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3 years ago

Given that f(x) = 2x − 5, find the value of x that makes f(x) = 15.

Mathematics

1 answer:

Vladimir79 [104]3 years ago

8 0

Answer:

Step-by-step explanation:

so you replace all the x's with 15 and it becomes

2×15-5

2×15=30

30-5=25

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A particle moves on the hyperbola xy=18 for time t≥0 seconds. At a certain instant, y=6 and dydt=8. What is x that this instant?

professor190 [17]

Answer:

The value of x at this instant is 3.

Step-by-step explanation:

Let $x\cdot y = 18$ , we get an additional equation by implicit differentiation:

$x\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0$ (1)

From the first equation we find that:

$x = \frac{18}{y}$ (2)

By applying (2) in (1), we get the resulting expression:

$\frac{18}{y}\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0$ (3)

$y\cdot \frac{dx}{dt}=-\frac{18}{y}\cdot \frac{dy}{dt}$

$\frac{dx}{dt} = -\frac{18}{y^{2}} \cdot \frac{dy}{dt}$

If we know that $y = 6$ and $\frac{dy}{dt} = 8$ , then the first derivative of x in time is:

$\frac{dx}{dt} = -\frac{18}{6^{2}} \cdot (8)$

$\frac{dx}{dt} = -4$

From (1) we determine the value of x at this instant:

$x\cdot \frac{dy}{dt} = -y\cdot \frac{dx}{dt}$

$x = -y\cdot \left(\frac{\frac{dx}{dt} }{\frac{dy}{dt} } \right)$

$x = -6\cdot \left(\frac{-4}{8} \right)$

$x = 3$

The value of x at this instant is 3.

4 0

3 years ago

If the temperature is dropping at a rate of 2° per hour how many hours will it take to drop 15°

Tju [1.3M]

Answer:

7 1/2

Step-by-step explanation:

If it drops 2 per hour, and you need it to drop 15, divide 15 by 2 and you’ll get 7.5 or 7 1/2

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3 years ago

Luanne wants to have $3275 in her bank account in 10 years. How much money should she deposit if her account earns 7.5% interest

Mekhanik [1.2K]

A. $1589.01

I solved this by a simple trial and error by inputing each answer into the equation.

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3 years ago

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What is the slant height of a regular pyramid if its lateral area is 160 units² and the perimeter of the base is 40 units?

SSSSS [86.1K]

Answer:

The slant height of a regular pyramid is $l=8\ units$

Step-by-step explanation:

we know that

The lateral area of a regular pyramid is equal to

$LA=\frac{1}{2}Pl$

where

LA is the lateral area

P is the perimeter of the base

l is the slant height

we have

$LA=160\ units^{2}$

$P=40\ units$

substitute in the formula and solve for l

$160=\frac{1}{2}(40)l$

$160=20l$

$l=160/20$

$l=8\ units$

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3 years ago

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If 40% of the students in the class are boys, and if there are 15 girls in the class, then how many students are in the class? *

OleMash [197]

Answer:

Step-by-step explanation:

15/6.0=2.5

2.5x4=10

2.5x6=15

10+15=25

10 boys and 15 girls

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3 years ago

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