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brilliants [131]
2 years ago
13

F(x) = -2x^5 + x^4 + x^2 -2; find f(-3) and f(4)

Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
8 0

Answer:

f(-3) = 574

f(4) = -1778

Step-by-step explanation:

f(x) = -2x^5 + x^4 + x^2 -2

f(-3) = -2(-3)^5 + (-3)^4 + (-3)^2 -2

\implies f(-3) = -2(-243) + 81 + 9 -2

\implies f(-3) = 486 + 81 + 9 -2

\implies f(-3) = 574

f(4) = -2(4)^5 + (4)^4 + (4)^2 -2

\implies f(4) = -2(1024) + 256 + 16 -2

\implies f(4) = -2048 + 256 + 16 -2

\implies f(4) =-1778

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Eva bought 3 rainbow trout for dinner. They weighed 3 Ib 5 oz, 2 Ib 12 oz, and 3 Ib 8 oz. She cut off the heads and the tails an
Y_Kistochka [10]

The amount of waste is 22 oz

<h3>How to determine the waste amount?</h3>

The weights of the 3 rainbow trouts are:

3 Ib 5 oz, 2 Ib 12 oz, and 3 Ib 8 oz.

The total weight is:

Total = 3 Ib 5 oz + 2 Ib 12 oz + 3 Ib 8 oz

Evaluate the sum

Total = 8 Ib 25 oz

The amount she was left with is 8 Ib 2 oz

Subtract this amount from the total

Waste = 8 Ib 25 oz - 8 Ib 2 oz

Evaluate

Waste = 22 oz

Hence, the amount of waste is 22 oz

Read more about sum and difference at:

brainly.com/question/10739762

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8 0
2 years ago
A line tangent to the curve f(x)=1/(2^2x) at the point (a, f(a)) has a slope of -1. What is the x-intercept of this tangent?
kirza4 [7]

Answer:

x-intercept = 0.956

Step-by-step explanation:

You have the function f(x) given by:

f(x)=\frac{1}{2^{2x}}   (1)

Furthermore you have that at the point (a,f(a)) the tangent line to that point has a slope of -1.

You first derivative the function f(x):

\frac{df}{dx}=\frac{d}{dx}[\frac{1}{2^{2x}}]  (2)

To solve this derivative you use the following derivative formula:

\frac{d}{dx}b^u=b^ulnb\frac{du}{dx}

For the derivative in (2) you have that b=2 and u=2x. You use the last expression in (2) and you obtain:

\frac{d}{dx}[2^{-2x}]=2^{-2x}(ln2)(-2)

You equal the last result to the value of the slope of the tangent line, because the derivative of a function is also its slope.

-2(ln2)2^{-2x}=-1

Next, from the last equation you can calculate the value of "a", by doing x=a. Furhtermore, by applying properties of logarithms you obtain:

-2(ln2)2^{-2a}=-1 \\\\2^{2a}=2(ln2)=1.386\\\\log_22^{2a}=log_2(1.386)\\\\2a=\frac{log(1.386)}{log(2)}\\\\a=0.235

With this value you calculate f(a):

f(a)=\frac{1}{2^{2(0.235)}}=0.721

Next, you use the general equation of line:

y-y_o=m(x-x_o)

for xo = a = 0.235 and yo = f(a) = 0.721:

y-0.721=(-1)(x-0.235)\\\\y=-x+0.956

The last is the equation of the tangent line at the point (a,f(a)).

Finally, to find the x-intercept you equal the function y to zero and calculate x:

0=-x+0.956\\\\x=0.956

hence, the x-intercept of the tangent line is 0.956

5 0
2 years ago
If a Tv screen is 20in wide and 15in high, what is the length?
yuradex [85]
20:15 which reduces to 4:3 or 4/3 or 4 to 3 , hope that helped have a good day
5 0
3 years ago
4 thousands 7 hundreds = 47
motikmotik
If there is 4 thousands and 7 hundreds is 4,700
4 0
2 years ago
Find the value of x pls help
4vir4ik [10]

Answer:

x = 15°

Step-by-step explanation:

First Identify the angle of x by subtracting 180° - 120° = 60°

Always remember when you see a straight line the line measures 180°

So the angle of x = 60° but not the value of x so use the given equation to find the value of x

3x + 15 = 60°

3x  - 15 = -15°

3x = 45

x = 15°

7 0
2 years ago
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