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3 years ago

Differentiate the function. f(x) = ln(25 sin^2(x))

1 answer:

8 0

Use the chain rule.
Let u = 25sin²(x), such that dy/dx = dy/du · du/dx

$\frac{dy}{dx} = \frac{1}{25sin^{2}(x)} \cdot 50cos(x) \cdot sin(x)$
$\frac{dy}{dx} = \frac{2cos(x) sin(x)}{sin^{2}(x)}$

$\frac{dy}{dx} = 2cot(x)$

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A number is called evil if it has 666 in it. How many 7 digit numbers are evil?

defon

Step-by-step explanation:

There are 5 different positions of 666:

666////

/666///

//666//

///666/

////666

The forward dashes represent any number from 0 to 9.

Case 1: "666////"

Number of ways = 10⁴ = 10,000.

Case 2: The other positions.

Since the 1st forward dash cannot be 0 (leading digit),

Number of ways for each position = 9 * 10³ = 9,000

Number of ways for all 4 positions = 9,000 * 4 = 36,000.

Total evil numbers = 10,000 + 36,000 = 46,000.

5 0

3 years ago

lan has a flower pot in the shape of a rectangular prism . The base of the flower pot is 36 square inches . The flower he's plan

JulijaS [17]

Answer:

108

Step-by-step explanation:

volume = area of the base * height
Area of the base = 36 square inches .
The height = 3 inches
36 * 3 = 108

4 0

4 years ago

87 POINTS PLZ HELP Aman is adding –17 + 9. He wants to write –17 as the sum of two numbers so that one of the numbers, when adde

Pie

Consider number 17. You know that

17=9+8.

Then for negative numbers you have the same rule (with respect to sign -):

-17=(-9)+(-8).

Since (-9)+9=9+(-9)=9-9=0, you have that

-17+9=(-9)+(-8)+9=(-9+9)+(-8)=0+(-8)=-8.

Answer: -17=(-9)+(-8).

5 0

3 years ago

What theorem can be used to prove that the two triangles are congruent?

choli [55]

The answer is D)
SSS

6 0

3 years ago

All vectors are in Rn. Check the true statements below:

Oduvanchick [21]

Answer:

A), B) and D) are true

Step-by-step explanation:

A) We can prove it as follows:

$Proy_{cv}y=\frac{(y\cdot cv)}{||cv||^2}cv=\frac{c(y\cdot v)}{c^2||v||^2}cv=\frac{(y\cdot v)}{||v||^2}v=Proy_{v}y$

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that $||Ax||=\sqrt{(A_1 x)^2+\cdots (A_n x)^2}$ . Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then $||Ax||=\sqrt{(x_1)^2+\cdots (x_n)^2}=||x||$ .

C) Consider $S=\{(0,2),(2,0)\}\subseteq \mathbb{R}^2$ . This set is orthogonal because $(0,2)\cdot(2,0)=0(2)+2(0)=0$ , but S is not orthonormal because the norm of (0,2) is 2≠1.

D) Let A be an orthogonal matrix in $\mathbb{R}^n$ . Then the columns of A form an orthonormal set. We have that $A^{-1}=A^t$ . To see this, note than the component $b_{ij}$ of the product $A^t A$ is the dot product of the i-th row of $A^t$ and the jth row of $A$ . But the i-th row of $A^t$ is equal to the i-th column of $A$ . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then $A^t A=I$

E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.

In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set $\{u_1,u_2\cdots u_p\}$ and suppose that there are coefficients a_i such that $a_1u_1+a_2u_2\cdots a_nu_n=0$ . For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then $a_i||u_i||=0$ then $a_i=0$ .

5 0

3 years ago