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oksian1 [2.3K]
2 years ago
14

A 40-foot pipe is cut into three sections. The longest section is three times as long as the shortest, and the middle-sized sect

ion is 5 feet longer than the shortest. Complete the diagram
by giving a and b as expressions involving x. Do not solve the problem.
P = 40 ft
12
X
b
21
X
P
1
a
Length of
middle-sized
Length of
shortest
section
Length of
longest
section
section
Mathematics
1 answer:
PtichkaEL [24]2 years ago
5 0

Answer:

P=40

a + b + x = P

a = 3x    

b = x + 5

substitute for b & y

3x + (x+5) + x = 40

Step-by-step explanation:

longest section 1 = a

mid length section 2 = b

shortest section 3 = x

P=40

a + b + x = P

a = 3x    

b = x + 5

substitute for b & y

3x + (x+5) + x = 40

5x + 5 = 40

5x = 35

x = 7

b = 12

a = 21

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Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x.
Leni [432]

Answer:

a)

g(2.9) \approx -6.6

g(3.1) \approx -3.4

b)

The values are too small since g'' is positive for both values of x in. I'm speaking of the x values, 2.9 and 3.1.

Step-by-step explanation:

a)

The point-slope of a line is:

y-y_1=m(x-x_1)

where m is the slope and (x_1,y_1) is a point on that line.

We want to find the equation of the tangent line of the curve g at the point (3,-5) on g.

So we know (x_1,y_1)=(3,-5).

To find m, we must calculate the derivative of g at x=3:

m=g'(3)=(3)^2+7=9+7=16.

So the equation of the tangent line to curve g at (3,-5) is:

y-(-5)=16(x-3).

I'm going to solve this for y.

y-(-5)=16(x-3)

y+5=16(x-3)

Subtract 5 on both sides:

y=16(x-3)-5

What this means is for values x near x=3 is that:

g(x) \approx 16(x-3)-5.

Let's evaluate this approximation function for g(2.9).

g(2.9) \approx 16(2.9-3)-5

g(2.9) \approx 16(-.1)-5

g(2.9) \approx -1.6-5

g(2.9) \approx -6.6

Let's evaluate this approximation function for g(3.1).

g(3.1) \approx 16(3.1-3)-5

g(3.1) \approx 16(.1)-5

g(3.1) \approx 1.6-5

g(3.1) \approx -3.4

b) To determine if these are over approximations or under approximations I will require the second derivative.

If g'' is positive, then it leads to underestimation (since the curve is concave up at that number).

If g'' is negative, then it leads to overestimation (since the curve is concave down at that number).

g'(x)=x^2+7

g''(x)=2x+0

g''(x)=2x

2x is positive for x>0.

2x is negative for x.

That is, g''(2.9)>0 \text{ and } g''(3.1)>0.

So 2x is positive for both values of x which means that the values we found in part (a) are underestimations.

6 0
3 years ago
How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid to obtain a mixture containing a
Nuetrik [128]

Answer:

40 quarts.

Step-by-step explanation:

Let x =quarts of the 50% solution

so, according to the question

the typical mixture equivalent equation will be like this

.50x + .20(20) = .40(x+20)\\.50x + 4 = .40x + 8\\.50x - .40x = 8 - 4\\.10x = 4\\x = 4/.10 \\x = 40

so the answer will be 40 quarts of 50% solution should be added.



5 0
2 years ago
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Answer:

Step-by-step explanation:

Yo when you get these kind of questions you can use desmos calculator, for the future.

5 0
2 years ago
HELP PLZ I NEED IT
vladimir2022 [97]

Answer:

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Step-by-step explanation:

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3 0
3 years ago
On a 1:5 scale drawing of a car one part is 8 inches how long will the actual car part be
lina2011 [118]
40, because if the ratio is 1:5 then we can times 8 by 5 to get 40 (I think :P)
5 0
3 years ago
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