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3 years ago

3 times a number X subtracted from 18 is less than -90 write an inequality for the statement above

Mathematics

1 answer:

emmainna [20.7K]3 years ago

5 0

18-3x<-90. Hope this helps! :)

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At what points on the given curve x = 4t3, y = 3 + 40t − 2t2 does the tangent line have slope 1?

dexar [7]

ANSWER

The points are:

(32,-85)

and

$( \frac{500}{27} , \frac{577}{9} )$

EXPLANATION

The given parametric equation that defines the curve is:

$x = 4 {t}^{3}$

$y = 3 + 40t - 2 {t}^{2}$

We differentiate to get,

$\frac{dx}{dt} = 12 {t}^{2}$

$\frac{dy}{dt} = 40 - 4t$

The slope of the tangent is given by;

$\frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} }$

$\frac{dy}{dx} = \frac{12 {t}^{2} }{40 - 4t}$

For the slope to be 1, then we must solve the following equation for t.

$\frac{12 {t}^{2} }{40 - 4t} = 1$

$12 {t}^{2} = 40 - 4t$

$12 {t}^{2} + 4t - 4 0 = 0$

$3{t}^{2} + t - 10 = 0$

$(t + 2)(3t - 5) = 0$

$t = - 2 \: \: or \: \: t = \frac{5}{3}$

When t=-2, we put -2 into the expression for x and y to get

x=4(-2)³ and y=3+40(-2)-2(-2)²

This implies that,

x=32, y=-85

Hence one point is (32,-85)

Similarly, when

$t = \frac{5}{3}$

$x = \frac{500}{27} ,y = \frac{577}{9}$

Another point is

$( \frac{500}{27} , \frac{577}{9} )$

7 0

2 years ago

2(x-2)^2+3 and 3(x+1)^2+5 rewrite in standard form

garri49 [273]

5x^2-2x+19 is the answer

6 0

3 years ago

Without looking it up- what is -2317 - (-5294)?

vovangra [49]

Answer:

=2977

Step-by-step explanation:

-2317 - (-5294)

-2317 + 5294

2977

4 0

2 years ago

Read 2 more answers

What is the 9th term for the following sequence<br><br> 1, 4, 7, 10<br> (Yeah I mean 9th, not nth)

Irina-Kira [14]

Answer:

1,4,7,10,13,16,19,22,25. 25 is the 9th term. hope this helps

Step-by-step explanation:

- Zombie

5 0

2 years ago

There are 99 males and 121 females participating in a marathon. What percent of the participants are female?

ioda

To do this, we first want to see how many participants there are in total by adding both males and females.

$99+121=220$

Now we know that there were 220 total participants, but only 121 were females.

This allows us to set up the fraction 121/220= the percent female.

$\frac{121}{220} =0.55$

or 55%

8 0

2 years ago