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vivado [14]
2 years ago
13

Sheila paid $8.68 for 7 flower plants. How much did she pay for each plant?

Mathematics
1 answer:
Olin [163]2 years ago
8 0

Answer:

$1.24 per plant

Step-by-step explanation:

You just have to divide the total amount paid by the number of flowers.

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Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x. (
True [87]
So it tells us that g(3) = -5 and g'(x) = x^2 + 7.

So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))

now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16 

Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84

So we have our linear approximation for the two. 

If you wanted to, you could check your answer by finding g(x).  Since you know g'(x), take the antiderivative and we will get 
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35

So just to check our linear approximations use that to find g(2.99) and g(3.01)

g(2.99) = -5.1597
g(3.01) = -4.8397

So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer.  Not a bad method if you ever need to use it. 
5 0
3 years ago
Consider the following statement: The square of a prime number is not prime. (a) Write this as an if-then statement, using caref
Hitman42 [59]

The square of a prime number is not prime.

a) let x ∈ R, If x  ∈ {prime numbers}, then x^{2}∉{prime numbers}

there says that if x is a real and x is in the set of the prime numbers, then the square of x isn't in the set of prime numbers.

b) Prove or disprove the statement.

ok, if x is a prime number, then x only can be divided by himself. Now is easy to see that x^{2} = x*x can be divided by himself and x, then x*x is not a prime number, because can be divided by another number different than himself

7 0
3 years ago
Comeplete the equation of the line whose slope is -2 and y-intercept is (0,-8)
Annette [7]

Answer:

y = -2x - 8

Step-by-step explanation:

The formula for a slope line is

y = mx + b

"m" is the slope that's given in the problem, and b is simply the y value of the y-intercept, which is also given.

I hope this helps!

6 0
3 years ago
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In how many different ways can all the letters of the word zookeeper be arranged?
vampirchik [111]
An infinite amount seeing as you can have infinite of each number
6 0
3 years ago
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Using the U- Substitution u=sqrt(2x), integral form 2-8 dx/ sqrt(2x) + 1 is equivalent to ...
AleksAgata [21]
We will use u-substitute:u= \sqrt{2x} , \frac{du}{dx}= \frac{1}{ \sqrt{2x} }= \frac{1}{u}Then for substitution:dx=u du. and integral becomes:\int { \frac{u}{u+1} } \, du = \int { \frac{u+1-1}{u+1} } \, du= \int{1} \, du- \int { \frac{1}{u-1} } \, dx=u-ln(u+1)=\sqrt{2x}-ln( \sqrt{2x}+1). Now we will change the values of limits: \sqrt{16}-ln( \sqrt{16}+1)-( \sqrt{4}-ln( \sqrt{4}+1))=4-ln(5)-2+ln(3)=2+ln(0,6)=2-0.51=1.49

8 0
3 years ago
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