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2 years ago

The diameter of the base of the cone measures 8 units. The height measures 6 units. What is the volume of the cone?

1 answer:

8 0

The volume of the cone will be given by:
volume,v=1/3πr^2h
radius,r=8/2=4 units
height,h=6 units
thus;
v=1/3*π*4^2*6
v=32π cubic units

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Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4

Dmitry [639]

Answer:

$\boxed{\sf Standard-form :x + 4y -17=0 }\\$

$\boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}$

Step-by-step explanation:

Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,

$\longrightarrow x + 4y = 7\\$

Firstly convert it into slope intercept form of the line which is y = mx + x , as ;

$\longrightarrow 4y = -x + 7 \\$

$\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\$

On comparing it to y = mx + c , we have ,

$\longrightarrow m =\dfrac{-1}{4}\\$

$\longrightarrow c =\dfrac{7}{4}\\$

Now as we know that the slope of two parallel lines is same . Therefore the slope of the parallel line will be ,

$\longrightarrow m_{||)}=\dfrac{-1}{4}\\$

Now we may use point slope form of the line as ,

$\longrightarrow y - y_1 = m(x-x_1) \\$

On substituting the respective values ,

$\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}\\$

$\longrightarrow y -5=\dfrac{-1}{4}(x+3)\\$

$\longrightarrow 4(y -5 ) =-1(x +3) \\$

$\longrightarrow 4y -20 = - x -3 \\$

$\longrightarrow x + 4y -20+3=0\\$

$\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\$

Again the equation can be rewritten as ,

$\longrightarrow y - 5 = \dfrac{-1}{4}(x +3) \\$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5 \\$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4} \\$

$\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{ y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\$

6 0

2 years ago

I GIVE BRAINLILEST

stich3 [128]

Answer:

96 kilograms

Step-by-step explanation:

32x3=96 just trust me I don'T know how to explain

6 0

3 years ago

What is not a multiple of 7

salantis [7]

Answer:

34 is not a mulitple of 7

5 0

2 years ago

Emergency! I don't get this really well. Please help! -(8-2n)=8-2(12-3n)

Naddik [55]

Answer:

n = 2

Step-by-step explanation:

2n - 8 = -2 (-3n + 12) + 8

2n - 8 = -(-6n + 24) + 8

2n - 8 = 6n - 24 + 8

2n - 8 = 6n - 16

-4n = -8

Divide each side by 4

n = 2

3 0

3 years ago

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I need help asap thank you

ddd [48]

The answer is H to your question

8 0

3 years ago

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