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Sedaia [141]
3 years ago
6

Find y’ for y=7sec^3x

Mathematics
1 answer:
laiz [17]3 years ago
6 0
Taking the derivative of 7 times secant of x^3:
We take out 7 as a constant focus on secant (x^3)
To take the derivative, we use the chain rule, taking the derivative of the inside, bringing it out, and then the derivative of the original function. For example:
The derivative of x^3 is 3x^2, and the derivative of secant is tan(x) and sec(x).
Knowing this: secant (x^3) becomes tan(x^3) * sec(x^3) * 3x^2. We transform tan(x^3) into sin(x^3)/cos(x^3) since tan(x) = sin(x)/cos(x). Then secant(x^3) becomes 1/cos(x^3) since the secant is the reciprocal of the cosine.

We then multiply everything together to simplify:

sin(x^3) * 3x^2/ cos(x^3) * cos(x^3) becomes

3x^2 * sin(x^3)/(cos(x^3))^2

and multiplying the constant 7 from the beginning:

7 * 3x^2 = 21x^2, so...

our derivative is 21x^2 * sin(x^3)/(cos(x^3))^2


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Laurie buys four bags of candy with 10 pieces of candy in each bag. Her father then gives her 5 more pieces of candy. Laurie wan
lina2011 [118]

Answer:

3 pieces left over

Step-by-step explanation:

Laurie has a total of 45 pieces of candy, if she has 6 friends, you can do

45 \div 6 = 7.5

each friend can get 7 pieces of candy

7 \times 6 = 42

if each friend gets 7 pieces, you have used 42 pieces out of you total 45

45 - 42 = 3

which leaves 3 pieces left over.

3 0
3 years ago
Steve's bedroom measures 12 feet by 13 feet. Ricardo's bedroom measures 8 feet by 14
lina2011 [118]

Answer: Steve's bedroom has the greater area.

Step-by-step explanation: The formula for area is Area = Length x Width.

So all you have to do to figure this out is multiply the Width of the rooms by the length.

So Steve's room is 12ft X 13ft = 156ft

Ricardo's room is 8ft X 14ft = 112ft

156ft > 112ft

Steve's room has a greater area.

4 0
3 years ago
The gradiant y=2x³-5x+1 at point (2,7)​
olga2289 [7]

Given:

The equation of the curve is:

y=2x^3-5x+1

To find:

The gradient (slope) of the given curve at point (2,7).

Solution:

We have,

y=2x^3-5x+1

Differentiate the given equation with respect to x.

y=2(3x^2)-5(1)+(0)

y'=6x^2-5

Now we need to find the value of this derivative at (2,7).

y'_{(2,7)}=6(2)^2-5

y'_{(2,7)}=6(4)-5

y'_{(2,7)}=24-5

y'_{(2,7)}=19

Therefore, the gradient (slope) of the given curve at point (2,7) is 19.

8 0
2 years ago
In ΔEFG, the measure of ∠G=90°, EF = 95 feet, and FG = 26 feet. Find the measure of ∠F to the nearest degree.
Firdavs [7]

Answer:

74.4°

Step-by-step explanation:

Given

  • ∠G=90° => ΔEFG is a right triangle
  • EF = 95 feet
  • FG = 26 feet

Use sine law to find ∠F

As we know:

Sin(GEF)/ GF = Sin(EGF)/EF

<=> Sin(GEF) / 26 = Sin(90)/95

<=>Sin(GEF) / 26 = 1/95

<=> Sin(GEF)  = 26/95

<=> ∠GEF ≈ 15.8°

=> ∠F = 180° - ∠G - ∠GEF

∠F = 180° - 90° - 15.8° = 74.4°

3 0
3 years ago
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A staff has<br> lines and<br> spaces.
Lisa [10]

Answer:

That's true. It does have 5 lines and 4 spaces.

Step-by-step explanation:

Ion know if it's a true or false question but I hope I helped ya.

If you don't understand my answer, hmu in the comments.

<u><em>< Sarah ></em></u>

6 0
3 years ago
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