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3 years ago

The sum of 5 consecutive even numbers is 200 what is the fifth number in this sequence?

1 answer:

7 0

Find the average of the numbers(the middle number) by dividing 200 by 5 to get 40. Since the numbers count by two, we would add four to get the value of the last number: 44.

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Consider the following. f(x, y, z) = x2yz − xyz8, P(6, −1, 1), u = 0, 4 5 , − 3 5 (a) Find the gradient of f. ∇f(x, y, z) = (b)

Darina [25.2K]

Answer:

a) ∇f(x, y, z) = (2xyz − yz⁸, x²z − xz⁸, x²y − 8xyz⁷)

b) ∇f(6, −1, 1) = (-11, 30, 12)

c) Duf(6, −1, 1) = 84/5

Step-by-step explanation:

Given

f(x, y, z) = x²yz − xyz⁸

P(6, −1, 1)

u = (0, 4/5, − 3/5)

a) ∇f(x, y, z) = ?

We apply

fx(x, y, z) = 2xyz − yz⁸

fy(x, y, z) = x²z − xz⁸

fz(x, y, z) = x²y − 8xyz⁷

then

∇f(x, y, z) = (2xyz − yz⁸, x²z − xz⁸, x²y − 8xyz⁷)

b) ∇f(6, −1, 1) = (2*6*(-1)*1 − (-1)(1)⁸, (6)²(1) − (6)(1)⁸, (6)²(-1) − 8(6)(-1)(1)⁷)

⇒ ∇f(6, −1, 1) = (-11, 30, 12)

c) Duf(6, −1, 1) = ∇f(6, −1, 1)*(0, 4/5, − 3/5) = (-11, 30, 12)*(0, 4/5, − 3/5)

⇒ Duf(6, −1, 1) = 0 + 24 - 36/5 = 84/5

5 0

3 years ago

if y varies directly as the square root of x and y=87 when x=625, find y if x =390625. Round off your answer to the nearest hund

natta225 [31]

Answer:

2175

Step-by-step explanation:

y = k sqrt(x)

x = 625

y = 87

87 = k * sqrt(625)

87 = k * 25

87/25 = k

k = 3.48

y = 3.48 * sqrt(390625)

y = 3.48 * 625

y = 2175

6 0

2 years ago

Please help please help please help please help please help please help look at the thingy pls help

attashe74 [19]

Answer:

The slopes of line segments AC and AD are same or constant i.e $\frac{1}{3}$

Step-by-step explanation:

We need to find slopes of AC and AD and tell if they are same or not.

The formula used to calculate slope is: $Slope=\frac{y_2-y_1}{x_2-x_1}$

Finding slope of AC

We have A=(3,2) and C=(0,1)

Finding slope using formula:

We have $x_1=3, y_1=2, x_2=0,y_2=1$

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{1-2}{0-3}\\Slope=\frac{-1}{-3}\\Slope=\frac{1}{3}$

So, Slope of AC is $\frac{1}{3}$

Finding slope of AD

We have A=(3,2) and C=(9,4)

Finding slope using formula:

We have $x_1=3, y_1=2, x_2=9,y_2=4$

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{4-2}{9-3}\\Slope=\frac{2}{6}\\Slope=\frac{1}{3}$

So, Slope of AD is $\frac{1}{3}$

So, the slopes of line segments AC and AD are same or constant i.e $\frac{1}{3}$

3 0

3 years ago

The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches. Men the same

masha68 [24]

Answer: The z-scores for a woman 6 feet tall is 2.96 and the z-scores for a a man 5'10" tall is 0.25.

Step-by-step explanation:

Let x and y area the random variable that represents the heights of women and men.

Given : The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches.

i.e. $\mu_1 = 64$ $\sigma_1=2.7$

Since , $z=\dfrac{x-\mu}{\sigma}$

Then, z-score corresponds to a woman 6 feet tall (i.e. x=72 inches).

[∵ 1 foot = 12 inches , 6 feet = 6(12)=72 inches]

$z=\dfrac{72-64}{2.7}=2.96296296\approx2.96$

Men the same age have mean height 69.3 inches with standard deviation 2.8 inches.

i.e. $\mu_2 = 69.3$ $\sigma_2=2.8$

Then, z-score corresponds to a man 5'10" tall (i.e. y =70 inches).

[∵ 1 foot = 12 inches , 5 feet 10 inches= 5(12)+10=70 inches]

$z=\dfrac{70-69.3}{2.8}=0.25$

∴ The z-scores for a woman 6 feet tall is 2.96 and the z-scores for a a man 5'10" tall is 0.25.

6 0

3 years ago

Plz help. Will give brainliest

Rina8888 [55]

Answer:

1200 / 3 = 400 Calories per Liter

7 0

3 years ago