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crimeas [40]
2 years ago
5

Find f. f ''(x) = −2 + 36x − 12x2, f(0) = 8, f '(0) = 18 f(x) =

Mathematics
1 answer:
Alik [6]2 years ago
8 0
Integrate <span>f ''(x) = −2 + 36x − 12x2 with respect to x:

f '(x) = -2x + (36/2)x^2 - (12/3)x^3 + c.  Find c by letting x = 0 and using f(0)=8.

Then f '(0) = -2x + 18x^2 - 4x^3 + c = 18 (which was given).

Then             -0      + 0      - 0 + c = 18, so c = 18 and 

f '(x) = </span>-2x + 18x^2 - 4x^3 + 18.

Go through the same integration process to find f(x).
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The marching band walks 1/15 miles in 1.5 minutes. At this rate, how many minutes will it take to complete 1 mile? Record your a
ipn [44]

Answer:

It will take 22.5 minutes to complete 1 mile

Step-by-step explanation:

From the question,

The marching band walks 1/15 miles in 1.5 minutes

First we will determine the miles cover in 1 minute

If the marching band walks 1/15 miles in 1.5 minutes

then, they will cover x miles in 1 minute

x = \frac{1/15 * 1}{1.5}\\

Then,

x = \frac{1/15 }{1.5}

x = 2/45 miles

∴ 2/45 miles are covered in 1 minute

Now,

If 2/45 miles are covered in 1 minute

Then, 1 mile will be covered in y minute

y = \frac{1 * 1}{2/45}

y =\frac{1}{2/45} \\y = \frac{45}{2}\\

∴ y = 22.5 minutes

Hence, it will take 22.5 minutes to complete 1 mile

6 0
2 years ago
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associ
OleMash [197]

Answer:

Each associate costs the client $700 per day, so a associates will cost the client 700a dollars per day. Each partner costs the client $1500 per day, so p partners will cost the client 1500p dollars per day. The total amount charged 700a+1500p :$14100:

700a+1500p=14100

700a+1500p=14100

Since there were a total of 11 lawyers assigned to the case (associates and partners), we know a+pa+p must equal 11.11.

a+p=11

a+p=11

\underline{\text{Write System of Equations:}}

Write System of Equations:

​

700a+1500p=

700a+1500p=14100

14100

a+p=11

11

8 0
2 years ago
20 pts please help!
sweet-ann [11.9K]
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2 years ago
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What is the y-intercept of the polynomial f(x)f(x) f(x) defined below? Write the y-value only. f(x)=−4x2+x5+10x3+5x+8x4f(x)=-4x^
zhannawk [14.2K]

Answer:

y = 0

Step-by-step explanation:

Given

f(x) = 4x² +x⁵ +10x³ +5x+8x⁴

Required

Determine the y intercept

The y intercept of a function is a point where x = 0

So, we have to substitute 0 for x in the above function

f(x) = 4x² +x⁵ +10x³ +5x+8x⁴ becomes

f(0) = 4(0)² +(0)⁵ +10(0)³ +5(0)+8(0)⁴

f(0) = 4 * 0 + 0 + 10 * 0 + 5 * 0 + 8 * 0

f(0) = 0 + 0 + 0 + 0 + 0

f(0) = 0

Substitute y for f(0)

y = 0

Hence, the y intercept is 0

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