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2 years ago

Simplify the expression (-12c5)(3c4)

Mathematics

1 answer:

ycow [4]2 years ago

4 0

Answer:

$-36{c}^{9}$

Step-by-step explanation:

According to the Product-to-Power Exponential Rule, whenever you multiply similar bases, you keep the base and add the exponents.

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A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

dusya [7]

The sum of arithmetic series is given by:
Sn=n/2(a1+an)
where:
n=number of terms
a1=first term
an=nth term
but
n=18, an=275, Sn=4185
plugging the values in the formula we get:
4185=18/2(a1+275)
simplifying this we get:
4185=9(a1+275)
dividing through by 9 we get:
465=a1+275
thus
a1=465-275
a1=190

Answer: first number is 190

3 0

2 years ago

The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)

Lemur [1.5K]

Answer:

Cardiac output: $F=0.055 L\s$

Step-by-step explanation:

Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.

To Find : Find the cardiac output.

Solution:

Formula of cardiac output: $F=\frac{A}{\int\limits^T_0 {c(t)} \, dt}$ ---1

A = 3 mg

$\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt$

Do, integration by parts

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}$

Substitute the value in 1

Cardiac output: $F=\frac{3}{54.49}$

Cardiac output: $F=0.055 L\s$

Hence Cardiac output: $F=0.055 L\s$

4 0

2 years ago

Devon exercised the same amount of time each day for 5 days last week. e His exercise included walking and swimming. e Each day

prohojiy [21]

I think that Devon swam at least 35 minutes each day for 5 days because if he exercised 225 minutes and each day he walked for 10 minutes then if you divide 225 by 5 you get 45 so every day he exercised 45 minutes and since he walked for 10 minutes you subtract 10 from 45 which gives you 35 so he swam for 35 minutes.

8 0

2 years ago

The angle measures associated with which set of ordered pairs share the same reference angle

Trava [24]

Answer:

Option 3 is right.

Step-by-step explanation:

Reference angle of x is obtained by either 180-x, 180+x. or 360-x depending on the posiiton of terminal whether II quadrant or iv quadrant, or iii quadrant, etc.

In whatever way we find reference angles,

cos will remain cos only and sin will remain sin only there may be only changes in sign.

Of all the ordered pairs given, we find that I, II, and Iv there is a switch over form cos to sine and sin to cos. Hence these options cannot be for reference angles.

III option is $(-\frac{1}{2} ,\frac{-\sqrt{3} }{2} )(\frac{1}{2} ,\frac{\sqrt{3} }{2} )$