Joy is giving ice cream cones to some children at a carnival. She has 8 chocolate ice cream cones, 10 vanilla ice cream cones, a
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9514 1404 393
Answer:
- 13 ft
- (a) 1 second; (b) t = 0, t = 1/2
Step-by-step explanation:
<h3>1. </h3>Let w represent the length of the wire. Then the height of attachment is (w-1). The Pythagorean theorem tells us a relevant relation is ...
5² +(w -1)² = w²
w² -2w +26 = w² . . . . . . . eliminate parentheses, collect terms
26 = 2w . . . . . . . . . . . . add 2w
13 = w . . . . . . . . . . . . divide by 2
The length of the wire is 13 feet.
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<h3>2. </h3>(a) When h = 0, the equation is ...
0 = -16t^2 +8t +8
Dividing by -8 puts this into standard form:
2t^2 -t -1 = 0
Factoring, we get ...
(2t +1)(t -1) = 0
The positive value of t that makes a factor zero is t = 1.
It will take 1 second for the gymnast to reach the ground.
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(b) When h = 8, the equation is ...
8 = -16t^2 +8t +8
Subtract 8 and divide by 8 to get ...
0 = -2t^2 +t
0 = t(1 -2t) . . . . factor out t
Values of t that make the factors zero are ...
t = 0
t = 1/2
The gymnast will be 8 feet above the ground at the start of the dismount, and 1/2 second later.
ANSWER
The rule is given by the relation,
EXPLANATION
We need to check and see if there is a constant difference between the y-values.
We can see that, there is a constant difference of 2.
This means that the table represents a linear relationship.
Let the rule be of the form,
Then the points in the table should satisfy the above rule.
So let us plug in
This implies that,
Our rule now becomes,
We again plug in another point say, (-1,-1) in to equation (1) to get,
we solve for m now to obtain,
We now substitute back in to equation (1) to get
The rule is given by the relation,
EXPLANATION
We need to check and see if there is a constant difference between the y-values.
We can see that, there is a constant difference of 2.
This means that the table represents a linear relationship.
Let the rule be of the form,
Then the points in the table should satisfy the above rule.
So let us plug in
This implies that,
Our rule now becomes,
We again plug in another point say, (-1,-1) in to equation (1) to get,
we solve for m now to obtain,
We now substitute back in to equation (1) to get