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1 year ago

What is the slope of a line perpendicular to the line whose equation is 5x - y = -7.

1 answer:

3 0

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

$5x-y=-7\implies 5x-y+7=0 \\\\\\ \stackrel{\stackrel{m}{\downarrow }}{5} x+7=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so a line perpendicular to that one above will have a slope of

$\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{5\implies \cfrac{5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{5}}}$

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I need some help with this calculus 1 implicit diffrention problem?

katen-ka-za [31]

Answer:

y" = -24 / y³

Step-by-step explanation:

6x² + y² = 4

Take the derivative of both sides with respect to x.

12x + 2y y' = 0

Again, take the derivative of both sides with respect to x.

12 + 2y y" + y' (2y') = 0

12 + 2y y" + 2(y')² = 0

Solve for y' in the first equation.

2y y' = -12x

y' = -6x/y

Substitute and solve for y":

12 + 2y y" + 2(-6x/y)² = 0

12 + 2y y" + 2(36x²/y²) = 0

12 + 2y y" + 72x²/y² = 0

6y² + y³ y" + 36x² = 0

y³ y" = -36x² − 6y²

y" = (-36x² − 6y²) / y³

Solve for y² in the original equation and substitute:

y² = 4 − 6x²

y" = (-36x² − 6(4 − 6x²)) / y³

y" = (-36x² − 24 + 36x²) / y³

y" = -24 / y³

7 0

2 years ago

The mean income per person in the United States is $44,500, and the distribution of incomes follows a normal distribution. A ran

Artist 52 [7]

Answer:

We conclude that the residents of Wilmington, Delaware, have higher income than the national average

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $44,500

Sample mean, $\bar{x}$ = $52,500

Sample size, n = 16

Alpha, α = 0.05

Sample standard deviation, s = $9,500

a) First, we design the null and the alternate hypothesis

$H_{0}: \mu = 44,500\text{ dollars}\\H_A: \mu > 44,500\text{ dollars}$

We use one-tailed(right) t test to perform this hypothesis.

c) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{52500 - 44500}{\frac{9500}{\sqrt{16}} } = 3.37$

b) Rejection rule

If the calculated t-statistic is greater than the t-critical value, we fail to accept the null hypothesis and reject it.

Now,

$t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis. We conclude that the residents of Wilmington, Delaware, have higher income than the national average

5 0

2 years ago

What is the number whose 4/5 is 144?

anyanavicka [17]

Answer:

180

Step-by-step explanation:

Multiply 144 by the reciprocal of $\frac{4}{5}$ , that is

The reciprocal of $\frac{4}{5}$ is $\frac{1}{\frac{4}{5} }$ = $\frac{5}{4}$ , then

$\frac{5}{4}$ × 144 = $\frac{5(144)}{4}$ = 180

3 0

2 years ago

In the figure, angle D measures 45° and angle E measures 87°. What is the measurement of angle H?

scZoUnD [109]

Hat means y + z = 180.

y is thrice than z means y = 3 * z. 

replace y with 3 * z in the equation of y + z = 180 to get 3 * z + z = 180. 

combine like terms to get 4 * z = 180. 

solve for z to get z = 180 / 4 = 45 degrees. 

since y = 3 * z, then y = 3 * 45 = 135 degrees. 

y = 135
z = 45 

y + z = 180 becomes 135 + 45 = 180
y = 3 * z = 135 = 3 *45 

solution is confirmed to be good.

3 0

2 years ago

Read 2 more answers

Svana wants to solve the equation x - 1.0675 = 3x - 4145.

AysviL [449]

Answer: D

Step-by-step explanation:

Given that Svana wants to solve the equation 1/2x - 1.0675 = 3x - 4145.

This equation is a system of equations which can be solved by using simultaneous equation methods.

But if she uses a graphing program to graph the equations y = 1/2x - 1.0675 and y = 3x - 4.145

The solution of 1/2x - 1.0675 = 3x - 4.145. Will be the point of intersection of the two equation.

Trace the point of intersection to the x - axis and also to the y - axis.

The solution to the system of equations is ( 1.231, - 0.452 )

3 0

2 years ago

Read 2 more answers