|x-(-12)| if x>-12 ill give brainlyest if corect

A cup of tea with initial temperature of I = 85C^(circ) is left in the room with a constant temperature A = 21^(circ). In one mi

tatyana61 [14]

Answer:

45.9° after 1 hour
22° after 264 minutes

Step-by-step explanation:

The temperature can be modeled by a decaying exponential function with an initial value of (85° -21°) = 64° and a vertical offset of 21°. The temperature T as a function of time t can be written as ...

T(t) = 21 +64(63/64)^t . . . . where t is in minutes and T is in degrees

The ratio 63/64 is the fraction of the initial temperature difference that remains after 1 minute.

We are asked for two points on the curve described by this function:

T(60)
t when 22 = T(t)

__

(a) T(60) = 21 +64(63/64)^60 ≈ 45.88

The temperature after 1 hour will be about 45.9 °C.

__

(b) Solving for t, we get ...

22 = 21 +64(63/64)^t . . . . fill in the value of T

1 = 64(63/64)^t . . . . . . . . . subtract 21

1/64 = (63/64)^t . . . . . . . . .divide by 64

log(1/64) = t·log(63/64) . . . take the log

log(1/64)/log(63/64) = t ≈ 264.08 . . . . divide by the coefficient of t

The temperature of the tea will be 22° after 264 minutes.

6 0

2 years ago

I need to solve the equation please help me

lesantik [10]

Answer:

$\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}$

Step-by-step explanation:

We are given the equation:

$4\sin^2(x)+6\sin(x)+2=0$

First, we can divide everything by 2:

$2\sin^2(x)+3\sin(x)+1=0$

Notice that we have an equation in quadratic form. Namely, if we make a substitution where u = sin(x), we acquire:

$2u^2+3u+1=0$

Solve for u. Factor:

$(2u+1)(u+1)=0$

Zero Product Property:

$2u+1=0\text{ or } u+1=0$

Solving for both cases:

$\displaystyle u=-\frac{1}{2}\text{ or } u=-1$

And by substitution:

$\displaystyle \sin(x)=-\frac{1}{2}\text{ or } \sin(x)=-1$

For the first case, recall that sin(x) is -1/2 for every 7π/6 and every 11π/6. Hence, for the first case, our solutions are:

$\displaystyle x=\frac{7\pi}{6}+2n\pi \text{ and } x=\frac{11\pi}{6}+2n\pi, n\in\mathbb{Z}$

Where n is an integer.

For the second case, sin(x) is -1 for every 3π/2. Thus:

$\displaystyle x=\frac{3\pi}{2}+2n\pi$

All together, our solutions are:

$\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}$

4 0

2 years ago

I just need help with this lol

n200080 [17]

I'll help with a few because no-one wants to just do your homework

there is the formula way or the intuitive way

(-19, -2) (-17, -10)

now slope is (difference in y)/ (difference in x)

or

(y2 - y1)/(x2 - x1) the formula. where x2 just means the second x

formula way:

(-19, -2) (-17, -10)

(-10 - (-2))/ (-17 - (-19)) ReM: Negative on number and in the formula

(-10 + 2)/ (-17 +19) = -8/2 slope is - 8/2

intuitive way

(-19, -2) (-17, -10)

(difference in y)/ (difference in x)

lets looks at the ys

-2 and -10; how many steps from -2 to -10? -8 the diff in y

lets looks at the xs

-19 to -17; how many steps from -19 to -17? + 2 the diff in x

so its -8/2

3 0

3 years ago

One number is 2/5 of another number. the sum of the two numbers is 35. find the two numbers. use a comma to separate your answer

Ivan

We have x = (2/5)y and x + y = 35;
then, (2/5)y + y = 35;
2y + 5y = 175;
7y = 175;
y = 27;
x = 35 - 27;
x = 8;

4 0

2 years ago

Given the function f(x)= x^2 + 3x-4 determine the average rate of change of the function over the interval −8≤x≤−1.

PolarNik [594]

Answer:

Step-by-step explanation:

hi

4 0

2 years ago