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GaryK [48]
2 years ago
12

B) Simplify (4ab^2)^3​

Mathematics
1 answer:
Rudiy272 years ago
3 0

Answer:

64a^{3} b^{6}

Step-by-step explanation:

(4ab^2)^3

=> 4^{3} a^{3} b^{6}

=> (4 \times  4 \times 4) a^{3} b^{6}

=> 64a^{3} b^{6}

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Select the correct answer. which hyperbola has both foci lying in the same quadrant? a. b. c. d.
faltersainse [42]

The hyperbola having both foci lying in the same quadrant is <u>(y - 16)²/9² - (x + 1)²/12² = 1</u>, making the <u>4th option</u> a right choice.

For the hyperbola with an equation of the form (x - h)²/a² - (y - k)²/b² = 1, the foci in on the points (h + c, k) and (h - c, k), where c = √(a² + b²).

For the hyperbola with an equation of the form (y - k)²/a² - (x - h)²/b² = 1, the foci in on the points (h, k + c) and (h, k - c), where c = √(a² + b²).

<u>Among the options</u>:

(a) (x - 24)²/24² - (y -1)²/7² = 1.

The equation is of the form (x - h)²/a² - (y - k)²/b².

h = 24, k = 1, a = 24, b = 7.

c = √(a² + b²) = √(24² + 7²) = √(576 + 49) = √625 = 25.

Thus, foci are at the points (h + c, k), (h - c, k) = (24 + 25, 1), (24 - 25, 1) = (49, 1), and (-1, 1), which are in different quadrants.

(b) (y - 12)²/5² - (x - 6)²/12² = 1.

The equation is of the form (y - k)²/a² - (x - h)²/b².

h = 6, k = 12, a = 5, b = 12.

c = √(a² + b²) = √(5² + 12²) = √(25 + 144) = √169 = 13.

Thus, foci are at the points (h, k + c), (h, k - c) = (6, 12 + 13), (6, 12 - 13) = (6, 25), and (6, -1), which are in different quadrants.

(c) (y - 16)²/15² - (x - 2)²/8² = 1.

The equation is of the form (y - k)²/a² - (x - h)²/b².

h = 2, k = 16, a = 15, b = 8.

c = √(a² + b²) = √(15² + 8²) = √(225 + 64) = √289 = 17.

Thus, foci are at the points (h, k + c), (h, k - c) = (2, 16 + 17), (2, 16 - 17) = (2, 33), and (2, -1), which are in different quadrants.

(d) (y - 16)²/9² - (x + 1)²/12² = 1.

The equation is of the form (y - k)²/a² - (x - h)²/b².

h = -1, k = 16, a = 9, b = 12.

c = √(a² + b²) = √(9² + 12²) = √(81 + 144) = √225 = 15.

Thus, foci are at the points (h, k + c), (h, k - c) = (-1, 16 + 15), (-1, 16 - 15) = (-1, 31), and (-1, 1), which are in the same quadrants (QUADRANT II).

Thus, the hyperbola having both foci lying in the same quadrant is <u>(y - 16)²/9² - (x + 1)²/12² = 1</u>, making the <u>4th option</u> a right choice.

Learn more about the foci of a hyperbola at

brainly.com/question/9384729

#SPJ4

For the options, refer the image.

7 0
2 years ago
Please help, ill give brainliest!
grigory [225]

Answer:

x=18 y=9

Step-by-step explanation:

6 0
2 years ago
The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. A random sample
oksano4ka [1.4K]

Answer:

t=\frac{55.82-56}{\frac{0.77}{\sqrt{49}}}=-1.636      

Step-by-step explanation:

Data given and notation      

\bar X=55.82 represent the sample mean

s=0.77 represent the standard deviation for the sample      

n=49 sample size      

\mu_o =56 represent the value that we want to test    

\alpha represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)      

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the mean is less than 56, the system of hypothesis would be:      

Null hypothesis:\mu \geq 56      

Alternative hypothesis:\mu < 56      

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:      

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)      

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic      

We can replace in formula (1) the info given like this:      

t=\frac{55.82-56}{\frac{0.77}{\sqrt{49}}}=-1.636      

4 0
3 years ago
So i figured out the first but I don't know the rest please help?
Pani-rosa [81]
For the first two, multiply 13 in place of the X. For example, 4(13)+71 = 123.
6 0
2 years ago
Suppose that the cost of producing n pairs of shoes is given by the expression c(n)=30+5n. the average cost of producing a pair
makkiz [27]
<h3>Given</h3>

c(n)=30+5n\\a(n)=\dfrac{c(n)}{n}

<h3>Find</h3>

\dfrac{d}{dn}(a(n))\quad\text{at n=10}

<h3>Solution</h3>

\dfrac{d}{dn}(a(n))=\dfrac{d}{dn}\left(\dfrac{30+5n}{n}\right)=\dfrac{d}{dn}\left(30n^{-1}+5\right)\\\\=-30n^{-2}\\\\=-30\cdot 10^{-2}\qquad\text{at n=10}\\\\=-0.30

The derivative of the average cost function at n=10 is -0.30.

7 0
3 years ago
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