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Ierofanga [76]
3 years ago
7

What is the slope of a line perpendicular to the line containing the points (4,-7) and (-5,-1)? Express your answer as a common

fraction.
40 POINTS!!!!!!

if not right i report
Mathematics
1 answer:
just olya [345]3 years ago
6 0

Answer:

3/2

Step-by-step explanation:

Slope 1 = (-1+7)/(-5-4) = 6/(-9) = -2/3

Slope 2 perpendicular to Slope 1 :

-1 ÷ -⅔ = 3/2

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An island is 1 mi due north of its closest point along a straight shoreline. A visitor is staying at a cabin on the shore that i
Elanso [62]

Answer:

The visitor should run approximately 14.96 mile to minimize the time it takes to reach the island

Step-by-step explanation:

From the question, we have;

The distance of the island from the shoreline = 1 mile

The distance the person is staying from the point on the shoreline = 15 mile

The rate at which the visitor runs = 6 mph

The rate at which the visitor swims = 2.5 mph

Let 'x' represent the distance the person runs, we have;

The distance to swim = \sqrt{(15-x)^2+1^2}

The total time, 't', is given as follows;

t = \dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}

The minimum value of 't' is found by differentiating with an online tool, as follows;

\dfrac{dt}{dx}  = \dfrac{d\left(\dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}\right)}{dx} =  \dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} }

At the maximum/minimum point, we have;

\dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} } = 0

Simplifying, with a graphing calculator, we get;

-4.72·x² + 142·x - 1,070 = 0

From which we also get x ≈ 15.04 and x ≈ 0.64956

x ≈ 15.04 mile

Therefore, given that 15.04 mi is 0.04 mi after the point, the distance he should run = 15 mi - 0.04 mi ≈ 14.96 mi

t = \dfrac{14.96}{6} +\dfrac{\sqrt{(15-14.96)^2+1^2}}{2.5} \approx 2..89

Therefore, the distance to run, x ≈ 14.96 mile

6 0
2 years ago
-3x^2 – 24x – 13 = -13
Fudgin [204]
\begin{gathered} -3x^2-24x-13=-13 \\ \text{ Express it as:} \\ 3x^2+24x+26=0 \\ 3x^2+24x=-26 \\ 3(x^2+8x+16)=?-26 \\ 3(x+4)^2=48-26 \\ 3(x+4)^2=22 \end{gathered}

oh,

3 0
1 year ago
What is the scientific notation of 68000
Dmitry [639]
OOHHH!! I like sci not! Okay, so you take the decimal ( which in this case is at the end: 68000. ) and move it over as many times as needed until it gets in between the, in this case, 6 and 8. ( 6.8000 ). You need to show exactly how many times it was actually moved so you multiply that number time 10^ whatever place. In this question, it'll be to the 4th place because you move the decimal over 4 times. The answer will be 6.80 x 10^4 OR -written in short hand- 6.8x10E4 
8 0
3 years ago
Read 2 more answers
Find the particular solution of the differential equation that satisfies the initial condition(s). f ''(x) = x−3/2, f '(4) = 1,
sweet [91]

Answer:

Hence, the particular solution of the differential equation is y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x.

Step-by-step explanation:

This differential equation has separable variable and can be solved by integration. First derivative is now obtained:

f'' = x - \frac{3}{2}

f' = \int {\left(x-\frac{3}{2}\right) } \, dx

f' = \int {x} \, dx -\frac{3}{2}\int \, dx

f' = \frac{1}{2}\cdot x^{2} - \frac{3}{2}\cdot x + C, where C is the integration constant.

The integration constant can be found by using the initial condition for the first derivative (f'(4) = 1):

1 = \frac{1}{2}\cdot 4^{2} - \frac{3}{2}\cdot (4) + C

C = 1 - \frac{1}{2}\cdot 4^{2} + \frac{3}{2}\cdot (4)

C = -1

The first derivative is y' = \frac{1}{2}\cdot x^{2}- \frac{3}{2}\cdot x - 1, and the particular solution is found by integrating one more time and using the initial condition (f(0) = 0):

y = \int {\left(\frac{1}{2}\cdot x^{2}-\frac{3}{2}\cdot x -1  \right)} \, dx

y = \frac{1}{2}\int {x^{2}} \, dx - \frac{3}{2}\int {x} \, dx - \int \, dx

y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x + C

C = 0 - \frac{1}{6}\cdot 0^{3} + \frac{3}{4}\cdot 0^{2} + 0

C = 0

Hence, the particular solution of the differential equation is y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x.

5 0
3 years ago
What percent of 56 is 42?
svetoff [14.1K]

Answer:

nicki monaj is the queen of rap

Step-by-step explanation:

periodt purr

8 0
3 years ago
Read 2 more answers
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