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2 years ago

A model of a volcano has a height of 12 in., and a diameter of 12 in.

Mathematics

2 answers:

solong [7]2 years ago

6 0

Answer:

452.16 cm³

Step-by-step explanation:

I assume the shape of the volcano is a cone.

V = (1/3)πr²h

r = d/2 = 12 in./2 = 6 in.

V = (1/3)(3.14)(6 in.)²(12 in.)

V = 452.16 in.²

Scilla [17]2 years ago

5 0

Answer:

Step-by-step explanation:

Radius r = 6 inches

Height h = 12 inches

volume of cone = πr²h/3 ≈ 3.14∙6²∙12 = 1,356.48 in³

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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 $a_i=0$ .

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3 years ago

The shape below is transformed to another shape.

netineya [11]

Answer:

Option 4 is the image of the given figure.

Step-by-step explanation:

We are given that,

The shape EFGHCD is transformed to form another shape.

From the options, we see that,

Figure 2 and 3 does not have the same vertices as that of the figure.

So, they are discarded.

Since, after transforming a figure, we get a new figure.

So, the vertices cannot have same name as that of the original figure.

So, option 1 is discarded.

Thus, we get,

Option 4 is the image of the given figure after transformation as shown below.

5 0

2 years ago

Read 2 more answers

Which equation is the inverse of y = 2x^2 - 8?

evablogger [386]

Answer: A

Step-by-step explanation:

$y=2x^2-8$

1. Swap x and y.

$x=2y^2-8$

2. Solve for the new y.

Add 8

$x+8=2y^2$

Divide by 2.

$\frac{x+8}{2}=y^2$

Extract the square root.

$\sqrt{\frac{x+8}{2} }=y$

6 0

3 years ago

Please answer right away

Delicious77 [7]

Answer:

independent

Step-by-step explanation:

Since no one else answered, figured you wouldn't mind if I do. :-), and you didn't use any CAPS.

How those two events (even and greater than 9) relate?

independent: YES. Can one happen without the other? Certainly. You see (1,1) is an even number that is not greater than 9. Equally, you see (6,5) which is greater than 9, but is not an even number.

inclusive: No, since there's a least one case where a pair number is not greater than 9. The opposite is also true... at least 1 number > 9 that is not even.

Mutually exclusive: No, since there numbers that are even AND greater than 9 (6,4) for example.

Conditional: No. Does one need the other to happen? Absolutely not.

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2 years ago

Need help asap!! close to running out of time to turn this in!

poizon [28]

You’re answer could be either the first or last one

7 0

2 years ago