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Basile [38]
3 years ago
10

2

Mathematics
1 answer:
goldfiish [28.3K]3 years ago
4 0

Answer:

The volume of can A is half the volume of can B.

Step-by-step explanation:

Given

Can A and Can B

Required

The true statement

For Can A, we have:

h =8

r = 0.5

The volume is:

Volume = \pi r^2h

This gives:

V_A = \pi * 0.5^2 * 8

V_A = \pi * 2

V_A = 2\pi

For Can B, we have:

h =4

r = 1

The volume is:

Volume = \pi r^2h

This gives:

V_B = \pi * 1^2 * 4

V_B = \pi  * 4

V_B = 4\pi

So, we have:

V_A = 2\pi

V_B = 4\pi

By comparison, (d) is correct

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Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 ? 9x2 ? 108x + 2, [?3, 4]
SVEN [57.7K]
Assuming the question marks are minus signs
to find max, take derivitive and test 0's and endpoints

take derivitive
f'(x)=18x²-18x-108
it equal 0 at x=-2 and 3
if we make a sign chart to find the change of signs
the sign changes from (+) to (-) at x=-2 and from (-) to (+) at x=3
so a reletive max at x=-2 and a reletive min at x=3

test entpoints

f(-3)=83
f(-2)=134
f(3)=-241
f(4)=-190

the min is at x=3 and max is at x=-2
4 0
3 years ago
Find the distance between the points (13, 20) and (18, 8).<br> 13<br> 7<br> 11
Lana71 [14]

Answer:  13

Step-by-step explanation:

See attached graph.

A third point (18,20) may be added to the two given points to form a right triangle with sides 5 and 12.  The distance, x, between the original two points is given by x^2 = 5^2 + 12^2

x^2 = 25 + 144

X^2 = 169

x = 13

5 0
3 years ago
The profit at a chocolate shop can be represented using the function f(x)=3x−95, where x is the number of chocolate truffles sol
xz_007 [3.2K]
The slope is the constant rate of change. In this case, the number is being multiplied by 3 each time

The slope is 3
“x represents number of chocolate truffles sold each day”
Represents amount of chocolate truffles sold per day
7 0
2 years ago
-3x+2-5x-7=4x+2 what is the first step solve this<br> equation?
Triss [41]

Answer: x = -0.58

Step-by-step explanation:

-3x+2-5x-7=4x+2

First step, collect like terms

-3x -5x-4x = 2-2+7

-12x = 7

x = 7/-12

x = -0.58

5 0
3 years ago
Two isosceles triangles share the same base. Prove that the medians to this base are collinear. (There are two cases in this pro
Anna71 [15]

Answer:

Given: Two Isosceles triangle ABC and Δ PBC having same base BC. AD is the median of Δ ABC and PD is the median of Δ PBC.

To prove: Point A,D,P are collinear.

Proof:

→Case 1.  When vertices A and P are opposite side of Base BC.

In Δ ABD and Δ ACD

AB= AC   [Given]

AD is common.

BD=DC  [median of a triangle divides the side in two equal parts]

Δ ABD ≅Δ ACD [SSS]

∠1=∠2 [CPCT].........................(1)

Similarly, Δ PBD ≅ Δ PCD [By SSS]

 ∠ 3 = ∠4 [CPCT].................(2)

But,  ∠1+∠2+ ∠ 3 + ∠4 =360° [At a point angle formed is 360°]

2 ∠2 + 2∠ 4=360° [using (1) and (2)]

∠2 + ∠ 4=180°

But ,∠2 and ∠ 4 forms a linear pair i.e Point D is common point of intersection of median AD and PD of ΔABC and ΔPBC respectively.

So, point A, D, P lies on a line.

CASE 2.

When ΔABC and ΔPBC lie on same side of Base BC.

In ΔPBD and ΔPCD

PB=PC[given]

PD is common.

BD =DC [Median of a triangle divides the side in two equal parts]

ΔPBD ≅ ΔPCD  [SSS]

∠PDB=∠PDC [CPCT]

Similarly, By proving ΔADB≅ΔADC we will get,  ∠ADB=∠ADC[CPCT]

As PD and AD are medians to same base BC of ΔPBC and ΔABC.

∴ P,A,D lie on a line i.e they are collinear.




3 0
3 years ago
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