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astra-53 [7]
1 year ago
12

Find the derivative of f(x) =2x^2 -4x + 3

Mathematics
1 answer:
iren [92.7K]1 year ago
5 0

Derivatives

Find the derivative of the function:

f(x)=2x^2-4x+3

The following rules are applied:

\begin{gathered} (x^n)^{\prime}=n\cdot x^{n-1} \\ (kx)^{\prime}=k \\ (k)^{\prime}=0 \end{gathered}

Where k and n are constants.

Applying the rules:

\begin{gathered} f^{\prime}(x)=2(2x)-4+0 \\ Operate\colon \\ f^{\prime}(x)=4x-4 \end{gathered}

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Y is inversely proportional to x, when Y = 2, x = 4.<br><br>Find the value of x when Y = 4.
ratelena [41]

The value of x when y =4 is 2

<h3>How to solve for x?</h3>

An inverse proportion is represented as:

k = yx

Where

k represents the constant of proportion

When y = 2, x = 4.

So, we have:

k =2 * 4

k = 8

Substitute k = 8 in k = yx

So, we have:

yx = 8

When y = 4, we have:

4x = 8

Divide by 4

x = 2

Hence, the value of x when y =4 is 2

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8 0
2 years ago
Plz hurry!!!! thank you!!!!
Nikitich [7]

Answer:

Area of trapezium = 4.4132 R²

Step-by-step explanation:

Given, MNPK is a trapezoid

MN = PK and ∠NMK = 65°

OT = R.

⇒ ∠PKM = 65° and also ∠MNP = ∠KPN = x (say).

Now, sum of interior angles in a quadrilateral of 4 sides = 360°.

⇒ x + x + 65° + 65° = 360°

⇒ x = 115°.

Here, NS is a tangent to the circle and ∠NSO = 90°

consider triangle NOS;

line joining O and N bisects the angle ∠MNP

⇒ ∠ONS = \frac{115}{2} = 57.5°

Now, tan(57.5°) = \frac{OS}{SN}

⇒ 1.5697 = \frac{R}{SN}

⇒ SN = 0.637 R

⇒ NP = 2×SN = 2× 0.637 R = 1.274 R

Now, draw a line parallel to ST from N to line MK

let the intersection point be Q.

⇒ NQ = 2R

Consider triangle NQM,

tan(∠NMQ) = \frac{NQ}{QM}

⇒ tan65° = \frac{NQ}{QM}

⇒ QM = \frac{2R}{2.1445}

QM = 0.9326 R .

⇒ MT = MQ + QT

          = 0.9326 R + 0.637 R  (as QT = SN)

⇒ MT = 1.5696 R

⇒ MK = 2×MT = 2×1.5696 R = 3.1392 R

Now, area of trapezium is (sum of parallel sides/ 2)×(distance between them).

⇒ A = (\frac{NP + MK}{2}) × (ST)

       = (\frac{1.274 R + 3.1392 R}{2}) × 2 R

       = 4.4132 R²

⇒ Area of trapezium = 4.4132 R²

5 0
3 years ago
PLEASE HELP, I WILL MARK BRAINLIEST FOR THE FIRST CORRECT ANSWER))
madam [21]

Answer:

The volume of this cylinder is 9184.5 cubic feet.

Step-by-step explanation:

The area of a circle is \pi r^2 and the volume of a cylinder with that base is just that area times the height:

V=\pi r^2\times h

Here, we're given the diameter, but we need the radius. The radius of a circle is just half of the diameter:

r=30\times0.5=15

Next, you can use that radius to calculate the area of the base:

A=3.14\times15^2\\A=3.14\times225\\A=706.5

Finally, multiply that by the height to find the volume of the cylinder:

V=706.5\times13\\V=9184.5

The volume of this cylinder is 9184.5 cubic feet.

7 0
3 years ago
Which number is greater and by how much?
Lana71 [14]

Answer:

A

Step-by-step explanation:

first option, as the decrease percentage is applicated on a greater number than the original

e.g.

A

a= 10

B

10 + 50% = 15

15 - 50% = 7,5

A will be greater then B by 25%

4 0
2 years ago
Which collection of three side lengths will NOT form a triangle?
Juli2301 [7.4K]
Just multiply each line then whatever one doesnt have 180 as the answer choose it
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3 years ago
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