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3 years ago

What are the solutions of f(x)=3x2-x+3 and what is the y-intercept?

Mathematics

1 answer:

expeople1 [14]3 years ago

7 0

Answer:

y intercept is (0, 3)

Step-by-step explanation:

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Find the equation of the sphere if one of its diameters has endpoints (-8, -3, -10) and (-6, 1, -4) which has been normalized so

alex41 [277]

Answer:

The equation is $x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0$

Step-by-step explanation:

From the question we are told that

The diameter endpoints is (-8, -3, -10) and (-6, 1, -4)

Generally the equation of a sphere with center coordinates (a, b , c ) and radius r is mathematically represented as

$(x - a )^2 + (y -b )^2 + (z -c)^2 = r^2$

Now since we are given the endpoints of the diameter then we can obtain the center coordinates as follows

$(a, b , c) = [ \frac{ -8 +(-6)}{2} , \frac{-3 + (1)}{ 2} , \frac{ -10 + (-4)}{2} ]$

$(a, b , c) = [ -7 , -1.5 , -7 ]$

Now the length of the diameter is evaluated as

$|d| = \sqrt{ (-8 - (-6 ))^2 + ( -3 - (1) )^2 + ( -10 - (-4))^2 }$

$|d| = \sqrt{56 }$

$|d| = \sqrt{4 * 14 }$

$|d| = 2 \sqrt{ 14 }$

Now the radius is mathematically represented as

$r = \frac{|d|}{2}$

$r = \frac{ 2 \sqrt{14} }{2}$

$r = \sqrt{14}$

$(x - -7 )^2 + (y --1.5 )^2 + (z --7)^2 = ( \sqrt{14} )^2$

$(x +7 )^2 + (y +1.5 )^2 + (z +7)^2 = 14$

$x^2 + 14 x + 49 + y^2 + 3y + 2.25 +z^2 14z + 49 = 14$

$x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0$

4 0

4 years ago

Solve the equation y-12=4y

andre [41]

Hi there!

$y - 12=4y 

We need to subtract 4y from both sides 

y-12-4y = 4y - 4y 

3y - 12=0 

3y = 0 + 12 

3y=12 

Divide both sides by 3 

-3y/3 = 12/-3 

y= -4$

8 0

3 years ago

528 a weekend.<br> 10% of 480 is 48<br> 480 + 48 = 528

GrogVix [38]

Answer:

ffhjjrhjzxuzdjzdjzsjezjdifi

5 0

2 years ago

20. Which expression is equal to 3(5x - 6) - 2(4x + 5)

Yuki888 [10]

Your answer is 7x-28

5 0

3 years ago

I need help ASAP :/ I need the explanation

PtichkaEL [24]

Is 17x-2 supposed to be angle T? This is a bad question; demand better from your teachers.

Let's assume 17x-2 = angle T. S is a right angle because it's subtended by a diameter, Thales' Theorem. R is half 116 degrees, so 58 degrees. T is complementary, T=90-58=32 degrees.

17x -2 = 32

17x = 34

x = 2

Answer: 2

6 0

4 years ago