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3 years ago

Please Help Quickly!!!

Mathematics

1 answer:

Sophie [7]3 years ago

5 0

It's the value of $\dfrac{\mathrm dy}{\mathrm dx}$ when $x=1$ :

$y=x^2\implies\dfrac{\mathrm dy}{\mathrm dx}=2x$

When $x=1$ , the derivative/slope is 2, so the answer is C.

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Find the area of a trapezoid Explain please

djverab [1.8K]

Answer:

Step-by-step explanation:

Area = a+b/2 * h

6+10/2= 8

8*4 = 32

7 0

3 years ago

A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate

Lyrx [107]

Answer:

Therefore the rate change of height is $\frac{1}{\pi}$ m/s.

Step-by-step explanation:

Given that a vertical cylinder is leaking water at rate of 4 m³/s.

It means the rate change of volume is 4 m³/s.

$\frac{dV}{dt}=4 \ m^3/s$

The radius of the cylinder remains constant with respect to time, but the height of the water label changes with respect to time.

The height of the cylinder be h(say).

The volume of a cylinder is $V=\pi r^2 h$

$=( \pi \times 2^2\times h)\ m^3$

$\therefore V= 4\pi h$

Differentiating with respect to t.

$\frac{dV}{dt}=4\pi \frac{dh}{dt}$

Putting the value $\frac{dV}{dt}$

$\Rightarrow 4\pi \frac{dh}{dt}=4$

$\Rightarrow \frac{dh}{dt}=\frac{4}{4\pi}$

$\Rightarrow \frac{dh}{dt}=\frac{1}{\pi}$

The rate change of height does not depend on the height.

Therefore the rate change of height is $\frac{1}{\pi}$ m/s.

3 0

3 years ago

8X + 1 = 49. what is X?

Zolol [24]

Answer:

5 0

3 years ago

Read 2 more answers

Which statements are true about the ordered pair (-1,-4) and the system of equations?

rewona [7]

Answer:

1.When (-1,-4) is substituted into the first equation, the equation is false. FALSE

2. When (-1,-4) is substituted into the first equation, the equation is true. TRUE

3. When (-1,-4) is substituted into the second equation, the equation is false.

FALSE

4. When (-1,-4) is substituted into the second equation, the equation is true. TRUE

5.The ordered pair (-1,-4) is a solution to the system of linear equations .TRUE

6.The ordered pair (-1,-4) is not a solution to the system of linear equations.

FALSE

Step-by-step explanation:

Here, the given set if equations are:

x - y = 3

7 x - y = - 3

Now, substituting the given value (-1,-4) in the given equations, we get

(1) Substitute (-1, -4) in first equation:

x - y = 3 : (-1, -4)

⇒ (-1) - (-4) = -1 + 4 = 3 = Right Side

So, the equation x - y = 3 holds TRUE for (-1,-4)

(2) Substitute (-1, -4) in second equation:

7 x - y = - 3 : (-1, -4)

⇒ 7(-1) - (-4) = -7 + 4 = -3 = Right Side

So, the equation 7 x - y = - 3 holds TRUE for (-1,-4)

Now, the given options are:

When (-1,-4) is substituted into the first equation, the equation is false. FALSE, equation is satisfied.

When (-1,-4) is substituted into the first equation, the equation is true.

TRUE

When (-1,-4) is substituted into the second equation, the equation is false.

FALSE, the given equation is satisfied.

When (-1,-4) is substituted into the second equation, the equation is true.

TRUE

The ordered pair (-1,-4) is a solution to the system of linear equations .

TRUE,as the given point satisfies both the equations.

The ordered pair (-1,-4) is not a solution to the system of linear equations.

FALSE,as the given point satisfies the equation.

4 0

3 years ago

For f(x) =4x+1 g(x)=x²-5, find (f•g)(x)

Inessa05 [86]

Answer:

(f · g)(x) = 4x³ + x² - 20x - 5

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Combining Like Terms
Expand by FOIL (First Outside Inside Last)

Step-by-step explanation:

Step 1: Define

f(x) = 4x + 1

g(x) = x² - 5

(f · g)(x) is f(x)g(x)

Step 2: Find (f · g)(x)

Substitute: (f · g)(x) = (4x + 1)(x² - 5)
Expand [FOIL]: (f · g)(x) = 4x³ - 20x + x² - 5
Combine like terms: (f · g)(x) = 4x³ + x² - 20x - 5

3 0

3 years ago

Read 2 more answers