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svet-max [94.6K]
3 years ago
12

(28 POINTS)

Mathematics
1 answer:
cestrela7 [59]3 years ago
3 0

Answer:

(a) -\sqrt{10}y

(b) -\sqrt{3}y

Step-by-step explanation:

(a) \sqrt{10y^{2}} can also be written as \sqrt{10} x \sqrt{y^{2}}

the \sqrt{y^{2}} = ± y

Therefore :

\sqrt{10y^{2}} = ±\sqrt{10}y

since it was given that y < 0 , then the factor will be -\sqrt{10}y

(b) \sqrt{3y^{2}} can also be written as : \sqrt{3} x \sqrt{y^{2}}

Therefore , one of the factor is -\sqrt{3}y

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Use The Divergence Theorem To Calculate The Surface Integral and Sis a sphere centered at the origin with a radius of 2. Confirm
marin [14]

Answer: hi your question is incomplete below is the complete question

Use the Divergence Theorem to calculate the surface integral S F dS   with F x y z = , , and S is a sphere centered at the origin with a radius of 2. Confirm your answer by computing the surface integral

answer : surface integral = 384/5 π

Step-by-step explanation:

Representing  the vector field as

F ( x, y , z ) = ( a^3 + y^3 ) + ( y^3 + z^3 ) + ( Z^3 + x^3 ) k

assuming the sphere ( s) with radius = 2 be centered at Origin of the vector field.

Hence the divergence will be represented as :

Attached below is the detailed solution

6 0
3 years ago
What equality is shown above
Bogdan [553]

Answer: If you see this line solid its > or equal too this > with line underneath

If you see line broken it's only >

Y>_ - 1/4x+2

Step-by-step explanation:

Starts at 2 on y then next pt go down 1 and 4 to the right

6 0
3 years ago
Suppose the weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams. The weights
user100 [1]

Answer:

a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b) The weight that 80% of the apples exceed is of 78.28g.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.

This means that \mu = 85, \sigma = 8

a. Find the probability a randomly chosen apple exceeds 100 g in weight.

This is 1 subtracted by the p-value of Z when X = 100. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{100 - 85}{8}

Z = 1.875

Z = 1.875 has a p-value of 0.9697

1 - 0.9696 = 0.0304

0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b. What weight do 80% of the apples exceed?

This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.

Z = \frac{X - \mu}{\sigma}

-0.84 = \frac{X- 85}{8}

X - 85 = -0.84*8

X = 78.28

The weight that 80% of the apples exceed is of 78.28g.

5 0
2 years ago
Which is the range of the function f(x) = (9)×?
Anna [14]

Using it's concept, it is found that the range of the function f(x) = 9^x is given by:

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<h3>What is the range of a function?</h3>

It is the set that contains all possible output values for the function.

In this problem, the function is:

f(x) = 9^x

For <u>exponential functions without vertical shifts</u>, as is the case in this problem, the range is given by:

all real numbers greater than 0.

More can be learned about the range of a function at brainly.com/question/10891721

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4 0
2 years ago
What is the square root of 100?
natulia [17]

Answer:

10

Step-by-step explanation:

the answer is 10 because 100 divided by 10 is 10

Please mark Brainliest

3 0
2 years ago
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