All categories

3 years ago

1. In a four-hour TV program, the commercials show 10% of the time.

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

6 0

Answer:

Step-by-step explanation:

I have devided10/100 I hope you can understand from the picture posted there

You might be interested in

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

seropon [69]

Answer:

$h'(x)=\frac{3r^{2}}{2\sqrt{r^3+5}}$

Step-by-step explanation:

1) The Fundamental Theorem of Calculus in its first part, shows us a reciprocal relationship between Derivatives and Integration

$g(x)=\int_{a}^{x}f(t)dt \:\:a\leqslant x\leqslant b$

2) In this case, we'll need to find the derivative applying the chain rule. As it follows:

$h(x)=\int_{a}^{x^{2}}\sqrt{5+r^{3}}\therefore h'(x)=\frac{\mathrm{d} }{\mathrm{d} x}\left (\int_{a}^{x^{2}}\sqrt{5+r^{3}}\right )\\h'(x)=\sqrt{5+r^{3}}\\Chain\:Rule:\\F'(x)=f'(g(x))*g'(x)\\h'=\sqrt{5+r^{3}}\Rightarrow h'(x)=\frac{1}{2}*(r^{3}+5)^{-\frac{1}{2}}*(3r^{2}+0)\Rightarrow h'(x)=\frac{3r^{2}}{2\sqrt{r^3+5}}$

3) To test it, just integrate:

$\int \frac{3r^{2}}{2\sqrt{r^3+5}}dr=\sqrt{r^{3}+5}+C$

5 0

2 years ago

Find the minimum value of the function f(x)=x^2+5x-6

mash [69]

<h3><u>Explanation</u></h3>

Method 1 (Formula)

$\begin{cases}h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{2a} \end{cases}$

The vertex of Parabola is the maximum/minimum point depending on the value of a.

Find Vertex

<u>h-value</u>

$h = - \frac{5}{2(1)} \\ h = - \frac{5}{2}$

<u>k-value</u>

$k = \frac{4(1)( - 6) - {(5)}^{2} }{4(1)} \\ k = \frac{ - 24 - 25}{4} \\ k = \frac{ - 49}{4} \\ k = - \frac{49}{4}$

The minimum value is the value of k. Therefore the minimum value is - 49/4 at x = -5/2.

Method 2 (Derivative)

This is Calculus method. We simply differentiate the function then substitute y' = 0.

Differentiate Function

$f'(x) = 2 {x}^{2 - 1} + {5x}^{1 - 1} - 0 \\ f'(x) = 2x + 5$

Substitute f'(x) = 0

$0 = 2x + 5 \\ - 5 = 2x \\ - \frac{5}{2} = x$

Substitute x = -5/2 in the original equation.

$f(x) = {( - \frac{5}{2} )}^{2} + 5( - \frac{5}{2} ) - 6 \\ f(x) = \frac{25}{4} - \frac{25}{2} - 6 \\ f(x) = \frac{25}{4} - \frac{50}{4} - \frac{24}{4} \\ f(x) = \frac{25}{4} - \frac{74}{4} \\ f(x) = - \frac{49}{4}$

<h3><u>Answer</u><u /></h3>

<u> $\sf{the \: \: minimum \: \: value \: \: is \: \: - \frac{49}{4} \: \: at \: \: x = - \frac{5}{2} }$ </u>

4 0

3 years ago

Please Find the value of x

Simora [160]

X = 101 + 41
x = 142

hope it helps

8 0

3 years ago

Read 2 more answers

Hollow spheres with a radius of 8 cm whose shell is 2.5 cm thick. About how much chocolate will go into making wash sphere?

Nonamiya [84]

About $2078.20cm^3$ chocolate will go into making wash sphere .

<u>Step-by-step explanation:</u>

Here we have , Hollow spheres with a radius of 8 cm whose shell is 2.5 cm thick. We need to find About how much chocolate will go into making wash sphere .Let's find out:

Basically we need to find the volume of hollow sphere , We know that volume of hollow sphere is :

⇒ $Volume = \frac{4\pi }{3}(r_1^3-r_2^3)$ .............(1)

According to question ,

$r_1=8cm\\r_2=2.5cm$

Putting these values in equation (1) :

⇒ $Volume = \frac{4\pi }{3}(8^3-2.5^3)$

⇒ $Volume = \frac{4\pi }{3}(496.38)$

⇒ $Volume = \frac{4(3.14) }{3}(496.38)$

⇒ $Volume =2078.20cm^3$

Therefore , About $2078.20cm^3$ chocolate will go into making wash sphere .

3 0

3 years ago

Read 2 more answers

How to find the angle of triangle only knowing the right angle?

katrin [286]

There are many different ways to figure this out but may I ask you one question....do you know whether the two legs are congruent or just the right angle?

3 0

3 years ago