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2 years ago

7

What is the solution to the equation? 2 x squared plus 4 equals 20 Choose all answers that are correct.

1 answer:

Stolb23 [73]2 years ago

8 0

$2x^2+4=20\ \ \ \ |subtract\ 4\ from\ both\ sides\\\\2x^2=16\ \ \ \ \ |divide\ both\ sides\ by\ 2\\\\x^2=8\iff x=\pm\sqrt8\\----------------------------\\\sqrt8=\sqrt{4\cdot2}=\sqrt4\cdot\sqrt2=2\cdot\sqrt2=2\sqrt2\ \ \ |use\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\-----------------------------\\therefore\ your\ answer\ is\ -2\sqrt2\ and\ 2\sqrt2\to\boxed{a\ and\ c}$

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An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per second. The pyramid, at the top, h

UNO [17]

Answer:

$\frac{225}{16} cm/s$

Step-by-step explanation:

We are given that

$\frac{dV}{dt}=25cm^3/s$

Side of base=4 cm

l=w=4 cm

Height,h=12 cm

We have to find the rate at which the water level rising when the water level is 4 cm.

Volume of pyramid= $\frac{1}{3}lwh=\frac{1}{3}l^2h$

$\frac{l}{h}=\frac{4}{12}=\frac{1}{3}$

$l=\frac{1}{3}h$

Substitute the value

$V=\frac{1}{27}h^3$

Differentiate w.r.t t

$\frac{dV}{dt}=\frac{3}{27}h^2\frac{dh}{dt}$

Substitute the values

$25=\frac{1}{9}(4^2)\frac{dh}{dt}$

$\frac{dh}{dt}=\frac{25\times 9}{16}=\frac{225}{16} cm/s$

5 0

3 years ago

Which of the following reveals the minimum value for the equation 2x^2 − 4x − 2 = 0?

12345 [234]

Answer:

$2(x-1)^{2}=4$

Step-by-step explanation:

<u><em>The options of the question are</em></u>

2(x − 1)2 = 4

2(x − 1)2 = −4

2(x − 2)2 = 4

2(x − 2)2 = −4

we have

$2x^{2} -4x-2=0$

This is a vertical parabola open upward

The vertex represent the minimum value

The quadratic equation in vertex form is

$y=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

so

Convert the quadratic equation in vertex form

Factor 2 leading coefficient

$2(x^{2} -2x)-2=0$

Complete the squares

$2(x^{2} -2x+1)-2-2=0$

$2(x^{2} -2x+1)-4=0$

Rewrite as perfect squares

$2(x-1)^{2}-4=0$

The vertex is the point (1,-4)

Move the constant to the right side

$2(x-1)^{2}=4$

3 0

2 years ago

Solve on the interval [0/2pi]<br><br> 1-cos(theta) = (1/2)

Airida [17]

Answer:

Final answer is $x=\frac{\pi}{3}$ and $x=\frac{5\pi}{3}$ .

Step-by-step explanation:

Given equation is $1-\cos\left(\theta\right)=\frac{1}{2}$

Now we need to find the solution of $1-\cos\left(\theta\right)=\frac{1}{2}$ in given interval $[0, 2\pi ]$ .

$1-\cos\left(\theta\right)=\frac{1}{2}$

$-\cos\left(\theta\right)=\frac{1}{2}-1$

$-\cos\left(\theta\right)=-\frac{1}{2}$

$\cos\left(\theta\right)=\frac{1}{2}$

which gives $x=\frac{\pi}{3}$ and $x=\frac{5\pi}{3}$ in the given interval.

Hence final answer is $x=\frac{\pi}{3}$ and $x=\frac{5\pi}{3}$ .

6 0

2 years ago

Alan, Bill, and Calvin are playing a game with collectible cards. At the moment, Alan has 11 less than 2 1/2 times the number of

kramer

Bill has 12 cards. I figured this out by making a table and drawing an equation:

7 0

2 years ago

Please help with this

vovikov84 [41]

Step-by-step explanation:

$= \frac{14\pi}{6}$

$= \frac{ \cancel{14}\pi}{ \cancel6}$

$= \frac{7\pi}{3}$

$= \frac{6\pi + \pi}{3}$

$= \frac{6\pi}{3} + \frac{\pi}{3}$

$= 2\pi + \frac{\pi}{3}$

$= 0 + \frac{\pi}{3}$

$= \frac{\pi}{3} \: \text{where} \: \frac{\pi}{3} < 2\pi$

The answer is B.

4 0

2 years ago