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3 years ago

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If the distance between two objects is increased, the gravitational attraction between them will: increase decrease remain the s

ame

2 answers:

natulia [17]3 years ago

8 0

It decreases
The further two objects are, the gravitational attraction decreases and the closer two objects are, the gravitational attraction increases

Elena-2011 [213]3 years ago

6 0

Answer:

B. decrease

Step-by-step explanation:

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Matthew is 3 times as old as jenny. in 7 years, he will be twice as old as she will be then. how old is each now? Explain how to

Nataliya [291]

Let m and j be the current ages of Matthew and Jenny, respectively.

Now, Matthew is 3 times as old as Jenny, so the variables are in the following relation:

$m=3j$

In 7 years, both of them will be 7 years older, i.e. their ages will be m+7 and j+7, and Matthew will be twice as old:

$m+7=2(j+7)$

Now, remembering that m=3j, we can rewrite the second equation as

$3j+7=2j+14 \iff j = 7$

So, Jenny is 7 and Matthew is 21 (he's 3 times older).

In fact, in 7 years, they will be 14 and 28, and Matthew will be twice as old.

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3 years ago

An airplane descends 2.5 miles to an elevation of 7.55 miles. Find the elevation of the plane before its descent. The initial el

Zielflug [23.3K]

Answer:

8.75!

Step-by-step explanation:

the answer is x-2.5=6.25

6.25+2.50=8.75

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3 years ago

Hello please help help

irinina [24]

9514 1404 393

Answer:

48°

Step-by-step explanation:

ΔACB is isosceles, so angles A and B have the same measure. The measure of angle C in that triangle is ...

∠C = 180° -2(69°) = 42°

Angle C in ΔCDE has the same measure. Angle D is the complement of that:

∠D = 90° -42° = 48°

_____

The relations we used are ...

the sum of angles in a triangle is 180°
base angles of an isosceles triangle are congruent
vertical angles are congruent
acute angles in a right triangle are complementary

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3 years ago

A box with a rectangular base and open top must have a volume of 128 f t 3 . The length of the base is twice the width of base.

noname [10]

Answer:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

Step-by-step explanation:

Given

$Volume = 128ft^3$

$L = 2W$

$Base\ Cost = \$9/ft^2$

$Sides\ Cost = \$6/ft^2$

Required

The dimension that minimizes the cost

The volume is:

$Volume = LWH$

This gives:

$128 = LWH$

Substitute $L = 2W$

$128 = 2W * WH$

$128 = 2W^2H$

Make H the subject

$H = \frac{128}{2W^2}$

$H = \frac{64}{W^2}$

The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

$A = LW + 2(WH + LH)$

The cost is:

$Cost = 9 * LW + 6 * 2(WH + LH)$

$Cost = 9 * LW + 12(WH + LH)$

$Cost = 9 * LW + 12H(W + L)$

Substitute: $H = \frac{64}{W^2}$ and $L = 2W$

$Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)$

$Cost =18W^2 + \frac{768}{W^2}*3W$

$Cost =18W^2 + \frac{2304}{W}$

To minimize the cost, we differentiate

$C' =2*18W + -1 * 2304W^{-2}$

Then set to 0

$2*18W + -1 * 2304W^{-2} =0$

$36W - 2304W^{-2} =0$

Rewrite as:

$36W = 2304W^{-2}$

Divide both sides by W

$36 = 2304W^{-3}$

Rewrite as:

$36 = \frac{2304}{W^3}$

Solve for $W^3$

$W^3 = \frac{2304}{36}$

$W^3 = 64$

Take cube roots

$W = 4$

Recall that:

$L = 2W$

$L = 2 * 4$

$L = 8$

$H = \frac{64}{W^2}$

$H = \frac{64}{4^2}$

$H = \frac{64}{16}$

$H = 4$

Hence, the dimension that minimizes the cost is:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

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2 years ago

One of the mutually exclusive results of an activity conditional probability 2. a combination of one or more outcomes independen

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Outcome - <span>one of the mutually exclusive results of an activity
probability - </span><span>a measure of likelihood of a given result
compound events - </span><span>events involving two or more activities
event - </span><span>a combination of one or more outcomes
independent events - </span>compound events whose outcomes do not affect each other
conditional probability - <span>probability of one event given that another has occurred</span>

4 0

3 years ago