Given f(x) = -3x-1 find x when f(x) = 11

Please help me:) !!!!!!

Naily [24]

Answer:

Please find the solution in the image attached below.

Step-by-step explanation:

Tcos60 -2T sin(90-theta) = 0

Tcos60 = 2T(cos theta)

cos 60 = 2cos theta

cos60 = 2cos theta

1/4 = cos theta

theta = 75.5

So the angle to the vertical = 90-75.5 = 14.5

S

Resolving perpendicular

Tsin60 + 2Tsin75.5 - 2g = 0

T(sin 60 + 2sin75.5) = 2g

T = 19.6/sin 60 + 2sin75.5

T = 19.6/1.936 + 0.866

T = 19.6/2.802 = 7.0N

Hope this helps!

6 0

3 years ago

Ty worked 4 hours and earned $28. At this rate, how much would he earn in 9 hours?

lora16 [44]

Answer:

63

Step-by-step explanation:

Ty worked 4 hours ad earned $28. This means that he earned $7 per hour. So, 7 times 9 is equal to 63. Which means that Ty will earns $63 in 9 hours.

3 0

3 years ago

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A 12 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the

ira [324]

Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.

Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.

Pythagoras theorem, $x^{2} + y^{2} = (12)^{2}$ --->(1)

Given, $\frac{dx}{dt}= 2feet/second$ at x=3

Put x=3 in Pythagoras theorem equation (1)

$(3)^{2} + y^{2} = 144$

$y^{2} = 144 - 9$

$y^{2}$ = 135

y = 11.61

Derive equation (1) w.r.t to 't'

$2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$ ---->(2)

substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall

$2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0$

12 + 23.22 $\frac{dy}{dt}$ = 0

$\frac{dy}{dt}= \frac{-12}{23.22}$

$\frac{dy}{dt} = -0.518$

Hence, using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.

Learn more about Pythagoras theorem here

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5 0

2 years ago

The attention span of children (ages 3 to 5) is claimed to be Normally distributed with a mean of 15 minutes and a standard devi

Agata [3.3K]

Answer:

If the observed sample mean is greater than 17.07 minutes, then we would reject the null hypothesis.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 15 minutes

Sample size, n = 10

Alpha, α = 0.05

Population standard deviation, σ = 4 minutes

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 15\text{ minutes}\\H_A: \mu > 15\text{ minutes}$

Since the population standard deviation is given, we use one-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Now, $z_{critical} \text{ at 0.05 level of significance for one tail} = 1.64$

Thus, we would reject the null hypothesis if the z-statistic is greater than this critical value.

Thus, we can write:

$z_{stat} = \displaystyle\frac{\bar{x} - 15}{\frac{4}{\sqrt{10}} } > 1.64\\\\\bar{x} - 15>1.64\times \frac{4}{\sqrt{10}}\\\bar{x} - 15>2.07\\\bar{x} > 15+2.07\\\bar{x} > 17.07$

Thus, the decision rule would be if the observed sample mean is greater than 17.07 minutes, then we would reject the null hypothesis.

6 0

4 years ago

7x - 20 = 2x - 3(3x + 2)

olga nikolaevna [1]

Answer:

x=1

Step-by-step explanation:

7x - 20 = 2x - 3(3x + 2)

Distribute

7x -20 = 2x -9x -6

Combine like terms

7x-20 =-7x -6

Add 7x to each side

7x+7x-20 =-7x+7x -6

14x -20 = -6

Add 20 to each side

14x-20+20 =-6+20

14x = 14

Divide by 14

14x/14=14/14

x=1

6 0

3 years ago

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