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3 years ago

A yellow ball, a red ball, a white ball and a

Mathematics

1 answer:

OleMash [197]3 years ago

4 0

Answer:

1/4 chance (this is equal to 25% as a percentage or 0.25 as a decimal)

Step-by-step explanation:

There are 4 balls and only one can be first. As there is only 1 yellow ball, there is 1/4 chance that the yellow ball is picked first.

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At what point on the paraboloid y = x2 + z2 is the tangent plane parallel to the plane 3x + 2y + 7z = 2? (if an answer does not

Nikitich [7]

If $f(x, y, z) = c$ represent a family of surfaces for different values of the constant $c$ . The gradient of the function $f$ defined as $\nabla f$ is a vector normal to the surface $f(x, y, z) = c$ .

Given the paraboloid

$y = x^2 + z^2$ .

We can rewrite it as a scalar value function f as follows:

$f(x,y,z)=x^2-y+z^2=0$

The normal to the paraboloid at any point is given by:

$\nabla f= i\frac{\partial}{\partial x}(x^2-y+z^2) - j\frac{\partial}{\partial y}(x^2-y+z^2) + k\frac{\partial}{\partial z}(x^2-y+z^2) \\ \\ =2xi-j+2zk$

Also, the normal to the given plane $3x + 2y + 7z = 2$ is given by:

$3i+2j+7k$

Equating the two normal vectors, we have:

$2x=3\Rightarrow x= \frac{3}{2} \\ \\ -1=2 \\ \\ 2z=7\Rightarrow z= \frac{7}{2}$

Since, -1 = 2 is not possible, therefore there exist no such point on the paraboloid $y = x^2 + z^2$ such that the tangent plane is parallel to the plane 3x + 2y + 7z = 2.

4 0

4 years ago

Given: AB≅ BC and AK ≅ KC, ∠AKE ≅ ∠CKP, Prove: ∆AKE ≅ ∆CKP PLEASE HELP!!!!!!!!!!!!!

timofeeve [1]

Answer:

Step-by-step explanation:

Given:

AB ≅ BC

AK ≅ KC

∠AKE ≅ ∠CKP

To Prove:

ΔAKE ≅ ΔCKP

Statements Reasons

1). AB ≅ BC 1). Given

2). ∠BAC ≅ ∠BCA 2). Property of Isosceles triangles

3). ∠EKA ≅ ∠PKC 3). Given

4). ΔAKE ≅ ΔCKP 4). ASA Postulate of congruence

Hence ΔAKE ≅ ΔCKP.

3 0

3 years ago

Kevin sold a box of 28 books at a yard sale for a total of $54.64. He sold the paperback books for $1.68 each and sold the hardc

vivado [14]

Answer:

x + y = 28

1.68x + 2.44y = 54.64

Step-by-step explanation:

Let x = paperback books and y = hardback books

x+y =28

We know that paperbacks cost 1.68 and hardback cost 2.44

1.68x + 2.44y = 54.64

We have 2 equations and 2 unknowns

x+y =28

1.68x + 2.44y = 54.64

8 0

3 years ago

Lisa took a survey of her classmates' favorite sport and recorded their genders. The results are in the table below:

Igoryamba

Answer:

0.43

Step-by-step explanation:

8 0

3 years ago

If h(x) is the inverse of f(x), what is the value of h(f(x))? оо 0 1 ООО o f(x)

mart [117]

Answer:

Step-by-step explanation:

If h(x) is the inverse of f(x) them h(f(x)) = x.

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4 years ago