Add 35kg 15g and 17.05kg

MakcuM [25]

9514 1404 393

Answer:

1.3363

Step-by-step explanation:

The basic idea here is to find an expression for the direction vector between a point on L1 and a point on L2. Then, solve for the points on L1 and L2 that make that vector perpendicular to both lines L1 and L2. (The dot product of direction vectors is zero.) The distance between the points found is the shortest distance between the lines.

__

Let P be a point on L1. Then the parametric equation for P is ...

P = (6t, 0, -t) . . . . . . origin + t × direction vector

Let Q be a point on L2. The direction vector for L2 is given by the difference between the given points. It is (4-1, 1-(-1), 6-1) = (3, 2, 5). Then the parametric equation for Q is ...

Q = (3s+1, 2s-1, 5s+1) . . . . (1, -1, 1) + s × direction vector

The direction vector for PQ is ...

Q -P = (3s+1-6t, 2s-1, 5s+1+t)

The dot product of this and the two lines' direction vectors will be zero:

(3s+1-6t, 2s-1, 5s+1+t)·(6, 0, -1) = 0 = 13s -37t +5 . . . perpendicular to L1

(3s+1-6t, 2s-1, 5s+1+t)·(3, 2, 5) = 0 = 38s -13t +6 . . . perpendicular to L2

The solution to these equations is ...

s = -157/1237

t = 112/1237

Then (Q-P) becomes (94, -1551, 564)/1237, and its length is ...

|PQ| = √(94² +1551² +564²)/1237 ≈ 1.3363

The distance between the two lines is about 1.3363 units.

8 0

3 years ago

I need some help with this

masya89 [10]

Answer:

A, C, D

Step-by-step explanation:

Consider triangles NKL and NML. These triangles are right triangles, because

$m\angle K=m\angle M=90^{\circ}$

In these right triangles:

$\overline{NL}\cong \overline {NL}$ - reflexive property;
$\angle KLN\cong \angle MLN$ - given

Thus, triangles NKL and NML by HA postulate. Congruent triangles have congruent corresponding parts, so

$\overline{KN}\cong \overline{NM}\\ \\\overline{KL}\cong \overline{LM}\ [\text{option D is true}]$

Since

$\overline{KN}\cong \overline{NM},$

then

$7x-4=5x+12\\ \\7x-5x=12+4\\ \\2x=16\\ \\x=8\ [\text{option A is true}]\\ \\MN=KN=7\cdot 8-4=56-4=52\ [\text{option C is true}]$

Option B is false, because KN=52 units.

Option E is false, because LN is congruent KN, not LM

4 0

3 years ago

Suppose researchers test 100 college students, whose ages range from 18 to 23. They also test 100 people at a nearby community c

prisoha [69]

Answer:

b. You would conclude that the differences in the average scores can be traced to differences in the working memory of the two groups.

Step-by-step explanation:

Though the average scores of the two sets could have lead to various conditions, but retentive ability deminishes with respect to an increase in age. With respect to the age of the elderly people involved, it is expected that some of them would not be able to retain information for a long period of time. Thus, their average score is 72%.

The college students' are younger, so it is expected that they should be able to retain more information. That ability is one of the reasons why their average score is 85%.

It can be concluded from the research that the differences in the average scores is probably due to the working memory of the two groups.

6 0

3 years ago

Write an inequality that expresses the range in the volume of acceptable tennis balls.

Rudik [331]

Answer:

the smallest number is the lower bound and the largest number is the upper bound, your inequality would be

8.2 ≤ x ≤ 9.5, where x represents the volume of tennis balls.

4 0

3 years ago

Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equat

vlabodo [156]

Answer:

y = 360(1.03)x

Step-by-step explanation:

$F = P x (1 + i)^n$

F is the future worth, P is the present worth, I will be the interest rate, and n is the number of years. $F = ($360)(1.03)^x$

The principal amount of the money = $360

Annual rate of interest = 3%

Thus, the amount after x years which is increased by 3%.

Since, this amount represented by y,

The required equation that represents the amount of money in Josiah’s account, y, after x years is, $= 360(1+\frac{3}{100} )^x\\ = 360(1+0.03 )^x\\ = 360(1.03 )^x$

This amount represented by y,

Therefore, the required equation that represents the amount of money in Josiah’s account, y, after x years is,

$y = 360(1.03 )^x$

Hope this helps you!

Have a nice evening! ;)

5 0

3 years ago

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Add 35kg 15g and 17.05kg​

Add 35kg 15g and 17.05kg