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adoni [48]
3 years ago
10

If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1)

= −3, g '(3) = 2, then find h '(1) if h(x) = f(x) g(x).
See attached

Mathematics
1 answer:
worty [1.4K]3 years ago
7 0
Hello,

h(x)'=(f(x)*g(x))'=f'(x)*g(x)+f(x)*g'(x)
h(1)=f'(1)*g(1)+(f(1)*g'(1)=-4*3+4*(-3)=-24
Answer B

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Find the perimeter. Simplify your answer completely.
Vladimir79 [104]

Answer:119 4/7

Step-by-step explanation:

2/14+6/14+2/14+4/14+1/14+3/14+4/14= 22/14

10+35+10+12+24+15+12=118

118 22/14

119 8/14

119 4/7

5 0
2 years ago
Read 2 more answers
You’re instructed to prepare for a promotional candle sale you will use to test the popularity of the two redesigned candles. Wi
Anuta_ua [19.1K]

Answer:

THE SMALLEST FORMS:

- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3

- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3

- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3

- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3

The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost  per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.

THE BIGGEST FORMS:

- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3

- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3

- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3

- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3

The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is  0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle

The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market,  you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.

If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.

Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:

Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4

The new length is 10-4=6 and the new width is 2+4=6.

Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)

7 0
2 years ago
A population of butterflies grows in such a way that each generation is simply 1.5 times the previous generation. There were 350
kap26 [50]

Answer:

378.5 or just 378

Step-by-step explanation:

This is a linear model with x representing the number of generations that's gone by, y is the number of butterflies after x number of generations has gone by, and the 350 represents the number of butterflies initially (before any time has gone by.  When x = 0, y = 350 so that's the y-intercept of our equation.)

The form for a linear equation is y = mx + b, where m is the rate of change and b is the y-intercept, the initial amount when x = 0.

Our rate of change is 1.5 and the initial amount of butterflies is 350, so filling in the equation we get a model of y = 1.5x + 350.

If we want y when x = 19, plug 19 in for x and solve for y:

y = 1.5(19) + 350

y = 378.5

Since we can't have .5 of a butterfly we will round down to 378

7 0
3 years ago
I need help plsssssssssssssssssssssss
Slav-nsk [51]

Answer:

7x + 34 = 90

-34          -34

7x = 56

Divide by 7 on both sides:

X = 8 degrees

A right angle equals 90 degrees so that must mean angle 7x + 34 must equal to 90 so we solve for x.

A triangle equals = 180 degrees

A quadrilateral equals = 360 degrees

A right angle equals = 90 degrees

A straight line equals = 180 degrees

8 0
3 years ago
Read 2 more answers
Which is true regarding the sequence below?
strojnjashka [21]
What? Add more detail please
7 0
3 years ago
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