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3 years ago

The volume of an object is given as a function of time by V = A + B t + C t4 . Find the dimension of the constant C

Mathematics

1 answer:

aksik [14]3 years ago

5 0

Answer:

The dimensions of constant C are of $[L^{3}T]^{-4}$

Step-by-step explanation:

It is given that

$V(t)=A+Bt+Ct^{3}$

Since the dimensions of volume are $[L^{3}]$

Each of the term shall have a dimension of $[L^{3}]$ since they are in addition.

Thus for third term we can write

Thus we have

$[L^{3}]=[C][T^{4}]\\\\\therefore [C]=[L^{3}][T^{-4}]$

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After 60 minutes a train has moved 60 miles toward its destination.

Fantom [35]

Answer:

1 mile per minute

Step-by-step explanation:

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2 years ago

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Deonte invested 200000at his bank for 10 years if he earned 130000 what was the interest rate the bank gave him

Volgvan

Answer:

The interest rate the bank gave Deonte is 6.5%.

Solution:

Given, Deonte invested 200000 at his bank for 10 years

He earned 130000

We have to find what was the interest rate the bank gave him.

Now we know that, simple interest $=\frac{\text {amount} \times \text {rate} \times \text {time}}{100}$

So, by substituting our values in above formula,

$130000=\frac{200000 \times \text { rate } \times 10}{100}$

Interest rate $\times$ 20000 = 130000

Interest rate $\times$ 2 = 13

$\text { Interest rate }=\frac{13}{2}=6.5 \%$

Hence, the interest rate given by bank is 6.5% to Deonte.

8 0

3 years ago

Help me solve this please

damaskus [11]

1) A quadratic will have no real roots when its discriminant is negative

$0 = ax^2 + bx + c = x^2 + 2k x + (4k-3)$

$d = b^2 - 4ac = (2k)^2 - 4(1)(4k-3) = 4k^2 - 16k + 12 < 0$

Dividing by 4,

$k^2 - 4 k + 3 < 0 \quad\checkmark$

We have a positive coefficient on k^2 so this parabola is a CUP (concave up positive) so has a minimum at the vertex. If the vertex y value is less than zero, the inequality will be true in the range between the zeros.

$(k-3)(k-1)$

That's true for

$1 < k < 3$

2) We look for the meet of the line and the parabola:

$2x + k + 2 = 2x^2 + (k+2)x + 8$

$0 = 2x^2 + kx + (6-k)$

For two intersections we need a positive discriminant:

$k^2 - 4(6-k)(2) > 0$

$k^2 + 8k - 48 > 0$

$(k+12)(k-4) > 0$

That's means two negative or two positive, so

$k < 12$ or $k > 4$

6 0

3 years ago

Which of the following steps is needed to inscribe a circle in a triangle?

xxTIMURxx [149]

Construct two angle bisectors of the triangle

Answer:

Option (D) is correct

Step-by-step explanation:

We have to contruct two angle bisectors of the triangle.

various steps to inscribe the circle in a triangle are

First draw a triangle
Draw angle bisector of one angle
Draw angle bisector of another angle
Extent these angle bisectors, where they meet that point will be called the incenter
From incenter draw prependicular to any side of the triangle
The length from the point where the prependicular touches the side of triangle to the point of incenter will be radius.
Use this radius and draw the incircle.

6 0

3 years ago

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Jose pays 8 payments of $4 each to a game store. He returns one game and receives $20 back. What is the change to the amount of

Katyanochek1 [597]

Answer:

the answer would be -12

Step-by-step explanation:

32- 20=12

The change to the amount of money he has is -$12 because

she has $12 less than she started with

6 0

3 years ago