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

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]:

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

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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)

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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)

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!

Given Dimension :-

To find :-

Solution :-

Volume :- 9.3 × 4 × 4 cm³

Volume = 148.8 cm³

Answer:

Step-by-step explanation:

In the question we have .

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 ,

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]

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

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.

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.

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.

Answer:

C

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

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

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

Answer:

THIS ANSWER IS CORRECT

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Step-by-step explanation:

BRAIN LESS ANSWER

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!!

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!

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:

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:

Answer:

20% of (50 cm)= 10 Centimeters

Step-by-step explanation:

calculator!

Answer:

10 cm

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

Answer:

=18/20

Step-by-step explanation:

• 25 - 7 = 18

• 30 - 10 = 20

= 18/20

if u reduce = 9/10

Answer:

problem 18=E

problem 20= 135

problem 19= 14

problem 21= -2

problem 22= 0.5

Answer:

the explanation is in the picture

Answer:

0.10

Step-by-step explanation:

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!

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

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

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.

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

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)

#1

Vertex (2,3)

#2

Vertex (-2,-3)

#3

Vertex (-3,-2)

#4

Vertex (3,2)

Answer:

5

Step-by-step explanation:

14-9=5

Answer:

2,197 is D

Explanation:

4/3 * 3.14 * 13^3 =

2,197

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]