How do I find the scale factor

A 0.3 ml dose of a drug is injected into a patient steadily for 0.65 seconds. At the end of this time, the quantity, , of the dr

Darya [45]

Use the compound interest formula: A=P(1+i)^t.

P is the initial amount of the drug, 0.3ml.
i is - 0.0035.
t is in seconds.

You'll get:
A=0.3(1-0.0035)^t.

Sub in any value on t to find out how many ml are left t seconds after injection.

The 0.65 second injection time does not seem to be relevant as the question clearly states that the exponential decay starts AFTER the injection is completed.

4 0

3 years ago

Which angle is a horizontal translation of the first angle?

grin007 [14]

Step-by-step explanation:

B becuase it keeps the same orientation and have the same distance from each point and they both produce rigid motion.

A is a reflection.

C is a dilation.

D is a rotation.

3 0

2 years ago

The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term

Salsk061 [2.6K]

Answer:

The first three terms of the geometry sequence would be $1$ , $5$ , and $25$ .

The sum of the first seven terms of the geometric sequence would be $127$ .

Step-by-step explanation:

Let $d$ denote the common difference of the arithmetic sequence.

Let $a_1$ denote the first term of the arithmetic sequence. The expression for the $n$ th term of this sequence (where $n\!$ is a positive whole number) would be $(a_1 + (n - 1)\, d)$ .

The question states that the first term of this arithmetic sequence is $a_1 = 1$ . Hence:

The third term of this arithmetic sequence would be $a_1 + (3 - 1)\, d = 1 + 2\, d$ .
The thirteenth term of would be $a_1 + (13 - 1)\, d = 1 + 12\, d$ .

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let $r$ denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

$\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d$ .

Ratio between the third term and the second term of the geometric sequence:

$\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}$ .

Both $(1 + 2\, d)$ and $\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)$ are expressions for $r$ , the common ratio of this geometric sequence. Hence, equate these two expressions and solve for $d$ , the common difference of this arithmetic sequence.

$\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}$ .

$(1 + 2\, d)^{2} = 1 + 12\, d$ .

$d = 2$ .

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be $1$ , $(1 + (3 - 1) \times 2) = 5$ , and $(1 + (13 - 1) \times 2) = 25$ , respectively.

These three terms ( $1$ , $5$ , and $25$ , respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be $r = 25 /5 = 5$ .

Let $a_1$ and $r$ denote the first term and the common ratio of a geometric sequence. The sum of the first $n$ terms would be:

$\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}$ .

For the geometric sequence in this question, $a_1 = 1$ and $r = 25 / 5 = 5$ .

Hence, the sum of the first $n = 7$ terms of this geometric sequence would be:

$\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}$ .

7 0

2 years ago

How can you tell a graph is proportional

Flura [38]

Answer:

If the line passes through the orgin

Step-by-step explanation:

6 0

2 years ago

Suppose , varies jointly with g and v, and j = 2 when g = 4 and v= 3.

kap26 [50]

Answer:

j = 44/3

Step-by-step explanation:

j varies jointly as g and v. This can be represented mathematically as:

$j \alpha gv\\j = kgv$ .............(1)

Where k is a constant of proportionality

j = 2 when g = 4 and v = 3

Substitute these values into equation (1)

2 = k * 4 * 3

2 = 12 k

k = 1/6

when g = 8 and v = 11:

j = (1/6) * 8 * 11

j = 44/3

7 0

3 years ago