All categories

3 years ago

Which of the following is the equation of a circle whose center is at the origin and whose radius is 4?

1 answer:

4 0

$\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{0}{ h},\stackrel{0}{ k})\qquad \qquad 
radius=\stackrel{4}{ r}
\\\\\\
(x-0)^2+(y-0)^2=4^2\implies x^2+y^2=16$

You might be interested in

n engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that

BartSMP [9]

Answer:

The calculated t- value = 1.11 > 2.89 at 0.025 level of significance

Null hypothesis is rejected

The engineer designed the valve such that it would produce a mean pressure is not equal to 5.4

Step-by-step explanation:

Step(i):-

Given mean of the Population (μ) = 5.4

Given sample size 'n' = 9

Mean of the sample (x⁻) = 5.7

Standard deviation of the sample (s) = 0.81

Step(ii):-

Null Hypothesis: H₀: The engineer designed the valve such that it would produce a mean pressure of 5.4

H₀: μ = 5.4

Alternative Hypothesis : H₁: μ ≠ 5.4

Level of significance = 0.025

Test statistic

$t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }$

$t = \frac{5.7 -5.4}{\frac{0.81}{\sqrt{9} } }$

t = 1.11

Degrees of freedom

ν = n-1 = 9-1 =8

t₀.₀₁₅ , ₈ = 2.89

The calculated t- value = 1.11 > 2.89 at 0.025 level of significance

Null hypothesis is rejected

The engineer designed the valve such that it would produce a mean pressure is not equal to 5.4

7 0

3 years ago

PLEASE HELP !! 40 POINTS ! ILL GIVE BRAINLIEST

xenn [34]

The answer is NOQ and MLJ

3 0

3 years ago

The set notation of [-5,16) is?

valentina_108 [34]

Answer: $\left\{x | x \in \mathbb{R}, \ -5 \le x < 16\right\}$

=======================================================

Explanation:

We have some number x such that x is a real number, so we write that as $x \in \mathbb{R}$ which is saying "x is in the real number set".

The portion $-5 \le x < 16$ is how x is restricted. This means x can be -5 or larger, but also must be smaller than 16.

This is from the interval notation [-5, 16). The square bracket means we include -5 as part of the interval, but we exclude 16 because of the curved parenthesis.

The curly braces surrounding everything indicates that we have a set of values.

-----------------

Side note:

If x is an integer, then we can get this roster set {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} showing all of the integers between -5 and 16, including -5 but excluding 16.

Though chances are your teacher will want you to stick to real numbers rather than just integers.

4 0

4 years ago

Find the general solution of <img src="https://tex.z-dn.net/?f=2cos%282x%20%2B%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20%29%20%3D%20%5Cs

Aleks04 [339]

Answer:

$\large\boxed{x=-\dfrac{\pi}{4}+k\pi\ \text{or}\ x=k\pi\ \text{for}\ k\in\mathbb{Z}}$

Step-by-step explanation:

$2\cos\left(2x+\dfrac{\pi}{4}\right)=\sqrt2\qquad\text{divide both sides by 2}\\\\\cos\left(2x+\dfrac{\pi}{4}\right)=\dfrac{\sqrt2}{2}\to2x+\dfrac{\pi}{4}=\pm\dfrac{\pi}{4}+2k\pi\\\\2x+\dfrac{\pi}{4}=-\dfrac{\pi}{4}+2k\pi\ \vee\ 2x+\dfrac{\pi}{4}=\dfrac{\pi}{4}+2k\pi\qquad\text{subtract}\ \dfrac{\pi}{4}\ \text{from all sides}\\\\2x=-\dfrac{2\pi}{4}+2k\pi\ \vee\ 2x=2k\pi\qquad\text{divide all sides by 2}\\\\x=-\dfrac{\pi}{4}+k\pi\ \vee\ x=k\pi\ \text{for}\ k\in\mathbb{Z}$

5 0

4 years ago

What are the four arithmetic means between -10 and 35?

Nuetrik [128]

Answer:

-1, 8, 17, 26

Step-by-step explanation:

35 - (-10) = 45

45/5 = 9

-10 + 9 = -1

-1 + 9 = 8

8 + 9 = 17

17 + 9 = 26

3 0

3 years ago