Answer:
The value of t is 1.75 years.
Step-by-step explanation:
Given that simple interest formula is I = (P×R×T)/100. So you have to substitute the following values into the formula :
Carey solves the equation 4(2x-1)+5=3+2(x+1) by applying the distributive property on both sides of the equation. The result is
2 answers:
Carey should combine 8x with 2x and all other terms as one term by applying distributive property
<u>Solution: </u>
Given that,
Carey solves the equation 4(2x – 1) + 5 = 3 + 2(x + 1) by applying the distributive property on both sides of the equation.
The result is 8x – 4 + 5 = 3 + 2x + 2.
Now, Carey then wants to combine like terms.
We have to find which are the terms Carey should combine?
If we observe clearly then there are two different types of terms, one with variables and others are numerical
Now let us make the like terms one side of “=”
Then, 8x – 2x = 3 + 2 + 4 – 5 ⇒ 6x = 4 ⇒ x =
Hence, carey should combine 8x with 2x and all other terms as one term
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Answer:
Take a look of the image below, we can think on this problem as a problem of two triangle rectangles.
We can see that both triangles share the adjacent cathetus, then the height of the flagpole is just the difference between the opposite cathetus.
Remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus)
So, if we define H as the height of the cliff
X as the distance between the observer and the cliff
and h as the height of the flagopole
we can write:
tan(40°) = H/X
tan(45°) = (H + h)/X
Notice that we have two equations and 3 variables (we should have the same number of equations than variables) then here is missing information, and we can't get an exact solution for the height of the flagpole.
But we can write it in terms of the height of the cliff H, or in terms of the distance between the observer and the cliff.
We want to find the value of h.
If we take the quotient between both equations, we get:
Tan(45°)/Tan(40°) = (H + h)/H
1.192 = (H + h)/H
1.192*H = H + h
1.192*H - H = h
0.192*H = h
So the height of the flagpole is 0.192 times the height of the cliff.
Answer:
0.015 radians per second.
Step-by-step explanation:
They tell us that at the moment the speed would be 6 ft / s, that is, dx / dt = 6 and those who ask us is dθ / dt.
Which we can calculate in the following way:
θ = arc sin 100/200 = pi / 6
Then we have the following equation of the attached image:
x / 100 = cot θ
we derive and we are left:
(1/100) * dx / dt = - (csc ^ 2) * θ * dθ / dt
dθ / dt = 0.01 * dx / dt / (- csc ^ 2 θ)
dθ / dt = 0.01 * 6 / (- csc ^ 2 pi / 6)
dθ / dt = 0.06 / (-2) ^ 2
dθ / dt = -0.015
So there is a decreasing at 0.015 radians per second.
