u = 1+3e<span>-x</span>
so that (Don't forget to use the chain rule on e<span>-x</span>.)
du = 3e<span>-x</span>(-1) dx = -3e<span>-x</span> dx ,
or
(-1/3)du = e<span>-x</span> dx .
However, how can we replace the term e<span>-3x</span> in the original problem ? Note that
.
From the u-substitution
u = 1+3e<span>-x</span> ,
we can "back substitute" with
e<span>-x</span> = (1/3)(u-1) .
Substitute into the original problem, replacing all forms of x, getting
(Recall that (AB)C = AC BC .)
Y=mx+b
x=number of newspapers
37.5 earned for 5 newspapers
37.5=5m+b
earned 75 and deliverd 20 newpapers
75=20m+b
we have
37.5=5m+b and
75=20m+b
multiply first equaiton by -1 and add to other equaiton
-37.5=-5m-b
<u>75=20m+b +</u>
37.5=15m+0b
37.5=15m
divide both sides by 15
2.5=m
sub back to find b
75=2.5(20)+b
75=50+b
minsu 50 both sides
25=b
y=2.5x+25 is lnear funtion
Answer:
See below in bold.
Step-by-step explanation:
A. (x + 7)^2 + (y - 7)^2 = 10.
This is the equation of a circle.
It is NOT a function
One to many correspondence.
B. y = x^2 + 2x - 3
This is a parabola which opens upwards.
It is a function.
For 2 values of x ( except at the vertex) there is one value of y so it is
many to one correspondence.
The common difference of the AP is -2 ⇒ A
Step-by-step explanation:
The formula of the nth term of AP is , where
- a is the first term
- d is the common difference between the consecutive terms
∵ The 8th term of an AP is -17
∴ n = 8 and
- Substitute n by 8 and by -17 in the formula above
∴ -17 = a + (8 - 1)d
- Simplify the right hand side
∴ -17 = a + 7d
∵ The 14th term is -29
∴ n = 14 and
- Substitute n by 14 and by -29 in the formula above
∴ -29 = a + (14 - 1)d
- Simplify the right hand side
∴ -29 = a + 13d
Now we have system of equations
a + 7d = -17 ⇒ (1)
a + 13d = -29 ⇒ (2)
Multiply equation (1) by -1 to eliminate a
-a - 7d = 17 ⇒ (3)
Add equations (2) and (3)
∴ 6d = -12
- Divide both sides by 6
∴ d = -2
The common difference of the AP is -2
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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Given the expression, 8x^2 + 1, the coefficient of the term 8x^2 is 8, while the constant is 1.
Therefore, the correct answer is D) 8.
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