It's actually (-9)... think of it as a hot air balloon, the positivies being balloons and the negatives being sandbags or weights.
You have 7 sandbags/weights and add 9 more sandbags/weights, causing u to go lower, therefore, *negative* 9
Hope that helped! :))
The length of the altitude is 9.5 cm.
The altitude bisects the base of the equilateral triangle (this is because the two sides emerging from the vertex are equal). This gives us a right triangle with leg 5.5 and hypotenuse 11. We use the Pythagorean theorem:
5.5² + h² = 11²
30.25 + h² = 121
Subtract 30.25 from both sides:
30.25 + h² - 30.25 = 121 - 30.25
h² = 90.75
Take the square root of both sides:
√h² = √90.75
h = 9.5
Answer:
maybe
Step-by-step explanation:
Dora is apparently assuming the dimensions are integers. In that case she is correct.
If the dimensions are unconstrained, the perimeter will be largest when a pair of opposite sides will be the smallest measure allowed.
For some perimeter P and side length x, the area is ...
A = x(P/2 -x)
Conversely, the perimeter for a given area is ...
P = 2(A/x +x)
This gets very large when x gets very small, so Dora is correct in saying that the side lengths that are as small as they can be will result in the largest perimeter. We have no way of telling if her assumption of integer side lengths is appropriate. If it is not, her statement makes no sense.
Answer:
DE = about 41.843 (rounded to nearest thousandth)
EF= 34.276 (rounded)
Step-by-step explanation:
For DE, we know that the shorter side (the opposite side) is 24, while the angle across form it is 35°. We can use trigonometry to figure this out. SinФ equals the opposite side (in this case, 24) divided by the hypotenuse. Set sinФ equal to a ratio of the sides like this:
sin(35) = 
x represents the hypotenuse length, which we don't know; 35 is the angle measure. Next, isolate x so that the equation looks like this:
= x
You will need a calculator for the next part. (and make sure you're in degree mode!). evaluate sin(35) and divide 24 by that value. That is DE's length. DE = about 41.843 (rounded to nearest thousandth)
For EF, we can just use Pythagorean theorem now that we know the other sides' values.
EF^2 + 24^2 = DE^2
*a calculator might also be useful for this part.
EF= 34.276 (rounded)
E = 1/2 m v^2
E = 1/2 (0.145) (40)^2
E = 0.0725 x 1600
E = 116 kg m^2/s^2
1 joule = 1 kg m^2/s^2
so here E in joules is 116 joules
so E = 116 joules
