Answer:
6 feet tall.
Step-by-step explanation:
The boy is 4 ft tall, but he casts a 6 ft long shadow. You need to find how long a shadow would be if a person/thing was just 1 ft tall.
To do this, you would need to divide 4 by 4, and 6 by 4 as well.
6/4 is 1.5, or 1 and a half.
If a person (or a thing) is 1 foot tall, the statue will cast 1 and a half feet long shadow.
The statue casts a 9 ft long shadow.
Since we already figured out 1 ft = 1 and 1/2 ft shadow, and since the statue casts a 9 foot long shadow, you need to divide 9 by 1.5.
(You'll get 6.)
This means that the statue is 6 feet tall, and it casts a 9 foot long shadow.
Let the number of History books be x. Then:-
x + x - 59 = 343
2x = 402
x = 201
So there are 201 History books and (201 - 59) = 142 Chemistry books.
Answer:
a. 3/4 inches per minute
b. -1 1/8 inches per minute
c. B is fastest; 1 1/8 is more than 3/4
Step-by-step explanation:
A <em>change</em> is a <em>difference</em>. A <em>rate of change</em> is <em>one difference divided by another</em>, usually the change in y-value divided by the change in x-value.
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<h3>a.</h3>
The change in elevation is the difference between the elevation at the end of the period (6 inches) and the elevation at the beginning of the period (3 inches). The change in time period is the difference between the end time (8 min) and the beginning time (4 min).
change in elevation per minute = (6 -3 inches)/(8 -4 min)
= (3 inches)/(4 min) = 3/4 inches/minute
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<h3>b.</h3>
Similarly, ...
change in elevation per minute = (3 -7 1/2 inches)/(18 -14 min)
= (-4 1/2 inches)/(4 min) = -1 1/8 inches/minute
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<h3>c.</h3>
We know that 3/4 is more than -1 1/8, but when we talk about the "fastest rate of change", we're generally interested in the magnitude--the value without the sign. That means we understand a rate of change of -1 1/8 inches per minute to be "faster" than a rate of change of 3/4 inches per minute.
The rate of change from Part B is fastest. 1 1/8 inches per minute is more than 3/4 inches per minute.
Recall that
d/dx sech(x) = - sech(x) tanh(x)
d/dx tan⁻¹(x) = 1/(1 + x²)
Then by the chain rule,
dy/dx = - sech(x) tanh(x) / (1 + x²)
Answer:
angle a is 116 degrees
Step-by-step explanation:
ok so first we have to make everything equal to 180 because every triangle is 180 degrees so it would be written like this:
(14x + 4) + (5x - 1) + (2x + 9) = 180
Then, we solve for x and x equals 8
After this we plug 8 back into the angle so it would be written like this:
14(8) + 4
This equals 116 degrees.
