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4 years ago

Please help. 10 points

Mathematics

1 answer:

Goshia [24]4 years ago

6 0

1. You must apply the formula for calculate the volume of a cone and and the volume of a cylinder. Then, you must sum both volumes to obtain the volume on the figure attached.

2. Volume of the cone:

Vcone=1/3(πr²h)

π=3.14
r=4 mm/2
r=2 mm
h=3 mm

3. When you substitute the values above into the formula, you obtain:
<span>
Vcone=1/3(πr²h)
</span> Vcone=12.56 mm³

4. The volume of the cylinder is:

Vcylinder=<span>πr²h
</span>
π=3.14
r=4 mm/2=2 mm
h=2 mm

5. <span>When you substitute the values above into the formula, you obtain:
</span>
Vcylinder=25.12 mm³

6. The volume of the figure is:

Vt=Vcone+Vcylinder
Vt=12<span>.56 mm³+25.12 mm</span>³
Vt=37.68 mm³

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Here we are given that the Alligator's tail length t varies directly as its body length b.

Using this given information and taking k as constant of proportionality, we get this equation :

$t=kb$ .................(1)

Now we are given:

body length (b) = 4 feet

tail length (t) = 2.5 feet

plugging these values in equation (1) we have,

$2.5=k*4$

from here we can calculate the value of k, dividing both sides by 4

k=2.5/4 = 0.625.............(2)

Now we have to find tail length of alligator if body length is 3.2 feet.

so plugging b=3.2 and k=0.625 in equation (1)

$t=3.2 * 0.625$

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3 years ago

1 Simplify the ratio of 464: 128

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Answer:

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3 years ago

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A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 80 p

avanturin [10]

Answer:

small = 35 pounds

large = 45 pounds

Step-by-step explanation:

Let x = large boxes

y = small boxes

two equations can be derived from the question

x + y = 80 equation 1

60x + 65y = 4975 equation 2

multiply equation 1 by 60

60x +60y = 4800 equation 3

subtract equation 2 from 3

5y = 175

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substitute for y in equation 1

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3 years ago

Find the equation of the line tangent to y = -3x2 + x - 5 at x = -1

SVEN [57.7K]

$\boxed{y+9=7(x+1)}$

<h2>Explanation:</h2>

The Point-Slope form of the equation of a line is given by:

$y-y_{0}=m(x-x_{0}) \\ \\ \\ Where: \\ \\ m:Slope \\ \\ (x_{0},y_{0}):A \ point$

To find the equation of the line tangent to $y=-3x^2+x-5 \ at \ x=-1$ , we need to take the derivative:

$\frac{dy}{dx}=-6x+ 1$

The slope of the line tangent to $y=-3x^2+x-5$ at $x=-1$ can be found evaluationg $x=1$ in the derivative:

$\frac{dy}{dx}\Bigr\rvert_{x=-1}=-6x+ 1 \\ \\ \\ \frac{dy}{dx}\Bigr\rvert_{x=-1}=-6(-1)+ 1 \\ \\ \\ m=\frac{dy}{dx}\Bigr\rvert_{x=-1}=7$

Finding the point:

$x_{0}=-1 \\ \\ Then: \\ \\ y_{0}=-3(-1)^2-1-5=-9 \\ \\ (x_{0},y_{0})=(-1,-9)$

Finally, our line is:

$y-(-9)=7(x-(-1)) \\ \\ \boxed{y+9=7(x+1)}$

The representation of this problem is shown below.

<h2>Learn more:</h2>

Derivative of functions: brainly.com/question/2142425

#LearnWithBrainly

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3 years ago

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7 and 3 both go into 21.

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Michael drank 6/21 quart of milk.

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Joel drank 7/21 quart of milk.

Add together 7/21 and 6/21 to get 13/21, the total amount of milk they both drank from the quart.

Now, subtract 13 from 21 to find how many quarts are left. Simplify if necessary.
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Since you can't simplify, there is 8/21 quart of milk left.
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