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Elza [17]
2 years ago
13

Find the slope of the line that passes through (10,3) and (3,12).

Mathematics
1 answer:
Gnoma [55]2 years ago
5 0

Answer:

-9/7

Step-by-step explanation:

slope \: of \: line  \\  \\ =  \frac{12 - 3}{3 - 10}  \\  \\  =  \frac{9}{ - 7}  \\  \\  =   - \frac{9}{7}

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An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of
Helga [31]

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = \pi r^{2} \frac{h}{3}

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm

We will now find the volume of the cone.

Volume of cone  \pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}

We know the density of ice is 0.93 grams per 1cm^{3}

1cm^{3} =0.93g\\\frac{168175\pi }{24}  cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g(Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = \pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}

Volume of cone being melted = New Volume - Original volume

= \frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = \pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = 5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= \frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

4 0
1 year ago
Solve for a.
egoroff_w [7]

Answer: a=\sqrt{\frac{30}{23} }

Step-by-step explanation:

23a^2=30

Divide by 23

a^2=\frac{30}{23}

Extract the square root.

a=\sqrt{\frac{30}{23} }

3 0
3 years ago
Pls help I’m failing asap
Kryger [21]

Answer:

The equation 2d + 18 = 24 can help find the number of days Jerry has been doing sit-ups.

Step-by-step explanation:

During the first day, Jerry did 18 sit-ups, and he proceeded to do 2 more sit-ups each following day, so the expression to represent this situation is 2d + 18. Because he did 24 sit-ups today, to find the number of days he did sit-ups, the equation to solve is 2d + 18 = 24.

4 0
3 years ago
What is the distributive property of 2 times 8
malfutka [58]
2*8 using <span>distributive property
= 2(3+5)
= 6+ 10
= 16</span>
5 0
3 years ago
What is 10 times 90 divided by -19
Semenov [28]
10 times 90 is 900, and divided by -19 is -900/19.
5 0
3 years ago
Read 2 more answers
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