I'm really confused on how to do this problem :/

Tell whether the angles are complementary or supplementary. Then fir<br> the value of x.

Helga [31]

Answer:

Step-by-step explanation:

4. 10x + 30 = 90

10x = 60

x = 6

complementary

5. 4x + 40 + 3x = 180

7x + 40 = 180

7x = 140

x = 20

supplementary

4 0

2 years ago

What is the area of the rectangle written in simplest form

Valentin [98]

Answer:

option D

Step-by-step explanation:

5/6 x 4/6

Multiply the numerators only.

it will give you--> 20/6

You can simplify this down by dividing 20 by 6 giving you 3 remainder 2

Putting this in fraction form would give you 32/6 which can be simplified to

3 1/3 ft^2

8 0

3 years ago

What expression is equivalent to

Wittaler [7]

Answer:

c) x^6 y^11 z^6

Step-by-step explanation:

When multiplying exponents with the same variables, you add them.

so x^4(x^2) would be 4+2 and therefore x^6.

keep in mind this doesn't apply for different variables

(xy^2)(x^2y) will not be added!!

4 0

3 years ago

A news item is spreading by word of mouth through a population of size 12,000 people. After t days, the number of people (in tho

Lilit [14]

Answer:

a) 2.303

b) $f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

c) 1.3609

e) $\frac{dy}{dx}=0.04y(12-y)$

f) 4.5 thousand people(smaller)

7.5 thousand people (larger)

e) t=7.93 days (smaller)

t=10.06 days (larger)

g) 1.44

Step-by-step explanation:

The given function is $y=f(t)=\frac{12}{1+75e^{-0.48t}}$

To find how many thousand people have heard the news after 6 days, we substitute to get:

$f(6)=\frac{12}{1+75e^{-0.48*6}}=2.303$ thousands.

b) We rewrite to get: $f(t)=12(1+75e^{-0.48t})^{-1}$

We differentiate using the chain rule to obtain:

$f'(t)=-12(1+75e^{-0.48t})^{-2}\cdot 75e^{-0.48t}\cdot -0.48$

This simplifies to:

$f'(t)=432e^{-0.48t}(1+75e^{-0.48t})^{-2}$

We rewrite as positive index to get:

$f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

c) To find the rate at which the news is spreading after 8 days, we substitute t=8 into $f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$ to get:

$f'(8)=\frac{432e^{-0.48\cdot 8}}{(1+75e^{-0.48\cdot 8})^{2}}=1.3609$

d) The solution to the logistic differential equation:

$\frac{dy}{dt}=ky(M-y)$

is

$y=\frac{M}{1+be^{-Mkt}}$

By comparison, M=12, and $Mk=0.48$

$12k=0.48\\k=0.04$

The differential equation is:

$\frac{dy}{dx}=0.04y(12-y)$

e) To how many people have heard the news when its rate of spread is 1.35 thousand per day, we equate the differential equation to 1.35 and so for t first.

$\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}=1.35$

This gives us: t=10.06 ot t=7.93

We substitute the times into the function to get:

$f(7.93)=\frac{12}{1+75e^{-0.48\cdot7.93}}$ =4.5 thousand: smaller value

$f(10.06)=\frac{12}{1+75e^{-0.48\cdot10.06}}=7.5$ thousand: Larger value

f) The two times that the news is spreading at rate 1.35 thousand people per day are:

$t=7.93$ days: Smaller value

$t=10.06$ : Larger value

g) To find the fastest rate at which the news spread we take the second derivative and equate it to zero.

$f''(t)=0$

This corresponds to where the horizontal line is tangent to

$f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

From the graph the point of tangency is:

(8.99,1.44)

Therefore the fastest rate at which the news spread is 1.44

7 0

3 years ago

the speeders scccer team charged $12 to wash each car at a fundraiser car wash. the team collected a total of $672 by the end of

snow_lady [41]

All u have do do is add 12 ×56 and u will get 627 so they will wash 56 cars

4 0

3 years ago