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Gnom [1K]
2 years 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]2 years 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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Help me out with this question (geometry)
nadezda [96]

Answer:

116

Step-by-step explanation:

13x-1 = 2(6x+4)

13x-1 = 12x+8

x=9

6 0
3 years ago
One of two complementary angles is 12 degrees greater than the other. Find the measure of the larger angle.
stiks02 [169]

Answer:

39,51

Step-by-step explanation:

Complementary angles add to 90 degrees

Let one angle be x

The other angle is x+12

x+ x+12 = 90

Combine like terms

2x+12 = 90

Subtract 12 from each side

2x+12-12 = 90-12

2x = 78

Divide each side by 2

2x/2 = 78/2

x =39

The other angle is 39+12 =51

8 0
3 years ago
(1/4)^3+(3/4)^3+3(1/4)(3/4)(1/4+3/4)
bogdanovich [222]
The answer should be 1
6 0
3 years ago
PLEASE HELP ME I WILL MARK BRAINLIEST!!!
alexandr402 [8]

1. One way to approach this is to convert the magnitude and direction of each force to rectangular coordinates.

... first force = 90(cos(30°), sin(30°)) = (77.94, 45.00)

... second force = 50(cos(160°), sin(160°)) = (-46.98, 17.10)

Then their sum is

... resultant force = first force + second force = (30.96, 62.10)

The magnitude is found using the Pythagorean theorem:

... resultant magnitude = √(30.96^2 + 62.10^2)

... ... = √(958.52+3856.41) = √4814.93

... ... = 69.39

The resultant direction can be found using the definition of the tangent function.

... tan(α) = 62.10/30.96 = 2.01

... α = arctan(2.01) = 63.55°

The (magnitude, direction) of the resultant force are (69.39, 63.55°).

_____

(Note that rounding introduced an error of 0.05° in the direction.)

2. Using DeMoivre's theorem, the magnitude of the 4th root is the 4th root of the magnitude, and the angle of the 4th root is 1/4 of the angle (and its aliases).

... fourth root = 256^(1/4)∠((240°+k*360°)/4) = 4∠(60°+k*90°) . . . . k=0, 1, 2, 3

7 0
3 years ago
What is equal to 4/5
nikitadnepr [17]
8/10 is equal to 4/5.

7 0
3 years ago
Read 2 more answers
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