Explanation

Given sinθ = 3/5, 1st quadrant

Use identity: sin²θ + cos²θ = 1

(3/5)² + cos²θ = 1  

9/25 + cos²θ = 1  

cos²θ = 1 - 9/25 = 16/25  

cosθ = ±4/5

In 1st quadrant both sin and cos are positive.  

So cosθ = 4/5.

Last verified on 04-05-2026

Explanation

• Mitochondria are called the powerhouse of the cell.
• Because they produce Adenosine Triphosphate (ATP).
• ATP is the energy currency of the cell.
• ATP provides energy for different cellular activities such as movement, growth, and transport.
• Energy is produced through aerobic cellular respiration using oxygen and الغذائی molecules.
• They are found in the cytoplasm of most eukaryotic cells.
• Richard Altmann first described mitochondria in 1890.

Main Parts of a Cell:

1. Cell membrane → Outer protective layer
2. Nucleus → Controls cell activities
3. Cytoplasm → Jelly-like material between membrane and nucleus

Last verified on 09-05-2026

Explanation

• Pakistan is located at a key crossroads of Asia.
• It connects South Asia, Central Asia, and the Middle East.
• This strategic location increases its political and economic importance.
• It also plays a key role in trade and regional connectivity.
• Major routes and projects pass through Pakistan.

Last verified on 25-05-2026

Explanation

• “At the eleventh hour” means at the very last moment.
• It refers to doing something just before it is too late.
• Example: He submitted the form at the eleventh hour.

Last verified on 14-05-2026

Explanation

Area of a triangle = 1/2 _ base _ height

Let old base = B, old height = H.  

Old area = 1/2 _ B _ H

New base = B + 25% of B = B + 0.25B = 1.25B  

New height = H - 20% of H = H - 0.20H = 0.80H

New area = 1/2 _ 1.25B _ 0.80H  

= 1/2 _ 1.00 _ B _ H  

= 1/2 _ B * H

New area = old area. It stays the same.

Last verified on 25-05-2026

Explanation

Put a = 1 into a² + b² = 170.

1² + b² = 170  

1 + b² = 170  

b² = 170 - 1  

b² = 169  

b = 13 or b = -13

So b equals 13 or -13.

Last verified on 25-05-2026

Explanation

A triangle is classified based on its angles.

If one angle is 90°, it is a right-angled triangle.

The given triangle has angles 30°, 60°, and 90°.

Since it contains a 90° angle, it is a right triangle.

Last verified on 25-05-2026

Explanation

Write (14x + 10)/(x(x + 5)) = A/x + B/(x + 5)

Multiply both sides by x(x + 5):

14x + 10 = A(x + 5) + Bx

Now find A and B by plugging in values for x:

Put x = 0:

14_0 + 10 = A(0 + 5) + B_0

10 = 5A

A = 2

Put x = -5:

14_(-5) + 10 = A(0) + B_(-5)

-70 + 10 = -5B

-60 = -5B

B = 12

So (14x + 10)/(x(x + 5)) = 2/x + 12/(x + 5)

Last verified on 25-05-2026

Explanation

For f(x) = x² - x, find f(5) and f(3) separately then subtract.

f(5) = 5² - 5 = 25 - 5 = 20  

f(3) = 3² - 3 = 9 - 3 = 6  

Now f(5) - f(3) = 20 - 6 = 14  

Last verified on 25-05-2026

Explanation

y ∝ 1/x³ means y = k / x³ where k is a constant.

Step 1: Find k using y = 32 when x = 2

32 = k / 2³

32 = k / 8

k = 32 * 8 = 256

Step 2: Use k to find y when x = 4

y = 256 / 4³

y = 256 / 64

y = 4

Last verified on 25-05-2026