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3 years ago

An orchard sells 6 lb of apples for

Mathematics

1 answer:

Arte-miy333 [17]3 years ago

5 0

Answer:

Oc= 2.25p

Step-by-step explanation:

13.50/6 equals $2.25 for each pound, so since we don't know the number of pounds being purchased we represent it with a variable, p, so 2.25 * p

2.25p

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A cake is removed from a 310°F oven and placed on a cooling rack in a 72°F room. After 30 minutes the cake's temperature is 220°

Fynjy0 [20]

Answer:

The time is 135 min.

Step-by-step explanation:

For this situation we are going to use Newton's Law of Cooling.

Newton’s Law of Cooling states that the rate of temperature of the body is proportional to the difference between the temperature of the body and that of the surrounding medium and is given by

$T(t)=C+(T_0-C)e^{kt}$

where,

C = surrounding temp

$T(t)$ = temp at any given time

t = time

$T_0$ = initial temp of the heated object

k = constant

From the information given we know that:

Initial temp of the cake is 310 °F.
The surrounding temp is 72 °F.
After 30 minutes the cake's temperature is 220 °F.

We want to find the time, in minutes, since the cake's removal from the oven, at which its temperature will be 100°F.

To do this, first, we need to find the value of k.

Using the information given,

$220=72+(310-72)e^{k\cdot 30}\\\\72+238e^{k30}=220\\\\238e^{k30}=148\\\\e^{k30}=\frac{74}{119}\\\\\ln \left(e^{k\cdot \:30}\right)=\ln \left(\frac{74}{119}\right)\\\\k\cdot \:30=\ln \left(\frac{74}{119}\right)\\\\k=\frac{\ln \left(\frac{74}{119}\right)}{30}$

$T(t)=72+(310-72)e^{(\frac{\ln \left(\frac{74}{119}\right)}{30}\cdot t)}$

Next, we find the time at which the cake's temperature will be 100°F.

$100=72+(310-72)e^{(\frac{\ln \left(\frac{74}{119}\right)}{30}\cdot t)}\\72+238e^{\frac{\ln \left(\frac{74}{119}\right)}{30}t}=100\\238e^{\frac{\ln \left(\frac{74}{119}\right)}{30}t}=28\\e^{\frac{\ln \left(\frac{74}{119}\right)}{30}t}=\frac{2}{17}\\\ln \left(e^{\frac{\ln \left(\frac{74}{119}\right)}{30}t}\right)=\ln \left(\frac{2}{17}\right)\\\frac{\ln \left(\frac{74}{119}\right)}{30}t=\ln \left(\frac{2}{17}\right)\\t=\frac{30\ln \left(\frac{2}{17}\right)}{\ln \left(\frac{74}{119}\right)}\approx 135.1$

4 0

3 years ago

Let V be the vector space P3[x] of polynomials in x with degree less than 3 and W be the subspace

Pepsi [2]

By definition, the span of two vectors is the set of all possible linear combinations of said vectors. So, any element in W is obtaining by choosing two numbers a,b and building

$a(7-8x-8x^2)+b(x^2-(5+6x)) = -8ax^2-8ax+7a+bx^2-6bx-5b$

(a)

So, you can show a nonzero polynomial in W by choosing any values of a and b, as long as they're not both zero. To keep it as simple as possible, we can choose for example a=1, b=0 and we obtain one of the base vectors of W:

$7-8x-8x^2$

(b)

Factoring the powers of x, we see that a generic polynomial in W looks like

$(b-8a)x^2-(8a+6b)x+7a-5b$

So, we must build a polynomial

$dx^2+ex+f$

such that it is not possible that

$\begin{cases}d=b-8a\\e=8a+6b\\f=7a-5b\end{cases}$

For example, let's try the polynomial $x^2+x+1$

We should solve the system

$\begin{cases}b-8a=1\\8a+6b=1\\7a-5b=1\end{cases}$

And you can check that it has no solutions. So, the polynomial $x^2+x+1$ does not belong to W. On the other hand, it surely belongs to V, because it is a polynomial with degree less than 3. So, the polynomial $x^2+x+1$ belongs to V/W.

7 0

4 years ago

bob switches cell phone plans from Verizon to Tmobile. the monthly cost of his new plan is half the cost of his old plan, plus h

EastWind [94]

First you need to divide 70 by 2 in order to cut it in half which would give you 35. Then add 27.50 and you get 62.5. Subtract that from 70 and you get 7.50 so he saved $7.50 each month

4 0

4 years ago

Distance between (1,2) and (4,6)

White raven [17]

Answer:

Step-by-step explanation:

6-4 over 2-1

2 over 1

I hope this is correct and have a great day

6 0

3 years ago

Yoryi bought an Apple Watch for $470. He paid $200 at the time of purchase and will make monthly payments of $30 to finish payin

inysia [295]

Answer:

9 months

Step-by-step explanation:200+30m=470

30m=270

m=9

He will pay for 9 months

8 0

3 years ago