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emmainna [20.7K]
1 year ago
12

Evaluate dydx at x=2 for the function below. y=6u^3+5u+2, where u=−3x^2−4x+9

Mathematics
1 answer:
bekas [8.4K]1 year ago
6 0

Step-by-step explanation:

y = 6u {}^{3}  + 5u + 2

y = 6( - 3 {x}^{2}  - 4x + 9) {}^{3}  + 5( - 3 {x}^{2}  - 4x + 9) + 2

Use the chain rule.

\frac{dy}{dx}  = 6(3)( - 3 {x}^{2}  - 4x + 9) {}^{2} ( - 6x  -  4) + 5( - 6x - 4)

18( - 3 {x}^{2}  - 4x + 9) {}^{2} ( - 6x - 4) + 5( - 6x - 4)

Factor out -6x-4,

( - 6x - 4)(18( - 3 {x}^{2}  - 4x + 9) {}^{2}  + 5)

Know plug in x=-2 to evaluate the derivative

( - 6(2) - 4)(18( - 3(2) {}^{2}  - 4(2) + 9) {}^{2}  + 5)

( - 16)(18(( - 12) - 8 + 9)) {}^{2}  + 5)

- 16(18( - 11) {}^{2}  + 5)

- 16(2183)

- 34928

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A car travels 30 – miles in
hodyreva [135]

Answer:

45.3 miles/h

Hope this will help you

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Find the length of YZ
emmainna [20.7K]
Larger triangle’s base length

a^2 + b^2 = c^2
a^2 + 3^2 = 8^2
a^2 = 8^2 - (3^2)
sqrt(a^2) = sqrt(55)
a = sqrt(55)
__________________

Smaller triangle’s base length:

The same formula applies.
a^2 + 3^2 = 5^2
a^2 = 5^2 - (3^2)
sqrt(a^2) = sqrt(16)
a = 4
____________

The finale!

Add the two side lengths of a, which is sqrt(55) + 4 (exact answer)
or... 11.416 (unrounded to thousandths place)

Good luck to you!
5 0
3 years ago
Plz help me out with this and do show work I will be waiting.... btw u will be marked brainliest!!!!!! Fast plz
pychu [463]

Answer:

x=16°

Step-by-step explanation:

5*x-30=2*(x+18)

For the second, I'd say it is:

5*x-30=2*x+18  

Let's solve both.  

5*x-30=2*(x+18)

5x-30=2x+36

3x=66

x=22  

5*x-30=2*x+18

3x+48

x=16°

8 0
3 years ago
To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then s
inysia [295]

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

5 0
3 years ago
What is the unit rate of 4 ticket for 35$
Paraphin [41]

Answer:35/5 = 8.75$ per ticket

Step-by-step explanation:

7 0
2 years ago
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