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2 years ago

Solve the quadratic equation given. 6x2 - 24 = 0

1 answer:

6 0

${6x}^{2} - 24 = 0 \\ = > 6( {x}^{2} - 4) = 0 \\ = > 6 {((x)}^{2} - {(2)}^{2} ) = 0 \\ = > 6(x - 2)(x + 2) = 0 \\ = > 6(x - 2) = 0 \: \: \: or \: \: 6(x + 2) = 0 \\ = > 6x - 12 = 0 \: \: \: or \: \: \: 6x + 12 = 0 \\ = > x = 2 \: \: \: or \: \: \: x = - 2$

Hope you could get an idea from here.

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3 years ago

Simplify the expression csc(-x)/1+tan^2x)

Charra [1.4K]

Assuming ya meant $\frac{csc(-x)}{1+tan^2(x)}$

to slimplify, we use a variation of the pythagorean identity and a decomposition into the sin and cos

for the pythaogreaon identity
$cos^2(x)+sin^2(x)=1$
divide both sides by $cos^2(x)$
$1+tan^2(x)=sec^2(x)$ since $\frac{sin(x)}{cos(x)}=tan(x)$
subsitute
$\frac{csc(x)}{sec^2(x)}$

recall that $csc(x)=\frac{1}{cos(x)}$
also that cos(x) is an even function and thus cos(-x)=cos(x)
therfore $csc(-x)=\frac{1}{cos(-x)}=\frac{1}{cos(x)}=csc(x)$
so we get

$\frac{csc(x)}{sec^2(x)}$
decompose them into $\frac{1}{cos(x)}$ and $\frac{1}{sin^2(x)}$ to get $\frac{\frac{1}{cos(x)}}{\frac{1}{sin^2(x)}}$
multiply by $\frac{sin^2(x)}{sin^2(x)}$ to get
$\frac{sin^2(x)}{cos(x)}$
we can furthur simlify to get
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5 0

3 years ago

Read 2 more answers

A cone-shaped water cup has a height of 3.3 inches and a diameter of 2.7 inches. One fluid ounce is equivalent to 1.8 cubic inch

DaniilM [7]

Answer:

3.5 fluid ounces

Step-by-step explanation:

In this question, we are asked to calculate the capacity in fluid ounce of a cone-shaped cup.

To solve this, we need to calculate the volume of the cup.

Mathematically, the volume of a cone =

1/3 * π * r^2 * h

Where r = d/2 = 2.7/2 = 1.35 inches

h = 3.3 inches

By substituting this, we have

V = 1/3 * 3.14 * 1.35^2 * 3.3 = 6.3 cubic inch

Now we proceed to calculate the capacity

From the question, we are told that ;

1 fluid ounce = 1.8 cubic inch

This means

x fluid ounce = 6.3 cubic inch

x = 6.3/1.8

x = 3.5 fluid ounces

8 0

3 years ago

Read 2 more answers