Answer:
<DAB = 120
Step-by-step explanation:
7)
<DAB = ?
<DAB + <DCB = 180
so
16x + 8 + 8x + 4 = 180
24x + 12 = 180
24x = 168
x = 7
<DAB = 16(7) + 8 = 120
Answer:
-2.5
Step-by-step explanation:
Here in this question, we are interested in calculating the z-score for a student that had a particular mark at the test
To calculate the z-score, we need to use a mathematical formula
Mathematically;
z-score = (x - mean)/SD
From the question;
x = 76
mean = 86
standard deviation SD = 4
Plugging these values in the equation, we have;
z-score = (76-86)/4 = -10/4 = -2.5
The answer would be -1/6 or -0.166667
<h2>9.</h2><h3>Given</h3>
<h3>Find</h3>
- linear approximation to the volume when the radius increases 0.4 cm
<h3>Solution</h3>
The equation for volume of a sphere is
... V = (4/3)π·r³
Differentiating gives
... dV = 4π·r²·dr
Filling in the given numbers gives
... change in volume ≈ 4π·(15 cm)²·(0.4 cm)
... = 360π cm³ ≈ 1130.97 cm³ . . . . . . volume of layer 4mm thick
<h2>11.</h2><h3>Given</h3>
- an x by x by 2x cuboid with surface area 129.6 cm²
- rate of change of x is 0.01 cm/s
<h3>Find</h3>
<h3>Solution</h3>
The area is that of two cubes of dimension x joined together. The area of each such cube is 6x², but the two joined faces don't count in the external surface area. Thus the area of the cuboid is 10x².
The volume of the cuboid is that of two cubes joined, so is 2x³. Then the rate of change of volume is
... dV/dt = (d/dt)(2x³) = 6x²·dx/dt
We know x² = A/10, where A is the area of the cuboid, so the rate of change of volume is ...
... dV/dt = (6/10)A·dx/dt = 0.6·(129.6 cm²)(0.01 cm/s)
... dV/dt = 0.7776 cm³/s
