All categories

3 years ago

The gradient of the curve

Mathematics

1 answer:

AleksAgata [21]3 years ago

3 0

Answer:

Coordinate of P is (-2, -3)

Step-by-step explanation:

Gradient is the derivative of the curve:

$y = {3x}^{2} + 11x + 7 \\ \\ \frac{dy}{dx} = 6x + 11$

but dy/dx is -1 :

$6x + 11 = - 1 \\ 6x = - 12 \\ x = - 2$

substitute for x :

$y = 3( - 2) {}^{2} + 11( - 2) + 7 \\ y = - 3$

You might be interested in

Which table shows a proportional relationship between X and Y?

Pachacha [2.7K]

The answer is B because for every x input there is a y output

6 0

3 years ago

Given cos = -2/5 a in quadrant III and cos b = 1/4, b in quadrant I find

BigorU [14]

I guess you mean $\cos a=-\dfrac25$ . Since $a$ is in quadrant III, we expect $\sin a$ . Then

$\sin a=-\sqrt{1-\cos^2a}=-\dfrac{\sqrt{21}}5$

Since $b$ is in quadrant I, we expect $\sin b>0$ , so that

$\sin b=\sqrt{1-\cos^2b}=\dfrac{\sqrt{15}}4$

Now,

$\sin(a+b)=\sin a\cos b+\cos a\sin b=-\dfrac{2\sqrt{15}+\sqrt{21}}{20}$

$\cos(a+b)=\cos a\cos b-\sin a\sin b=\dfrac{3\sqrt{35}-2}{20}$

and

$\tan(a+b)=\dfrac{\sin(a+b)}{\cos(a+b)}=-\dfrac{2\sqrt{15}+\sqrt{21}}{3\sqrt{35}-2}$

5 0

4 years ago

Exspress 0.0008235 in scientific notation

UNO [17]

Step-by-step explanation:

0.0008235

scientific notation=

$8.235 \times {10}^{ - 4}$

8 0

3 years ago

In a hydroelectricity production, water falls from a dam into a turbine wheel 49 m below. What is the velocity of water at the t

svlad2 [7]

Answer:

31m/s

Step-by-step explanation:

Using the equation of motion

v² = u² + 2gH

H is the height of fall = 49m

g is the acceleration due to gravity = 9.8m/s²

u is the initial velocity = 0m/s

v² = 0² + 2(9.8)(49)

v² = 960.4

v = √960.4

v = 30.9m/s

v ≈ 31m/s

Hence the velocity of water at the turbine is 31m/s

6 0

3 years ago

If line AB is parallel to line RS, find the value of x.

kozerog [31]

Answer: 125 degrees

Step-by-step explanation: <MTB and angle x are corresponding therefore congruent (Equal Measure) so the answer would be 125 degrees.

6 0

3 years ago