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3 years ago

Choose the most appropriate name for the function described below.

2 answers:

4 0

T(p) would be an accurate answer. This situation likens to the f(x) function, where y is the function of x and so dependent on x. The cost of the tomatoes is dependent on the price per pound, so cost would be in the f place and price per pound would be in the (x) place.

ziro4ka [17]3 years ago

4 0

Answer:C: the total price depends on the number of pounds

Step-by-step explanation:

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What is the slope of the line through (1, -1) and (5. – 7)?

Vladimir [108]

Answer:

-3/2

Step-by-step explanation:

Given two points, we can find the slope by

m = (y2-y1)/(x2-x1)

= (-7 - -1)/ (5-1)

= (-7+1)/(5-1)

= -6/4

= -3/2

6 0

3 years ago

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Sarah says that 26 divided by 8 equals 14 divided 4 because both are "3 R2. show her mistake using decimal division

mezya [45]

26/8=3.25
14/4=3.5
You must show your work.

8 0

3 years ago

Which correctly describes how to determine the measure of angle 1?

Kitty [74]

Answer:

Step-by-step explanation:

The 81° angle and angle 2 are corresponding angles so angle 2 must measure 99°. Angles 1 and 2 are supplementary angles so angle 1 must measure 81°.

7 0

3 years ago

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Martin modeled the distance, y, that runners traveled during a race a function of the time, that they ran. Which would best desc

Mama L [17]

Answer:

All positive real numbers

Step-by-step explanation:

Given

The model can be represented as:

$y = f(x)$

$y = distance$

$x = time$

Required

Determine the domain

This means that we list out possible values of x.

If x represents time, then it is impossible for x to be negative.

This implies that x can take any value as long as it is greater than or equal to 0.

<em>Hence, the domain is all positive real numbers</em>

4 0

3 years ago

The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T min

dolphi86 [110]

This is a doozy. I actually have another form of the equation for cooling, and it's in Celcius (so I convert) and seconds (we can switch back to minutes in the end). The Celcius and Fahrenheit don't matter because it's the time we are interested in and as long as we use the C and F equivalents, we're fine. Promise. The formula is as follows: $T(t)= T_{s}+( T_{0}- T_{s})e ^{-kt}$ . It's really easy to use. T(t) is the ending temperature; $T_{s}$ is the room temp; $T_{0}$ is our initial temperature of the liquid; e is Euler's number, k is the constant of variation, and t is the time in seconds. In Celcius, our temps are as follows: 180 F = 82.2 C; 100 F = 37.8 C; 75 F = 23.9 C; 80 F = 26.7 C. 10 minutes is 600 seconds. Filling in our formula with all of that, we will solve for k. Then we will use that k value to solve for the time in the question we are told to answer. Let's do this. $37.8=23.9+(82.2-23.9)e ^{-600k}$ . Simplifying a bit we have $37.8=23.9+(58.3)e ^{-600k}$ . Subtracting 23.9 from both sides we have $13.9=58.3e ^{-600k}$ . divide both sides by 58.3 to get $.2384219=e ^{-600k}$ . At this point in your mathematical career, I'm assuming that since you're doing this, you're studying natural and common logs. The base of a natural log is e, therefore, if we take the natural log of e, they both "undo" each other and cancel each other out completely. So let's do that. $ln(.2384219)=-600k$ . Simplifying on the left gives us $-1.433713=-600k$ . Dividing both sides by -600 gives us a k value of .002389. Now we will do the equation again, using that k value, to solve for how long it takes for the coffee to cool to 80 F (26.7 C). $26.7=23.9+(82.2-23.9)e ^{-.002389t}$ . Simplifying a bit again gives us $26.7=23.9+(58.32)e ^{-.002389t}$ . Subtracting 23.9 from both sides gives us $2.8=(58.32)e ^{-.002389t}$ . We will now divide both sides by 58.32 to get $.0480109=e ^{-.002389t}$ . Again we will take the natural log of both sides to "undo" the e: $ln(.0480109)=-.002389t$ . The natural log of .0480109 is -3.036325671. So, dividing both sides by the negative decimal on the right gives us $\frac{-3.036325671}{-.002389}=t$ and t = 1270.9 seconds. Divide that by 60 to get the time in minutes. t = 21.1826...so 21 minutes. Phew!!!

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3 years ago

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