Find the 11th term of the geometric sequence 10, 20, 40, ...

At the instant that a cake is removed from the oven, the temperature of the cake is 350°F. After 10 minutes, the cake's temperat

BARSIC [14]

Once the cake is removed from the oven, it has been exposed to the room temperature of 70°F. After 10 minutes, the cake's temperature decreased to 200°F, which is 150°F cooler than it initially was (350°F). As for the what is asked, 90°F is 260°F cooler than its original temperature (350°F).

This problem can be expressed in a ratio:
10mins:150°F = N:260°F
where N is how long it will take for cake to cool to 90°F

150°FxN=10x260
150N=2600
N=2600/150
N=17.33
N≈20 minutes

Thus, it takes approximately 20 minutes for the cake to cool to 90°F

8 0

4 years ago

From the top of the Eiffel Tower, a jogger is spotted heading toward the tower. When at position A, the angle of depression of t

8090 [49]

325 meters if using full height of 324 meters for tower
277 meters if using observation platform height of 276 meters.
When the depression is 37 degrees, you can create a right triangle with the angles 90, 37, and 53 degrees. The distance from a point directly underneath the observer will be:
h/tan(37)
where
h = height of the observer.

And when the depression is 72 degrees, the distance will be:
h/tan(72)
So the distance between the two points will be the absolute value of:
h/tan(72) - h/tan(37)
=(tan(37)h)/tan(37)tan(72) - tan(72)h/(tan(37)tan(72))
=(tan(37)h - tan(72)h) /(tan(37)tan(72))
=h(0.75355405 - 3.077683537)/(0.75355405 * 3.077683537)
=h(0.75355405 - 3.077683537)/(0.75355405 * 3.077683537)
=h(-2.324129487/2.319200894)
=h*-1.002125125

And since we're looking for absolute value
=h*1.002125125

As for the value of "h" to use, that's unspecified in the problem. If you take h
to be the height of the Eiffel Tower, then it's 324 meters. If you take h to be
the highest observation platform on the Eiffel Tower, then it's 276 meters. In
any case, simply multiply h by the value calculated above:
=h*1.002125125
=324*1.002125125
= 324.6885406 m

=h*1.002125125
=276*1.002125125
=276.5865346

6 0

4 years ago

Rebecca went swimming yesterday. After a while she had covered one fifth of her intended distance. After swimming six more lengt

alukav5142 [94]

Answer:

Option E.

Step-by-step explanation:

Let the intended length of Rebecca's swimming is = x units

and we assume the length of the pool = l units

Now it is given in the question that " She covers one fifth of her intended distance "

That means distance covered = $\frac{x}{5}$

" After swimming six more lengths of the pool she had covered one quarter of her intended distance"

So $\frac{x}{5}+6(l)=\frac{x}{4}$

$6l=\frac{x}{4}-\frac{x}{5}$

$6l=\frac{x}{20}$

x = 20×(6l)

x = 120l

Therefore, Rebecca has to complete 120 lengths of the pool.

Option E is the answer.

4 0

3 years ago

A number consists of two digits. The number is 2 more than 8 times the sum of the digits, and if 54 is subtracted from the numbe

Gennadij [26K]

Let the units digit = x

Let the 10s digit = y

Equations

10y + x - 2 = 8 * (x + y) (1)

10y + x - 54 = 10x + y (2)

Equation 1

10y + x - 2 = 8 * (x + y) Remove the brackets on the right

10y + x - 2 = 8x + 8y Subtract 8y from both sides

10y - 8y + x - 2 = 8x Subtract 8x from both sides

2y + x - 8x - 2 = 0 Combine

2y - 7x - 2 = 0 (3)

Equation 2

10y + x - 54 = 10x + y Subtract 10x

10y - 9x - 54 = y Subtract y from both sides.

9y - 9x - 54 = 0 Divide by 9

y - x - 6 = 0 Multiply by 2

2y - 2x - 12 = 0 (4)

Solution

Subtract (3) - (4)

2y - 7x - 2 = 0

2y - 2x - 12 = 0

- 5x + 10 = 0 Subtract 10 from both sides.

- 5x = - 10 Divide by - 5

x = 2

Use (4) to find y

2y - 2x - 12 = 0 Let x =2

2y - 2(2) - 12 = 0 Remove the brackets

2y - 4 - 12 = 0 Combine

2y - 16 = 0 Add 16 to both sides.

2y = 16 Divide by 2

y = 8

Answer 82

I'll leave the check to you, but the answer of 82 is correct.

4 0

4 years ago

Zachary sold 1/2 of a 40-acre lot. He then sold 3/5 of the remaining lot. What fraction of the land did he sell in all? (Write t

Mazyrski [523]

4/5 acres of the land were sold.
40* 1/2 = 20
20* 3/5 = 12
12+20= 32
32/40 = 4/5 simplified

4 0

3 years ago