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3 days ago

T varies inversely as the square root of u.t = 3 when u = 4.Find t when u = 49.

1 answer:

6 0

t = $\frac{6}{7}$ Step-by-step explanation: Since t varies inversely with the square root of u, the equation that represents them is

t = $\frac{k}{\sqrt{u} }$ ← k represents the constant of variation. To determine k, apply the condition t = 3 when u = 4, thus

k = t $\sqrt{u}$ = 3 × $\sqrt{4}$ = 3 × 2 = 6

t = $\frac{6}{\sqrt{u} }$ ← equation of variation. When u = 49, then

t = $\frac{6}{\sqrt{49} }$ = $\frac{6}{7}$

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22.Island A is 160 miles from island B. A ship captain travels 170 miles from island A and then finds that he is off course and

babunello [8402]

We can summarize that

By applying the law of cosines:

c² = a² + b² - 2abcos(C)

where:

a,b, and c represent the triangle's sides and C denotes the angle opposing side c.

Let us assign:

a=170 miles

b=200 miles

c=160 miles

Thus, we establish:

160² = 170² + 200² - 2(170)(200)cos(C).

We now aim to solve for C.

25,600 = 28,900 + 40,000 - 68,000cos(C).

25,600 - 28,900 - 40,000 = -68,000cos(C).

-43,300=-68,000cos(C).

Thus, cos(C)=0.6367.

C=arc cos(0.6367)--------> C=50.45°.

Consequently, the captain should adjust toward island B by

180 - 50.45 = 129.55 degrees.

The final answer is

129.55 degrees

6 0

28 days ago

−7x−50≤−1 AND−6x+70>−2

PIT_PIT [9101]

Answer:

$-7\geq x$ and $[-7,12)$ expressed in interval notation.

Step-by-step explanation:

A compound inequality $-7x-50\leq -1\text{ and }-6x+70>-2$ has been provided. Our task is to determine the solution for this inequality.

Initially, we will address each inequality independently, followed by merging the findings by combining the overlapping intervals.

$-7x-50\leq -1$

$-7x-50+50\leq -1+50$

$-7x\leq 49$

By dividing with a negative number, it is necessary to reverse the inequality sign:

$\frac{-7x}{-7}\geq \frac{49}{-7}$

$x\geq -7$

$-6x+70>-2$

$-6x+70-70>-2-70$

$-6x>-72$

Again, dividing by a negative requires flipping the inequality sign:

$\frac{-6x}{-6}$

$x$

In combining both intervals, we will arrive at:

$-7\geq x$

Thus, the solution for the inequality provided is $-7\geq x$ and $[-7,12)$ in interval notation.

7 0

1 month ago

Triangle MRN is created when an equilateral triangle is folded in half. Triangle N R M is shown. Angle N R M is a right angle. A

Inessa [8989]

Answer:

El valor de x es 4.

Explicación paso a paso:

Se indica que el triángulo MRN surge al doblar un triángulo equilátero por la mitad.

Esto sugiere que el triángulo equilátero original es MNO y que NR actúa como bisectriz perpendicular (una línea que divide un segmento en dos partes iguales formando un ángulo recto).

La longitud del lado del triángulo es

NO = NS + SM = 6 + 2 = 8

Dado que un triángulo equilátero tiene todos sus lados iguales y NR es la bisectriz perpendicular, se tiene que

RM = MO/2 = 8/2 = 4

El valor de x es 4.

7 0

27 days ago

Read 2 more answers

During batting practice, two pop flies are hit from the same location, 2 s apart. The paths are modeled by the equations h = -16

Inessa [8989]

Answer:

2.5 seconds after the initial ball was struck.

Step-by-step explanation:

The height equations are:

h = -16t² + 56t

h = -16t² + 156t - 248

At the point where the balls intersect, both heights are alike, therefore:

-16t² + 56t = -16t² + 156t - 248

-16t² + 56t + 16t² - 156t + 248 = 0

- 100t + 248 = 0

248 = 100t

t = 248/100

t = 2.48 ≈ 2.5

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1 month ago

"There are 3 teams of 18 employees working today. Company policy says that we need to have 1 supervisor for every 8 employees on

tester [8808]

They require six supervisors.

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1 month ago

Read 2 more answers

T varies inversely as the square root of u.t = 3 when u = 4.Find t when u = 49.​

T varies inversely as the square root of u.t = 3 when u = 4.Find t when u = 49.