the width is 34 and the length is 24cm. Using the same formula, we can find the area of the little square.

Little square

A

r

e

a

=

L

W

=

24

34

=

816

The area is enclosed in the area of the big square minus the area of the little square.

3360

816

=

2544

So the area enclosed is

2544

c

m

2

Step-by-step explanation:

Marissa drew and labeled 4 triangles on grid paper as shown below. Which triangle appears to be an obtuse triangle

Answers

The triangle that must appear to be obtuse mmust have one of its angle to be greater than 90 but less than 180 degrees:

What are obtuse triangles?

Obtuse triangles are triangles that has one of theor angles to greater than 90 degrees.

Most obtuse triangles has two acute angles (angles less than 90 degrees) and a obtuse angle (angles between  90 and 180 degrees)

Hence the triangle that must appear to be obtuse mmust have one of its angle to be greater than 90 but less than 180 degrees:

Learn more on obtuse triangle here: https://brainly.com/question/3250447

Which sum does the model below represent?
+
+
+
+
ĐO
oo ooo
0 4+(-7) = -3
O 4+ 7 = 11
O 8+(-3) = 4
O 11+ (-4) = -3

Answers

Answer:

THIS ANSWER IS CORRECT

----------------------------------------------

Step-by-step explanation:

BRAIN LESS ANSWER

Find the missing number in the following fraction calculation
/7 ÷10 =3/35

Answers

x=6

Step-by-step explanation:

x ÷ 7 ÷10 = 3/35

(Use trial & error - since I knew x<7)

6/7 ÷ 10 = 3/35

Or

3/35 x 10

(then, simplify it to 6/7 or ÷ that by 1/7 to get 6)

Hope this helps!

4
Select the correct answer from each drop-down menu.
A circle is rotated around a vertical axis. The circle does not intersect the axis.
Complete the following statement.
The three-dimensional shape resulting from the rotation is a
with a
center.

Answers

If the circle is rotated about the vertical axis then it forms the shape of a sphere with the same center.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A circle is rotated around a vertical axis. The circle does not intersect the axis.

The three-dimensional shape resulting from the rotation will be

If the circle is rotated about the vertical axis then it forms the shape of a sphere with the same center.

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ1

What percent of 50 (is)40?

Answers

Answer:

80% :)

Step-by-step explanation:

We divide to solve this!!

40/50 = 0.8

Now multiply to get a percent!!

0.8 x 100 = 80%

Have an amazing day!!

Please rate and mark brainliest!!

How many, Inch cubes fit into a rectangular prism that measures 4 Inches long, 5 Inches wide, and
Inches high?
C. 780
A. 130
D. 1,040
B. 260

Answers

780 (or c)


I think this is correct because 4 x 5 = 20 x 5 = 100 and 100 x 5 = 500

500 + 280 = ????

780

If rectangle ABCD were rotated 90° clockwise about the origin to create rectangle A'B'C'D', which set of sides would be parallel in the resulting image?

I. A'B' and D'C'
II. A'D' and D'C'
III. A'B' and A'D'
IV. A'D' and B'C'

A.
I and II only
B.
I and IV only
C.
II and III only
D.
I, II, III, and IV

answers is B

Answers

Answer: B. I and IV only

Step-by-step explanation:

     We can look at the rectangle already graphed. Since it is being rotated, parallel sets of sides will be parallel in ABCD and A'B'C'D'

I. A'B' and D'C'

      -> True

II. A'D' and D'C'

      -> False

III. A'B' and A'D'

      -> False

IV. A'D' and B'C'

      -> True

This means your answer is option B.

I and IV only

i don't have much time left could someone help me super quickly (trinomials) btw you could get extra 50 points from a previous question on my profile (only if you want) i would really appreciate if i could have help understanding things

Answers

Answer:

(a)  [tex](x-2)(x+4)[/tex]

zeros: x = 2, x = -4

vertex: (-1, -9)

(b)  [tex]-(x+2)(x+7)[/tex]

zeros: x = -2, x = -7

vertex = (-4.5, 6.25)

Step-by-step explanation:

To factor a quadratic in the form [tex]ax^2+bx+c[/tex]:

Find 2 two numbers (d and e) that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]Rewrite [tex]b[/tex] as the sum of these 2 numbers: [tex]d+e=b[/tex]Factorize the first two terms and the last two terms separately, then factor out the comment term.

To find zeros of a factored quadratic in the form [tex](ax+b)(cx+d)[/tex]

Set each of the parentheses to zero and solve for [tex]x[/tex]

The midpoint between the two zeros is the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute this into the given equation.

