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3 years ago

Identify an equation in point-slope form for the line perpendicular to

Mathematics

1 answer:

LenaWriter [7]3 years ago

3 0

Answer:

A. y - 7 = -4(x + 2)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are.

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A chain has a ribbon tied to it every 2/3 foot. If the chain is 10 2/3 feet long, how many ribbons are tied to the chain??

patriot [66]

Answer:

16 ribbons

Step-by-step explanation:

Given the length of the chain as 10 $\frac{2}{3}$ and there is a ribbon tied to it every $\frac{2}{3}$ , we can take the total length of the chain and divide by the measure of $\frac{2}{3}$ :

$10\frac{2}{3}=\frac{32}{3}$

$\frac{\frac{32}{3}}{\frac{2}{3}}=\frac{32}{3}*\frac{3}{2}=\frac{96}{6}=16$

When dividing with fractions, we use the rule of 'keep/change/flip' to keep the first fractions, change the operation to multiplication and flip the second fraction.

7 0

3 years ago

Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4

arsen [322]

we are given

$R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k$

now, we can find x , y and z components

$x=cos(8t),y=sin(8t),z=8ln(cos(t))$

Arc length calculation:

we can use formula

$L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt$

$x'=-8sin(8t),y=8cos(8t),z=-8tan(t)$

now, we can plug these values

$L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt$

now, we can simplify it

$L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8sec(t) dt$

now, we can solve integral

$\int \:8\sec \left(t\right)dt$

$=8\ln \left|\tan \left(t\right)+\sec \left(t\right)\right|$

now, we can plug bounds

and we get

$=8\ln \left(\sqrt{2}+1\right)-0$

so,

$L=8\ln \left(1+\sqrt{2}\right)$ ..............Answer

5 0

3 years ago

Which number line shows the solutions to n > 3?ヽ(°◇° )ノ

balu736 [363]

It is the first number line :)

3 0

4 years ago

Read 2 more answers

If a hose waters 5/7 of a lawn in 2 hours, how much time will it take to water the entire lawn?

jarptica [38.1K]

Ok well check it out work out how long it took to hose 1/7 the of the lawn which is 2/5 hours. Times that by 7 to get the whole lawn: 7 x 2/5 = 2.8 hours hope that helps

8 0

4 years ago

There are approximately 1.2×10 to the eighth household in the US if the average household uses 400 gallons of water each day wha

lana [24]

Answer:

$Total = 4.8 * 10^{10}$