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3 years ago

Evaluate -5x2 − 8x + 1 when x = -3.

Mathematics

1 answer:

Dafna11 [192]3 years ago

5 0

Answer:

Step-by-step explanation:

-5 x 2 - 8x + 1

= -5 x 2 - 8(3) + 1

= -10 - (-23)

= 13

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A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station. Find the ra

Anika [276]

Answer:

The rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.

Step-by-step explanation:

Given information:

A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station.

$z=1$

$\frac{dx}{dt}=430$

We need to find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

$y=2$

According to Pythagoras

$hypotenuse^2=base^2+perpendicular^2$

$y^2=x^2+1^2$

$y^2=x^2+1$ .... (1)

Put z=1 and y=2, to find the value of x.

$2^2=x^2+1^2$

$4=x^2+1$

$4-1=x^2$

$3=x^2$

Taking square root both sides.

$\sqrt{3}=x$

Differentiate equation (1) with respect to t.

$2y\frac{dy}{dt}=2x\frac{dx}{dt}+0$

Divide both sides by 2.

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

Put $x=\sqrt{3}$ , y=2, $\frac{dx}{dt}=430$ in the above equation.

$2\frac{dy}{dt}=\sqrt{3}(430)$

Divide both sides by 2.

$\frac{dy}{dt}=\frac{\sqrt{3}(430)}{2}$

$\frac{dy}{dt}=372.390923627$

$\frac{dy}{dt}\approx 372$

Therefore the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.

6 0

4 years ago

A circle centered at the origin has a radius of 10 units. The terminal side of an angle, Theta, intercepts the circle in Quadran

Tanzania [10]

Since the circle is centered at the origin, we can use the equations
x² + y² = r²
x = r cos θ
y = r sin θ

We know y = 8 and r = 10. Solving for x
x² + 8² = 10²
x = 6

From this equation:
x = r cos θ
6 = 10 cos θ
cos θ = 6/10 = 0.6

7 0

3 years ago

Please explain how to do this!

irakobra [83]

Ask ur mom she can knows

5 0

3 years ago

PLEASE HELP I WILL MARK BRAINLIEST

Lelu [443]

Answer:

$27 \: {km}^{2}$

Step-by-step explanation:

Given is the shape of a trapezoid.

Therefore,

Area of the trapezoid

$= \frac{1}{2} (2 + 7) \times 6 \\ \\ = 9 \times 3 \\ \\ = 27 \: {km}^{2}$

5 0

3 years ago

Need help with this.

skelet666 [1.2K]

Answer:

-5/2(3x+4)<6-3x (multiply with -5/2)

-15/2x-10<6-3x (multiply with 2)

-15x-20<12-6x (change sides)

-15x+6x<12+20

-9x<12+20

-9x<32

x>-32/9

Hope this will help u :)

3 0

4 years ago