Explanation

Work = Men × Days = 120 × 30 = 3600 man-days

If 80 men work: 3600 ÷ 80 = 45 days

Explanation

Let apple = x, orange = y

5x + 4y = 340

Try options:

B) 5×40 + 4×20 = 200 + 80 = 340 

Explanation

Total students = 35 → Total height = 35 × 161 = 5635 cm

14 girls = 14 × 151 = 2114 cm

So, 15 girls = (2114 + x) → x = height of 1 girl = assume x = 151

Total height of 15 girls ≈ 15 × 151 = 2265

Total height of boys = 5635 - 2265 = 3370

Mean height of 20 boys = 3370 ÷ 20 = 169 cm

Explanation

Eccentricity of ellipse is 0 < e < 1

If e = 0, ellipse becomes a perfect circle

Explanation

You gave the equation:  

xy² + xy = 8x  

We are to find dy/dx at the point (1, 2).

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Step 1: Differentiate both sides implicitly with respect to x:

d/dx(xy²) + d/dx(xy) = d/dx(8x)

Use product rule:  

d/dx(xy²) = x·d/dx(y²) + y²·d/dx(x) = x·2y·dy/dx + y²  

d/dx(xy) = x·dy/dx + y  

d/dx(8x) = 8

So the full derivative becomes:  

x·2y·dy/dx + y² + x·dy/dx + y = 8

Now plug in x = 1, y = 2:

1·2·2·dy/dx + 4 + 1·dy/dx + 2 = 8  

=> 4·dy/dx + 4 + dy/dx + 2 = 8  

=> 5·dy/dx + 6 = 8  

=> 5·dy/dx = 2  

=> dy/dx = 2/5

Explanation

limₓ→0 (sin(ax) / sin(bx))

Divide the numerator and the denominator by x:

= limₓ→0 [(sin(ax)/x) ÷ (sin(bx)/x)]  

= (a/b) × limₓ→0 [sin(ax)/(ax)] ÷ [sin(bx)/(bx)]

As x → 0, sin(kx)/(kx) → 1, so:

Answer: a / b

Explanation

The point where two boundary lines of a solution region (in linear programming or systems of inequalities) intersect is called a  Vertex

Explanation

[−73^7]^6 = 7x

First, simplify the left-hand side:  

= (−73^7)^6  

= −73^(7×6) = −73^42  

So:

−73^42 = 7x  

Now solve for x:  

x = (−73^42) / 7

Explanation

• Distance to school = 2 km

• Speed = 4 km/h

• Time = ?

Step 1: Use the formula

Time=Distance​.Speed=2/4​=0.5 hours

Step 2: Convert 0.5 hours to minutes

$$0.5 times 60 = 30 text{ minutes}$$

Explanation

cosecθ − cotθ = (1 - cosθ) / sinθ