Factor f(x) = 6x^4 - 9x^3 - 57x^2

The quotient of n and -4 is 8. What is the value of n?

Phoenix [80]

Answer:

n = -32

Step-by-step explanation:

quotient means divide

n/-4 = 8

Multiply each side by -4

n/-4 *-4 = 8*-4

n = -32

8 0

4 years ago

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 43 ft/s. Its height

Lina20 [59]

Answer:

Instantaneous Velocity at t = 1 is 20 feet per second

Step-by-step explanation:

We are given he following information in the question:

$y(t)=43t-23t^{2}$

B) Instantaneous Velocity at t = 1

$y(1) = 43(1)-23(1)^2 = 20$

A) Formula:

Average velocity =

$\displaystyle\frac{\text{Displacement}}{\text{Time}}$

1) 0.01

$y(1 + 0.01)=y(1.01) = 43(1.01)-23(1.01)^{2} = 19.9677\\\\\text{Average Velocity} = \dfrac{y(1.01)-y(1)}{1.01-1} =\dfrac{19.9677-20}{1.01-1}= \dfrac{-0.0323}{0.01} = -3.230000 \text{feet per second}$

2) 0.005 s

$y(1 + 0.005)=y(1.005) = 43(1.005)-23(1.005)^{2} = 19.984425\\\\\text{Average Velocity} = \dfrac{y(1.005)-y(1)}{1.005-1} =\dfrac{19.984425-20}{1.005-1} = -3.1150000 \text{feet per second}$

3) 0.002 s

$y(1 + 0.002)=y(1.002) = 43(1.002)-23(1.002)^{2} = 19.993908\\\\\text{Average Velocity} = \dfrac{y(1.002)-y(1)}{1.002-1} =\dfrac{19.993908-20}{1.002-1} = -3.0460000 \text{feet per second}$

4) 0.001 s

$y(1 + 0.001)=y(1.001) = 43(1.001)-23(1.001)^{2} = 19.996977\\\\\text{Average Velocity} = \dfrac{y(1.001)-y(1)}{1.001-1} =\frac{19.996977-20}{1.001-1} = -3.0230000 \text{feet per second}$

3 0

3 years ago

Kate scored 85,78,72, and 81 on 4 math tests. What score does she need on the fifth test to have at least an 80 average?

Elan Coil [88]

I am not good in this kind of question so maybe 84?

suppose the full marks for each of them is 100 so for 5 of them it will be 500 cause if you if you multiply 100 full marks by 5 it will be 500

so the answer to this question is maybe 84?

cause if you add all of them with 84 the outcome will be 400 and if you divide the 400 by 5 it will be 80

4 0

3 years ago

A farmer in China discovers a mammal hide that contains 37% of its original amount of C-14. Find the age of the mammal hide to t

Naya [18.7K]

Answer: 54678 years

Step-by-step explanation:

This can be solved by the following equation:

$N_{t}=N_{o}e^{-\lambda t}$ (1)

Where:

$N_{t}=54\%=0.54$ is the quantity of atoms of carbon-14 left after time $t$

$N_{o}=1$ is the initial quantity of atoms of C-14 in the mammal hide

$\lambda$ is the rate constant for carbon-14 radioactive decay

$t$ is the time elapsed

On the other hand, $\lambda$ has a relation with the half life $h$ of the C-14, which is $5730 years$ :

$\lambda=\frac{ln(2)}{h}=\frac{ln(2)}{5730 years}=1.21(10)^{-4} years^{-1}=0.000121 years^{-1}$ (2)

Substituting (2) in (1):

$0.54=1e^{-(0.000121 years^{-1}) t}$ (3)

Applying natural logarithm on both sides of the equation:

$ln(0.54)=ln(1e^{-(0.000121 years^{-1}) t})$ (4)

$-0.616=-(0.000121 years^{-1}) t$ (5)

Isolating $t$ :

$t=\frac{-0.616}{-0.000121 years^{-1}}$ (6)

$t=54677.68 years \approx 54678 years$ (7) This is the age of the mammal hide

8 0

3 years ago

I just don't know what to do for this at all.

True [87]

Answer:

40 degrees

Explanation:

A supplementary angle is when two angles add up to equal 180 degrees. So to figure out that one it would be 180-140=40. The other angle is 40 degrees.

8 0

3 years ago

Factor f(x) = 6x^4 - 9x^3 - 57x^2 - 18x +24