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Nastasia [14]
3 years ago
8

A particle travels along the x-axis such that its position at time t is given by the function x(t)= 2t^2+t. What is the average

speed of this particle over the interval 2 is less than or equal to t which is less than or equal to 10
A-4

B-200

C-32

D-25
Mathematics
1 answer:
Lapatulllka [165]3 years ago
8 0

Answer:

4: A

Step-by-step explanation:

Mathematically, the average speed over a particular range will be;

f’(b)-f’(a)/(a-b)

In this case; a = 2 and b = 10

So we have the following;

f’(x) = 4t + 1

f’(10) = 4(10) + 1 = 41

f’(2) = 4(2) + 1 = 9

So we have the average speed change as;

(41-9)/(10-2)

= 32/8 = 4

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Suppose you take $25,000 and deposit some of it into a savings account that pays 2.2% interest. You then take the rest of the mo
FromTheMoon [43]

Answer:

The amount deposited in the savings account is $11,494.12

The amount deposited in the CD account is $13,505.88

Step-by-step explanation:

Firstly, let’s calculate the amount of interest;

Interest = Amount at end of 10 years - amount deposited= 31,648 -25,000 = 6,648

Let the amount deposited in the savings account be $x while the amount deposited in the CD account be $y

Mathematically;

x + y = 25,000 ••••••••••(i)

Now the formula for simple interest is;

PRT/100

where P is the amount deposited, r is the rate and T is the time

On the savings account, amount of interest generated will be;

(x * 2.2 * 10)/100 = 22x/100

On the CD act, amount of interest generated will be;

(y * 3.05 * 10)/100 = 30.5y/100

The addition of both give the total interest;

22x/100 + 30.5y/100 = 6648

Multiply through by 100

22x + 30.5y = 664800 •••••••(ii)

From i, x = 25,000 - y

Substitute this into ii

22(25000-y) + 30.5y = 664800

550,000 -22y + 30.5y = 664,800

8.5y = 664,800-550,000

8.5y = 114,800

y = 114,800/8.5

y = $13,505.88

x = 25,000 -y

x = 25,000 - 13,505.88

x = $11,494.12

3 0
3 years ago
A sphere has a radius of 12 inches. A second sphere has a radius of 9 inches. What is the difference of the volumes of the spher
just olya [345]

Answer:

Solution given;

for sphere

radius [r]:12inches

another

radius [R]:9inches

Now

difference in volume of sphere:

volume of sphere of having radius [r-R]

=\frac{4}{3} πr³-\frac{4}{3} πR³

=\frac{4}{3} π(12³-9³)

= 1332π cubic inches

The volume of the larger sphere is <u>___1332</u>__π cubic inches greater than the volume of the smaller sphere.

3 0
3 years ago
If the triangles are similar, what is the value of x?
Sav [38]

Answer:

the answer to your question is D. d=54

4 0
3 years ago
Today, everything at a store is on sale. The store offers a 20% discount.
Mila [183]
Answer: $14.40

10% of $18 = $1.80 (just divide it by 10)
$1.80 x 2 = $3.60
20% of $18 = $3.60

since it’s a discount, you subtract from the original price so:

$18 - $3.60 = $14.40
8 0
2 years ago
A and b are positive integers. Find <img src="https://tex.z-dn.net/?f=-2a%2B3b" id="TexFormula1" title="-2a+3b" alt="-2a+3b" ali
lord [1]

A could be 2 while B could be 3, so -2a+3b turns into -4+9, which equals 5.

From what I know you can't really solve a a single equation with two-variables so it's just a matter of trial and error.

Just try plugging in a small number like 2 for a just to try it and you get 8b^2=72.

Divide everything by 8 to isolate b and you get that b^2=9.

Square root everything and you'll find that b=3. This is just one possible combination, I'm sure there are many more but this is obviously the one that was intended to be found.

Now that we know that a=2 and b=3 just plug them into the equation.

-2(2)+3(3)=?

-4+9=?

5

Sorry about having to use this ^ symbol, the equation maker is not working.

7 0
3 years ago
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