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Vlad
13 days ago
7

If p+pq is 4 times p-pq, and pq does not equal to 0, which of the following has exactly one possible value? A)p B)q C)pq D)p+pq

Mathematics
1 answer:
Inessa [9K]13 days ago
8 0
D is the correct option since it represents a combination where neither p nor a equals zero.
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What is a rational number that is located between 31.5 and 31.6
Svet_ta [9518]
A rational number refers to any number that can be written as a fraction, such as 2, -3, 2/3, etc.

Essentially, any non-repeating number found between 31.5 and 31.6 would suffice.

Examples include: 31.51, 31.52, 31.568, 31.599

I suggest 31.55 since it’s straightforward and can be expressed as the fraction: 361/20

4 0
9 days ago
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Consider this equation: –2x – 4 + 5x = 8 Generate a plan to solve for the variable. Describe the steps that will be used.
tester [8842]

The equation given is –2x – 4 + 5x = 8, and the task is to find the value of x. To start, combine like terms and reorganize the equation:

-2x + 5x = 8 + 4
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1 month ago
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Frank has X stamps and Chris has 8 more than 7 times the number of stamps Frank has. How many stamps do Frank and Chris have in
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I think the right answer is D. 8x+8;
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5 0
11 days ago
Aubrey's dinner cost \$85$85dollar sign, 85. She tips the waitstaff 30\%30%30, percent for excellent service.
tester [8842]
Aubrey's dinner totaled $85. For excellent service, she tips the waitstaff 30%. The tip amount is $25.5. To calculate the tip, we start with the total cost of the dinner, which is $85, and apply the 30% tip rate. So, 30% of $85 is calculated as: Tip = 30% of 85. This results in Aubrey tipping the waitstaff $25.5.
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8 days ago
Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.
Inessa [9006]

Answer:

Wyjaśnienie krok po kroku:

Załóżmy, że prostokąt ma wierzchołki (x,y,z) w dodatnim oktancie.  Prostokątny pudełko musi być symetryczne względem wszystkich trzech osi.

Wtedy jego boki to

2x,2y,2z

Objętość = 8xyz

Maksymalizuj objętość przy założeniu

x^2+y^2+z^2 =1

tj. g(x,y,z) = x^2+y^2+z^2 -1=0

Użyj mnożników Lagrange'a, mamy

∇f(x,y,z)=λ∇g(x,y,z)przy maksimum

∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)

8yz=2λx8xz=2λy8xy=2λz

Dzieląc otrzymujemy

\frac{y}{x} =\frac{x}{y} \\x^2=y^2

Podobnie y^2=z^2

Zatem otrzymujemy 3x^2 =1\\x = \frac{1}{\sqrt{3} }

Stąd wymiary to

(2x,2y,2z)

<pzatem wymiary="" to="">

\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} } )

</pzatem>
3 0
24 days ago
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