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3 years ago

Write an inequality to model the situation. the maximum speed on the highway , x is 55 mi/h

Mathematics

2 answers:

Mekhanik [1.2K]3 years ago

8 0

Answer:

We have been given the maximum speed on the highway which is 55 mi/hr

So, it has to be less than or equal to 55 because maximum it can go up to 55.

The required inequality will be $x\leq55$

We can take an example of a moving car on a highway which is moving with the speed of 45 mi/hr

And also the stationary car on highway because its speed will be zero which is satisfying the inequality condition.

OLEGan [10]3 years ago

6 0

A maxm speed of 55 mph means that the speed has to be lexx than or equal to 55

x <= 55

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Let ρ = x3 + xe−x for x ∈ (0, 1), compute the center of mass.

hram777 [196]

The center of mass is mathematically given as

$\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}$

<h3>What is the center of mass.?</h3>

Determine the center of mass in one dimension:

Represent the masses at the respective distances.

$\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\end$

We calculate the total mass of the system.

$\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}$

Step 03: Calculate the moment of the system.

$\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}$

we calculate the center of mass.

$\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}$

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2 years ago

Sail with the equation by completing the square x^2+8x=-3

maxonik [38]

Answer:

The solutions are $x=-4(+/-)\sqrt{13}$

Step-by-step explanation:

we have

$x^{2} +8x=-3$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2} +8x+16=-3+16$

$x^{2} +8x+16=13$

Rewrite as perfect squares

$(x+4)^{2}=13$

square root both sides

$x+4=(+/-)\sqrt{13}$

$x=-4(+/-)\sqrt{13}$

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3 years ago

Which proportion can you use to find the value of a?

Ugo [173]

<u>Given</u>:

The given triangle is a similar triangle.

The length of the hypotenuse is 18 units.

The length of the leg is a.

The length of the part of the hypotenuse is 16 units.

We need to determine the proportion used to find the value of a.

<u>Proportion to find the value of a:</u>

We shall find the proportion to determine the value of a using the geometric mean leg rule.

Applying the leg rule, we have;

$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$

Substituting the values of hypotenuse, leg and part, we get;

$\frac{18}{a}=\frac{a}{16}$

Thus, the proportion used to find the value of a is $\frac{18}{a}=\frac{a}{16}$

Hence, Option D is the correct answer.

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3 years ago

Mrs. Williams is deciding between two field trips for her class. The Science Center charges $135 plus $3 per student. The Dino D

Marianna [84]

Set it up like a regular equation. I used:
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As you can see, however, I inserted the "less than" symbol rather than the equal sign because values greater than a certain value can also equal "x". Solve it like a normal equation and you will arrive at:
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This means that, as long as x is greater than 45, "6x" will be greater than "3x+135". Thus, if you bring 46 students, the Science Center will cost less.

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solniwko [45]

Answer:

use a ruler stupid duhhhh!11

Step-by-step explanation:

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