Bonus Question:
a. Consider the function f(x) = ax^2 + c
Find f'(x)

b. Point A (-2, 5) lies on the graph of y = f(x).
The gradient of the tangent to this graph at A is -6. Find the value of a.

c. Find the value of c.

Please answer this question and please show your work too. Anyone who is able to do this correctly will receive 50 points from me. (This assignment is about Derivatives)

Answer:

(5,3)

Step-by-step explanation:

1. Translation 5 units right, so the x-coordinates goes to 5.

2. Translation 5 units under, so the y-coordinates goes to 3.

So . the answer is (5, 3)

Given:

The vertices of a triangle are [tex](1,1),(-1,-1),(-\sqrt{3},\sqrt{3})[/tex].

To prove:

The given vertices are the vertices of an equilateral triangle.

Solution:

Distance formula:

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

Let the vertices of the triangle are [tex]A(1,1),B(-1,-1),C(-\sqrt{3},\sqrt{3})[/tex]. Then, by using the distance formula, we get

[tex]AB=\sqrt{(-1-1)^2+(-1-1)^2}[/tex]

[tex]AB=\sqrt{(-2)^2+(-2)^2}[/tex]

[tex]AB=\sqrt{4+4}[/tex]

[tex]AB=\sqrt{8}[/tex]

Similarly,

[tex]BC=\sqrt{(-\sqrt{3}-(-1))^2+(\sqrt{3}-(-1))^2}[/tex]

[tex]BC=\sqrt{(1-\sqrt{3})^2+(1+\sqrt{3})^2}[/tex]

[tex]BC=\sqrt{(1)^2+(\sqrt{3})^2-2\sqrt{3}+(1)^2+(\sqrt{3})^2+2\sqrt{3}}[/tex]

[tex]BC=\sqrt{1+3+1+3}[/tex]

[tex]BC=\sqrt{8}[/tex]

And,

[tex]CA=\sqrt{(1-(-\sqrt{3}))^2+(1-\sqrt{3})^2}[/tex]

[tex]CA=\sqrt{(1+\sqrt{3}))^2+(1-\sqrt{3})^2}[/tex]

[tex]CA=\sqrt{(1)^2+(\sqrt{3})^2+2\sqrt{3}+(1)^2+(\sqrt{3})^2-2\sqrt{3}}[/tex]

[tex]CA=\sqrt{1+3+1+3}[/tex]

[tex]CA=\sqrt{8}[/tex]

Clearly, [tex]AB=BC=CA[/tex].

Since all sides of the given triangle are equal, therefore the given vertices are the vertices of an equilateral triangle.

Hence proved.

Answer: 103 degrees

Step-by-step explanation: all angle of a regular triangle always add up to 180. so 62+15=77. and 180 - 77= 103

Answer:

A. 103 degrees

Step-by-step explanation:

In a triangle, the sum of angle measures is equal to 180 degrees, so by adding 62 & 15, & subtracting it from 180 you get the third angle measure of 103.

Answer:

not defined

Step-by-step explanation:

[tex] {x}^{2} = 56 - 2000 - 15637 \\ {x}^{2} = - 1758[/tex]

For A)

arcsin(11/15)=angle of elevation

47.17=angle of elevation

For B)

tan(47.17)=11/x

11/tan(47.17)=x

10.2=x

Answer:

8 books were in each box

Step-by-step explanation:

According to the Question,

Assume X is the Number of Books In Each Box.

Algebraic Expression,

4X + 3 = 35

4X = 35 - 3

4X = 32  ⇔  X=8 books in Each Box.

Answer:

32 ft³

Step-by-step explanation:

put r= 2 ft

V= 4/3x 3 X 2³

V= 32 ft³

I got this answer with help form Gauthmath App you can check out the app on Play Store and App store.

Answer:

8

Step-by-step explanation:

Given:

13 - 0.75w + 8x

where,

w = 12

x = 1/2

13 - 0.75w + 8x

Substitute the value of w and x into the equation

= 13 - 0.75(12) + 8(1/2)

= 13 - 9 + 8/2

= 13 - 9 + 4

= 8

Therefore,

13 - 0.75w + 8x = 8

Answer:

u r ANS

Step-by-step explanation:

7/3 on number line

Mark above ANS as branliest

Answer:

I believe the correct answer is 49.

Step-by-step explanation:

If this answer is incorrect let me know and I will fix it. I'm sorry in advance if it is wrong.

Answer:

42 crickets

Step-by-step explanation:

6 x 7= 42

Answer:

the surface area of cylinder is 1733.28 inches²

hope it helps

have a nice day

Answer:

The 2 option :)

Step-by-step explanation:

The Chords : QL ,SM , Secant : NR , Tangents : a  and b , Diameter : QL, ,radii: PT , QT and TL therefore the Option A is the correct answer.

A circle is a round shaped figure , whose all points are in the same plane and at same distance from a single point known as center.

A secant is a segment that passes through 2 points on a circle, It is an infinite extension of a chord.

A tangent touches a circle at exactly one point and never enters the interior of the circle.

A chord is a line segment which connects two point on the circle.

