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3 years ago

Give the final simplified result.

Mathematics

1 answer:

grin007 [14]3 years ago

3 0

Answer:

-8 a

Step-by-step explanation:

i simplified -3 a (70+3a) wich came out to negative eight A

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Let a=x^2+4. Use a to find the solutions for the following equation:

Helga [31]

(x^2+4)^2 + 32 = 12x^2 + 48 .... a = x^2 + 4
(x^2 + 4)^2 + 32 = 12(x^2 + 4) 
a^2 + 32 = 12a 
a^2 - 12a + 32 = 0 
(a - 8)(a - 4) = 0 
a = 8 and a = 4 

for a = 8 ... 8 = x^2 + 4 ... x^2 = 4 ... x = +/- 2 
for a = 4 ... 4 = x^2 + 4 ... x^2 = 0 ... x = 0 

x = -2, 0, +2 so your answer is going to be e

4 0

3 years ago

Read 2 more answers

Henry's baseball practice starts at 2:00 pm. It lasts 1 hour and 45 minutes. What time does he get out of baseball practice? Wri

Andrew [12]

Answer:

3:45

Step-by-step explanation:

because if you add 2 to 1 it is 3 and that is 3pm and it says 2:00 and the 00 are the minutes minutes so you can add those in and it will be 45 so 3:45

5 0

3 years ago

Help I don't know how to do this

Vilka [71]

Answer:

P(t) = 282.2(1.009)^t

Step-by-step explanation:

Look at the attached image.

Hope you can read my handwriting. the image cut off the right side, b = 1.009213324... but question asks to round to nearest thousandth so it's 1.009

For the second part just use the equation to find P when t = -1 and see if P is less than (underpredicts) the number from the question or greater than (overpredicts) the number. I haven't calculated it but I think it will be smaller and thus underpredicts just from looking at the numbers when t = -1

6 0

3 years ago

A company manufactures running shoes and basketball shoes. The total revenue (in thousands of dollars) from x1 units of running

Alborosie

Answer:

$x_1 =2 , x_2=7$

Step-by-step explanation:

Consider the revenue function given by $R(x_1,x_2) = -5x_1^2-8x_2^2 -2x_1x_2+34x_1+116x_2$ . We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).

$\frac{dR}{dx_1} = -10x_1-2x_2+34 =0$

$\frac{dR}{dx_2} = -16x_2-2x_1+116 =0$

From the first equation, we get, $x_2 = \frac{-10x_1+34}{2}$ .If we replace that in the second equation, we get

$-16\frac{-10x_1+34}{2} -2x_1+116=0= 80x_1-2x_1+116-272= 78x_1-156$

From where we get that $x_1 = \frac{156}{78}=2$ . If we replace that in the first equation, we get

$x_2 = \frac{-10\cdot 2 +34}{2}=\frac{14}{2} = 7$

So, the critical point is $(x_1,x_2) = (2,7)$ . We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives and check if the criteria is fulfilled in order for it to be a maximum. We get that

$\frac{d^2R}{dx_1dx_2}= -2 = \frac{d^2R}{dx_2dx_1}$

$\frac{d^2R}{dx_{1}^2}=-10, \frac{d^2R}{dx_{2}^2}=-16$

We have the following matrix,

$\left[\begin{matrix} -10 & -2 \\ -2 & -16\end{matrix}\right]$ .

Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is $(-10)\cdot (-16) - (-2)(-2) = 156>0$ and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum

8 0

3 years ago

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Make b the subject of P = 1/2 a b² + c where b is positive. (3 marks)

mote1985 [20]

That’s the answer to the question

8 0

2 years ago