Please help with numbers 2-5. thank you

Two water tanks release water at the same time. • Water tank A holds 6,000 gallons of water and water is released from this tank

Ksenya-84 [330]

Answer:

Step-by-step explanation:

its A

7 0

3 years ago

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A ladder is resting against a wall. The ladder and the ground make an angle of 45° and the ladder is 7 ft from the wall. How lon

vichka [17]

The ladder is 10 ft long (9.899 ft to be more precise).

6 0

3 years ago

The point A, with coordinates (0,a,b) lies on the line l1, which has equation:

Luda [366]

a) The solution of the system is: (λ, a, b) = (- 5, - 11, - 26).

b) The coordinates of the point P are (x, y, z) = (- 16 / 3, - 43, 152 / 3).

c) Vectors AP and PB are collinear for their ends lie on the line. The ratio AP : PB is 83.248 : 73.491 (1.133 : 1).

<h3>How to analyze a line equation in vector form</h3>

a) In this problem we have a equation of the line in vector form, whose form is:

r = (5, 19, - 1) + λ · (1, 6, - 5)

Now we find the value of λ for the case r = (0, a, b):

(0, a, b) = (5, 19, - 1) + λ · (1, 6, - 5)

5 + λ = 0

19 + 6 · λ = a

- 1 + 5 · λ = b

The solution of the system is: (λ, a, b) = (- 5, - 11, - 26).

b) Then, the following condition must be fulfilled:

OP • PB = 0

(5 + λ, 19 + 6 · λ, - 1 + 5 · λ) • [(4, 13, 4) - (5 + λ, 19 + 6 · λ, - 1 - 5 · λ)] = 0

(5 + λ, 19 + 6 · λ, - 1 + 5 · λ) • (- 1 - λ, - 6 - 6 · λ, 5 + 5 · λ) = 0

(5 + λ) · (- 1 - λ) + (19 + 6 · λ) · (- 6 - 6 · λ) + (- 1 + 5 · λ) · (5 + 5 · λ) = 0

- (5 + λ) · (1 + λ) - 6 · (19 + 6 · λ) · (1 + λ) + 5 · (- 1 + 5 · λ) · (1 + λ) = 0

- (5 + 6 · λ + λ²) - 6 · (19 + 25 · λ + 6 · λ²) + 5 · (- 1 + 4 · λ + 5 · λ²) = 0

- 5 - 6 · λ - λ² - 114 - 150 · λ - 36 · λ² - 5 + 20 · λ + 25 · λ² = 0

- 12 · λ² - 136 · λ - 124 = 0

There are two solutions: λ₁ = - 1, λ₂ = - 31 / 3, whose points P are:

r₁ = (5, 19, - 1) + (- 1) · (1, 6, - 5)

r₁ = (4, 13, 4)

r₂ = (5, 19, - 1) + (- 31 / 3) · (1, 6, - 5)

r₂ = (- 16 / 3, - 43, 152 / 3)

Then, the coordinates of the point P are (x, y, z) = (- 16 / 3, - 43, 152 / 3).

c) Vectors AP and PB are collinear for their ends lie on the line. The ratio can be found by using the magnitudes of each vector:

Vector AP

AP = (- 16 / 3, - 43, 152 / 3) - (0, - 11, - 26)

AP = (- 16 / 3, - 32, 230 / 3)

AP = √(AP • AP)

AP ≈ 83.248

Vector PB

PB = (4, 13, 4) - (- 16 / 3, - 43, 152 / 3)

PB = (28 / 3, 56, - 140 / 3)

PB = √(PB • PB)

PB ≈ 73.491

The ratio AP : PB is 83.248 : 73.491 (1.133 : 1).

To learn more on lines: brainly.com/question/17188072

#SPJ1

8 0

2 years ago

Find the measures of angle AOC and angle COB in the graph

OleMash [197]

The line perfectly cuts the 90 degree angle in half, as shown by the proportional x and y movement. Meaning that the angles are both 45 degrees

5 0

4 years ago

Which shows the following expression after the negative exponents have been eliminated? m^7 n^3/ mn^-1 assume m=0 and n=0

aliina [53]

Given expression is $\frac{m^7n^3}{mn^{-1}}$ .

where $m \neq 0, n \neq 0,$

Now we have to simplify this and find the next step so that negative exponent gets eliminated.

We know that when negative exponent changes sign, then it moves from numerator to denominator or from denominator to numerator as shown in the formula:

$x^{-m}=\frac{1}{x^m}$

or $\frac{1}{x^{-m}}=x^{m}$

n has negative exponent in denominator so it will move to numerator and we get:

$\frac{m^7n^3n^1}{m}$

or $\frac{m^7n^3n}{m}$

Hence final answer is $\frac{m^7n^3n}{m}$ .

8 0

3 years ago

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