Answer:
- 575.6 N at 40°
- 451.7 N at 55°
Step-by-step explanation:
Angles are measured from the direction of motion, so the "force made good" is the force in the rope multiplied by the cosine of the angle. If the forces in the ropes (in Newtons) are represented by x and y, then we have ...
x·cos(40°) +y·cos(55°) = 700
In order for the resultant to be in the direction of motion, the forces perpendicular to the direction of motion must cancel.
x·sin(40°) - y·sin(55°) = 0
Here, we have assumed that the positive direction for measuring 40° is the negative direction for measuring 55°. That is, the angles are measured in opposite directions from the direction of motion.
Any of the usual methods for solving systems of linear equations can be used to solve this set. My preference is to use a graphing calculator. It gives the answers summarized above.
Answer:
5hrs & 30mins
Step-by-step explanation:
In scientific notation, a number is usually?.?*10^??
for example:
1.3*10^-2
To write it in standard notation you can simply multiply it out
for example:
0.013
So you must be reflecting over the y=x line so your quadrates would be (4,-2) (5,-4) (3,-9)
Step-by-step explanation:
We assume that the advertising rates in this journal for full-page ads is x ($/ad); the rate for half-page ads is y ($/ad).
The revenue for 3 full page ads are: 3x ($)
The revenue for 5 half page ads are: 5y ($)
One issue of a journal has 3 full-page ads and 5 half-page ads, generating $6340.
=> The total revenue for 3 full page and 5 half page ads are $6340
=> 3x + 5y = 6340
The revenue for 4 full page ads are: 4x ($)
The revenue for 4 half page ads are: 4y ($)
One issue of a journal has 4 full-page ads and 4 half-page ads, generating $6625.
=> The total revenue for 4 full page and 4 half page ads are $6625
=> 4x + 4y = 6625 (1)
We have:
+) 3x + 5y = 6340
=> 5y = 6340 - 3x
=> y = (6340 - 3x)/5 = 1268 - 0.6x
Replace <em>y = 1268 - 0.6x </em>into (1), we have:
4x + 4y = 6625
⇔4x + 4(1268 - 0.6x) = 6625
⇔ 4x + 5072 - 2.4x = 6625
⇔ 1.6x = 1553
⇔ x = 1553/1.6 = 970.625
=> y = 1268 - 0.6x = 1268 - 0.6*970.625= 1268 - 582.375 = 685.625
So the advertising rate for full page ads is $970.625, for half-page ads is $685.625
