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3 years ago

12

A retired math teacher takes his grandson shopping. He tells his grandson that they can spend x

1 answer:

leva [86]3 years ago

4 0

Answer:

Addition, 83.6

Step-by-step explanation:

x - 72.6 = 11, x = 83.6

The grandson must add 72.6 to both sides to solve for x.

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The daily recommended allowance of vitamin C for a sixth grader is 45 mg. 1 orange has about 75% of the recommended daily allowa

Elden [556K]

Answer:

about 33.75 mg

Step-by-step explanation:

75% of 45 mg is ...

0.75 × 45 mg = 33.75 mg

About 33.75 mg of vitamin C are in one orange.

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You might be asked to round this to 34 mg.

3 0

3 years ago

Simplify 14 to the power of 15 over 14 to the power of 5

BartSMP [9]

Answer:

1. Use Quotient Rule

{14}^{15-5}

2. Simplify

{14}^{10}

3 Simplify.

289254654976289254654976

Step-by-step explanation:

6 0

3 years ago

What is the awnser to this equation

Scorpion4ik [409]

Answer:

14..........................

7 0

3 years ago

I need help on this. Can someone please help me??

Veronika [31]

Answer: A

Step-by-step explanation: if you want me to explain just comment

4 0

3 years ago

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

4 years ago