MATHEMATICS HIGH SCHOOL

What is the indefinite integral of 6sin(3t) dt?

Answers

Answer 1

Answer:

Answer:

$\displaystyle \int {6sin(3t)} \, dt = -2cos(3t) + C$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals
[Indefinite Integrals] Integration Constant C

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int {6sin(3t)} \, dt$

Step 2: Integrate Pt. 1

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int {6sin(3t)} \, dt = 6\int {sin(3t)} \, dt$

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Set u: $\displaystyle u = 3t$
[u] Differentiate [Basic Power Rule, Multiplied Constant]: $\displaystyle du = 3 \ dt$

Step 4: integrate Pt. 3

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int {6sin(3t)} \, dt = 2\int {3sin(3t)} \, dt$
[Integral] U-Substitution: $\displaystyle \int {6sin(3t)} \, dt = 2\int {sin(u)} \, du$
[Integral] Trigonometric Integration: $\displaystyle \int {6sin(3t)} \, dt = -2cos(u) + C$
Back-Substitute: $\displaystyle \int {6sin(3t)} \, dt = -2cos(3t) + C$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

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Solve the system of equations

Answers

Answer:

Step-by-step explanation:

You can solve it by substitution, by setting the first equation to y=1-x.

Replace the y in the equation by y=1-x.

4x + 3(1-x) = 8.

Distribute the 3.

4x + 3-3x = 8

Combine like terms.

x + 3 = 8

x =5

Plug 5 into y=1-x.

y=1-5

y= -4

A triangle formed by the sides 3.8cm ,3.7 cm, and 5cm is

Answers

By the Pythagoras theorem we know that the if the square of the longest side of the triangle is equal to the sum of the square of other two sides.

The triangle formed by the sides 3.8 cm ,3.7 cm, and 5 cm is acute angle triangle.

How to find the type of triangle?

By the Pythagoras theorem we know that the if the square of the longest side of the triangle is equal to the sum of the square of other two sides. Thus,

For a triangle to be right angle triangle,

$c^2=a^2+b^2$

By this law it is observed that,

For a triangle to be acute angle triangle,

$c^2<(a^2+b^2)$

For a triangle to be obtuse angle triangle,

$c^2>(a^2+b^2)$

The sides of the given triangle are 3.8 cm ,3.7 cm, and 5 cm.

Here the longest side is 5 cm. Thus check the type of triangle using above formula. Longest side,

$c^2=5^2\nc^2=25$

Other two sides,

$a^2+b^2=3.8^2+3.7^2\na^2+b^2=14.44+13.69\na^2+b^2=28.13$

Therefore,

$25<28.13\n$

Hence the triangle formed by the sides 3.8 cm ,3.7 cm, and 5 cm is acute angle triangle.

Learn more about the type of triangle here;

brainly.com/question/2644832

It is a scalene triangle because none of the sides are the same!

In 2006, there were 2,573 computer viruses and other security incident. During the next 7 years, the number of incidents increased by about 92% each year.

Answers

Answer:

Total number of virus after 7yrs= 247484.7 virus

Step-by-step explanation:

Total number of virus after 7yrs = 2573(1+0.92)⁷ = 247484.7 virus

(–2, –3) is the image produced by applying the composition T -2.4 rx to a point. What are the coordinates of the preimage?A.
(0, –1)
B.
(0, 1)
C.
(3, 4)
D.
(0, 7)

Answers

Answer:

D. (0,7)

Step-by-step explanation:

We are given that,

The point (-2,-3) is transformed by the composition $T_(-2,-4)\circ R_(x)$ .

That is, the point is first reflected across x-axis and then translated 2 units to the left and 4 units up.

So, the rule for the transformation is (x,y) → (x,-y) → (x+2,-y+4)

Thus, the image of (-2,-3) is given by,

(-2,-3) → (-2,3) → (-2+2,3+4) = (0,7)

That is, the image of (-2,-3) after transformation is (0,7).

So, option D is correct.

One positive number exceeds 4 times another positive number by 3. The product of the two numbers is 351. What are the two numbers? A) 6 and 9
B) 6 and 24
C) 9 and 39
D) 25 and 29

Answers

Hello,
Answer C 9 and 39.

Let a the first and b the second
a=4b+3
a*b=351

==>b*(4b+3)=351
==>4b²+3b-351=0
Δ=9+4*4*351=5625=75²
==>b=(-3-75)/8 =-9.75 ==>a=4*(-9.75)+3=-36 (excluded) a>0
or b=(-3+75)/8=9 and a=4*9+3=39

How to solve a mixed fraction?

Answers

To solve a mixed fraction you will have to multiply the mixed number by the denominator then add the numerator for example:
7 3/4 you are gonna go 7x4=28 then you are gonna take that 28 and add 3 to it so it would be 31. I hope that helped some c:

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