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Mathematics

1 answer:

Mumz [18]2 years ago

8 0

Step-by-step explanation:

multiplying expressions.

remember every term of one expression has to be multiplied with every term of the other expression, and the results are added up (while considering their individual signs, of course).

(-3×3 + 2x - 4)(3x - 2)

(-9 + 2x - 4)(3x - 2)

(-13 + 2x)(3x - 2) = -13×3x + -13×-2 + 2x×3x + 2x×-2 =

= -39x + 26 + 6x² - 4x = 6x² - 43x + 26

let's do the other multiplication and compare the result with the result of 1 :

(-13 + 2x)(2x - 3) = -13×2x + -13×-3 + 2x×2x + 2x×-3 =

= -26x + 39 + 4x² - 6x = 4x² - 32x + 39

no, this product is not the same as in 1.

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A cooler has a temperature of 32 degrees Fahrenheit. A bottled drink is placed in the cooler with an initial temperature of

FinnZ [79.3K]

Answer:

$k \approx 0.44$

Step-by-step explanation:

Given function:

$f(t) = (ce)^{-kt}+32$

As per question statement:

Initial temperature of bottle is 70 $^\circ F$ .

i.e. when time = 0 minutes, f(t) = 70 $^\circ F$

$70 = ce^{-k\times 0}+32\\\Rightarrow 38 = ce^{0}\\\Rightarrow c = 38$

After t = 3, f(t) = 42 $^\circ F$

$42 = 38 \times e^{-k\times 3}+32\\\Rightarrow 42-32 = 38 \times e^{-3k} \\\Rightarrow 10 = 38 \times e^{-3k} \\\Rightarrow e^{3k} = \dfrac{38}{10}\\\Rightarrow e^{3k} = 3.8\\\\\text{Taking } log_e \text{both the sides:}\\\\\Rightarrow log_e {e^3k} = log_e {3.8}\\\Rightarrow 3k \times log_ee=log_e {3.8} (\because log_pq^r=r \times log_pq)\\\Rightarrow 3k \times 1=log_e {3.8}\\\Rightarrow 3k = 1.34\\\Rightarrow k = \dfrac{1.34}{3}\\\Rightarrow k \approx 0.44$

Hence, the value is:

$k \approx 0.44$

8 0

4 years ago

The vertex of this parabola is at (2, -4). When the y-value is -3, the x-value is -3. What is the coefficient of the squared ter

lyudmila [28]

Answer:

The squared term is 1/25

Step-by-step explanation:

The parabola equation in the vertex form is

$y = a \times (x - h)^2 + k$

where point (h,k) is the vertex and a is the squared term. In this case h = 2 and k = -4. On the other hand, we know that y = -3 and x = -3 are in the parabola. Replacing these values in the formula gives

$-3 = a \times (-3 - 2)^2 - 4$