-------------------------------------------------------------------------------------

Question (a)

Factored

Factor  [tex]y=x^2+2x-8[/tex]

[tex]ac=-8[/tex]  and  [tex]d+e=2[/tex]

[tex]\implies d=4[/tex] and [tex]e=-2[/tex]

Rewrite [tex]2x[/tex] as [tex]+4x-2x[/tex]:

[tex]\implies x^2+4x-2x-8[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies x(x+4)-2(x+4)[/tex]

Factor out common term [tex](x+4)[/tex]:

[tex]\implies (x-2)(x+4)[/tex]

Zeros

[tex]\implies (x-2)=0\implies x=2[/tex]

[tex]\implies (x+4)=0\implies x=-4[/tex]

Vertex

[tex]\sf x-value=\dfrac{2+(-4)}{2}=-1[/tex]

[tex]\sf y-value=(-1)^2+2(-1)-8=-9[/tex]

Vertex = (-1, -9)

-------------------------------------------------------------------------------------

Question (b)

Factor  [tex]y=-x^2-9x-14[/tex]

[tex]ac=14[/tex]  and  [tex]d+e=-9[/tex]

[tex]\implies d=-7[/tex] and [tex]e=-2[/tex]

Rewrite [tex]-9x[/tex] as [tex]-7x-2x[/tex]:

[tex]\implies -x^2-7x-2x-14[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies -x(x+7)-2(x+7)[/tex]

Factor out common term [tex](x+7)[/tex]:

[tex]\implies (-x-2)(x+7)[/tex]

Factor [tex](-x-2):-(x+2)[/tex]

[tex]\implies -(x+2)(x+7)[/tex]

Zeros

[tex]\implies -(x+2)=0\implies -x-2=0 \implies x=-2[/tex]

[tex]\implies (x+7)=0\implies x=-7[/tex]

Vertex

[tex]\sf x-value=\dfrac{-2-7}{2}=-4.5[/tex]

[tex]\sf y-value=-(-4.5)^2-9(-4.5)-14=6.25[/tex]

Vertex = (-4.5, 6.25)

Simplifying please help i don’t know how to do this

Answers

Answer:

8,400

Step-by-step explanation:

840*10^1 = 8400

Answer:

8400

Step-by-step explanation:

840 * 10 = 8400

When multiplying by 10 in this scenario, simply add a zero to the end of the number.

A pyramid has a square base that has an area of 144 square feet. If the slant height of each triangular face is 10 in, what is the total surface area of the pyramid?

Answers

Answer:

Total Surface Area

= 384 sq ft

Step-by-step explanation:

To find Total Surface Area, add up the areas of all the sides of the shape. A square based pyramid has five sides, a square bottom and four triangular sides. Luckily all four sides are the same, so just one calculation for these.

Area of square base is given.

A = 144 sq ft

Since the base is a square the length of the side of the square is 12, because 12×12 is 144.

The side of the square base is the base of the triangular side.

Area of a triangle:

A = 1/2•b•h

A = 1/2(12)(10)

A = 60

The area of one triangular face is 60. There are four of these.

A = 4(60)

A = 240

This is the area of all the triangular faces.

Add them all up.

A (TOTAL)

= 144+240

= 384 sq ft

Hewo

My question:
1/2÷4 but if you could! draw a model plsss

Answers

Answer:

0.125

Step-by-step explanation:

So since we have 1/2 we will convert that to half of a pie... (the half circle)

We need to divide by four so we take that half of a pie and slice it into four parts... each part is now equivalent to our answer...

Equation... (as follows)

0.50 / 4 = 0.125

to check our work 0.125 x 4 = 0.50...

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!

Seven students in class A and ten students in class B ate pizza. There are 25 students in class A and 30 students in class B. What fraction of the class didn't eat pizza?

Answers

Answer:

=18/20

Step-by-step explanation:

• 25 - 7 = 18

• 30 - 10 = 20

= 18/20

if u reduce = 9/10

171% of x = 3388, Find x and find 500% of x.

Answers

Answer:

0.10

Step-by-step explanation:

What is the sum of the
greatest common factor and the least common
multiple of 4 and 10?
A 18
B 20
C 22
D 24

Answers

Answer:

C

Hope This Helps! :) Please Give Brainliest if this does!

Solve the equation by factoring. z2 – 6z – 27 = 0

z = –3 or z = 9
z = –3 or z = –9
z = 3 or z = –9
z = 3 or z = 9

Answers

Answer:

The value of z = -3 or z = 9

Step-by-step explanation:

Given equation => z² – 6z – 27 = 0

=> z² - 9z + 3z - 27 = 0

=> z(z -9 ) +3 (z - 9 ) = 0

=> (z + 3) (z - 9)

=> z = -3 or z = 9

Answer:z = –3 or z = 9

Step-by-step explanation:

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