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Gnom [1K]
1 year ago
10

10. Find

%5Csin%20t%7D_1%5Csqrt%7B1%2Bu%5E%7B4%7D%7Ddu%5Cright%29dt%5Ctext%7B.%7D" id="TexFormula1" title="\frac{d^{2}}{d x^{2}}\int ^x_0\left(\int ^{\sin t}_1\sqrt{1+u^{4}}du\right)dt\text{.}" alt="\frac{d^{2}}{d x^{2}}\int ^x_0\left(\int ^{\sin t}_1\sqrt{1+u^{4}}du\right)dt\text{.}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
RideAnS [48]1 year ago
3 0

Let g(t) denote the inner integral. By the fundamental theorem of calculus, the first derivative is

\displaystyle \frac{d}{dx} \int_0^x g(t) \, dt = g(x)

Then using the FTC again, differentiating g gives

\displaystyle \frac{dg}{dx} = \frac{d}{dx} \int_1^{\sin(x)} \sqrt{1+u^4} \, du = \boxed{\cos(x) \sqrt{1+\sin^4(x)}}

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Zoe counts 5 times as many black kittens as white kittens for sale at the pet store. she counts a total of 25 kittens how many m
malfutka [58]

Let us say that:

a = black kittens

b = white kittens

 

We know that:

a = 5 b

a + b = 25

 

Therefore:

5 b + b = 25

6 b = 25

b = 4.17

But we cannot have a fraction value for the number of kittens, so round off:

b = 4

 

So a is:

a = 25 – 4 = 21

 

<span>Hence Zoe counts additional 1 black kitten.</span>

3 0
2 years ago
Which is the graph of f(x) = –(x + 3)(x + 1)?
Lostsunrise [7]

Answer:

Option 2

Step-by-step explanation:

We know that the graph will face down (the negative sign)

We also know that the vertex should be (-2, 1)

Therefore, option 2 is the solution

5 0
2 years ago
Read 2 more answers
What are the solutions of the equation x^4 + 6x^2 + 5 = 0? Use u substitution to solve.
Radda [10]

Answer:

second option

Step-by-step explanation:

Given

x^{4} + 6x² + 5 = 0

let u = x², then

u² + 6u + 5 = 0 ← in standard form

(u + 1)(u + 5) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 1 = 0 ⇒ u = - 1

u + 5 = 0 ⇒ u = - 5

Change u back into terms of x, that is

x² = - 1 ( take the square root of both sides )

x = ± \sqrt{-1} = ± i ( noting that \sqrt{-1} = i ), and

x² = - 5 ( take the square root of both sides )

x = ± \sqrt{-5} = ± \sqrt{5(-1)} = ± \sqrt{5} × \sqrt{-1} = ± i\sqrt{5}

Solutions are x = ± i and x = ± i\sqrt{5}

3 0
2 years ago
Which one of the following statements is true of perpendicular lines? A. They intersect to form an obtuse angle. B. They interse
quester [9]
They intersect at one point
6 0
3 years ago
Read 2 more answers
If a = -3, find the value of 3a²<br><br>​
guajiro [1.7K]

Step-by-step explanation:

given

a = - 3

3a² = 3 * ( -3) ²

= 3 * 9

= 27

The value of 3a² is 27.

8 0
2 years ago
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