A diameter is a chord that passes through the center of the circleThe radius is half of the diameter of the circle

Based on the above definitions

Chords : QL ,SM

Secant : NR

Tangents : a  and b

Diameter : QL

radii: PT , QT and TL

To know more about Circle

https://brainly.com/question/11833983

#SPJ2

Answer:

hypotenuse = 7.3

Step-by-step explanation:

the length two legs of the given triangle are 7 and 2 respectively.

using pythagoras theorem

a^2 + b^2 = c^2

7^2 + 2^2 = c^2

49 + 4 = c^2

53 = c^2

[tex]\sqrt{53}[/tex] = c

7.3 = c

Step-by-step explanation:

you only need to provide an example ?

if your question here is complete, then the full set is

{1,7,8}

and these are all possible subsets (pick any one you like) :

{1}, {7}, {8}, {1,7}, {1,8}, {7,8}

and formally also

{}, {1,7,8}

the empty set is a subset of every set, and the whole set itself is also formally a subset.

Answer:1) 32.  2).  3) 21.  4) 4

Step-by-step explanation: 1) 4*8=32m, 2) I don't know, 3) 6*7=42 for the area of a square but since a triangle half it so its 21, An the last is by 4 for example 4*10=40 but if doubled its 20*8 and that equals 160. and 160/40=4

Answer:

D

Step-by-step explanation:

3 - 7 = -4 and 3(3) + 2(-7) = -5, so D is the only choice that is correct for both inequalities.

Answer:

Gradient = -3

Step-by-step explanation:

The gradient of the graph = change in y/change in x

Change in y = the vertical distance = 3 units

Change in x = the run/horizontal distance = 1 unit

The line slopes downward, so it's a negative gradient.

Thus:

Gradient = 3/1 = -3

Step-by-step explanation:

- 1⅔ < -¼

__________________

Answer:

8a) 3x

8b) 3 × x

8c) (2/3)x

8d) x/2

8e) 1/x

9a) 4x - 7

9b) x + 1/x

9c) 5(x + 2)

9d) x/(x + 4)

9e) (x/8) + x

Answer:

6,9,12

Step-by-step explanation:

A triangle cannot be considered a triangle unless the sum of the smaller two of the sides is greater than the larger side.

Answer:

(6, 9, 12)

Hope that this helps!

Answer:

D

Step-by-step explanation:

point C is on the y with the value 2 so y=2 and x=z=0

Answer:

Option : The product of the roots is - 4

Step-by-step explanation:

[tex]3x^2 + 9x - 12 = 0\\\\3x^2 + 12x - 3x - 12 = 0\\\\3x(x+4) -3(x+4) = 0\\\\(3x - 3) (x+ 4) = 0\\\\[/tex]

Therefore the roots are -4 and 1

The product of the roots are -4 x 1 = -4

Answer:

d bro. pay attention at order of triangle's vertices

Answer:

P'=(0,3)

Step-by-step explanation:

P'=(-5+5, 7-4)

Answer:

If I understand this right, the answer is $48.00

Step-by-step explanation:

If they pay $1.50 three times a month just times $1.50 by 12 because there are 12 days in a month, then you get 16, then you times 16 by 3 and you get 48.

(I hope this is right lol)

Answer:

$54.00

Step-by-step explanation:

3 transactions × $1.50 per transaction = $4.50 per month

$4.50 × 12 months in a year = $54.00

Answer:

[tex]\frac{3}{10} , 0.48 , 0.73[/tex]

Step-by-step explanation:

In order to put this number in order from least to greatest, we have to turn them into fractions with the same denominator, so firstly we write down all of the decimals as fractions, and we will get...

[tex]0.48 = \frac{48}{100} \\\\0.73 = \frac{73}{100}[/tex]

Now, we need to find the smallest number that is divisible by 100 and by 10, and this number will be the least common denominator. The smallest number that is divisible by 100 and by 10 is 100, therefore 100 is the least common denominator. Now we have to make all of the fractions have the denominator of 100 and we do that in the following way...

[tex]\frac{48}{100}= \frac{48}{100}\\\\\frac{73}{100} = \frac{73}{100}\\\\\frac{3}{10} = \frac{(3)(10)}{(10)(10)} = \frac{30}{100}[/tex]

By looking at this we need to understand that...

[tex]\frac{30}{100}<\frac{48}{100}<\frac{73}{100}[/tex]

Therefore...

[tex]\frac{3}{10} < 0.48 < 0.73[/tex]

Step-by-step explanation:

my answer is in the image above

p has to be greater than or equal to 8 root 2

Answer:

2355in³

Step-by-step explanation:

3.14(5)²×30=2355 in³

Answer:

Answer:94.2

Answer:94.2Step-by-step explanation:

Answer:94.2Step-by-step explanation:3.14(5)²×30

Answer:94.2Step-by-step explanation:3.14(5)²×303.14×25×30

Answer:94.2Step-by-step explanation:3.14(5)²×303.14×25×303.14×5×6

= 94.2

i am sorry if it is not correct

Answer:Number 1

a. eleven thousand and twelve

b. four thousand three hundred and fifteen

c. twenty one thousnad and ten

Answer:Number 2

a.I one thousand

II one tousand

b.I hundreds

II cero

c.I ten thousands

II sixty thousand