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3 years ago

Solve 4 square root of 3 = 8cos

Mathematics

1 answer:

sukhopar [10]3 years ago

4 0

Therefore $\theta = 30^\circ$

Step-by-step explanation:

Given,

$4\sqrt{3 } =8 cos \theta$

$\Leftrightarrow cos \theta =\frac{4\sqrt{3} }{8}$

$\Leftrightarrow cos \theta =\frac{\sqrt{3} }{2}$

$\Leftrightarrow cos \theta =cos 30^\circ$

$\Leftrightarrow \theta = 30^\circ$

Therefore $\theta = 30^\circ$

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3 years ago

Read 2 more answers

A rectangular prism has a length of 12 feet, a width of 6 feet, and a height of 2 feet.

aliina [53]

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3 years ago

A rock is thrown upward from a bridge that is 57 feet above a road. The rock reaches its maximum height above the road 0.76 seco

bekas [8.4K]

answer:

$f(t) = -9.9788169(t -0.76)^2 +57$

Step-by-step explanation:

On this question we see that we are given two points on a certain graph that has a maximum point at 57 feet and in 0.76 seconds after it is thrown, we know can say this point is a turning point of a graph of the rock that is thrown as we are told that the function f determines the rocks height above the road (in feet) in terms of the number of seconds t since the rock was thrown therefore this turning point coordinate can be written as (0.76, 57) as we are told the height represents y and x is represented by time in seconds. We are further given another point on the graph where the height is now 0 feet on the road then at this point its after 3.15 seconds in which the rock is thrown in therefore this coordinate is (3.15,0).

now we know if a rock is thrown it moves in a shape of a parabola which we see this equation is quadratic. Now we will use the turning point equation for a quadratic equation to get a equation for the height which the format is $f(x)= a(x-p)^2 +q$ , where (p,q) is the turning point. now we substitute the turning point

$f(t) = a(t-0.76)^2 + 57$ , now we will substitute the other point on the graph or on the function that we found which is (3.15, 0) then solve for a.

0 = a(3.15 - 0.76)^2 + 57

-57 =a(2.39)^2

-57 = a(5.7121)

-57/5.7121 =a

-9.9788169 = a then we substitute a to get the quadratic equation therefore f is

$f(t) = -9.9788169(t-0.76)^2 +57$

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3 years ago