Answer:
b = 252 in
Step-by-step explanation:
cos theta = adjacent side over hypotenuse
cos 38 = b/ 320
Multiply each side by 320
320 cos 38= b/320 * 320
320 cos 38 = b
252.1634412 =b
To the nearest whole number
252 =b
Answer:
f(x) > 0 over the interval ![(-\infty,-4)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C-4%29)
Step-by-step explanation:
If f(x) is a continuous function, and that all the critical points of behavior change are described by the given information, then we can say that the function crossed the x axis to reach a minimum value of -12 at the point x=-2.5, then as x increases it ascends to a maximum value of -3 for x = 0 (which is also its y-axis crossing) and therefore probably a local maximum.
Then the function was above the x axis (larger than zero) from
, until it crossed the x axis (becoming then negative) at the point x = -4. So the function was positive (larger than zero) in such interval.
There is no such type of unique assertion regarding the positive or negative value of the function when one extends the interval from
to -3, since between the values -4 and -3 the function adopts negative values.
This is probably related to the increased availability of calves providing a greater opportunity for learning, and the adaptation of a more predatory behavior by some grizzly bears in Yellowstone.
Hope this helps :)
<span>x = 18 and the length of each side of the triangle is 29.
This is a matter of reading the descriptions and converting to mathematical notation.
"QRS is an equilateral triangle"
We now know that all three sides of the triangle have the same length.
"If QR is seven less than twice x". So we can write
QR = 2x - 7
"RS is 61 less than 5 times x". So we can write
RS = 5x - 61
"QS is 11 more than x". And we can write
QS = x + 11
And because we already know that they all have the same length, then we can set those equations equal to each other. Let's just pick 2 of them. Will use the length of QR and QS because they look the simplest and then will solve for x.
QR = 2x - 7
RS = 5x - 61
QS = x + 11
2x - 7 = x + 11
x - 7 = 11
x = 18
So we now know that x = 18. Let's check to make sure all three equations have the same value.
QR = 2x - 7 = 2*18 - 7 = 36 - 7 = 29
RS = 5x - 61 = 5*18 - 61 = 90 - 61 = 29
QS = x + 11 = 18 + 11 = 29
And they all are equal, so 18 is the correct value for x.</span>