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Mathematics

1 answer:

posledela3 years ago

7 0

Answer:

Step-by-step explanation:

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Find the obtuse angle the line y-2x=7 makes with the x- axis

Kazeer [188]

In analytical geometry, there are already derived equations to find the distance of lines and points as well as the angle made between two lines. As special case is when the other line is one of the coordinate axis. Then, the formula can be simplified to

tan θ =m, where m is the slope of the equation

In the next step, we also incorporate operations of calculus. Since the slope is equal to Δy/Δx, this is equivalent to dy/dx in calculus. Therefore, you can find the slope by differentiating the equation in terms of x.

y-2x=7
y = 2x+7
dy/dx = 2 =m

So,

tan θ = 2
θ = tan⁻¹(2)
θ = 63.43°

5 0

3 years ago

Solve this question

love history [14]

Answer:

$\frac{4x - 11}{2} \leqslant 3x - 3 < 4 \\ \\ = > \frac{4x - 11}{2} \leqslant 3x - 3 \: and \: 3x - 3 < 4 \\ \\ < = > 4x - 11 \leqslant 6x - 6 \: \: and \: \: 3x < 7 \\ \\ < = > 2x \geqslant - 5 \: \: and \: \: x < \frac{7}{3} \\ \\ < = > \frac{ - 5}{2} \leqslant x < \frac{7}{3}$

=> the greatest integer is 2

the smallest integer is -2

3 0

3 years ago

To obtain information on the corrosion-resistance properties of a certain type of steel conduit, 45 specimens are buried in soil

Fiesta28 [93]

Answer:

The sample has not met the required specification.

Step-by-step explanation:

As the average of the sample suggests that the true average penetration of the sample could be greater than the 50 mils established, we formulate our hypothesis as follow

$H_0$ : The true average penetration is 50 mils

$H_a$ : The true average penetration is > 50 mils

Since we are trying to see if the true average is greater than 50, this is a right-tailed test.

If the level of confidence is α = 0.05 then the $z_\alpha$ score against we are comparing with, is 1.64 (this is because the area under the normal curve N(0;1) to the right of 1.64 is 0.05)