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3 years ago

Find cos(a), if cos(a)^4 - sin(a)^4 = 1/8

Mathematics

1 answer:

Alex17521 [72]3 years ago

5 0

Answer:

3/4, -3/4

Step-by-step explanation:

Using the difference of squares we can change things around.

cos(a)^4 - sin(a)^4

(cos^2(a) + sin^2(a))((cos^2(a) - sin^2(a)) then sin^2 + cos^2 = 1

cos^2(a) - sin^2(a) Using the same identity sin^2 = 1 - cos^2

cos^2(a) - (1 - cos^2(a))

cos^2(a) - 1 + cos^2(a)

2*cos^2(a) - 1

So let's use this.

2*cos^2(a) - 1 = 1/8

2*cos^2(a) = 9/8

cos^2(a) = 9/16

cos(a) = +/- 3/4

so 3/4 can be positive or negative

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10. Given that the total distance travelled is 4 km and that the initial aceleration is 4 m/s², find:a) the value of V.b) the va

andrezito [222]

The initial deceleration is 4 m/s^2, so this means that considering the first line segment, $\frac{V-100}{T}=-4 \implies V=100-4T$ .

The total distance traveled is 4 km, which is equal to 4000 meters. This is equal to the area under the graph, so $400T-\frac{1}{2}(100-V)(5T)=4000$ .

$400(100-4T)-\frac{1}{2}(4T)(5T)=4000\\\\40000-1600T-10T^2=4000\\\\10T^2 +1600T-36000=0\\\\T^2 +160T-3600=0\\\\(T+180)(T-20)=0\\\\T=20 (T > 0)\\\\\therefore V=100-4(20)=20$

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1 year ago

Write a linear equation that passes through the point (2,-9) and has a slope of -5

Anna [14]

Answer:

y = -5x + 1

Step-by-step explanation:

<u>Given:</u>

The slope m = -5 and point (2, -9)

<u>Use point slope form:</u>

y - y₁ = m(x - x₁), where (x₁, y₁) is the given point

<u>So the equation is:</u>

y - (-9) = -5(x - 2)
y + 9 = -5x + 10
y = -5x + 1

3 0

3 years ago

Yes I wanted to know what is the answer

jek_recluse [69]

Answer:

14 flats

5 plants

Step-by-step explanation:

First you would do 89/6 but since that doesn’t divide nicely you can do 90/6 to get 15 then subtract 1 since the original number was 89 and you would get 14

The 14 times 6 would get you 84

Then subtract 84 from 89 and you get 5 plants left over ^^

7 0

2 years ago

Graph the inequality x<1

S_A_V [24]

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7 0

3 years ago

A volume of the cone is (1/3) the volume of a cylinder. The volume of the sphere is what fraction of the volume of the cylinder?

xenn [34]

Answer:

4/3

Step-by-step explanation:

To know this, let's write down the formulas for the volume of cylinder and sphere.

Vs = 4/3πr³ (1)

Vc = π r² h (2)

Now, we do have a little problem here and its the fact that the sphere do not have a height like the cylinder do. But in this case so if you want to have an idea of the fraction of the volume, we will assume that the cylinder has the same height as its radius. Assuming this we have the following:

Vs / Vc = 4πr³ / 3πr²h

Vs/Vc = 4πr³ / 3πr³

From here, we can cancel out the values of π and r³:

Vs/Vc = 4/3

Thus we can conclude that the volume of the sphere is 4/3 the volume of a cylinder.

Hope this helps

8 0

2 years ago