A rectangular steel plate expands as it is heated. Find the rate of change of area with respect to temperature T when the width is 1.6 cm and the length is 2.6 cm if d l divided by dt equals 1.1 times 10 Superscript negative 5 Baseline cm divided by degrees Upper C and dw divided by dt equals 8.9 times 10 Superscript negative 6 Baseline cm divided by degrees C. Round to one decimal place.

The variation rate is 4.07 × 10⁻⁵ cm²/ºC

Step-by-step explanation:

The relationship of the change in length as a function of the temperature, which are given in this problem can be written by the expression for the area of a rectangle

a = L × W

Differentiating both sides,

=

= W + L

The values they give us are

= 1.1 × 10⁻⁵ cm/ºC

= 8.9 × 10⁻⁶ cm/ºC

W = 1.6  cm

L= 2.6 cm

Substituting the values and calculating

= (1.6 × 1.1 × 10⁻⁵) + (2.6 × 8.9 × 10⁻⁶)

= (1.76 × 10⁻⁵) + (2.31 × 10⁻⁵)

=  4.07 × 10⁻⁵ cm²/ºC

The variation rate is 4.07 × 10⁻⁵ cm²/ºC

v = 1/3 a^2h

step-by-step explanation:

if the height is 57.7cm and the height of the slant edge is 18.2cm, then the volume is 1/3 a^2h.

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!