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3 years ago

Solve the equation x^4-64=0

Mathematics

2 answers:

ki77a [65]3 years ago

6 0

Answer:

Step-by-step explanation:

x^4=64

x^2= +- 8

x = +-sqrt2, x= +- i sqrt2

mina [271]3 years ago

4 0

Answer:

Step-by-step explanation:

x^4-64=0

factor

(x^2+8)(x^2-8)=0

zero property

x^2+8=0, x^2-8=0

x^2=0-8-8,

x^2=-8,

x^2=0+8=8,

x^2=8,

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

sqrt(8) & sqrt(-8),

gives you 2*sqrt(2) and -2*sqrt(2),

also, the square root of a negative number contains the imaginary number, i. Because sqrt(-1)=i, don't forget this formula.

So sqrt(-8)=2i*sqrt(2) and -2i*sqrt(2).

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A 1414-ft ladder leans against a wall at a point 55 feet above the ground. how far is the bottom of the ladder from the wall?

viva [34]

Assume ladder length is 14 ft and that the top end of the ladder is 5 feet above the ground.

Find the distance the bottom of the ladder is from the base of the wall.

Picture a right triangle with hypotenuse 14 feet and that the side opposite the angle is h. Then sin theta = h / 14, or theta = arcsin 5/14. theta is

0.365 radian. Then the dist. of the bot. of the lad. from the base of the wall is

14cos theta = 14cos 0.365 rad = 13.08 feet. This does not seem reasonable; the ladder would fall if it were already that close to the ground.

Ensure that y ou have copied this problem accurately from the original.

7 0

3 years ago

In triangle ABC, a = 9, c = 5, and angle B = 120°. Find the measure of angle A to the nearest degree. Show your work.

slamgirl [31]

Answer:

Angle A = 39°

Step-by-step explanation:

We are given that there is a triangle ABC where a = 9, c = 5 and angle B = 120° and we are to find the measure of angle A.

But first we need to find the side b using the law of cosine:

$b^2 = a^2 + c^2- 2a*c*cos(120)$

$b^2 = 81 + 25 - 2*9*5*(-0.5)$

$b=\sqrt{151}$

Now finding angle A using law of cosine:

$cos(A) = \frac{b^2+c^2-a^2}{2b*c}$

$cos(A) = \frac{151+25-81}{2*12.29*5}$

$cos A=0.7730$

$A=39.38$

Therefore, the measure of angle A = 39°.

7 0

3 years ago

Read 2 more answers

Write the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5)

Sedbober [7]

Answer: $\bold{y=-\dfrac{1}{3}x-1}$

Step-by-step explanation:

(4, 1) & (2, -5)

First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\$

Next, find the midpoint of (4, 1) and (2, -5):

$Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)$