Write the quotient in simplest form. Type answer as integer or a fraction

Mathematics

1 answer:

Usimov [2.4K]3 years ago

7 0

Answer:

$-\dfrac{1}{26}$

Step-by-step explanation:

$-\dfrac{12}{13}\div 24=\\\\-\dfrac{12}{13} \times \dfrac{1}{24}=\\\\-\dfrac{12}{13\times 24}=\\\\-\dfrac{1}{26}$

Hope this helps!

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P, Q & R form a right-angled triangle.

Naya [18.7K]

Answer:

m<RPQ = 22°

Step-by-step explanation:

Given:

m<SRQ = 90°

PS = PQ

m<SQR = 46°

Required:

m<RPQ

Solution:

m<SQR + m<SRQ + m<RSQ = 180°

Substitute

46° + 90° + m<RSQ = 180°

m<RSQ = 180° - 136°

m<RSQ = 44°

Find m<PSQ:

m<PSQ = 180° - m<RSQ (Angles on a straight line

m<PSQ = 180° - 44° (Substitution)

m<PSQ = 136°

Find m<RPQ:

∆QSP is an isosceles triangle with two equal base angles. Therefore:

m<RPQ = ½(180° - 136°)

m<RPQ = 22°

4 0

3 years ago

Find an equation for the plane that is tangent to the surface z equals ln (x plus y )at the point Upper P (1 comma 0 comma 0 ).

alexira [117]

Let $f(x,y,z)=z-\ln(x+y)$ . The gradient of $f$ at the point (1, 0, 0) is the normal vector to the surface, which is also orthogonal to the tangent plane at this point.

So the tangent plane has equation

$\nabla f(1,0,0)\cdot(x-1,y,z)=0$

Compute the gradient:

$\nabla f(x,y,z)=\left(\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y},\dfrac{\partial f}{\partial z}\right)=\left(-\dfrac1{x+y},-\dfrac1{x+y},1\right)$